The Journal of a Freelance Scientist

Male brain = Female brain ? Theater answers for you...

2012-02-06T15:11:00.019+01:00

Post Category > concept - article review - micro-publication - discussion - web - this blog - author's - miscellaneous

Those wondering what I am doing in life that prevented me so far from posting more often will now know. I have been working a lot lately on the piece of theater we actually play at the Museum "Le Vaisseau." Since January, we play it on stage in the 140-seats-auditorium, and people like it very much ! Roughly, the subject is : are there differences between the female brain and the male brain?

Translation of the title : "Pink-blue gray matter?"

Here is a picture of me doing my stuff on stage:

This is the kind of theater genre you are problably not accustomed to. Not only is it exclusively dealing with scientific subjects, which everybody knows as "Scientfic theater", but it is also played in two languages at the same time : german + french.

Writing a two-languaged piece of theater requires understanding how to lay out the whole thing for both without getting either bored. German people should not find it boring to sit there as the french text is being spoken, and conversely, which requires cleverly managing text and action in the right way.

In one chapter, the piece adresses a polemic issue as to why there are no woman among Fields Medal owners, that is, if girls/women are effectively worse at math than boys/men. And the story tells that girls are as good at math as boys with respect to their cerebral ability, but we (men) exert pressure on them so they lose self-confidence and fail. This is in the text and I am quite responsible for it, and proud of it :)

The piece lasts roughly 35-40 minutes. In conclusion, we do not claim there are differences between men and women regarding their brain, which would not have been fair, but simply that : if we are different, then there are things we can learn from each other and thus get both better at the same time.

In case you are in France, Strasbourg, please come and visit Le Vaisseau, and make a reservation. You won't regret it :)

Tschüss

2011-12-19T13:50:00.000+01:00

Post Category > concept - article review - micro-publication - discussion - web - this blog - author's - miscellaneous

Dear readers,

many of you probably noticed that LaTeX formulas do not work in an optimal way on this blog since a few weeks. This is unfortunately not due to myself. It seems like the server providing the java script I use for interpreting LaTeX code is being anyhow modified or so ; in any event, something has been changed, which I have no influence upon.

Sorry for that. Please enjoy the blog any way :)

J.C.

From one integer onto another

2011-10-24T20:51:00.009+02:00

Post Category > concept - article review - micro-publication - discussion - web - this blog - author's - miscellaneous

I wish today to present a mathematical object to you, which I (perhaps) invented myself ("perhaps" because I am too busy in life to check this up in the literature). This is in fact a generalization of arithmetic progression, which are sequences $\color{White}(u_i)_{i \in \mathbb{N}}$of the form:$\color{White}u_{n+1}=u_n+g$, where$\color{White}g$ is fixed, and can be generalized into forms like that.

The kind of generalized arithmetic progression, which I would like to present here corresponds to the diagram hereafter:

This is an instance of what I want to deal with... Imagine this is an interval on the natural axis (ordered from left to right), with one integer in each box. Red boxes represents integers of the sequence, white arrows indicate the jump between two successive values of the sequence and the blue arrow shows when everything comes back to the beginning. Such a sequence could be for example:

$\color{White}5,9,11,14,19,21,25,27,30,35,32,...$,etc.

To define this in the most general case, which I choose to call "concatenated Generalized Arithmetic Progression", one needs to define first the set$\color{White}G=\left\{g_1,g_2,...,g_k\right\}$of successive gaps, that is, the basic chunk of gaps. The cardinal of G is an integer and the values themselves can be taken from any ring. What is caracteristic is:

(1) the set of successive gaps is finite and ordered

(2) the succession of gaps cycles

Formally speaking, this reads:

$\color{White}u_{n+1}=u_n+g_{(n\mod k)+1}$

One can determine a closed formula for the pth value of the sequence through the equation:

$\color{White}u_p=u_0+g_1n_1+g_2n_2+...+g_kn_k$

With$\color{White}p=n_1+n_2+...+n_k$.

One demonstrates that the coefficients take the value:

$\color{White}n_i=\left\lfloor\dfrac{p}{k}\right\rfloor+\dfrac{1-\sigma(i-p\mod k)}{2}$

So the calculation of$\color{White}u_p$follows naturally.

Proof:

Since

$\color{White}u_{p}=u_0+\overbrace{g_1+g_2+\ldots+g_k+\ldots+g_1+g_2+\ldots+g_m}^{\text{p values}}\quad (1 \le m \le k)$

Then it comes that:

$\color{White}u_p=u_0+g_1n_1+g_2n_2+...+g_kn_k$

while the following always holds:

$\color{White}n_i=\begin{cases}\left\lfloor\frac{p}{k}\right\rfloor+1, & \text{if}\quad 1 \le i \le m\\ \left\lfloor\frac{p}{k}\right\rfloor+0, & \text{if}\quad m < i \le k\end{cases}$

Thus the coefficients$\color{White}n_i$are a function of the index i.

Now consider the function:

$\color{White}\mu(i)=\dfrac{1-\sigma(i-p\mod k)}{2}$

Where$\color{White}\sigma$is the sign function such that:

$\color{White}\sigma(x)=\begin{cases}-1, & \text{if}\quad 0 \ge x \\+1, & \text{if}\quad 0< x\end{cases}$

Then:

$\color{White}n_i=\left\lfloor\dfrac{p}{k}\right\rfloor + \mu(i)$

End of proof.

c-GAP sequences find applications in many areas of mathematics, the first of which is number theory. Let us consider now the following diagram:

It shows in blue a subset of the sequence of the set of integers, which are neither multiples of 2 (upper orange layer), nor multiples of 3 (lower orange layer). Clearly that set contains at least all prime numbers greater than 3 and can furthermore be generated by means of a c-GAP since (let's recall it here):

(1) the set of successive gaps is finite and ordered
(2) the succession of gaps cycles

Those 2 points are a direct consequence of the fact:

$\color{White}\begin{cases}x \mod 2 \equiv 0 \\x \mod 3 \equiv 0 \end{cases} \Rightarrow x=(2\times 3)n, \quad n \in \mathbb{N}$

The interest in considering this c-GAP is to minimize the cardinality of the set in which one screens great prime numbers using primality test. This c-GAP will simply be:

$\color{White}G=\left\{4,2\right\}$ ; $\color{White}u_{n+1}=u_{n}+g_{(n\mod k)+1}$ ; $\color{White}u_0=1$

Given the following general formula:

$\color{White}u_p=u_0+g_1n_1+g_2n_2$

And the fact that all elements of G are generated through the following:

$\color{White}g_k=3+(-1)^{k+1}$

We get a closed form for the pth value of the sequence:

$\color{White}u_p=1+ \sum_{k=1}^{2} (3+(-1)^{k+1}) \left(\left\lfloor\dfrac{p}{2}\right\rfloor + \dfrac{1}{2}(1-\sigma(i-p\mod k))\right)$

The latter may be used when looking for primes greater than 3 : it increases the speed of the screening as it filters up a large amount of values, of which we know they cannot be primes.

Remark:

This generalizes to the case in which all primes up to the kth one are known and placed in a set$\color{White}P_k=\{2,3,5,...,p_k\}$. Then there exists an application defined by:

$\color{White}P_k \mapsto G_{2,3,5,\ldots,p_k}=\{g_1,g_2,\ldots,g_m\}$

And the latter verifies the identity:

$\color{White}g_1+g_2+\ldots+g_m=2\times 3\times 5 \times \ldots \times p_k$

End of remark

Water, wind, air and me

2011-10-07T12:31:00.011+02:00

Post Category > concept - article review - micro-publication - discussion - web - this blog - author's - miscellaneous

Streaming waters make sense to me. I gaze at them whenever they flow down to places, where they will feel more at ease. Water has this fact in common with me that it is in search for both the best and the few at the same time. I know I could have been a river without feeling embedded in another, sleeping in some valley of my own.

Winds blow in a meaningful manner too – just like water and I, they let themselves be, let themselves be according to all rules of Nature. Outdoor they make my hair float, and I let them do this entanglement despite all my efforts in giving them a style, for I like when winds and I are just as one, resonating with each other. Indoor I let them lay my trees down, because wind and trees have a relationship of their own, which I adore perceiving without a move.

Even a piece of the air would be my realm, my kingdom; I need not to possess human jewels as I know there is so much more in each and every piece of the free sky. I am already rich of the mud, which sticks everyday to my soles, and a thousand bacteria or grains of sand in it is sure worth half a cup of stock options. And each time I inhale my surrounding, I feel like paid, redeemed, as air is like any other essential thing, that is, invisible.

So if I die tomorrow, or even now on my chair, do not think I am lost, in hell, or no more; no, don’t think I am weeping like a phantom, as with death loses one nothing, but, on the contrary, gains a ticket for the water, for winds, for the air.

No, if I die tomorrow, just think I went back home.

"Who works where" game: THE solution

2011-10-05T20:39:00.005+02:00

Post Category > concept - article review - micro-publication - discussion - web - this blog - author's - miscellaneous

This is the answer to the question in the last post "My neighbor who won the Nobel Prize"... I let you think a little more about it with this:

Have found now the answer? You can't wait any longer... Okay, here's for you:

Picture A was a photo of Jean-Marie Lehn's ISIS and Picture B was the "Institut de Biologie Moléculaire et Cellulaire" of Jules Hoffmann.

Next time, try to think faster :)

Best,

My neighbor who won the Nobel Prize

2011-10-04T20:43:00.015+02:00

Post Category > concept - article review - micro-publication - discussion - web - this blog - author's - miscellaneous

Jules Hoffmann is this year winner of the Nobel Prize in Medecine. Most importantly (at least for me), he works in Strasbourg, France... i.e., the town in which I live. Jules Hoffmann is in fact the second Nobel Prize winner here in Strasbourg with Jean-Marie Lehn, who has built here an Institute called ISIS, which means I have actually in my near neighborhood (less than 2 kilometers) two Nobel Prize Winners floating around.

Wow...

So let's make a little game: Here under are the two photos of the two Nobel-Prize-Winner-containing Institutes in Strasbourg.

Guess which institute is Jules Hoffmann's one and which is Jean-Marie Lehn's (solution available on this blog in a few days...)

A = ???
B = ???

Best,

Phenomenon + Model + Paradigm of the time = Compromise your theory

2011-10-03T12:54:00.077+02:00

Post Category > concept - article review - micro-publication - discussion - web - this blog - author's - miscellaneous

This is an important issue in phenomenological science to question about how a model should be interpreted. In fact, the more science evolves, the more it gets into the unobservable world, the more we should take care about how we trust in equations. Not a new debate, but I would like to adress today this hypothetical model:

This is a couple of objects (balls) having only 2 possible states$\color{White}u_1$and$\color{White}u_2$mutually repulsive, i.e., if the blue balls is in state$\color{White}u_1$, then the red ball must be in the state$\color{White}u_2$, and conversely. Now assume the system alternates endlessly from one state to the other: How should one model this?

Clearly, as both balls are tightly related to each other, so we have two correlated sub-systems, one may model it at once by means of one single 2-dimensional dynamical equation, for example a recursion of the form:

$\color{White}u_{n+1}=Wu_{n}$

If$\color{White}u$is the general state vector, then$\color{White}W$is a simple permutation matrix of the form:

$\color{White}W = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$

The alternating and interdependent movement is completely understood with the model since:

$\color{White}\begin{pmatrix} u_i \\ u_j \end{pmatrix}_{n+2}=W^{2} \begin{pmatrix} u_i \\ u_j \end{pmatrix}_{n}$

We have there modelled the dynamics of the system as a function of time$\color{White}n$.

It is an old tradition now to try and find what the dynamical system will be at equilibrium, or to better say, at infinity ($\color{White}n \rightarrow \mathcal{1}$), that is, perform fix point analysis. This is based on the fact that dynamical systems must tend naturally to an attractor, which corresponds to the search of a steady-state vector$\color{White}u_{s}$such that:

$\color{White}u_{s}=Wu_{s}$

The problem is, it is not relevant here to perfom the fix point analysis because this$\color{White}u_{s}$does not exist, as the system alternates endlessly, unless one enforces it in order to fit with the requirement of finding an equilibrium state... One might state that at infinity a fix point exists in a probabilistic form, so we get:

$\color{White} < u_{s} > =\begin{pmatrix} \frac{(u_1+u_2)}{2} \\ \frac{(u_1+u_2)}{2} \end{pmatrix}$

This heuristic interpretation says that, at infinity, the system may be either in one state or the other with probability 1/2 each. It clearly is neither wrong nor totally right, but in case the paradigms of the time requires the finding of a unique equilibrium state, one can imagine this is the only way to compromise cleverly... and get acceptance from peers.

Anyway, always bear this fact in mind when regarding a theory: discoverers turn their findings so they should not break too much in established things, but followers deduce things on that without considering this point.

Best,

Scientific poem

2011-10-01T14:50:00.016+02:00

Post Category > concept - article review - micro-publication - discussion - web - this blog - author's - miscellaneous

I wrote this last night:

Lost in a crowd of blind boxers feels the orphan
And so goes digging throughout the Earth

In search for his mother and his fleshy birth:

The very cause of him is worth the miss of an organ

So are we too, as protected by the science sky,

Orphans of an all very first shared Mother

Who gave birth to all pieces and each gather

In the fleshy hull we learned to name “I”

That out of smartness may raise Her presence

One day or another, did never get questionable

And so were drawn: the line, the dot and the ball

As unique words saying the Deep and the Essence

In cradle of logic, our minds wave like the Klein bottle

As the All led us here without an answer to the Null

And stating: “The clearer we see, the lesser we’re dull!”

We hope every “hence” prevents from any “addle”

Now realize: in the know must always die a gain

As the All and the Null cling endlessly to each other

And we should learn this last thing from our Mother:

The Whole will ever be born out of the Part again

J.C.

