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An example of an online game using evolution based upon the behaviour of multiple distributed users is Galactic Arms Race (GAR) (Hastings et al.,, 2009 This includes an genetic algorithm that evolves new weapons (based upon particle systems) according to the users’ current playing styles. In single-player mode, the wea... |
The Picbreeder system, described above, allows the evolution of 2D images. In 2011, Clune and colleagues introduced the EndlessForms |
website for the collaborative interactive evolution of 3D forms. EndlessForms like Picbreeder , is based upon an underlying CPNN representation of form (Clune and Lipson,, 2011 |
Also in 2011, a project was launched of a rather different nature to those discussed above. OpenWorm is an “open science” project to develop a detailed 3D dynamic simulation of the nematode C. elegans |
(Palyanov et al.,, 2012 . Although the simulation itself is not web-based, the core team are distributed across the world and have regular team meetings using web-based collaboration tools. The project website actively seeks to recruit new members to the team, including scientists, programmers, artists and writers. All... |
Kickstarter campaign that raised over US$120,000. A novel variety of WebAL was reported by Auerbach, ( 2012 . This work evolved 2D images with a similar representation to that used in Picbreeder . However, the key difference was that the fitness of each image was determined automatically rather than by user selection, ... |
Hickinbotham et al., ( 2013 describe work using the YouShare software-as-a-service infrastructure to create an online “ALife Zoo”. They demonstrate the potential of the system by setting up various well known ALife systems as services, including Tierra-as-a-service and |
Avida-as-a-service . The system allows software written on diverse architectures to be run in a consistent framework, and for web visitors to run and interact with the services for research, education, and archival purposes. |
Finally, another WebAL system with an educational flavour is Ludobots developed by Bongard and colleagues and launched in 2012. This is an infrastructure for teaching undergraduate-level evolutionary robotics using 3D simulations and other tools. The simulations are not web-based, but the website makes available a seri... |
Methodologies and Technologies The work summarised in the previous section demonstrates a variety of ways in which the Web can be used for A-Life research and applications. Some broad categories of methodology are outlined below (this is by no means an exhaustive list): |
Distributed computation It is becoming increasingly possible to use the Web as a distributed computation platform. Much of the work surveyed above involves some aspect of distributed computation. The HTML5 and related APIs such as |
Web Socket Web Workers and Web Storage make it easier to implement these kinds of distributed computation systems using native technology. Furthermore, a number of technologies are currently being developed to allow fast client-side processing at speeds approaching those of local binaries: Mozilla’s |
asm.js and Google’s Native Client are the most prominent of these. Human and hybrid computation Closely related to the idea of distributed computation on the Web, and also a feature of much of the work surveyed above, is the idea of |
human or hybrid computation , where some part of the computation is performed by human users of the system. A human based genetic algorithm was first proposed by Kosorukoff, ( 2001 , and there is a large literature on the more general areas of human computation and crowd creativity (for good reviews, see (Malone et al.... |
(Maher,, 2010 (Quinn and Bederson,, 2011 and (Yu et al.,, 2012 ). Cloud APIs The work by Auerbach, ( 2012 , described above, illustrates one way in which Cloud interfaces and APIs (in his case, |
Google Image Search ) may be used as components of computational intelligence systems. It is not hard to think of many other ways in which Cloud APIs could be employed to provide enhanced capabilities to WebAL systems. |
Persistent systems Most A-Life experiments typically run for a few hours, days, or maybe weeks on a local machine or compute cluster, data is collected, results are written up, and no further experimentation is done. A feature of web-based A-Life systems is that they are persistent and offer the possibility of on-going... |
and Picbreeder , discussed above, give some indication of the potential benefits of web-based experiments, and many other types of long-term experiment can be imagined. |
The Web as a Complex Environment Some of the early papers on WebAL, such as (Ray,, 1995 and (Langdon,, 2005 , discuss the possibility of A-Life agents roaming the Internet and evolving in the complex environment that it provides. Some of the experimental work discussed above shows aspects of this kind of free-roaming a... |
