Self-regulation

Three typical examples

Snow

The simplest example is that of the Neige: it is common of to observe because it is being white, i.e. reflects the majority the wavelengths which reach it, and thus melts of as much less quickly. If snow were being black, it would not exist about it less, but we would have less time to observe it. This example also shows that self-regulation:

does not require the life
does not require an intentional process to set up itself

This simple consideration marks the border between the Hypothèse Gaïa of James Lovelock, scientific assumption like another, and the Théorie Gaïa of aspect more mystical which was induced by it by some of its readers, and who is disputed - including by Lovelock itself.

Solutions plugged in chemistry

The chemical reactions answer a law of balance named Loi of action of mass which can be used to carry out solution-plug: such solutions show a pH much more stable in the presence of an acid or of a base that pure water would not do it: a self-regulation thus occurs.

Such buffer effect is observed in biology, and provides a stability favourable with good progress of the vital processes.

Self-regulation in the alive world

In the case of the beings which we name alive, the process darwinien of Natural selection constitutes a complex form of self-regulation: indeed, a species itself autorégule not (excluded by the exhaustion of its resources), but a system composed by preys and predatory autorégule according to a mechanism is described by the equation of Bernoulli - or else preys as predatory disappear.

Self-regulations of the cell are studied under the name of Homéostasie.

Physical self-regulation

Thermostat

Its principle of operation is described in the article specialized Thermostat.

Centrifugal governor of James Watt

The problem to make preserve at a steam engine a constant speed under the load without operating its levers constantly was posed and solved by James Watt. See the section How to ensure the regulation? of the Centrifugal governor article .

Self-regulation of the Sun

The operation of the Sun is at the base a continuous transformation of hydrogen into helium by fusion, with continuous loss of mass (4×106 tons a second).

Si for reasons of thermal agitation (heat of the thermonuclear reaction) the Sun increases by size, the result is a greater average spacing of the hydrogen atoms, therefore a deceleration of the reaction.
Reciprocally, a reduction in size results in a greater density of hydrogen and a greater frequency of the reactions of fusion.

Self-regulation in chemistry

Principle of Châtelier

The chemist Henry Chatelier noticed several phenomenon of stability in the chemical world: a reaction supported by heat, for example, absorbed some. A reaction supported by the pressure resulted in a greater absorption of gas, etc In a more general way:

Any action caused a reaction which would have had the opposite effect if it had occurred only .

It drew the law from it from stability of chemical balance which bears its name today.

http://mendeleiev.cyberscol.qc.ca/chimisterie/2002-2003/AMDery.html

Law of action of mass and buffer effect

The law of Châtelier, which was only qualitative, had given rise to other laws of the same order like that of Van' T Hoff . Work of Guldberg and Waage gave birth in 1864 to the Loi of action of mass, quantitative , which was very studied by Marcellin Berthelot and Svante Arrhénius (Berthelot was so admiring of this law that it came from there to suppose that chemistry would be soon a completed science ). The odd behavior of these chemical solutions which seemed to adapt as return the horns as a snail when they touch an obstacle revealed in the final analysis to be only one business of concentration of ions led spontaneously to minimize a chemical potential.

Self-regulation in biology

(case of only one organization, in opposition to the populations)

Glycemia

The self-regulation of the Glycémie in an organization is approached in this article.

Hormonal system

The hormones play a part of regulation in the organization, treated in the articles Hormone and Homéostasie.

Neuro-transmitter S

Immune system

Expression/promotion/inhibition and other regulations of genes

Self-regulation and economy

It can seem awkward to tackle in an article on the car regulation the question of the economy, field which arises in theory more from the will of the men that installation of natural mechanisms .

Technically, it would be to forget that these mechanisms in general set up at the knowledge of the men themselves (at least as a mechanism of regulation) and that the economic scene - which started with really emerging only towards XVIIIe and XIXe century - followed only by far the invention of the Monnaie, which existed already time of Babylon.

Pedagogically, the currency is something which we all use, and it is trying to illustrate self-regulation while being based on well-known concepts.

The currency

The Monnaie constitutes an effective tool of regulation of the tangible properties in an artisanal, rural or wandering company, and that for a stucturelle reason:

most favorable conditions of production (physical fine shape at the beginning of day, better ground, better animals) being exploited in first (see: Law of the decreasing outputs), the unit production costs increases in such a type of company with the produced quantities.