Best,

With Primetris any child will know of prime numbers

2011-09-28T21:57:00.021+02:00

Post Category > concept - article review - micro-publication - discussion - web - this blog - author's - miscellaneous

Working in a Museum for Science is quite stimulating for the brain, as long as one considers the hard searching for strategies with which to explain scientific concepts to children using the simplest words and the simplest means. One of the trickiest thing, I think, is to succeed in explaining children what prime numbers are. Prime numbers are taught in France when children are thirteen or so. Because one must learn first to divide and multiply numbers to be able to recognize certain numbers among integers, the prime numbers, being not dividable, it is not thought possible for younger children...

But, is it necessary to know of dividing integers to understand primes?

In fact, I recently concluded that knowing of division is no requirement. One can give to children younger than 10 or even 9 a set of N cubes, and ask them to fit them together so as to obtain a square or a rectangle. See now the picture below... It will work or will not, depending on the primality of N.

By means of many trials, failings (blue) and successes (orange) they learn through an experiment of their own what primes are...If the number N is no prime, then they will finally find the solution in orange, because $\color{White}N=A \times B$, i.e., the number of cubes they have been given is composite. In case they had N cubes in theirs hands with N being prime, they will endlessly try and assemble the cubes without any success. It is up to the explainer to help them conclude that prime numbers are those N for which it is impossible to build a squary form, whatsoever they do and even if for an eternity.

Furthermore, the greater the number N, the longer it is to find the A and the B making N, so the child performing the trials will "feel" that this can be used as a strategy for puzzling others, although without knowing precisely of RSA cryptography (for example).

I guess any child in the world having no particular mind impedement has the ability to understand this, and in some way, this is to me the best way ever to teach mathematics.

Best,

That man will win a Nobel Prize in Medecine

2011-09-24T14:00:00.007+02:00

Post Category > concept - article review - micro-publication - discussion - web - this blog - author's - miscellaneous

You may be now acquainted with this fact : I like forecasting future events, and especially, who is going to win the highest prize in science ever, i.e. the Nobel Prize... Thus I would like to introduce that man to your greedy brain:

His Name : Alexander van Oudenaarden.

Why are his discoveries so important to biology?

He and his team brilliantly succeeded in showing the world the following:

It is possible to model and predict the behaviour of genes in single cells, despite the awful noisy nature of gene expression in such systems.

As soon as 2001, he began modelling the expression of proteins with a simple linear model (see this article) which took into account the low number of molecules in a single cell, which generates high stochasticity due to the poissonian nature of the noise.

At this time, it was only theory.

In 2005, he published in Science (here) a study of synthetic gene network, for which a theoritical model has been established. This model is based on the use of statistical correlation between the expression of two genes through a cascade of transcription up/down-regulations. The fact is, the match between the stochastic model and the measurements is quasi perfect!

Alexander is a physicist of the MIT, who drifted to biology at a time where there is so much to discover in this area. We are so lucky to have a physicist interested in biology: he perfectly catched with his mind what the very need was.

Anyway, now believe 100% in his selection to the Nobel Prize.

Best,

VIVE LA REVOLUTION !

2011-07-14T21:20:00.002+02:00

Post Category > concept - article review - micro-publication - discussion - web - this blog - author's - miscellaneous

It's so fascinating to see...

... that human biological systems can't help resorting to the regularity of mathematical straight lines to show off their power and force.

Best,

Weakening the Erdös-Straus conjecture makes it a bliss

2011-07-14T00:29:00.013+02:00

Post Category > concept - article review - micro-publication - discussion - web - this blog - author's - miscellaneous

About the Erdös-Straus conjecture, Terence Tao published lately on his blog What's New his discovery of an upper boundary for the number of solution to the equation:

$\color{White}\dfrac{4}{n}=\dfrac{1}{n_1}+\dfrac{1}{n_2}+\dfrac{1}{n_3}$

One must demonstrate that for all$\color{White}n$there is at least one triple of integers$\color{White}(n_1,n_2,n_3)$solving the equation, which is still now an open problem. The fact is, such diophantian equations are a real pleasure playing with them, not only because this is technically interesting but also because it is all about pure mathematics. So let's play with it for a while...

One can reformulate it so to obtain the following:

$\color{White}4 n_1 n_2 n_3=p(n_3 n_2+n_1 n_3+n_2n_1)$

$\color{White}p$being any positive prime number. Interestingly, one can prove a "weakened" conjecture when considering that if the latter is true then the following is true as well :

$\color{White}e^{i\pi 4 n_1 n_2 n_3}=e^{i\pi p(n_3 n_2+n_1 n_3+n_2n_1)}$

And the latter is straightforwardly solved since on the one hand:

$\color{White}e^{i\pi 4 n_1 n_2 n_3}=1\quad\forall (n_1,n_2,n_3)\in\mathbb{N}^3$

And since on the other hand:

$\color{White}e^{i\pi p(n_3 n_2+n_1 n_3+n_2n_1)}=\begin{cases}-1, & \text{if }p(n_3 n_2+n_1 n_3+n_2n_1)\text{ is odd} \\ 1, & \text{if }p(n_3 n_2+n_1 n_3+n_2n_1)\text{ is even}\end{cases}$

For$\color{White}p=2$, $\color{White}p(n_3 n_2+n_1 n_3+n_2n_1)$ is trivially even, so one has:

$\color{White}e^{i\pi 4 n_1 n_2 n_3}=e^{i\pi 2(n_3 n_2+n_1 n_3+n_2n_1)}\quad\forall(n_1,n_2,n_3)\in\mathbb{N}^3$

For$\color{White}p>2$, since in this range$\color{White}p$is always odd and since$\color{White}\text{odd}\times\text{odd}=\text{odd}$, it is up to$\color{White}n_3 n_2+n_1 n_3+n_2n_1$to be even in order to resolve the weakened conjecture.

Recall now the following:

$\color{White}\text{odd}\times\text{odd}=\text{odd}$

$\color{White}\text{even}\times\text{even}=\text{even}$

$\color{White}\text{odd}\times\text{even}=\text{even}$

$\color{White}\text{odd}+\text{odd}=\text{even}$

$\color{White}\text{even}+\text{even}=\text{even}$

$\color{White}\text{odd}+\text{even}=\text{odd}$

Considering the latter and the following:

$\color{White}n_3 n_2+n_1 n_3+n_2n_1=n_{\sigma(3)} n_{\sigma(2)}+n_{\sigma(1)} n_{\sigma(3)}+n_{\sigma(2)}n_{\sigma(1)}$

i.e. invariance of the expression under indices cyclic permutation, one finds that there is for all p an infinity of triples with which to solve the weak conjecture.

If$\color{White}f(n_1,n_2,n_3)=n_3 n_2+n_1 n_3+n_2n_1$, then the four cases below suffice to demonstrate all possible cases:

$\color{White}f(\text{even},\text{even},\text{even})=\text{even}$$\color{White}f(\text{odd},\text{even},\text{even})=\text{even}$

$\color{White}f(\text{odd},\text{odd},\text{even})=\text{odd}$$\color{White}f(\text{odd},\text{odd},\text{odd})=\text{odd}$

Given that the setting of even integers has infinite cardinality, we prove in turn that for all prime$\color{White}p$there exists at least one triple of integers$\color{White}(n_1,n_2,n_3)$such that:

$\color{White}4 n_1 n_2 n_3\equiv p(n_3 n_2+n_1 n_3+n_2n_1) \pmod 2$

Hence we have solved a "weakened" Erdös-Straus conjecture.

The next step is now to use this in order to solve the real conjecture...

I'll think of it when I get the time for it ;)

Best,

Is there room for freelance science in the scientific community?

2011-07-11T10:32:00.007+02:00

oPost Category > concept - article review - micro-publication - discussion - web - this blog - author's - miscellaneous

Clearly, this is THE question. But I would first like to adress it in the following way: What justifies the fact that there should be feelance scientists?

By definition, a scientist who is not "freelance" is one that has an academic affiliation. The reason why a scientist should not have this affiliation could be:

Did not study at the university and lacks the University degrees

Has been fired and did not get hired since so

Is either too young (genius?) or too old (retired...) or has "impediments" to study science and get a position (handicapped,...) at the university

Comes from a poor country or had unrecognized degree in this country though having talent and skills (Eastern Europe, Africa, ...)

Became "the one who loses" in a machination when in applying to a grant

And many others...

There are in fact thousands of reasons why one may be put aside the mainstreaming academic system though having the talent to perform excellent research. This generates frustration and the need to do something anyway despite not belonging to the elite.

I think now of those students living in Greece. This country is at present about to get bankrupted... What if one out there is a very smart person who could in the future make great discoveries? According to "what is reasonable to do", he should turn down his project and give everything up.

I personnaly do not agree with that. My first argument is, good scientists are obstinate, so if they which to perform research even if having no academic position, that's good because it proves they fit with the main requirement for being a scientist, i.e. obstination.

The other thing is, science is a common good and as such it must be as much colloborative as possible.

Problems arise when there is a too much of information produced. It is clear that by publishing freely, many will not take quality into account and mislead others or have them wasting their time.

If they want to persuade about their achievements, freelance scientists must be quite meticulous and rigorous, perhaps more than affiliated ones.

Best,

Last month has been... symmetrical

2011-07-06T21:45:00.006+02:00

Post Category > concept - article review - micro-publication - discussion - web - this blog - author's - miscellaneous

Dear readers,

I can't resist showing you the statistics of The Journal of a Freelance Scientist recorded last month. Indeed I have been rewarded with the following:

Clearly, at the middle of June is a symmetry bar to be seen so the whole curve is in fact half a curve mirrored backward-forward with respect to it. I can't help seeing in this some theory, which could have great influence in the field of psychology. Do readers of JOFS surf it unconsciously when their brains decides it according to such a geometrical law ? If so, then it means JOFS renders you mathematically gifted (if you were not before...)

I hope next month will bring another inspiring curve.

So thank you again for this one :)

Best regards,

Linear chemistry under non commutative paradigm : so what?

2011-06-29T22:24:00.043+02:00

Post Category > concept - article review - micro-publication - [discussion] - web - this blog - author's - miscellaneous

In this short post, I would like to deal with the problem of determining a parameterized dynamics when it comes to non commutative models. By definition, a time-dependent process can be parametized using one single value, which is as anyone knows "time", simply noted $\color{White}t$

In reaction chemistry, a reversible order-1 scheme comprising 2 compounds A and B (i.e., exchange reaction) is primarily modelled with the following system of linear differential equations:

$\color{White}\frac{dx}{dt}=-\frac{dy}{dt}=-k_{+}x+k_{-}y$

It is no technical issue to resolve it using conventional methods, so we get the solution:

$\color{White}x(t)=x_{0}e^{-(k_{+}+k_{-})t}+(x_{0}+y_{0})\frac{k_{-}}{k_{-}+k_{+}}(1-e^{-(k_{-}+k_{+})t})$
$\color{White}y(t)=x_{0}e^{-(k_{+}+k_{-})t}+(x_{0}+y_{0})\frac{k_{+}}{k_{-}+k_{+}}(1-e^{-(k_{-}+k_{+})t})$

The latter is continuous and reaction events are hence considered over both a time and a state continuum.

However, if one identifies in the considered chemical reaction a recursive non-commutative characteristic, i.e., the fact that "event A before event B" does not yield the same as "event B before event A", continuity impairs correct modelling of the situation. Indeed, a finite sequence of recursive choices "AB or BA?" over time can be parameterized by means of a sequence of 0's and 1's with 0 standing for one case and 1 standing for the other (there's merely here an isomorphism allowing that), so a real-numbered parameter is no longer the need. The problem is, continuity of the solution implies uncountability of events whereas a sequence of 0's and 1's, even when infinite, will be a countable set.

Hence, a discrete model appears as the sine qua non condition as soon as non commutativity is to be managed by the theory.

When I first studied phenomenological non commutativity in the linear scheme above, which one commonly sketches in the form: $\color{White}A\rightleftharpoons B$, I began doing it with the two following matrices :

$\color{White}R=\begin{pmatrix}\kappa & 0 \\ 0 & 1 \end{pmatrix}\qquad P=\begin{pmatrix}1& 0 \\ (1-\kappa) & 1 \end{pmatrix}$

R models the reactional event : Reactant disappears according to ratio$\color{White}\kappa$.

P models the reactional event : Product appears according to ratio$\color{White}(1-\kappa)$.

One calculates the commutator to be:

$\color{White}[R,P]=\begin{pmatrix}0 & 0 \\ (1-\kappa)^2 & 0 \end{pmatrix}$

Thus I considered a state vector $\color{White}\varpi$on which to operate a linear random walk similar to the map shown here for the construction of De Rahm curves, i.e., to 2 affine functions:

$\color{White}\varpi_{n+1}\equiv \begin{cases} f_{0}(\varpi_{n})=RP\varpi_{n}\\f_{1}(\varpi_{n})=PR\varpi_{n}\end{cases}$

And the map:

$\color{White}\varpi_{n}=C_{b_0,b_1,..,b_n}\varpi_{0}$

where $\color{White}C_{b_0,b_1,..,b_n}=f_{b_0}\circ f_{b_1}\circ...\circ f_{b_n}$.

Interestingly, one can in this case easily determine a closed-form solution of the recursion for $\color{White}\varpi_{n}$ in the form $\color{White}\varpi_{b_0,b_1,..,b_n}$.

Considering the vector: $\color{White}\varpi=\begin{pmatrix}r \\ p \end{pmatrix}\$

The solution turns out to be:

$\color{White}\varpi_{b_0,b_1,..,b_n}=\begin{pmatrix}\kappa^n & 0 \\ (1-\kappa)(\kappa^{n-1+b_0}+\kappa^{n-1+b_2}+...+\kappa^{n-n+b_n+1}) & 1 \end{pmatrix}\ \varpi_{0}$

The parameter being a sequence of the set $\color{White} \left\{0,1\right\}^n$. n encodes time in number of steps while the sequence of 0's and 1's encodes the choice RP or PR at each step.

That first attempt had led me to a non commutative model of the exchange reaction scheme, which was very familiar since resembling the continuous one because of its time parameter.

In fact, this model has an interesting flaw rather than is a good model of the exchange scheme... By inspection, one finds that the only orbits acceptable with respect to mass conservation are all orbits of the form$\color{White}\varpi_{0,0,0,0,0,...,0}$. This corresponds to the fact that the product $\color{White}RP$ may be interpreted as: "Reactant disappears in first place, product appears in second" whereas $\color{White}PR$ "Product disappears in first place, reactant appears in second". Naturally the logic tells us the first statement is the correct one.

My first result was that non commutativity in the model fits with non commutativity in the reasoning.

Strang's strange figures and state superposition in rotating systems

2011-06-27T10:21:00.067+02:00

Post Category > concept - article review - micro-publication - discussion - web - this blog - author's - miscellaneous

Today I wish to try and convince you thanks to this post that making state measurements upon some deterministic oscillatory physical system may lead to a probabilistic theory as the choice for the most relevant way. To understand the idea, one must take into account two different observation viewpoints of this physical system:

1/ the internal one, embodied by Mr Schröd

2/ the external one, embodied by Mr Heise

Since Mr Schröd does belong to the physical system, he does not need to perform measurements upon the oscillator to observe it and his best model can be continuous:

$\color{White}\phi_{s}(t)=e^{i\theta t}$

On the contrary, Mr Heise does NOT belong to the system; as such he has no choice but to perform measurements of the system and record dot-wise its time-dependent evolution in order to analyze it visually. In doing so, Mr Heise has universal limitations to cope with: he may not expect continuous recording of the system but instead discrete ones, as he will not be able to “shoot” successive measurements in a range shorter than Plank’s time$\color{White}t_{P}$(according to the definition of this constant he wouldn’t be able to measure it). All in all, his model will be at the very best:

$\color{White}\phi_{m}(n)=e^{i\theta t_{P}n}$

The correspondence between Mr Heise's external model and Mr Schröd's internal model is obtained by searching$\color{White}t$ such that$\color{White}t=n t_{P}$.

The fact is, this apparently slight difference introduces probabilities in the observation field of Mr Heise, which Mr Schröd will not even know of. This is not due to the system itself – it remains deterministic and unperturbed – but is a direct consequence of the measurement upon the oscillating system.

Let us now consider two opposite cases:

Case A: the oscillator has low frequency/energy:

Scheme A shows the frequency on the Z-plane while diagram I (see below) depicts the time-dependent evolution of the system. In this case, Mr Schröd and Mr Heise observe the same deterministic phenomenon; Mr Heise should only deal with a subset of the total data generated by the oscillator.

Case B: the oscillator has high frequency/energy:

Now a particular effect takes place in Mr Heise’s external observation field, but not in Mr Schröd’s internal one. Indeed, Mr Schröd still observes oscillation of type I whereas Mr Heise will have to deal with observable data in the form of II, III or IV. This effect is better known as Strang’s figure, which occurs when the rotation angle$\color{White}\theta$is incommensurable within the circle.

How is this to be explained?

For example, figure B corresponds to the recording II.

We have the identity $\color{White} \theta=\pi-\delta$ which yields in turn an equivalent model for Mr Heise such that:

$\color{White}\phi_{m}(n)=e^{i(\pi-\delta) t_{P}n}$

Now resorting to Euler’s identity leads to the following:

$\color{White} e^{i\pi}=-1 \Leftrightarrow \left( e^{i\pi}\right)^n =\left( -1 \right)^n$

Which we can put into the first expression so to obtain:

$\color{White}\phi_{m}(n)=(-1)^n e^{i(-\delta) t_{P}n}$

The term$\color{White}(-1)^n$generates the superposition of 2 states both having frequency equalling to$\color{White}-\delta$out of 1 having frequency equalling to $\color{White}\theta$. The cases III and IV are similar to case II, obtained with angles $\color{White}\theta=\frac{\pi}{2}-\delta$ for III and $\color{White}\theta=\frac{\pi}{6}-\delta$ for IV.

A Strang’s figure consisting in $\color{White}k$superposed sine waves having each rotation angle $\color{White}\pm\delta$ needs the 2 following characteristics to hold:

$\color{White}\theta=\frac{2\pi}{k}\pm\delta$
$\color{White}\frac{2\pi}{k}\gg|\delta|$

It is clear that Mr Heise’s consciousness plays the key-role in this effect, as it is left to its own interpretation (i.e., his visual cortex in the brain) to bind together rows of distant dots to recover a continuous model in the form of two waves in place of one.

For all practical purposes, i.e., to fit with observations in the real world and to be able to persuade his peers about them, Mr Heise should then cleverly resort to probabilities rather than to desperately cling to the original deterministic model. In Mr Heise's observation field, the physical system regularly flips from one state to the other so his measurement has probability 0.5 to record the upper wave and probability 0.5 to record the lower one. For example, he then should describe the case II by means of a state vector:

$\color{White}\Phi_{m}=\frac{1}{2}|\phi_{\uparrow}\rangle+\frac{1}{2}|\phi_{\downarrow}\rangle$

where $\color{White}\phi_{\uparrow}=-\phi_{\downarrow}$and are both either the real part or the imaginary part of the orginal function$\color{White}\phi_{m}$.

Thanks to probabilities, Mr Heise has now the ability to describe the system but unlike Mr Schröd, he hence question a lot about how a deterministic rotation can lead to indeterminate observations…

Successful enhancement of JOFS

2011-06-25T00:24:00.004+02:00

Post Category > concept - article review - micro-publication - discussion - web - [this blog] - author's - miscellaneous

The Journal of a Freelance Scientist now includes...

$\color{White}u^2=v^2+w^2$

... Latex formulas!

BIG NEWS OF THE DAY !

2011-06-23T21:42:00.002+02:00

Post Category > concept - article review - micro-publication - discussion - web - [this blog] - author's - miscellaneous

The Journal of a Freelance Scientist has changed... Now it's dark.

.......Sorry for those who do not like it :(

................Welcome to those who prefer it this way :)

Non commutative geometry for the dummies - Part 2

2011-06-19T14:04:00.055+02:00

Post Category > concept - [article review] - micro-publication - discussion - web - this blog - author's - miscellaneous

The purpose of non commutative geometry is to describe the geometric objects which are related to certain algebraic structures. Though being relatively intuitive in case of commutative algebras, the situation becomes rather dazzling when considering non commutative ones... Just for the remembering, I recall that commutativity is the property of certain algebras in which the following holds for any two elements$\color{White}A$and$\color{White}B$of this algebra:

$\color{White}AB-BA=0$

On the contrary of the latter, one should talk about non commutative algebra.

The diagram hereafter compares particular instances of both cases (click on it for high resolution):

Each figure represents a particular geometry with the kind of algebra it is to be related to.

Case I is the most simple one: this is the pair of dots with one at +1 and the other at -1. One can relate that geometrical object, i.e. double-dot, to some algebraic object by means of the set $\color{White}\left\{-1,1\right\}$endowed with multiplication. This set is a subset of$\color{White}\mathbb{Z}$and a multiplicative group which is commutative (try this out yourself if not yet convinced).

Case II is not that more complicated than case I: it is the real line, i.e$\color{White}\mathbb{R}$. By considering the doublet $\color{White}(\mathbb{R},+)$ then again we show that all dots of the geometrical object (here the straight line) can be put into a relation with a commutative algebra (addition on$\color{White}\mathbb{R}$is commutative), so 2 dots of the geometry can be added to yield a third one of the line through the corresponding algebra.

Case III is a little bit more intricate than case I and II, though still very intuitive. The geometrical object under consideration is the circle. There are several possible algebras for this case, either$\color{White}SO(2)$, i.e. rotations in$\color{White}\mathbb{R}^2$, or $\color{White}U(1)$, i.e. multiplication in$\color{White}\mathbb{C}$with complex numbers having modulus 1. Once again those algebras are commutative, independently of the ground algebra ($\color{White}\mathbb{R}$or$\color{White}\mathbb{C}$) chosen. This is due to the fact that rotation in $\color{White}SO(2)$and addition in$\color{White}\mathbb{R}$are in relation to each other through the morphism: $\color{White}\mathbf{R}(a)\mathbf{R}(b)=\mathbf{R}(a+b)$, which preserves commutativity.

Case IV is the non commutative one. There the doublet$\color{White}(\left\{A,B\right\},\circ)$is considered, with$\color{White}A$and$\color{White}B$being non commutative square matrices of dimension at least 2x2 and $\color{White}\circ$a composition law. The geometrical object is in this case very different from that of the 3 previous cases. The many possibilities of multiplying$\color{White}A$and$\color{White}B$are shown here, which is a tree. The issue is then to determine if that algebra is closed, that is to say, if all products are bounded whatever the number of times the multiplication is performed. If$\color{White}A^n$and$\color{White}B^n$tends to limits as n tends to infinity, then it appears in the case presented here that any possible product is bound to a subset of$\color{White}\mathbb{R}$(as shown here projected onto the real line) As shown in this article or this one, the geometrical object can be in some cases the Cantor set or lead to some function of the Tagaki class. Both of these do not appear naturally when studying commutative algebras.

In any event, we are now sure that complex algebraic structures and their study can pave the way for us in searching for novel geometric objects.

What French geniuses really are

2011-02-13T22:55:00.004+01:00

Post Category > concept - article review - micro-publication - discussion -[web] - this blog - author's - miscellaneous

This is one thing every French knows : those who are allowed to study in the "Grandes Ecoles" will become the elite of the country taht is to say, our best engineers and our richest bosses ever. That is the reason why the selection phase is so hard, so wild. When I was around 18 or so I suffered a lot from this competition... I needed time to assimilite complicated concepts, and those like me were said to be too slow for such an ambition... And I went to the University.

Only a few of us would be allowed to take the "Concours des Grandes Ecoles" - i.e. big test with numerus clausus - even fewer to pass it. And those who succeeded became some sorts of Gods. And I have already been told that those who succeed are very, very (very) clever... They would know anything and everything because they passed the test... As compared to them, I felt like being nothing or so.

Okay, that's the way it is... I assumed not to be so intelligent as those who did it...

Thanks to Internet, I lately read what juries write after correcting the tests of the "Concours des Grandes Ecoles"... I am 32, and it has been my big, big, big laughing time.

Let's take a look at this

This is the test to be passed if you want to study in Centrale... Now let's read (and translate) the section dedicated to what were answers to questions in Mathematics. No later than the very first question one can read that:

"A large amount of candidates are unable to make the difference between "inclusion of sets" and "belonging to a set".

Nice start boy! Those geniuses simply do not manage to recognize whether the written symbol is an epsilon or a 90°-spinned U.

The text never ceased to tell us how lame they all are. Now a little further:

"Many candidates made the following statement : Tau equals to Tau' although they only proved that Tau and Tau' are included one in another"

Briefly speaking, those who knew the signification of inclusion simply assimilated it in the end with an equation! Good job indeed.

This happened in 2010... Well, one can hypothesize that it was a bad year, just like with wine and bad years... Let's take a look at this, which is the same Concours taking place in 2006.

First question : "No more than 5% of the candidates are aware of the geometrical meaning of t in the parameterized form x = a cos t , y=b sin t "

It seems like no less than 95% of those geniuses aren't even aware of the fact we are going to travel along the perimeter of an ellipse.

A little further again:

"Many candidates mix up in their mind hermitian product and scalar product"

Confusion, confusion, confusion... It seems to be irremediably what happens when one learns deep things by simply studying the surface of them, no?

Enough now...

In case you can read French, you will discover by poring over these pdf files the following: not a single applicant to these "Concours des Grandes Ecoles" knows really what he does at the moment, and it is all about giving a try to it. No one at the age of 20 may perform clear and profound mathematics, even after two years of training in the "Classes préparatoires"... Those crazy exams are nothing but mental massacres.

Nice to see that I was aware of this from the very start...

Best,

What's up - What's new ???

2011-02-10T20:11:00.002+01:00

Post Category > concept - article review - micro-publication - discussion - web - this blog -[author's] - miscellaneous

It's been a long time since I last posted anything to my blog. The reason is, a lot happened to me in the last months so I could not really take care of you, dear readers. Now I'm back, more ahead of anything than anyone could imagine (I just invented this expression)

So what's up with me?

In the middle of september I got recruited by some "Museum for Science and Technics" as a "pedagogic designer". The Museum is called "Le Vaisseau", which one can translate into "The Ship", and is dedicated to education to science and all the fun that can go with it.

Yes, I can hear some of you yelling at me : "Hey! What kind of job is this?"... Wait a minute. Let me explain this to you.

The aim of that Museum is to help "ordinary" people discover science and technics. To do so, never will they learn there deep theoritical stuffs in order to understand what, say, quantum physics is... On the contrary "Le Vaisseau" aims at making people understand complex phenomena even if their scientific background is low. It's all about interactivity with the many elements of the exhibition which they manipulate if they manage to understand a concept.

What pedagogic designers are then supposed to do is to create ways to explain science without teaching it. Workshops and big-show-like lectures are what we do here for a central task most of the time.

I must say I'm pretty excitated with my job at the time. I have many ideas as to how I can explain that or this by means of this or that...

Well that's it for now. See ya.

What am I up to?

2010-03-12T14:37:00.005+01:00

Post Category > concept - article review - micro-publication - discussion - web - [this blog] - author's - miscellaneous

It's been long since I last posted anything to my blog... I however do not forget what I promised, especially the "Noncommutative Geometry for the dummies - Part 2/2".

The fact is, I scientifically have a lot to do in the moment, which explains why I post so few... I am preparing an e-print for viXra about strong non-linearities in some important biochemical process, and the way one can work them out... During writing the manuscript, I stumbled upon something very new (I mean in the mathematical sense of it), and thought of re-arranging the e-print as to integrate that novel point in it... I finally realized this would ask for more investigation than firstly believed, and decided to write the e-print with the original equations only... Well, it is much effort needed anyway, as I really want to produce the most perfect papers ever.

That's it for now.

The era of necro-technologies

2010-02-26T20:12:00.055+01:00

Post Category > concept - article review - micro-publication - [discussion] - web - this blog - author's - miscellaneous

Big riots against nano lobbies

I am not sure whether the recent riot against nanotechnologies that occurred in Grenoble, France, was due to an absence of satisfactory education about what nanotechnologies really are, as the notorious defenders of the nano-revolution were lately saying. As a biochemist, I must say that I comprehend some of the technicalities involved in the field… But as a person not earning from them neither a position nor funds, I can claim lucid impartiality in the debate. As a hallmark of the polemic, let me point out here that militants ironically call nanotechnologies with the pun “necro-technologies”. “Necro”, in Greek, refers to the English word “death”. It means that their fear is deep, hence meaningful, and it must be respected. This fear is deeper than the fear of television that has been seen in the sixties. Television was said to render telly watchers stupid, unintelligent, brainless, dim-witted. It was though not accused to be causing death.

While nanotechnologies are said to be the revolution that society must undergo according the progress-must-be paradigm, those people are merely afraid for their life. Life is fragile, and losing it in the progress game is what they are quite scared of. Besides, those who defend nanotechnologies claim that those who are afraid simply do not have sufficient knowledge to objectively fear what they fear. But life can end, it is scientifically proven.

What do militants actually fear?

For sure, it is not about the particular technicalities involved, or about the properties of nanotubes or about whatsoever, but a question of common sense, which the scientists who found so many opportunities, recognition and funds in this field may have finally lost. It does not take an expert to realize that industrial lobbies does provide researchers with money to invent and demonstrate things to work, and does give not a single eurocent to check if it damages anything. And it would not be useless to remind them of the fact that, according to an old principle of scientific methodology, pros and cons must be weighed with equal effort before one can objectively claim that pros are permitted to win.

The fact is that cons are now barely emerging, while at the same time pros are so advanced that nano-products are now on the market. High investments never occur where pros and cons are regarded in half-half proportion, as nobody would sign projects and contracts up otherwise. Industrial lobbies want their money back as fast as possible, so they only consider the pros paradigm and leave the cons to in situ experimentation of risks, or burn them at the flame of cynicism. Anyone should realize that nothing bold would happen otherwise, or scarcely. If you find the latter so trivial that you think it was not worth mentioning it, but still blame militants for the way they manifest their fright about nanotechnologies, then you are incoherent, or simply not following the scientific standard line.

Bad memories are in minds

Remember how you, I, and all naïve populations were sold the so-called Genetically Modified Organisms. More or less verbatim, it sounded like: “GMO will save Africa from starvation”. So was the pitch of the soothing discourses. Hence, struggling against GMO was equivalent to killing Africa, and you became the nasty one if against… But high-technology development does occur if and only if huge amounts of funds are there available to make them happen, and huge amount of funds can only come from the richest industry, which allegedly seems to have always found Africa uninteresting for some reason. Monsanto has never had the main part of his market in Africa, which for now is still waiting for its genetically modified miracle. I am not even sure Africa was mentioned in Monsanto’s business plan. Nobody invests in starving Africa, but now GMO are in your plate. Anybody knows this by mind-processing a bit of common sense.

I would not be surprised to learn from objective psychological inspection (but empathy is still one using logical skills and current experience) that nanotechnology researchers are nothing but smart donkeys kicked at their back by the whippy spanking of the publish-or-perish stick, and attracted ahead thanks to the hope-to-be-awarded-the-Nobel Prize carrot. Industry is well aware of the fact that the researchers’ nice humanism makes them act in the way industry needs, and makes them speak well about their project while keeping them blind enough about the very aim of things. Everything fits, indeed.

To accept nanotechnologies, militants need to be convinced that nanotechnologies are essential for them, and that no one is going to pervert the potential that this technological advancement has. But History does tell any logic-based and memory-protecting mind, be it the one of an expert in nanosciences or not, that so it was not in the past. If it is true that a knife does not prove to be a weapon unless a hand takes it and kills with it, it is also true that industry does never include the ethics factor in its business plans and business models. Thus, stores and outlets sell cooking knives as well as hunting knives. Capitalism makes inventions available without considering moral responsibility in doing this, which it prefers leaving to the consumer’s choice of buying or not, i.e., the consumers awareness of consequences. In that rioting day, militants were showing off what they are aware of.

As we now know a lot of, asbestos was sold and installed in buildings before any has tested whether it causes cancer or not. Nuclear power reactors have mushroomed here and there, but not research laboratories where to discover how to recycle nuclear wastes having long decay half-life. Cigarettes were long sold without restriction until politicians found lung cancers to be too expensive for the healthcare system. I will let the reader self-enumerate other examples (there are so many).

The fact is that new technologies have always seeded their commercial success in the soil of legal systems, as they have always sown their seeds where constraining laws were lacking. The run in between the arrival of a product on the market, which is always first in place, and its control by the legal system, which is always second, is the time of all possible damages. At present, we are adapting our legal system to Google extreme strategies, aren’t we? Thanks to our long experience of capitalism, we now know too much of that phenomenon, no one can contradict this.

My own view-point?

My personal view is that to infinitesimally shrink devices and let them float around in the air would be not sane at all, not sound. If things are glued and well controlled, then forget the panic. I cannot help thinking of tiny acarids, which may trigger allergies when they are inhaled. When in the body, the immune system regards them not as lost objects but as intruders, and undergoes immune reaction against them, although being not pathogenic stricto sensu. But for bigger insects, like ants, it is not so: the immune system does not take them into account. In this fact, the size has its importance.

You may then say allergies are not so frequent in populations, and furthermore not lethal most of the time, and you would be right saying so. I would thus reply to you that acarids have evolved with human beings for millions of years within the same ecosystem according to each other. The worst case scenario might have been wiped away thanks the progressiveness of their concomitant emergence. On the contrary, nanotechnologies are created in closed idealized place, i.e., apart from humanized natural environments, and once they proved to be powerful enough, what if they are launched into the nature? Since they do not emerge out of the latter, they are de facto not in equilibrium state within it, and therefore are like a perturbation of it. All consequences are the response to this perturbation of brand-new species spawned in well-equilibrated system. And there are so many issues to be addressed in investigating what is going to happen after such a perturbation. Among the many questions that I find relevant, one is: Do macrophages phagocyte nano-particles? Are those white blood cells destroyed or rendered useless by them? If so, our immune system could be quite damaged by nano-particles, and then militants are right to act the way they do.

I am not against nanotechnologies. I am solely advocating the scepticism principle of Science.

Nano-conclusion

In the end, what militants want is… to not believe in nanotechnologies. Scepticism, to not believe but to aspire for objective arguments. Actually, this demand would make excellent scientists out of them, wouldn’t it? They do not feel at ease with what they do not objectively know of, like scientists do either. It’s not a lack of scientific education that they are suffering from, but on the contrary, they are benefiting from a plain use of it.

Dr. Alain Privat, a pending Nobel Prize winner

2010-02-22T19:02:00.061+01:00

Post Category > concept - article review - micro-publication - discussion - web - this blog - author's - [miscellaneous]

To echo back Steven Colyer’s posthumous Nobel Prizes series, I wish here to anticipate with this post about one future possible winner for the Nobel Prize in Medicine, who I personally regard as being worth this honorific title today, although he was not awarded it yet. I am triggering here the campaign.

Fast portrait for a long career
Dr. Alain Privat (see photograph) is nothing less than a physician and a researcher in Neurobiology at the “Institut National de la Santé Et de la Recherche Médicale” (INSERM) of Montpellier (France), who has been working on the nervous central system for about forty years, and as a consequence learned to know it as well as can be. During year 2003, he and his collaborators published a ground-breaking result in the field while attempting to address the following long-unanswered question: How does one regenerate the nervous fibres spanning from spine to limbs in patients who had their spine broken in an accident, and who for this reason have become handicapped and will be sitting in a wheel-chair their life long.

Battling for the handicapped
The main reason why quadriplegia and paraplegia are still at present irreversible after-effects of an accident is that the human nervous system has not the ability to compensate the losses by reconstructing the nervous system where it has been damaged, like lizards do with their tail after it was cut. In human adults, if it is true to say that the majority of neurons lose the ability to perform mitosis and thus to divide into daughter cells (except in hippocampus, our memory centre), it is nevertheless wrong to say that neurons lose their capacity to regenerate their axon, i.e., the long fibre that conduct electric signals from one point of the body to the other, and which is mainly disrupted in the handicaps mentioned above. Actually, the neurons of an adult are able to let bulge out and to throw a new axon away, a phenomenon called by experts “neuron sprouting”. It was observed in vitro, but not in vivo. Why so?

Overcoming the walls against sprouting
The smart hypothesis that Dr. Privat and his team tested in their article was that this property to sprout axons should be in vivo hindered by the scar which normally forms in an injured spine, the so-called “glial scar”. There are indeed, in my nervous system as well as in yours, many cells other than neurons, and which one calls with the generic name glial cells. So to say, it has long been an old tradition to focus on neurons when attempting to understand and to control what is happening in the nervous system; perhaps is it so because of the ramified form those cells have, which makes them so attractive at first sight. Instead, Dr. Privat and his collaborators have focused on what everybody had so far put aside, or even denigrated. Around neurons, the population of glial cells is indeed tremendous, and is – like everything in the body – not useless at all: glial cells regulate the parameters of the physiological milieu. When a lesion occurs in your spine, the fact is that some of your glial cells, precisely those called astrocyte, undergo hyperplasia, that is to say, growth of the cell body, which blocks the lesion area. The smart hypothesis was to state this would impair axon sprouting in an injured spine.

In mice, they succeeded in reducing the glial scar after spine lesion by using double knock-out mice for both the glial fibrillary acidic protein (GFAP) and the vimentin protein. Indeed, the two of these proteins was known previously to be major proteins of the astrocyte cytoskeleton, and one could well think that astrocytes could not trigger hyperplasia without them. By testing how control mice versus knock-out mice for those genes were able to efficiently run on a grid after spine lesion, Dr. Privat’s team demonstrated that reducing the glial scar helped better recover locomotion skills. Without the scar, the neurons of the wrecked area could now sprout an axon from spine towards limbs and thus reconstruct the impaired motion functionality.

I feel like adding here that this article has been published in a high standard journal, although it was neither Nature nor Science, but PNAS instead. Not that PNAS may be thought of as being a mediocre journal, as the fact is that PNAS is an important revue, i.e., one of the most cited journals worldwide, but PNAS impact factor is calculated to be less than that of Nature and Science. This result was worth winning Nature or Science, and the choice for PNAS still remains, at least to me, quite obscure. The publication has anyway caught the world’s attention.

Unforgettable encounter
I remember that 2003-2004 was the year that I passed the MSc Degree in Cellular and Molecular Biology, that is to say, the year of their incredible publication. The news had spread up throughout Montpellier that Dr. Alain Privat’s laboratory had finally achieved the unfeasible thing. I then felt like prospecting there rapidly, in case I was awarded the PhD grant. I sent an e-mail to him, carefully writing that I had plausible chance to be awarded the scholarship being my success in the first selection turn of the Ecole Doctorale. He accepted to have a talk with me at the University of Sciences and Technology, in his office. The latter was precisely situated on the campus.

In Montpellier, the University of Medicine lies inside an ancient gothic-styled building situated in the very centre of the town, from what, as I guess it, students and professors may think to acquire an aristocratic status. On the contrary, the University of Sciences and Technology, with its campus mostly built during the sixties, suffers from the pathetic style of socialist architectures. You would not believe a king to find a convenient throne here. Though being primarily a physician, who naturally would have belonged to the former, Dr. Alain Privat had his office not in the former, but well in the latter. A king is a king, even if sitting in a wooden castle.

While getting to the place of our appointment, anxiety was there in me so deep, as I was aware to be about to meet someone essential for the science world. For this reason only, I felt like having a soothing walk around the splendid sculpture placed in front of the main gate of the Faculty. The beauty I am writing about is offered to your eyes in the second photograph of this post (if you do not see it, then it simply means you are blind).

If you let my shortly drift off of the subject here, this fine-looking piece of artwork was smartly entitled Tribute to Confucius by its author, probably in case the uncultured scientists passing the entrance, which it evidently decorates, would have thought this was, in fact, a gigantic doughnut onto which a massive sausage was glued for ever, and hence would not seize the philosophy it symbolizes. In the years I was studying in Montpellier, some students, who without a doubt were pitiful vandals, climbed up onto the sausage with ropes and grapples in order to paint the top of it in white. Those pitiful vandals allegedly believed that mayonnaise was all the sculpture was missing. Fortunately for our delight, the mayonnaise is not shown on this photograph... I guess this is exactly what must happen in a world in which erudition is no longer the aim of scientists, and that is why I recommend this sculpture to be more conveniently placed in front of the University of Letters. True art must live, breathe and perspire where it belongs.

Anyway, after a few turns meditating around that unforgettable symbol, I escaped away to Dr. Privat’s office. There, he has been the first and the last researcher I have ever met having such a large desk and so a committed secretary. I remember a charismatic person, wearing a black cravat and a black costume, which made him so immense in front of me. He had this ability to impress much with his sayings, even with a few words. Right after I began talking, his telephone rang with an important call, and I went in another room for half an hour before I could resume my proposal. He said to me his laboratory was missing students, and that a PhD position could be made available in case I was granted the money. As I left his office, he encouraged me for what was going to happen after this day. This day has been the day I have thought to be the tiniest student in the world.

Defender of adult stem cells
On the 28th of April 2009, Dr. Privat gave an interview at the Assemblée Nationale in Paris so as to plead in favour of moratorium concerning the French laws in bioethics. The fact is that Dr. Privat’s research group is now attempting to provide injured spines with stem cells able to replace the lost cells with new ones grown out of stem cells graft. The very issue regarding stem cells is the how to obtain them, and until late 2006, one had to extract them from embryos, which ethically speaking is not trivially acceptable. The recently discovered iPS cells, which are common adult cells (in fact the most common of them, fibroblasts) that are totally re-programmed into stem cells by transfecting them with four genes have definitely changed the rules of the game. Stem cells will now be obtained using the cells of an adult skin, i.e., without killing an embryo, which makes the ethics less sensitive regarding that novel generation of stem cells research. Dr. Privat has asked for a moratorium regarding the French laws aiming at regulating such researches, given the rapid changes they are currently undergoing.

So, what lacks to make him a Nobel Prize winner? Probably nothing.

Noncommutative geometry for the dummies - Part 1

2010-02-16T13:01:00.113+01:00

Post Category > [concept] - article review - micro-publication - discussion - web - this blog - author's - miscellaneous

I am currently getting stuck with my work-in-progress aimed at developing, for the reaction chemistry field, some robust mathematical models which feature natural noncommutative components. In the meantime, I am preparing another manuscript, for which I have all things nearly done. Coarsely speaking, it is all about some multi-dimensional nonlinear processes known to be essential in bio-molecular networks, and which were so far thought to be not analytically integrable… I cannot however tell more about it now. It needs to be maximally proofread by me before I can post to viXra.org. I am tired of those independents posting too fast, too roughly, as if they were sending their post into the garbage can: as an independent, one must double the effort in reaching excellence. Coming soon anyway…

In any event, with this post I have decided to address the jagged issue (“jagged” because it hurts when one attempts a grabbing it) of presenting the main well-established outcomes in non-commutative geometry. Just asking virtually the great Pr. Alain Connes for an easy-to-grasp lecture on the subject, and you’ll get into something like this :

(Translation: "Sure! But, as you can see it, the explanation is non-commutative itself... And it unfortunately admits no inverse.")

As seen through this superbistically well drawn picture (self-flattering causes no harm), a popularized explanation may not be performed without physical damage :(

Reading Pr. Alain Connes’ book Noncommutative geometry is a tough task; quite a tough one, in fact. And I am well talking about “reading”, and not “comprehending”, which is a step beyond that. The way Pr. Connes writes (and perhaps, that he makes mathematics) is to me well in some French manner, i.e., it goes like a flowing development of constructions rather than a step-by-step rationalization of closed achievements. A picture of what I am meaning writing this would be that the former is someone pacing here and there throughout some unknown land, studying every woods and rocks whilst constantly making logical connections, whereas the latter consists in building huts where a convenient place has been revealed, and going further if and only if huts have been turned into a village. I guess that Pr. A. Connes does not need to stay long on a subject to master it. Many of your hard points are his trivialities so that, behind his flying intelligence, you are simply meant to be the running one.

We'll run anyway.

Among the many aspects in algebras of operators that Pr. Connes has addressed, there are however some that one can hope to understand. E.g., one easily understands that if two elements of some non-Abelian algebra do not commute, then the way one infers the value of unknowns in this algebra must be done with respect to the order in which operands are composed in the expression. And the way we handle the usual one-dimensional numbers - may they be natural, real or complex ones - gives a bad intuition about how to deal with the non-commutative issue.

Indeed, a non-commutative algebra generates a commutation table which is far more complicated than that of a commutative one. For instance, one should think of the multiplication rules between the basis elements i, j and k of quaternions or of the dihedral group D3: in the multiplication tables of these examples, there is no strict equalities regarding the elements mirrored apart the diagonal line, as it is the case in a commutative algebra. Then, one wise way to shunt one’s path through the awkward land of non-commutative asymmetry is to focus on traces.

By definition, a trace is a positive linear form such that:

$\color{White}Trace(AB)=Trace(BA)$

Because of the non-commutativity, the multiplication between A and B requires additional information about which is first and which is second; one should interpret that as being a restriction put on the algebra that both operands belong to. Instead, one may focus on an invariant application, the so-called “trace”, which unlike pure multiplication will be invariant under inversion of operands order; when resorting to a trace, some unifying characteristics can be seized without the need for considering one particular order or the other. In summary, the trace application bypasses the indeterminacy that non-commutativity introduces in the algebra.

In matrix algebras, the standard trace is the sum of all elements of the matrix diagonal. A. Connes’ discovered the importance of a generalized trace formula while calculating the so-called Chern character for Fredholm modules... The above formula does only consider two operands A and B, for which the formula is trivially always true. However, when considering more than two operands (say now the set A0, A1,..., An), the trace function applied to the multiplication of three or more operators has not automatically the property of independence cited above. It is however fundamental to gauge how far a trace can be invariant in a given algebra, as complex calculations with more than two operands may have their traces drifting away otherwise.

The fact is that, if not always true for any permutation of a set of multiplied operands, the trace is invariant under cyclic permutations , so we have the identity:

$\color{White}Trace(A_{1}A_{2}...A_{n})=Trace(A_{\sigma(1)}A_{\sigma(2)}...A_{\sigma(n)})$

where sigma permutes the indices accordingly. Given the latter, A. Connes has derived the notion of cyclic n-cocycle of some algebra, which may be interpreted as a generalized trace. E.g., a cyclic 2-cocycle is a functional tau verifying the two conditions hereafter:

a) $\color{White}\tau(A_{1},A_{2},A_{0})=\tau(A_{0},A_{1},A_{2})$

b) $\color{White}\tau(A_{0}A_{1},A_{2},A_{3})-\tau(A_{0},A_{1}A_{2},A_{3})+\tau(A_{0},A_{1},A_{2}A_{3})-\tau(A_{3}A_{0},A_{1},A_{2})=0$

a) demonstrates the cyclic invariance of tau as for the standard trace, while b) demonstrates the compatibility of this functional with both the addition and the multiplication. If both a) and b) are true, then tau is the character of a cycle on the corresponding algebra.

This is a functional similar to the one shown above which Jean Bellissard used to explain the plateaus observed in the quantum Hall effect, i.e., the fact that the Hall conductivity is in the form of a staircase-like function of the Fermi level jumping onto discrete values as the Fermi level is varied continuously. Using tools of the noncommutative geometry, Jean Bellissard has demonstrated the existence of an important element in the corresponding algebra, a projector E, given by the normal application at the surface of the metallic sheet of the experiment. This E may be deformed into a family of idempotents Et along with the continuous variation of the Fermi level. Then, a theorem stating that tau is stable for the whole family of idempotents, i.e.:

$\color{White}\tau(E_{u},E_{u},E_{u})=\tau(E_{v},E_{v},E_{v})$

with two distinct u and v, does the rest of the job. In his book, A. Connes claims that the functional tau is for this reason a good candidate for explaining the observed plateaus mentioned above.

At this stage, you may logically ask why the word “geometry” in the title of this post while what I have only been writing so far was about algebra. In fact, with the example of the quantum Hall effect, we begin addressing this point, as the family of idempotents is linked to the normal application at the surface of the metallic sheet of this experiment.

I will deal with that in the second part of this post, coming soon.

RECOMMENDED FURTHER READINGS: About non-commutativity, trace and statistical description, you can read Terence Tao's excellent post here.

We all dream of a nanoworld

2010-02-09T21:02:00.004+01:00

Post Category > concept - article review - micro-publication - discussion - web - this blog - [author's] - miscellaneous

This drawing appeared on my graphics tablet the day when I questioned about nanosciences, and how they are going to change our way of life. But will they change it in an ostentatious manner? According to their property of being so tiny that no one can see them, but so smart that they will be needed in every corner of the Earth (if one admits that spheres can have corners), I say no : we will not see them roaming around... An obvious time of paranoia is thus looming in front of us. I foresee populations will fear to be spied on by Governments, saying there are nano-eyes and nano-ears in their homes. Whether true or not true, paranoia will be the only way to tame one's ignorance. I then fear a Civil War against Nanocracy. Is there a logical way to establish that nanostuffs are surrounding your own environment? Click the strip above, and you may get the answer.

Power in the science world

2010-02-08T11:56:00.009+01:00

Post Category > concept - article review - micro-publication - discussion - web - this blog - [author's] - miscellaneous

Professor A had much self-confidence in himself when he talked to others about his own achievements, and when he met Doctor B in whatever scientific congress (details are not essential here), he began shedding his science at him:

- When are you going to present your work, asked Pr. A to Dr. B? Personally speaking, I have a presentation of my theory about the incompleteness of quark theory in the morning. I called this theory “the Mickey Mouse theory”. According to my groundbreaking vision, quarks would not be the very tiniest particles in the Universe. There are other particles, which are the ears of a Mickey Mouse head while quarks are in fact the head itself. It is revolutionary at all.

Dr. B was not that self-confident, but on the contrary rather filled up with doubts. Doubts about what he was searching for, doubts about whether he was doing well or not. Perhaps, he owed that modesty to the fact that he had not had his education in some prestigious university. Or maybe was this psychological fact more deeply embedded in his very self, as he questioned a lot about anything while others were always sure to be of the best kind. He was never sure about things, he constantly needed to prove. Dr. B did not dash towards success, this was his flaw. His natural tendency to produce mental question marks led him to work as a researcher in Physics. There had been, in fact, no better job for him.

Hearing about Pr. A’s Mickey Mouse theory, Dr. B could not help thinking that such a theory had the smell of a legend or a tale, at best a crackpottery of the first kind. Dr. B had so much learned about how to avoid peer’s attacks by using secure terminology in the discourse that he first thought Pr. A was one from a worst university than his, one who did not know yet how to spare himself a peer’s taunting. But Pr. A’s attitude was the one of an established person, who went throughout the place shaking hands, and who had abhorrence talking about subjects other than his.

Pr. A finally figured out Dr. B was not interesting enough for him. Indeed, Dr. B did not understand the Mickey Mouse theory, which was too abstract for him (Pr. A had seen the doubt in Dr. B’s eyes, which had been empty in the moment, and concluded it was too abstract for him). He then quitted Dr. B without a goodbye, and went away into a small group of reputed scientists where he shook some other many hands.

The relevant terminology for describing that group was Princeton, Cambridge, Nobel Prize, Nature journal, etc.

Clearly, Pr. A was part of the elite race. Having talked to Dr. B had been, in fact, one hazardous event of life which Pr. A had rapidly fixed by escaping from Dr. B, so he had not stayed too long with his feet in the mud. The two would never converse again with each other in the day.

The result was that Dr. B already knew what was going to happen to him. He knew now that, in the future, he will have to know everything about the Mickey Mouse theory; he knew that the state of the art in Physics was going to change this way, and he could not afford ignoring what everybody will have to know by heart around him. By not knowing Pr. A’s Mickey Mouse theory, the risk was to get excluded from the best circles he was now allowed to be in.

On the contrary, Pr. A. would not have to know anything about Dr. B’s achievement for the purpose of his own careering. Indeed, Dr. B aimed at using classical optical properties to help blind persons recover their sight; the equations he used for this were not groundbreaking at all.

In developing the Mickey Mouse theory, Pr. A estimated he did not need to learn how to not stay blind.

My first upload to viXra.org is now available online

2010-01-15T08:50:00.131+01:00

Post Category > concept - [article review] - micro-publication - discussion - web - this blog - author's - miscellaneous

Lately, I (finally) discovered where to upload the e-print of a research work I carried out in the last few years. This is meant to be a first theoritical achievement in providing biochemistry with an enhanced theory, of which in this post I present the most fundamental points it deals with. Hereafter is this e-print I am blogging about:

http://vixra.org/abs/1001.0018

In a previous post which you will find here, I had tried to convince you about how crucial it is to describe biochemical processes with a model seizing all aspects of topological complexity. In deed, many aspects of information management in living cells depend on whether or not that information is rendered fuzzy by the running dynamics and the gene network topology they have (see references). Complexity is thought in cellular genetic processes to let noise occur, and one fundamental question then arises with this: In cellular networks, is noise some necessary feature, or is noise some dynamical flaw that evolution has anyhow to cope with? To answer this, one has first to totally decipher where this fuzzyness comes from, what characteristics it has, how to model it in the best way. As we know it today, information is in living cells mostly in statistical form.

This article addresses the above issue when the equilibrium state of some linear exchange reaction (reversible first-order scheme) is considered. Its results (mathematics + numerics) emphasizes the fact that non-commutativity has a role to play in such systems, for the interesting reason that concentration exchange between two entities X and Y is at equilibrium not particularly ordered with respect to time: the simultaneous antagonist transformation of X into Y and Y into X can be achieved following two possible event sequences (former first latter second, or conversely), which the system is free to choose at random. This generates a rich amount of possible statistics, which has never been seen so rich in the past for linear schemes.

The whole theory highly depends on the existence of Planck's time, or more generally, on a shortest time interval below which no mass can be displaced from one place to another, provided the involved distance is at least so long as one Planck's length. There is indeed in exchange reactions always mass displacement (think of isomerization from one isomer to another with atoms moving inside the molecule) : Planck's length is so little (around 1.32e-35 m) that the considered movement does involve Planck's time naturally. This minimal time is there called the chronon of the theory, a notion first introduced in the scientific literature by Caldirola, and treated in this article as an open value so as to see all imaginable consequences.

On the left is the schematic representation of the situation. A hypothetical molecule, which has different isomer forms due to a second possible stable conformation, is let free to react at time t1 with every molecule being in the elbow-like isomer form. As time goes by, some of those elbow-like isomers will react into the product, which is the ruler-like isomer at time t2, following a first-order scheme. However, such a transformation requires the displacement in space-time of the green-blue chemical group over a distance generally wider than Planck's length, so we know there exists a duration named theta, which is thus the chronon of this reaction, below which no more product can be found to have appeared because of the fundamental impossibility that goes with this. The whole theory depends at fullest on such a limitation.

Formalization of such dynamics leads to a non-commutative theory. This article aims at demonstrating the interest of regarding non-commutativity as a standard of the description in chemical reaction processes. The statistics obtained by means of in silico approach could let you think of nonlinear reaction schemes and their complicated statistics (e.g. the chaotic logistic equation), though the considered scheme is well a linear one. And the theory presented here holds in the limit of high concentrations, which makes the theory somewhat eventually validated by some macroscopic experiments.

Let us only hope it'll come soon... <

Contribution for the Backreaction blog

2010-01-09T21:14:00.054+01:00

Post Category > concept - article review - micro-publication - discussion - [web] - this blog - author's - miscellaneous

This post is my contribution to the challenging issue proposed by Bee on:
http://backreaction.blogspot.com/2010_01_01_archive.html

Go there and read the interesting question, I could not resist answering it!