Crowdfunding While not related to WebAL technology as such, another important way in which the Web can enhance A-Life is through |
crowdfunding of research and applications. The OpenWorm project, discussed above, is one example of a research effort that has succeeded in raising significant funds through a Kickstarter campaign and other crowdfunding efforts. |
Steve Grand, author of the Creatures game discussed above, also successfully secured Kickstarter funding of nearly US$57,000 in 2011 to develop a new A-Life powered game, currently still under development. |
Another A-Life veteran, Jeffrey Ventrella, has also recently secured Kickstarter funding of over US$15,000 for his company Wiggle Planet to develop an augmented reality A-Life game. |
Between them, these three projects have raised nearly US$200,000 of funding through Kickstarter . These examples demonstrate that it is possible (although still far from easy) to obtain substantial funding for A-Life projects via crowdfunding. |
Looking Forward The preceding sections have looked at ways in which web technologies and A-Life techniques have been combined in domains as diverse as collaborative design, human computation, education, outreach, persistent and long-running experiments, the archiving, sharing, reproduction, and reuse of scientific expe... |
As web technology continues to develop, and particularly with the move towards native APIs in place of proprietary plugins, the potential for developing complex web-based A-Life research and applications grows greater each year. |
Whether or not a WebAL project is primarily focused on education or public outreach, the very nature of the Web means that WebAL research is inherently open and can reach a wide audience (unless steps are taken to actively prevent this). As funding councils around the world place increasing emphasis on the public under... |
Looking back over the research reviewed here, it is clear that great strides have been made over the last 18 years. However, as web technology and APIs develop, I have the feeling that current work is only the tip of the iceberg of what could be possible. |
The Wilderness Downtown , itself four years old now, still remains a great showcase of some of the possibilities of the HTML5 era, and yet there are undoubtedly many other possibilities, some as yet unimagined. Advances will doubtless be made in all of the areas outlined in the previous section, and likely in completel... |
It is a truly exciting time to be involved in WebAL research. I cannot predict what advances and achievements will be made over the next few years, but I look forward to witnessing what emerges, and eagerly await a WebAL system that gives me a similar sense of awe as when I first watched The Wilderness Downtown |
# Source: arxiv 1408.1529 # Title: Self-organization in complex systems as decision making # Sections: all # Downloaded: 2026-03-03T01:58:35.503320+00:00 |
Self-organization in complex systems as decision making V.I. Yukalov 1,2∗ and D. Sornette 1,3 Department of Management, Technology and Economics, |
ETH Zürich, Swiss Federal Institute of Technology, Scheuchzerstrasse 7, Zürich CH-8092, Switzerland Bogolubov Laboratory of Theoretical Physics, |
Joint Institute for Nuclear Research, Dubna 141980, Russia Swiss Finance Institute, c/o University of Geneva, 40 blvd. Du Pont d’Arve, CH 1211 Geneva 4, Switzerland |
Abstract The idea is advanced that self-organization in complex systems can be treated as decision making (as it is performed by humans) and, vice versa, decision making is nothing but a kind of self-organization in the decision maker nervous systems. A mathematical formulation is suggested based on the definition of p... |
Keywords : self-organization; complex systems; decision theory; probabilistic scenarios; behavioral biases Author for correspondence (yukalov@theor.jinr.ru) |
Introduction In order to avoid misunderstanding, we would like to stress from the very beginning that the main idea and the principal novelty of the present article is the demonstration that self-organization of complex systems can be described in precisely the same mathematical terms as decision making by human beings... |
for accomplishing the demonstration of the equivalence of self-organization and decision making. Before plunging into the mathematical formulation, we give in this introduction below the general feeling of the problem, which should help the reader to grasp the main ideas that will be mathematically proved in the follow... |
The universe is marvelously structured. Everywhere and at any scale one examines, one cannot escape a deep sense of wonder about the origin and meaning of the remarkable organizations that can be observed, exhibiting complex interplays between regularity and irregularity, order and disorder, periodicity and stochastici... |
Many thinkers and scientists have contributed to the rebuttal of the intelligent design argument. On pure logical grounds, the proposition that a designer creates by definition a design, which has some structure, does not reverse logically into the proposition that a structure is necessary by design, and thus requires ... |
More recently, great attention is being paid to the processes of self-organization in various networks, including neuron networks in the brain (Mainzer 2007; Chialvo 2010; Werner 2012; Fingelkurts et al. 2012) and of self-organization of various swarms and flocks (Vanni et al. 2011; Turalska et al 2011), where self-org... |
swarm intelligence . Complex behaviors of simple physical systems, imitating a kind of trivial intelligence, can be due to entropic forces (Wissner-Gross and Freer 2013). |
The goal of the present article is to suggest a novel level of understanding, combining self-organization of the complex system and decision making of that same complex system (without invoking the will and decision making of any controller or watchmaker). This is based on the recognition that the |
mathematical structures of self-organization and of decision making are identical. In other words, the process of self-organization corresponds to an endogenous decision making process, giving the impression that a superior intention is at work. While this view point has been made many times by philosophers of the scie... |
As any endeavor touching such big concepts and existential questions, there are many roots and precursors of our ideas, going back to Plato and Aristotle, Saint Anselm around 1000 AD and Kant. Perhaps the idea closest to our proposition is the one formulated by the German philosopher Kant. In 1790, in his Kritik der Ur... |
We prove the general proposition of the similarity between self-organization and decision making by developing an explicit mathematical formulation |
describing these processes in the frame of the same general probabilistic approach. Necessarily, such an approach has to be probabilistic for two reasons. First, a probabilistic approach is mathematically more general, including the deterministic one as a particular case. Second, observed processes in nature are practi... |
Armed with the notion that the description of any system requires a probabilistic framework, we can now give a first intuition of the correspondence between the processes of self-organization and decision making, which can be described in the frame of the same mathematical framework with just a slight change of termino... |
Self-organization is the process of evaluating the probabilities of system states in the search for the most stable state Decision making is the process of evaluating the probabilities of decision prospects in the search for the most preferable prospect |
We start Sec. 2 by explaining the intimate connection between the notions of stability and of probability, so that the system state is more probable, provided it is more stable. Then we give the general scheme outlining the analogies between the system states and decision prospects in the frame of the probabilistic rep... |
We would like to stress that our main aim is not to analyze in detail the behavior of particular systems, but to show that their final mathematical description can be realized in the same general probabilistic framework Particular examples that we mention for illustration can be already well understood. This does not i... |
System states as decision prospects The possibility of characterizing (i) the states of empirical systems as decision prospects and (ii) transitions between the states as if the system would be deliberating choosing the most stable, that is, the most preferable state, relies on the fact that observation and knowledge a... |
2.1 Relation between stability and probability Any complex system, under given external conditions, tends to occupy the most stable state. At the same time, the available states can be classified by their probabilities, so that the more stable state enjoys the higher probability. This relation between stability and pro... |
[MATH] , hence the minimization of free energy is equivalent to the maximization of probability. It is admissible to accept the entropy [MATH] |
as a thermodynamic potential. Then the system stability requires the maximization of the system entropy. At the same time, the system probability reads as |
[MATH] . Therefore, the larger entropy corresponds to the higher probability. In Sec. 5 below, we demonstrate that the same relation between stability and probability holds for nonequilibrium systems as well. For the latter systems, the higher stability is characterized by the smaller map multiplier, thus, by the large... |
2.2 Self-organization as search for the most preferable state A complex system can be in several macrostates corresponding to different levels of self-organization. The macrostates can be distinguished, e.g., by their order parameters (Landau and Lifshitz 1980; Yukalov and Shumovsky 1990; Sornette 2006) or by their ord... |
[MATH] . The total set of admissible states is denoted as [EQUATION] The main assumption is that each state [MATH] can be characterized by the related probability [MATH] satisfying the standard properties |
[EQUATION] For a while, we assume that such a probability measure can be defined. And the method of constructing the corresponding probabilities will be given in the following section. |
Here, the index [MATH] , enumerating the macrostates, is taken to be discrete. The case of a continuous index can be treated in the same manner, just replacing summation by integration. |
The set of all states can be ordered according to relations between the corresponding probabilities. The state [MATH] is said to be preferred to the state [MATH] if and only if |
[EQUATION] The states [MATH] and [MATH] are equivalent if and only if [EQUATION] And the state [MATH] is preferred or indifferent to [MATH] when |
[EQUATION] Comparing the states by using their probabilities makes it possible to define the least preferred and the most preferred states, which makes the set ( a complete lattice. An optimal state [MATH] is the state possessing the largest probability: |
[EQUATION] A self-organizing complex system behaves as if it would evaluate, by means of fluctuations, the probabilities of available macrostates, selecting from them the optimal state. This is analogous to the behavior of a decision maker who chooses, by deliberation, among a set of given alternatives, the optimal pro... |
2.3 Measures of system self-organization To define the level of self-organization, one usually considers the Shannon entropy [EQUATION] |
which is a positive quantity characterizing missing information (Shannon and Weaver 1949). Respectively, the Shannon information is minus the Shannon entropy, |
[EQUATION] The latter quantity, describing missing information, is negative. The larger the system entropy, that is, the smaller the Shannon information, the lesser the system self-organization. |
Another measure of self-organization is the von Foerster redundancy [EQUATION] in which [MATH] is the maximal value of entropy (von Foerster 1995; Pask 1996). The Shannon entropy ( ) is maximal for the uniform probabilities [MATH] , when [MATH] . The larger the redundancy, the higher the level of the system self-organi... |
According to von Foerster, when the system is certainly in a fixed state [MATH] , such that [MATH] then it is perfectly organized, with [MATH] . On the contrary, for the uniform distribution |
[MATH] , the system is not organized, with [MATH] A convenient measure is the Kullback-Leibler (1951, 1959) relative information |
[EQUATION] where [MATH] is a representative of an approximate, or trial, probability measure, based on the available additional information on the system, and satisfying the standard conditions |
[EQUATION] The Kullback-Leibler relative information, also called negentropy, is non-negative defined: [EQUATION] This follows from the Gibbs-Klein (Gibbs 1902; Klein 1931) inequality |
[EQUATION] The relative information is minimal when [MATH] and [MATH] coincide, [EQUATION] In the case of the uniform trial distribution [MATH] , the Kullback-Leibler relative information and Shannon information are connected by the equality |
[EQUATION] The form of the Kullback-Leibler information is similar to the expected log-likelihood function employed in statistics (Edwards 1972). The information measures are important for constructing the information functional that makes it possible to define the state probabilities for the considered complex systems... |
Principle of minimal information A pivotal role for defining the explicit form of the state probabilities is played by the principle of minimal information implying the minimization of an information functional. The origin of this principle is the maximization of entropy under given conditions (Gibbs 1902, 1928, 1931; ... |
3.1 Minimization of the information functional To define an information functional, one has, first, to introduce the representative ensemble, which is a pair [MATH] , where [MATH] |
implies the probability set [EQUATION] which is complemented by the available additional constraints making unique the system description (Gibbs 1928, 1931; Yukalov 1991, 2007). Such constraints are formulated as statistical averages, or expected values, of constraint functions: |
[EQUATION] with the index [MATH] enumerating the constraints. Then, the information functional can be written as [EQUATION] [EQUATION] |
where [MATH] and [MATH] are Lagrange multipliers guaranteeing the validity of constraints ( 16 ). The information functional is the sum of the Kullback-Leibler information measure and of those constraints that have been imposed on the system. |
The minimization of the information functional assumes the variational conditions [EQUATION] Introducing the global constraint [EQUATION] |
this results in the state probability [EQUATION] in which the normalization quantity [EQUATION] is called partition function. The parameter [MATH] is a Lagrange multiplier. |
The meaning of the principle of minimal information is in characterizing the probability distribution under the minimal information encoded in the statistical constraints. By specifying these constraints for concrete systems, one gets particular forms of the probability distribution. |
3.2 Minimization of the grand potential It may happen that the probabilities ( 20 ) depend on some additional set of parameters [MATH] , so that the state probability is |
[EQUATION] with the partition function [EQUATION] Substituting this into the information functional ( 17 ) yields [EQUATION] with a fixed global constraint |
[EQUATION] Since the latter is fixed, the minimization of the information functional with respect to the parameter set [MATH] is equivalent to the maximization of the partition function: |
[EQUATION] We can introduce the grand potential [EQUATION] In a thermodynamical system, [MATH] plays the role of temperature [MATH] More generally, [MATH] plays the role of a parameter measuring the level of noise. Then, from Eq. ( 23 ), it follows (Yukalov 2011) that the minimization of the information functional is e... |
[EQUATION] The above formalism applies beyond the description of thermodynamical systems at or close to equilibrium, also to quasi-equilibrium systems, when the notion of temperature is replaced by its more generalized version |
[MATH] giving a measure of the typical strength of the fluctuations of the system variables. As important practical applications, it is possible to enumerate a number of heterogenous condensed-matter systems displaying mesoscopic heterophase fluctuations (Yukalov 1981, 1991, 2003a; Shumovsky and Yukalov 1982). Then the... |
[EQUATION] characterizes the statistical weights [MATH] of qualitatively different mesoscopic fluctuations. Quasi-stationary self-organizing systems |
When the system parameters vary much slower than typical dynamical motions in the system, the latter can be treated as quasi-stationary. The principle of minimal information is often applied for describing self-organization in such quasi-stationary systems. Below we give a brief reminder of the known examples of variou... |
4.1 Probability of thermodynamic states Statistical systems, to which thermodynamics is applicable, are characterized by thermodynamic potentials, such as the free energy (Landau and Lifshitz 1980). Suppose that the system can acquire several thermodynamic states [MATH] corresponding to different thermodynamic phases s... |
[EQUATION] Assuming the uniform trial distribution [MATH] , the principle of minimal information gives [EQUATION] with the partition function |
[EQUATION] Here [MATH] is a Lagrange multiplier corresponding to the inverse temperature [MATH] Distribution [MATH] describes the probability that the thermodynamic system is in the state [MATH] . The sharpness of the distribution depends on the system size. |
4.2 Infinite statistical systems The typical situation for the so-called bulk statistical systems, such as condensed matter or gases, is to consider their large sizes by taking the thermodynamic limit, when the number of particles [MATH] composing the system is assumed to tend to infinity. In that case, the free energy... |
[EQUATION] whose order parameter provides the minimal free energy of the system, [EQUATION] Let some of the characteristic system parameters, either external or internal, be varying. For instance, this can be temperature. For any given governing parameter, such as temperature, the system always chooses the optimal stat... |
[EQUATION] [EQUATION] which is called phase transition. Since varying the governing parameters does not usually directly impose neither the type of the order parameter nor the related symmetry, but the system itself acquires the structure and symmetry of the optimal state, this process is termed self-organization. As f... |
4.3 Finite statistical systems There exists a large class of systems that contain many particles, in that sense being statistical, but at the same time, with the number of particles being finite, such that finite-size effects become important. Examples are trapped atoms, quantum dots, atomic nuclei, metallic grains, an... |
When the system is finite, with a finite number [MATH] of particles, then several macroscopic states can be realized, having nontrivial probabilities 27 ). In such a case, the phase transition between two different phases occurs with the characteristics that the state probabilities are not exactly one or zero, as for i... |
[EQUATION] to the inequality [EQUATION] The transition can be discontinuous or continuous. In any case, this corresponds to a probabilistic self-organization associated with phase transitions (Bouchaud and Georges 1990; Jona-Lasinio 2001). |
As physical illustrations of finite systems with coexisting phases, we can mention metallic grains that can be either in superconducting or normal states (von Delft 2001), atomic nuclei that can take different shapes (Gaudefroy et al. 2009), and nanosize spin clusters that can be either in magnetic or non-magnetic stat... |
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