On the other hand, these productions have they-even, because of same the law of the decreasing outputs applied by the consumer, a increasingly low utility . The economist Charles Gide gives like example the water bucket which one extracts from the well:

the first is used by priority to ensure the ration of water of the family
the second to be given to drinking with the cattle
the third to sprinkle the kitchen garden
the fourth to make a bit of toilet
the fifth wash the ground
the sixth to perhaps sprinkle some flowers of approval

The conjunction of the increasing unit costs and the decreasing unit value guarantees that one will arrive at a balance. There will exist one moment when one will not judge interesting any more to draw from the well, for this day, only one water bucket moreover. The point of balance reaches structurally , and obligatorily, in this precise case .

In the real-world, however:

the utilities can not be decreasing, but on the contrary increasing (if there exists only one telephone in the world, its utility for the world is null; the more there are some, the more the possible utility of each one increases or, at least, it is easy to show that it could not decrease.

the unit costs can not be increasing: if thousand readers need a newspaper, this one will cost relatively much. If it is a million readers, it will be possible to distribute the costs on a broader basis.

The existence of a single point of balance can then not be guaranteed. There can for example be several distinct which will be like as many local optima .

Competition

Competing self-regulation

In the case of the monopoly (competition of the various uses of the currency for the consumer)

Except very particular cases (water, medicine…), the producer cannot increase indefinitely his price, without what the consumer could in his turn reorientate his consumption. Thus, if it considers the voyages too expensive, it can decide to occupy its leisures with another thing like the cinema, the gardening or do-it-yourself.

In the case of oligopoly (pressure much stronger to the fall of the costs)

The “invisible hand” of Adam Smith

Metaphor of the invisible hand of Adam Smith (“the man is led by an invisible hand to fill an end which enters its intentions by no means; while seeking only its personal interest”). Thus the market autorégule and maximizes the only production; however, Smith had forgotten that its model did not regulate not the question of the Répartition. (It is necessary to consider this concept under its only technical aspect and not under possible aspects of propaganda or denigration of the liberal theory)

Other aspects of self-regulation in economy

Ricardo
Pareto and the scaling Laws: empirical law of the 80/20.

Limitations structural of self-regulation

Loss of effectiveness of the currency like regulator with the Industrial revolution.

increasing Importance of the standing fixed overhead : the law of the decreasing outputs , even overall true, locally becomes sometimes false.
associated Instability

> this technical phenomenon generates economic crises.

Analysis of Karl Marx (to also limit to the technical aspect )
Perverse effects of not-concavity.

Exemple of the Control Dated Cyber 72, which was Cyber 74 provided with delay lines.
Intel 486 SX, which was one 486 DX attached
“Golden delicious screwdriver” of IBM. Case of the “emulator VM” which was in fact a not-brakesman .

Problem of the regulation of the Immaterial . Consequences of some Deregulation S (the desert of the Mojave).

Self-regulation and policy

extreme Example: “the absolute monarchy moderated by the regicide” .
Feudality
Monarchy
bicameral Democratic system. Separation of the capacities

E. - U.
Europe

Comparison of the Poll of district and the Proportional as regards self-regulation.
the System of Hare
Paradox of Condorcet
Theorem of Arrow
Beyond Condorcet: Model of Marcotorchino and Michaud. Dated mining.

“In 1794, the marquis de Condorcet had to write “a literary” text of powerful mathematical contents. It was a question of determining the “average” man, the average equilateral triangle on the basis of several equilateral triangles. More generally, that can be seen in terms of vote in the majority relative. NR voters classify M candidates according to their preferences in the order. If one applies it to M produced, it is the table of the consumer's choices. Considering the state of mathematics of then, it was difficult to find a solution satisfactory with the rule of Condorcet. Even in the Sixties, a “expert” American Weles obtained the “Nobel Prize” of economy by issuing a “theorem” of the impossibility of the aggregation of the individual preferences and died blow second of Condorcet. However in the Eighties, Michaud and Marcotorchino raised the veil on the paradox. The paradox of Condorcet is not any more one. It is enough initially to code the answer of the individuals by 1 or 0, then by an algorithm of the simplex or a linear programming to maximize dispersion or in other words to increase the variance between classes (Lagrangian will have to be used) to find the solution with the rule of the vote in the majority relative”. (this comes from the site * http://perso.wanadoo.fr/aygosi/1P.html: to carry out a clarification )

Particular cases

Clientélisme
Corporatism
African System

Self-regulation of microsociétés

The Community GNU/Linux

GNU Linux

The Community Slashdot

See the system of self-regulation of Slashdot in the article Slashdot.

Pages 157 to 162 of the work of Steven Johnson Emergence (ISBN 0-140-287-752) also detail this phenomenon of self-regulation.