Dystopia

25 years in the future, I guess Google will have anyway already launched its new ground-breaking product named “Google Discovery”, totally free, handy, and easy-to-launch. This engine surely will extract from some Google’s private scientific publications database all relevant results, then mix that information bunch together in some bag of bits, which detractors will surely call “binary mud” (though it will not be), perform all logical connections between notions, theories, equations, everything, and thus painlessly engineer new brilliant physics discoveries. No doubt Google will at the ECS subsequently provide the very first non controversial unification of all physical forces, released in the optimized time of 0.1 seconds – one single click on Google’s site, and let’s go for it! I guess Google’s super-computer will be, at that time, the first non-human awarded the Nobel Prize ever. I can also foresee that Google's machine will utter no “Thank you very much” in Stockholm since having no feet to go there at all. I believe that Nature will write “this is a step forward” in its journal.

Following Nature’s positive claim, I foretell Google will rapidly make sense out of this, and create some Google Research Tools Suite, comprising Google Discovery, Google Theory, Google Experiment, Google R&D and Google SellTechnology. Without a doubt, there will be 5 such icons to click on Google’s site, each having eyes in the “o” looking at you when you are looking at them, plus smiling mouth underneath to get you in the mood for searching. Thanks to Google, in the future, scientific research will merely be entertaining and definitely hilarious.

I thus forecast that, having heard Nature’s call, academia will recognize that the competition is going to be played with Google, or will not be played at all. Following the least-effort-for-biggest-gain line, universities will test Google Discovery versus the researchers they hire, and obviously figure out how lame fleshy researchers can be. I guess many physicists will begin to remorse about the least action principle universality, which leads the philosophy of this, possibly deny the theorem in thoughtful publications just to give it a try, in vain. Becoming Google accounts, universities will smartly fire 95% of their slow organic researchers, and continue hiring until retirement the remaining 5% for clicking continuously on Google’s 5 icons. That 5% will be more than elite, knowing anything about everything, but clicking stupid icons all the time; they will constantly be asked to click faster than those of rival universities. Nobel Prizes will be awarded to best clickers of the decade. As usual, Nature will write this is “breaking through progress for science”.

In 25 years, Nature articles will be long-past routinely generated by Google Journal free article generator.

Utopia

In 25 years, I foresee that Garret Lisi will be recognized as the father of this emerging novel researcher species beginning to come into view at that time: scientists making science in order to solve issues, and not careering in order to obsessively grab some Nobel Prize. At that time, a Garrett Lisi Prize has been created by the Lisi Foundation, and the awarded person is given a medal bearing a picture of a surfing board across Shrödinger’s psi function. Scientists of that time are shocked when they are told that Dr Lisi was lynched 25 years ago for both publishing and surfing in his life, like we are shocked today learning that Dr Turing was lynched in the past for having invented the computer and being gay at the same time. A Lisi College for Physics and Good Times is going to be built at http://www.lisi-university.com/, which he will e-inaugurate cutting the bitmap of a ribbon with a click activating some chisel on the screen. At that time, young physicists envy Lisi, saying that he and only he was the one to understand everything, and that his detractors were old austere skilled-in-the-art frustrated unsuccessful scientists.

In that time, scientists are asked by academia to open up their minds. Universities want their researchers to go to museum, listen to music having emotion in it, watching paintings displaying sense with unspoken language, in order to educate their brain and make them aware of other things and other manners. In the future, universities will care about how sane their researcher’s mentality is, and understand the interest of liking art and getting inspired by it in their researches.

Ambition’s no longer the trend of the time; aggressiveness targeted at students and peers no longer exists.

A new generation of publishing system has emerged. At that time, scientists perform real-time publications directly on the Internet, building up knowledge daily, uploading equations and measurements day after day into an immense data pool. This data pool is frequently processed by means of logic analyzers, which connect ideas one to the others, weaving the great theory of all things with equally everyone’s contribution. Whether or not one’s contribution is right or wrong does no longer make sense, it is up to the logic analyzer to decide. At that time, and because of the fact that this ubiquitous new system does finely work, academic competition has ceased. Papers bibliography have become so interwoven and complicated that no one is now able to disparage other's paper without disparaging one's own work, which makes judgement objectivity purely impossible. Careering and killing others for success has become an old and regressive behaviour, which scientists are now laughing at.

In that time, at last we are doing science.

Sentence of the day

2010-01-08T11:36:00.009+01:00

Post Category > concept - article review - micro-publication - discussion - web - this blog - [author's] - miscellaneous

Among physicists, the dangerous ones are those wanting the whole great Universe to be assigned their name<

About micro-publication and its benefit for researchers

2010-01-04T21:10:00.105+01:00

Post Category > [concept] - article review - micro-publication - discussion - web - this blog - author's - miscellaneous

Freelance research is what one can define as the "scientific activity of searching and discovering scientific matter without being affiliated to an academy for it". The very harsh point with such a status, or to better say, with such a non-status, is to find the schedule to offer publications and inventions. Claiming independence is one thing, demonstrating and making sense with it is one another. In deed, if you found some way to become secure with a job, and have time spared to discover like you ever wished to, then why shouldn't it be your right to discover according to the following logic : "What is not forbidden is allowed"?... Since 2004, the date when I began practising as a freelance scientist while applying for PhD grants and jobs that never came, I have experienced a lot about how to perform sensible research works as a freelance participant. This is what I am exposing here with the term "micro-publication".

First of all, I would like to emphasize here the point that freelance research, or by more broad meaning "independent research", is not a fringe's activity. One can easily imagine that many scientists hired for carrying out researches in some field they are recognized to be competent in would like to attempt in some other field for which they have no institutionalized support. E.g. what if a climate researcher has a special personal questioning about, say, prime numbers? Or, what if a young researcher with competence in experimental biology would like to search for theories aiming at future possible researches he will perhaps carry out in the future? Others will tell him this is in vain, since out of the mainstream, so he will forget about this, and do not what he is told not to do. This is omitting that science is an ADVENTURE FOR PIONEERS, not the BUSINESS of an established BOURGEOISIE. What if Galileo had been sitting on the easy side of his epoch's establishments ? We all perhaps nowadays would still think Earth to be in the middle of the Universe, nothing less than this... With established science and the strict pertaining of scientists to institutions, we are tending to forget this major point of the scientist's Essence. Scientists are forward-movers, question-markers, discoverers, answerers : establishment in stones of things without afterwards is not and will never be in their deep nature. Every genuine scientist is somewhere independent, at least in its very heart.

Clearly, therapeutic research, as it is performed in biomedical science, or technological research, e.g. nanosciences, are not the concern of independent works, at least directly, because the final aim of such researches are bankable goals. However, putting the whole great science into the narrow box of that pair of fields equals to forgetting the philosophical part of science. And, forgetting the philosophical part of science is denying what it has been primarily invented for : to produce a culture of coherence not depending on God, that is to say, to free minds of believing. That is the reason why there is one science, but infinity of religions. One may call that part of science "ideologic research". To give an example of ideologic research, which nobody can be granted money for though it is important at all : the probabilistic nature of matter. Though this question does not leave minds quiet and is currently discussed, nobody adresses how this could be technically resolved. In deed, being able to assert that the matter is so or so does not explicitely bring out efficiency and industry enhancement, but only a world of wrong or right ideas. Physicists are solely asked, from time to time, to wonder and to deal with the subject for a little while, and that's it. Technical reasearches about how to relate matter behavior to a non bizarristic paradigm are apparently not worth it. To show how this particular issue could be adressed reasonably, I hope to publish in this blog what conception I have of it, in one of my many micro-publication.

The idea would be to perform super-collaborative works in a coherent bottom-up approach. The basic principle would be to offer independent researchers, be they partially or fully independent, a networking pool into which to throw small productions of theirs. Each small production may then be as a piece of a puzzle, of which the admitted format may allow to construct without much concertation the whole end picture. In my idea, micro-publications would be no more than publication like the good old classical ones we are accustomed to, but very short, and adressing one particular bold question of larger unresolved topics. E.g., "How to calculate the natural density of such a class of integer?" would be the initial question; then, give the technical solution to it; then, propose new questions to help others relay your work. Peu à peu could then profound works emerge, with an optional publishing in peer-reviewed journals. Using categorization algorithms like those used by Google, or some logical anchoring between micro-publications, on may even get an automation of how the whole work raises out of single works. In the end, i.e. when an interesting result has emerged, the list of participants could be data-mined so as to chart the namewise complete history of contributions. What format may fit with the requirements stated above is what I will be installing in that blog with my own works <

New design

2010-01-04T12:47:00.003+01:00

Post Category > concept - article review - micro-publication - discussion - web - [this blog] - author's - miscellaneous

For better comfort and clarity of your reading, this blog is now endowed with new guiding feature, placed as you may see at the very top of any new post. That bar under the title indicates square-bracketly the focus of the post, with the following meaning:

Concept.................... Proposal pointing out one special need in some current research field
Article review........... Focus on one paper or a topic-related bunch of scientific publications
Micro-publication.... Own rapid research work released in open research flux
Discussion................ Debate about a boiling subject of current research/science
Web.......................... Generally, links to web resources
This blog................... Information about The Journal of a Freelance Scientist
Author's .................. One special introspective text emitted by this blog's author
Miscellaneous.......... Open category

Best wishes <

Does a cell regulate its genes morphologically?

2010-01-02T15:48:00.110+01:00

In living cells, the way transcription factors perform their action throughout their own gene network should be not fully understood if we describe it without the morphological context. Until now, most studies aimed at modelling gene networks while neglecting this aspect. In this post, I am briefly showing that such an aspect remains crucial.

The general space-time pattern followed by transcription factors (Tf) is sketched in the strip hereafter:

A: RNAs of Tf are emitted, inside the nucleus, from source genes up to nearest translation destination sites (black dots stands for ribosomes).

B: messenger RNAs of Tf are translated into proteins of Tf in the rough endoplasmic reticulum boarding the nucleus membrane.

C: Tf are emitted from the nucleus membrane towards intra-nuclear genes where to perform their transcriptional activity, sometimes at their own gene when a self-regulation (feedback) exists.

In fact, it was demonstrated by chemists, notably specialists of reaction-diffusion systems at the Université Libre de Bruxelles, that such a situation should generate a concentration gradient spanning from side to side the nucleus interior. The scheme on the right is a representation of the corresponding laboratory experiment (top), and the shape of the subsequent stationary gradient (bottom). Typically, the molecule concentration (Tf here) must be maintained constant as a stationary entering flux Tf0 feeding the reaction volume with fresh reactant. Inside, Tf must be the reactant of a first-order irreversible reaction (gamma is the rate of the reaction) for the process to work. And, this can be put into the following simple PDE equation:

$\color{White}\dfrac{\partial}{\partial x}T\!f(x,t)=D\dfrac{\partial}{\partial x^2}T\!f(x,t)-\gamma T\!f(x,t)$

The latter can be solved at equilibrium state, and we obtain the following hyperbolic curve:

$\color{White}T\!f(r)=T\!f_0\dfrac{\cosh(\rho\sqrt{\frac{\gamma}{D}}r)}{\cosh(\rho\sqrt{\frac{\gamma}{D}})}$

Where rô is the volume radius, D is the diffusion constant, and:

$\color{White}r=\dfrac{x}{\rho}\qquad(0\le r \le1)$

It is clear that transcription factors, in the standard way we describe them, do have all the aspects of this experiment, so they can be thought to produce such gradients in real cellular situation. In deed, the decaying rate gamma is, anyhow, related to the ubiquitinylation of proteins, which occurs in every cells. One can also hypothesize that the entering flux of transcription factors may be maintained more or less constant, at least for the ones that are regularly used by the cell. Though, in real gene networks, the situation may be thought to be more complex than this model (e.g. it's been shown that many transcription factors oscillate in the time domain), modulation of the transcription factors level as a function of their position in the nucleus can not be definititely ousted: augmentation of complexity should rather come with non linear features, like emergence of space-time motifs.

Trivially, protein levels are, in gene networks, important. They can, for example, decide whether a gene will be set to an ON state, or not. Hence, if real, such a phenomenon would relate the function of a gene networks to the position of chromosomes in the nucleus, giving in turn rise to a novel view of the complexity we are studying. A way to measure this possibility is however still to be discoverd.

Mathematics and nematodes meet during a mapped motion

2010-01-01T13:08:00.278+01:00

On the 24th of December, appeared on arXiv a breathtaking article. This pre-publication, which was written by G. J. Stephens, B. Johnson-Kerner, W. Bialek, and W. S. Ryu, is, to say it in a few straightforward words, a brilliant achievement for the bio-mathematics field. In deed, this paper completely succeeds in relating at once genotype, phenotypic adaptation to environmental complexity, and a fine mathematical model encompassing all of this at once. All in one. Who would have thought this to be possible for a phenomenon as complicated as the swarming movement of worms ?... Those authors did. Pre-published on Christmas day, their paper was the gift to unwrap and to pore over.

This article is, actually, the follow-up of a previous published work. In the latter, the four same authors had shown that every inner complex movements of C. elegans may smartly be synthesized by means of four basic modes, which is what they call the four "eigenworms" of C. elegans. The latter squirms and twists, which, at first thought, may seem theoritically inextricable because of the high dimensionality it intuitively implies... Despite the complicatedness of this task, they proved that four dimensions only are efficient in describing the whole space of the nematode's shapes. The pending question was then: "How can this be that only four basic modes suffice for exploring all imaginable environments?".

This time, their new article aims at mapping the four modes mentioned above onto the worm's displacement on an agar bidimensional surface. First, they show that C. elegans loses memory of the trajectory it is chasing after that a typical time has been passed. After 10 seconds, the worm's behavior becomes fully Brownian, i.e., totally random. Before it, C. elegans performs better controlling of his motion. They further establish that the four stereotypic shapes, which they determine experimentally through an original measurement method of the curvature along the worm's body, can be formally combined in a non linear and differential expression. With the latter, they capture 80% of C.elegans's overall self-curvature. Then, they calculate the correlation between the inner worm's curvature that this mathematical form provides and the extrinsic motions followed by nematodes. Interestingly, correlation diagrams display beautiful circular motifs. This is the phenotype they model, which they link to the genotype by probing, together with wild types, two different mutants, namely dop-2 and dop-3, the two of which was shown to be defective in certain dopamine receptors. More precisely speaking, the latter were earlier proved to modulate foraging strategies of C. elegans, that is to say, the way it moves towards nutrients. And it works ! Dopamine is revealed here as an influential parameter on C. elegans's motion, which the mathematical map has the ability to encode. Hence, W. S. Ryu and his collaborators prove here that genotype, phenotype and mathematical model can be the three components of a complete and efficient theory of complex behaviors in animals.

After reading this article, one cannot help wondering what would such a methodology bring out if it was transposed to human beings. It is clear that we have more complicated patterns of movement than C. elegans has, but we cannot deny the fact that, in the everyday life, our movements are stereotypic. To drink water from a glass requires a way, which we perform with approximately the same manner everytime we drink, and which is probably the most adapted gesture to do so. When, at the same time, we drink and walk as if we were combining two modes, it anyhow resembles C. elegans composing complex movements with two of its four basic modes. Where is then our free-will in this? Can mathematical models absorb consciousness in their algebraic structure? Perhaps are free-will and consciousness somewhere in the way we play with stereotypic behaviors, like painters play with single colors, which themselves never fundamentally change... In deed, this article generates tons of profound questions.

Reference:http://arxiv.org/PS_cache/arxiv/pdf/0912/0912.4760v1.pdf

Tired of not being hired for science

2009-12-31T14:44:00.129+01:00

This is a misleading idea to assert that talent and work are altogether the key component of success. This is a wrong perspective to claim that they both do push you towards professional recognition. Talent and work are null and void compared to what brings power and money. With power and money can you possess talent and work, which, reciprocally speaking, is untrue as well as wrong, a thousand times and more. Being a rich person will bring you folks around laughing at your puns, even the crappiest of them, or when your pen has fallen out of your pocket, or when you say "Sorry, I didn't know you were behind the door!", and so on... With money can you say "Do this for me!" so it will be done. But as a poor man, you will have to think over your words to let the subtle absurdity and the charm in them perhaps attain the sparse crowd passing you by. And do not even try to order anything, because, as a poor man, you have no mouth to throw orders, you have only ears to receive them. Money is everything.

"You should work at school! Otherwise, you will have to clean up streets and floors for the rest of your life." I have been working hard at school, harder at the university. I have passed degrees with distinctions and honors, obtained a grant for the Master degree, which one obtains with good scores. Now I am not far away from cleaning up streets and floors, with five-hundred euros a month for a wage, and no creative or intelligence-demanding task to perform on the day. My job is such that I have to go where I am told to; a robot or a dog could for this misery qualify too. This work-for-sucess dogma, alas, remains what every young boys are taught by parents and teachers. Constantly. Repeatedly. Then, when the subsequent mature men seize how wrong this paradigm is, it's too late. They have been trapped by the system, and they have understood: If parents and teachers keep saying children to work and prove to have talent, this is not aimed to motivate children, no, but to solely acertain that they, as parents and teachers, have done their own job right. Thereby, parents spare themselves other's judgements on the way one must breed children, and teachers become well considered by schools hiring them. That's it. Working-at-school brave children allow their parents and teachers to succeed, nothing more. As a reward, parents and teachers should thank such good children for the hand given in their own social and professional recognition, but they usually do not, according to the golden rule: Never thank who you are using, or who you are using shall understand where your dependency, and hence his power on you, is. Money is everything, anyway.

My deepest error ever has been to think that work and talent were at least sufficient to grow up in the field of sciences. Science is my first love, and it probably will be the last. That is surely the reason why I always believed the scientific job to be the ideal of a job, in which the only excellence criterion is passion. But those who came wandering in laboratories and talked to established researchers certainly have heard a different music. They probably listened to those from whom words of rich excellence were flowing abundantly. Wasn't it sounding like: "First-class students are these who come from here, or from there", which in the end was where money is? How many are there, those researchers, to evaluate the competence of students at the wealth of their education place, even indirectly ? Though they do not frankly admit it, there are plenty of them ! The French culture is however ambiguous on this point, because the French culture treats money as if it were taboo, even when nothing can be done without it. My all first question entering a laboratory for real was: "Is there a whole budget for our team?". I was answered by my supervisor that so it was not. For every test tube, every erlenmeyer, every glove, one should make a request to the "Direction", which anyhow is directly linked to the "Ministère de la Recherche et de l'Enseignement supérieur", to obtain the budget for it, in a need-a-becher-phone-the-prime-minister fashion. Your research budget is a common good. The problem is that if you let an apple-tree in your garden, and say that anyone should cherry-pick fruits as much as pleased, can you be sure that the starved ones will be the more nurished by it? In my very personal conception of the situation, many will amass apples before other can eat... Most French researches are not accustomed to managing with a budget and research plan. They take from it the benefit of freedom, notably because they can randomly perform free research attempts without much justification. Most of them support the French system for themsleves, but advocate for others the ones in which budget and subject are inseparable. This is what they laud when they claim :"Good students are surely not in French universities", like I read once in an interview published in "La Recherche" of some French scientist, the name of whom has here no relevancy since he is surely not the only one to utter such a discourse. Are they worth something better than what they already have? If they had a budget, they could hire someone that fits with their criteria of excellence, couldn't they? Money is everything, didn't they forget it?

I think they did.

Noise & oscillations in gene networks : bibliography

2009-12-30T12:28:00.060+01:00

In order to corroborate my previous article called A flaw in the theory, and everything goes clearier networked, here is the bibliography, which, to replace my conclusions within the state of the art, must be read.

A/ Noisy expression of genes:

http://paulsson.med.harvard.edu/Web_pdfs/paulsson2004nature02257.pdf

http://www.pnas.org/content/98/15/8614.full.pdf+html

http://people.mbi.ohio-state.edu/baguda/AgudaLab/be700/hasty2001.pdf

http://vc.cs.nthu.edu.tw/home/paper/codfiles/tchsu/200906120413/Noise%20Propagation%20in%20Gene%20Networks(2005).pdf

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC125456/pdf/cde240.pdf

http://ccbs.bio.uci.edu/pdf/SBJC/SBJC_Week9.pdf

http://www.pnas.org/content/97/5/2075.full.pdf+html

http://eao.igc.gulbenkian.pt/ti/4u/PDBEBBiochemicalKinetics/NRG-2005-6-451.pdf

http://www.pnas.org/content/100/13/7714.full.pdf+html

B/ Oscillations in mathematical models:

http://www.zcam.tsinghua.edu.cn/~jzlei/teaching/sysbio2009/PIIS0896627300811940.pdf

http://elowitz.caltech.edu/publications/Repressilator.pdf

http://thecity.sfsu.edu/~wow/index_page/Strogatz2001Nature.pdf

http://www.pnas.org/content/99/2/679.full.pdf+html

http://www.pnas.org/content/99/9/5988.full.pdf+html

C/ In vivo oscillations:

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1682024/pdf/msb4100102.pdf

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2063883/pdf/jcb1730659.pdf

http://www.tbiomed.com/content/pdf/1742-4682-1-9.pdf

The model, which I have in this note briefly exposed is still controversial, mainly because many aspects of the time discretization are not fixed yet in it. This model should be better interpreted as a template on which to base future enhancements of multi-modal oscillatory genetic models. If experimentally true, consequences of this multi-modality would be without coming back. In ref. B - http://.../Strogatz2001Nature.pdf, the author states that, in networks, single elements are coupled to others according to the graph structure of that network, so that if one node self-oscillates, then it interacts with elements which it is connected to by resonating with them, transmitting thus its wavy behavior one to the next, in a regulatory cascade. And individually oscillating inter-connected nodes tends to synchronize and let a mean-field around a mean frequency emerge... For the time being, bimodality has been considered in gene networks, but not for the oscillating case. How a gene responds to another gene that controls it with bimodal oscillations is the sort of issue, which is now to be adressed, and which I am currently developing.

See you !

A flaw in the theory, and everything goes clearlier networked

2009-12-23T22:43:00.301+01:00

A few years ago (2004-2005), I began surveying gene networks like the one I am displaying on the right, when they are understood as an assemblage of well-defined sub-networks. Diagram sketches the typical action of a protein X performing either a positive or a negative action upon its own gene (grey box) through its binding to an upstream promoter sequence (white box). The protein Y is an intermediary form in the degradation pathway, and this intermediary form does stand for a simplication of the ubiquitinylation pathway, known to occur for almost every proteins. The alpha letter is the intensity of that self-performed activation/inhibition, while the r one is the transcription rate of that gene, considered to be of the leaky type. I'll leave an explanation about K's a little later on...

As a matter of fact, such a model has largely been studied during the last decade, in the framework of differential equations or by means of van Oudenaarden's models, but this is not what I was willing to reproduce... There, I wanted to investigate such a basic module from some other view-point, so as to answer whether or not considering complex modules as being particular arrangements of simpler modules communicating with each other would induce a rich paradigm. My idea was that biological sub-networks do exchange information, energy or mass with time limitations in the corresponding transfer because there exists a universal boundary playing its role in it, which is Planck's time... Physicists recognize that Planck's time is the time required by one photon to dart in void across Planck's length, the latter being the shortest distance ever at our current state of knowledge. Hence, if two biological sub-networks exchange information as fast as possible (envisage it in a rapid pingpong-like manner) this will not however be feasible in a laps quicker than a Planck's duration. In deed, whatsoever the shape of that information be, it should at most be transmitted so fast as a photon going from one system to the other, but no faster than this. Naturally, slower cases can be envisaged, but since those transfers must be embodied by particles, and since no lighter and faster particles than a photon exists for transmitting that information, then Planck's time should become the minimum time required in system-to-system transfers. Fundamentals are hence fixed.

The straightforward way to put in formal form what I am stating there above was to dismember that network into irreducible sub-networks, find the basic operators associated to each of these elementary components, then model the corresponding complex dynamics by fitting all parts together in a bottom-up manner, precisely like one does it with Legos. The collection of transformations I used for this re-construction is detailed hereafter:

Constants
$\color{White}K_{i}=e^{-k_{i}h}$

Remaining fluxes

$\color{White}R_{1}(x)=K_{1}x$
$\color{White}R_{-1}(y)=K_{-1}y$
$\color{White}R_{2}(y)=K_{2}y$

Added fluxes

$\color{White}A_{-1}(x,y)=x+(1-K_{-1})y$

$\color{White}A_{r}(x)=x+hr$

$\color{White}A_{1}(x,y)=y+(1-K_{1})x$

Transfer function

$\color{White}\varphi(\nu)=e^{-\alpha\nu}$

K's are obtained by integrating the three first-order irreversible reactions shown in the upper diagram not from time 0 up to time t but over h, which thus becomes the assumed chronon of the process. As a transfer function, I initially used this auto-inhibition exponential curve rather than the traditional sigmoidal one, i.e. the so-called Hill function, for the simplicity of it. The former is close in shape to the latter at low IC50, which makes the theory still meaningful for the time being.

Actually, my first re-construction of this networks dynamics brought nothing interesting at all. If, after it, an awkward trial of mine had not somehow come to play its part in the theater of my experiment, I would certainly not be writing about all of this now... Note that I am not scared of assuming that I do commit errors and void results, unlike what young researchers are commonly supposed to claim here and there, everyday and everytime, sometimes in inappropriate context, in order to sound competent, reliable, and worth working with (this is said one for all !)... In deed, I primarily experimentated the following system:

$\color{White}x_{t+h}=A_{-1}(R_{1}(x_{t})+A_{r}(0)\varphi(x_{t}),y_{t})$

$\color{White}y_{t+h}=R_{2}(A_{1}(x_{t},R_{-1}(y_{t})))$

This bi-dimensional map exactly models the scheme with which I launched this article. It yields a rather common dynamics evolving towards a flat steady state, so I felt unsuccessful at the moment with it. However, gazing a little closer at the latter led me to question about the fact that I was nesting functions at nodes of the network where several reactions were competing for one reactant. This is here particularly obvious for the case of y, which is involved in three maps that are composed with each other. Is there a prevailing order ? Apparently not. I began trying different orders, and came across what is coming next:

$\color{White}x_{t+h}=A_{-1}(A_{r}(R_{1}(x_{t}))\varphi(x_{t}),y_{t})$

$\color{White}y_{t+h}=R_{2}(A_{1}(x_{t},R_{-1}(y_{t})))$

The latter is, in fact, flawed (I mean with respect to the initial diagram) because it adds to the above network an irreversible dimerization of protein X, which I will not sketch here in detail, but that I had not put primarily in the network scheme. And, the interesting thing has been the orbits I derived from that mistake, which the following let you visually discover:

On the left are the time-dependent evolution of X (grey), and Y (blue)*. On the right is exactly the same dynamics now represented in the phase-space: $\color{White}X(t+1)=f(X(t))$ and $\color{White}X(t+3)=f(X(t))$. At first sight, I have rapidly been astonished by the latter because, as you can see, these two orbits generate both a couple of superimposed cycles, which corresponds to two different equiprobable oscillation modes of each orbit. I then wanted to chech how the Lyapunov's exponant evolved in such a bimodal situation. I thus computed it for both X and Y orbits, which gave the typical sort of result shown here underneath:

That pair of two green straight lines outlines what I interpreted as being 2 co-existing Lyapunov's exponants for the same orbit (here Y's one). This is, as far as I know, a feature yet not described in the literature of chaotic systems, and worth going further in its comprehension.

In the end, my feel about all of this was that I had seized something essential about gene networks, which is that they can both oscillate and be chaotic at the same time. This duality is something I scarcely found in the literature, where one finds rather one feature without the other, but not the two co-existing in the theory. However, I also directly felt the theoritical lack that a discretized model is better seen as an approximation method from which arising chaos should feel guilty and ashamed... This has given rise to a subsequent harsh fundamental work I swear to present to you in the future, in another article.

*For the enthusiasts who would like to reproduce this result, use the following set of values: X(0)=0, Y(0) = 0, h=1, alpha=1/2, r=1000, k1=log2/2, k-1=ln2/3, k2=ln2 in the second map, iterate long enough, and plot with OpenOffice.

Review of a mind-shaking physicist's Bible

2009-12-20T22:11:00.265+01:00

If I had to tell about one book that radically made me think science in a different fashion after I read it, then I would surely say this one: Sources and evolution of quantum physics - The founding texts, by Bruno Escoubès and José Leite Lopes. This is edited by EDP Sciences with the following French title: Sources et évolution de la physique quantique - Textes fondateurs. It may sound out of context for a biologist like the one I everyday try to be to refer to such a physicist's Bible, but one is enforced to admit reading it that no such a thing exists in the field of biology... In this miraculous volume, Dr Escoubès and Dr Leite Lopes piled up in one single publication the major early articles, which elevated quantum physics up to where it nowadays is. Written by Jean-Marc Lévy-Leblond, the foreword does state that if every contemporary writers may have pored over works of classical writers, if every contemporary painters may have contemplated paintings of influential classical painters, if every contemporary composers may have listened to classical composers to fine-tune themselves and adjust their work after them, all of this remains however untrue for contemporary physicists, who rather advocate amnesia about the past as a motto. Words are even more crual than this, accusing science to have for long been convinced that forgetting origins of ideas is the hallmark of a sane and sound science stepping towards progress, writes J.-M. Lévy-Leblond citing Whitehead's view on this point. This is what this book aims at warding off.

The whole relevant record lies therein. The discovery of radioactivity by H. Becquerel in the Comptes rendus de l'Académie des Sciences (1896) ; The quantized distribution of energy by M. Planck in Annalen der Physik (1901) ; The production and transformation of light by A. Einstein (1905) ; The existence of the nucleus in atoms by E. Rutherford (1911) ; W. Pauli (1925) ; E. Fermi (1926) ; S. Bose (1924) ; L. de Broglie (1923) ; E. Schrödinger (1926) ; W. Heisenberg (1925) ; M. Born, N. Bohr, R. Feynmann's Nobel prize speech... Even if translated from original language (mostly German and English) into French, original papers are impressing. It is clear that each author's personnality shows off through the scientific shibboleth. By reading those, one faces one's own definition of excellence. What is a revolutionary idea ? What makes a paper more important than another? While laying down words, were authors aware of the afterwards ? Were they already foreseeing consequences of what they were writing at the time ? May those same works have gone ingognito through the literature in slightly different condition? Did the authors fully control the effect of their idea, or was the name of their academy and/or the journal's impact factor doing ninety percent of the influence job ? Might someone else have written verbatim the same article ? In fact, that book answers many of those questions, though not always in the expected direction. E.g., E. Schrödinger's paper on his celebrated equation does contain no more than four papers in its references record, which are furthermore, here and there in footnotes, dispatched along with the text. "Worse" is the way L. de Broglie, in its first note about waves and quanta, does indicate only two references: one is a self-referencing to de Broglie's previous publication Journal de Physique, 6ème série, 3, 422, (1922) ; the second does refer to some proceedings written by M. Brillouin in Comptes rendus, 168, 1318 (1919), which anyhow refers to L. de Broglie's first note on waves and quanta. In fact, the outstanding results used for demonstration are, in these articles, announced without explicit referencing. In this first note, which was published in 1923, L. de Broglie starts up with the relation "h.nu = m.c^2", i.e. Planck's well-established relation equals to Einstein's well-established relation, the two of which were discovered twenty years ago, and the rest follows as naturally as can be. Concerning E. Schrödinger's paper, its famous author introduces his equation in a (rather) odd manner. In deed, E. Schrödinger assumes that the corresponding function must/should/may/might be in the form of a product of three functions, each of which depending on one variable x, y or z, i.e. the three spatial axes. The idea is that the Hamilton function for the energy had, in the past, always been solved with a sum of functions, which apparently was not satisfying for the electron. He then begins to investigate the problem of having his invention into the hamiltonian of electron's energy. All in all, it seems like, in the quest for a wavy description of matter, the momentary lack of papers in the field has been an open place in the town of creativity. Revolutions protrude where holes of knowledge are pending.

The other interesting aspect of this book is that it lets us plunge deeply into the psychology of these eternal discoverers; this book provides a subtle insight into their particular minds. Thus, W. Heisenberg offers an extremely brilliant introduction, in which he accuses with authority the previous assumptions in describing microscopic systems by means of quantities that cannot be observed, and hence builds up its argument in favor of a description based solely on observable quantities. During the entire text, he casts apart quantum theory and classical theory, following his line. Like the famous Hilbert's "Wir müssen wissen, wir werden wissen", W. Heisenberg exposes things with the typical germanic manner of that time : for order to be, certain things must be done. He details the information as if it were copied from a school book, and nobody could tell from reading it that the treated subject is so novel to science. Definitely, W. Heisenberg had clear ideas about what he was doing at the moment : a break in how to talk about the matter. E. Schrödinger's text goes somehow in the inverse direction... In fact, the divergence between W. Heisenberg and E. Schrödinger vision of matter shows through even in the style they wrote their article. While the former perfectly tidies up the course of his idea, the latter rather links ideas in a non linear manner, numbering equations (1), then (2), then (1'), then (1''), then (3), etc., advancing its seed argument alone, without providing a whole set of preventive logical connections and references, adding sometimes in a footnote that he missed another way to formulate the problem. At the end of the discussion, E. Schrödinger mentions the "joy" of having succeeded in representing microscopic systems in a more familiar scheme, that is to say, differential equation systems. In the end, E. Schrödinger appears as an enthusiast, a boiling brain, who seems to have gone all possible ways, even the riskiest of them, to work out an issue he could not stand anymore.

The conclusion to this unforgettable book is that great discoverers never perfectly look like what one thinks they had looked like in the past. One then reconsiders one's own vision of authority in scientific development, realizing that doubt and certainty are two inseparable elements of the thinking, which struggle one against the other until the latter has won upon the former, at least for a while. The truth, which is though what all have been searching for, is never claimed by those who, with their special conception, came across it... Did they know that the best way to announce it is to seed it, and then let it grow up in the reader's mind along with time ? This book will probably answer this question for you !

More about curlicues in the Zeta function

2009-12-19T11:33:00.100+01:00

Yes, I must be thankful to you, dear Anthony. In deed, you begged for some clearer (smarter?!) explanation about curlicues creation methodology with the Zeta function; I effectively re-read this previous post, which I plausibly wrote in the haste of blind enthusiasm, and seized at once why and what for such a request you had to me... True, not everyone is acquainted with the How, the What and the Where of experiencing Riemann's special series. The secret of this concealed handsomeness is, first, that an OpenOffice's spreadsheet does suffice in carrying out these calculations. Dear Anthony, then should you opt for two arbitrarily chosen real values, namely x and $\color{White}\gamma$, with which to define, according to your wish and will, the following:

$\color{White}Z(n)=\sum_{k=1}^n \frac{1}{k^{x-i\gamma}}$

If you compute it as a function of n, the latter will work out the rest for you... E.g., x = 0.3 and gamma = 50671.27 will eye-candy you with a "U" decorated with curlicues, one exactly looking like this "U" decorated with curlicues, which is to be seen right underneath:

Nice, but do not mislead yourself !... The current and old many studies, which deal with Riemann's Zeta function in the divergent domain, and for which much sweat is and was skin-oozed to prove that zeros have all real part equalling to 1/2, are about its analytic continuation to the whole z-plane. The so-called technique makes Zeta series converge where it otherwise would not. In that continued context, we forget about those curlicues I am now displaying at you, no matter how sad it is doing so.

Cordially yours

What Linux, bacteria and diplomats have in common

2009-12-16T14:03:00.126+01:00

Preemption is a concept, which one better encounters in computer sciences. Preempting is the ability of an Operating System (OS) to cleverly manage multi-tasking and is the opposite of collaborating, which is another way to manage multi-tasking. So what's the difference between them?

Collaborating OS (e.g. Windows 3.1) can run several programs at the same time, but it's up to each one to let another one run after it. Therefore there is always one program running and all the others waiting for it to stop before getting back on their own job. If it crashes, it doesn't crash alone and everything is lost... On the contrary preempting OS (e.g. Linux) manage hierarchically the whole bunch of running programs, that is to say, the OS supervises them like a mother does with her kids, letting them do their job one after the other according to priorities. Quite a smart way to handle the workflow of a computer, but did computers were the first endowed with this?

Clearly, the human brain preempts like human lungs breathe. The brain has this ability to let several thoughts run at the same time and put the less important aside for a while in order to concentrate efficiently on what is the most important as long as it remains unsolved... Then the less important can come into view in the next thinking step. Hence a diplomat trying to rule out political problems of the Middle East can both eat an apple and call the Ambassy without bugging, which would let a war break out in case of rotten fruit.

So can one find an instance of natural preempting operating system already there a long time ago?

       Thanks to Jacob and Monod we know there is one such instance in nature called Operon Lactose. The latter is the gene born by bacteria, which regulates their sugar consumption.

      Preemption in our good old bacteria is completely demonstrated by diauxie in Escherischia coli. When both glucose and lactose are present in the milieu, operon lactose gives highest priority to glucose consumption so E. coli will first absorb glucose and forget lactose. Once there is no glucose any more at disposal, operon lactose lets the metabolism absorb lactose as a new sugar source. Like computer preemption, preemption in a bacterium is a way of switching down one program (lactose absorption) in order to let another run (glucose absorption), though without leaving aside the potentiality to run the first.
       We can more or less conclude that bacteria like Escherischia coli use a Linux-inspired operating system for their own advantage, so I ask: What's the point in keeping using Windows as the standard when even bacteria, which natural selection hardly selected, show us that Linux is the only real OS on Earth?

About curlicues in Riemann's Zeta function

2009-12-15T21:46:00.028+01:00

This is an unkown stuff, but Riemann's zeta function and curlicues have much in common than one could guess. Before you continue the reading, I recommend taking a look at these pictures on the left.

How does one obtain such pictures?

First, consider the Zeta function in the complex domain, i.e., a harmonic series with constant complex power. Second, do not consider its analytic continuation but record only the way it diverges towards infinity - this can be done using openoffice sheets.

The upper picture represents the z-plane on which each nth dot is a partial sum of the series up to the nth rank. The lower picture shows the corresponding modulus.

The way Riemann's zeta function diverges seems to be interesting too. There are, as we see it, many attracting points towards which the series feels like converging, but which are in fact no limit so the series jumps onto another for a while, and another again, and this yields the curlicue motif in a perfect manner.

Nobody studies this eagerly and it's a shame as it's very nice watching this on the screen.

The deep history of the all of that

2009-12-14T08:38:00.043+01:00

Those interests of mine in Science, for so broad they are, are no madness, no whim of the day. What to be and to become without them ? Another me, surely, in place of that thinking self...
Biology. True, I graduated with it, in it, among the mediterranean breeze, in that Montpellier of my bygone studying time. Thank you to all of you, teachers and professors, who taught me with taste and passion the How, the Where and the When of the living and the dying thing. Thank you so much for never telling the What for, which you anyhow would not know. From their words, Science sounded like a shared place, where the knowing is and ever becomes, where the career careers off the stream when it is mainly wrong. Biology. Learn it yourself if you find the will to: In there will you encounter the weakness of mind when it plunges in itself. Think of life as a miracle, but bannish such a word from your mouth. In this lurks the inner discrepancy of the biologist, the paradox out of which she draws the daily energy of her researching...
Mathematics. So late it appeared to me essential. Essential now it is. How a thing would be what it is without being one rather than thousand? Stability of structures brings the one. Love brings the two and the many. War brings the minus (down to zero if made with good perfection). Man, she hurt you with a strong hearbeat of passion, but to tell things in the facts, she had you with straights of coal above her iris roundness, the topology of a look branding a male's soul, and you fell. Our brains long for number and geometry, for it is the mental way of escaping decaying and disorder, of denying universal entropy. Where is the mind when it counts and traces the world? Outside of it? Inside of it ? Probably in both... A reason why it finally catches up with you.
Physics. Back in the past of my childhood, in there remains the trouble of quantum in the form of never-healing illness. Remember... Science books and magazines in the house, that me being ten or less... I have had two eyes in those pages, once and ever again. Mum and Dan read this and had their mind changed right after... Shouldn't I either? "Too young", they said... I peeped in and then pored over. In the understood words, was electrons here and there at the same time to be read. Humanity had been constructed out of that wind-flying dust, they wrote. Ten was not an age for such a fuzziness, some trauma has been deep there in me up till now - I have been philosophically injured from ten to thirty. "Are we truly such cards castles of matter?", I wonder. Physics accepted... I do ever not.

Entering the skin of a freelance scientist

2009-12-13T22:39:00.003+01:00

In the scientific world, is there room for freelance research ? Many say: "It is fated to die !" - I have heard some writing this, read some saying so - others howl: "They are amateurs, crackpots... parasites!". There is no room for it, for them, for us - I know it more than ever - but there is a need, a deep need for freelance research in science - today more than it ever did. Personal wish ? Childish dream of mine ? Sure not. Here is a crucial requirement, for the deeps and the roots were lost... Surely, nobody expects triumphing crops from awkwardly engineered seeds of novelty, for hard and long it takes to have one germinating out of thousands of them drying in the furrow. One root of this new and gorgeous discovered wheat does bring a tiny meal, no bread, the only taste of hard working, as others say. Finally, established ones claim seeds have no meaning at all in cultivating wheat and growing things... Independent research is one man facing the Nature, nothing more. While being two with her, are there the voice, the carrot and the stick of an institution telling where and what to search for ? No, there are not... In his solitary, he is asking the Nature for a world of explanations... "Why did you made me chase the truth of logic instead of letting me sleep on the truth of God?", he says. No answer. Confused, he surely is - God was one he could talk to like he talked to other men... From now on will he be answered with the feedback of proper calculations. That is why he learns to speak this way, in the language of science. With the joy of finding comes the will of sharing. He wishes others to dig the furrow further on with him, begs and demands for a tie and a link. Pure is the discovery, but sinful is the turmoil around it. And he is laid down by others, for he has found on his own. Peers accuse him to try and steal the something the all call "The Nobel prize", and which they crave for... He and they did not speak a same language.