The Community Wikipedia

Wikipedia

Management system of contents Mambo

the CMS Mambo (in English)

Self-regulation and right of the Internet

In French

the share necessary of self-regulation in the right of the Internet, by Claude-Etienne Armingaud - http://armingaud.free.fr/dess-ntsi/docs/janus/autoregulation.pdf (File pdf)

See also the site of E-Lawyers:

http://www.e-juristes.org/rubrique.php3?id_rubrique=6 (data sheets)
http://www.e-juristes.org/rubrique.php3?id_rubrique=203 (legal day before)

In English

Site of bibliohèque of right of Santa Clara: * http://www.scu.edu/law/library/

Site of the library of right of Cornell: http://www.lawschool.cornell.edu/lawlibrary/guides/foreign2/

Emergent processes of self-regulation

Self-regulation in the field of the Free software

Self-regulation of the populations

See ecology, Gaïa

Prey-predatory models of Bernoulli

The linear model proposes the study of the evolution of a colony of preys in permanent growth:

$\ frac {dx_ {1}} {dt} = k*x_ {1}$

With the decrease of the colony of the predatory ones:

$\ frac {dx_ {2}} {dt} = - h*x_ {2}$

But the predatory ones can survive thanks to the preys:

$\ frac {dx_ {2}} {dt} = - h*x_ {2} + b*x_ {1}$

In the same way the colony of the preys it will decrease:

$\ frac {dx_ {1}} {dt} = k*x_ {1} - a*x_ {2}$

One will see in a advanced approach the model of Volterra-Lotka.

Bonds:

http://www.bretagne.ens-cachan.fr/math/people/gregory.vial/files/cplts/volterra.pdf

Space phases and field of stability

Raymond Lindeman and quantitative ecology

Structural stability, morphogenesis and emergence

Car-organization

Signature of chaos

Santa-Fe models

Dependant subjects

Theorists having worked on self-regulation

Thomas Malthus
Adam Smith
Charles Darwin
Nikolaï Kondratieff
Ross Ashby
Benoit Mandelbrot

Mathematics of self-regulation

Dynamic systems, mathematical continuations

A simple expression of self-regulation is that of the arithmético-geometrical continuations, very related to the Rétroaction:

$x (T) = a.x (T-1) + b$

The system is in balance when:

$x (T) = X (T-1)$

that is to say:

$x = a.x + b$

the point of balance is thus:

$x = \ frac {B} {1-a}$

When $|has| < 1$ , the continuation always converges towards the point of balance, whatever the initial value, and thus whatever the specific disturbance applied to the system.

When $|has| > 1$ or if $a = 1$ , the system diverges and tends towards the infinite one: it is an car-amplification.

If $a = -1$ , one has an oscillating system around $x_ {0}$ and $-x_ {0} +b$ :

$x_ {1} = - x_ {0} +b$

$x_ {2} = - x_ {1} +b = - (- x_ {0} +b)+b = x_ {0}$

and thus very prone to a specific disturbance, which modifies the point of oscillation.

Steady balance

Stability and instability (in weather)

Eigenvalues

When in the vicinity of one of its points of balances a system can be approximated by a linear model of feedback, then its eigenvalues is necessarily negative (what constitutes an expression of this stability).

http://mwt.e-technik.uni-ulm.de/world/lehre/basic_mathematics/di_fr/node27.php3

Circles of Gerschgorin

The exact of the eigenvalues, inconvenient calculation for the matrices of very great dimension, is not always essential. The theorem of Gerschgorin shows indeed that all these eigenvalues are located, in the complex plan, inside circles name circles of Gerschgorin . It is it should be noted that independently of self-regulation, these circles have a characteristic interesting: if they are disjoined, the matrix is invertible (what means in light that one can without particular difficulty “go up time” with regard to the evolution of the system, all the more far the precision from the linear approximation of the behavior of the system around this local point of stability is good.

http://mwt.e-technik.uni-ulm.de/world/lehre/basic_mathematics/di_fr/node27.php3

Equations of Volterra-Lotka

The equation of Volterra-Lotka governs at the beginning of the models made up of preys of the predatory ones; qualitatively:

more the preys are numerous and more the predatory ones will survive and to reproduce,
more the predatory ones are numerous with the following generation, more are the preys which will then be consumed.
that will lead to at the end of some time with a reduction in the preys, therefore with a famine of predatory and a reduction of their number

The result can be a deadened cycle, a not-deadened cycle, or an excursion which can result in the disappearance of the two species.

http://agreg-maths.univ-rennes1.fr/documentation/docs/volterra.pdf

Space of the phases

http://perso.wanadoo.fr/olivier.granier/meca/ex_og/esp_pha/esp_pha.htm

Criterion of Nyquist

http://www.eudil.fr/eudil/belk/dy3651.htm

See too

Random links: