Per Bak. How Nature Works. Oxford University Press, 1997.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....if then rules based on measures on the population. A simple approach may be to count the number of generations without fitness improvement and then increase the mutation variance temporarily Bak suggests the sandpile model as a simple approach to study many complex phenomena found in nature [14]. The sandpile model is an example of how self organized criticality (SOC) can be generated by very simple means. Named after Bak s work on self organized criticality. 0 0.2 0.4 0.6 0.8 1 (a) Deterministic annealing #(t) 0 0.2 0.4 0.6 0.8 1 (b) Deterministic non monotonic ....

....this model seems interesting, Greenwood et al. unfortunately only reported results on a rather simple two dimensional numerical problem [60] Hence, the performance on a broader selection of problems have not been examined yet. 5.5. 3 SOC extinction EA The idea of self organized criticality (SOC, [14]) has been used by Krink et al. to control the extinction rate in an EA [86] The approach is motivated by the fact that mass extinction in nature follows the power law distribution [111; 14] The SOC extinction EA use a so called sandpile model [14] to generate power law distributed numbers that ....

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Bak, P. (1996). How Nature Works. Copernicus, Springer-Verlag, 1st edition. 153

....search algorithms, which would choose to flip the spin that would decrease the energy the most. Extremal optimisation, however, chooses to flip the spin with rank k with a probability that is proportional to k . The use of this probability function is inspired by self organized criticality [54, 55, 56]. The value of that is best to use depends on the problem at hand, see [53, 57] 2.7 The first problem shown to be in NPC was the satisfiability problem [58] This was the first paper that asked questions about what problems were and were not solvable efficiently and also provided answers; it ....

P. Bak, How Nature Works. Oxford University Press, 1997.

....i.e. 20D = 1000 generations, Power law distributed numbers can be generated by x = 1 u 1 # , where u U(0, 1) is uniformly distributed, and # is a parameter determining the shape of the distribution. Another approach used in [10] is to log the avalanche sizes in the so called sandpile model [14]. 50D = 2500 generations, and 100D = 5000 generations. The four (minimization) problems are: Ackley F1(x) 20 e 20 exp # 0.2 # # # exp cos(2# x i ) Griewank F1(x) 1 4000 (x i 100) cos # i 1 Rastrigin F1(x) x ....

Bak, P.: How Nature Works. Copernicus, Springer-Verlag, New York, 1st edition, (1996)

....conclude that hybrid models of the standard GA and the PSO, could lead to further advances. Paleontological findings have revealed that mass extinction has been a common phenomenon in evolution [11] It has been suggested to be an important mechanism for evolutionary progress in biological world [12], since extinction allows the repopulation of niches and gives space for new adaptations. In the field of evolutionary algorithms, this idea has been the motivation for so called (mass ) extinction models, which has been introduced recently [13 15] It is therefore natural to ask if mass ....

P. Bak. How nature works. Springer-Verlag, NY, 1986

....Replacing more individuals by controlled mass extinction have been examined by Krink et al. 26, 27] This latter example uses the concept of Self Organized Criticality to control the frequency and strength of the events adding diversity. Self Organized Criticality (SOC) was introduced by Bak ([3]) to describe the frequency of an emergent property in complex systems. Typically, in complex systems the strength of an emergent property is inversely proportional to its frequency. Various complex systems follow this SOC relation e.g. species extinction rates in nature ( 3] or the ....

....was introduced by Bak ( 3] to describe the frequency of an emergent property in complex systems. Typically, in complex systems the strength of an emergent property is inversely proportional to its frequency. Various complex systems follow this SOC relation e.g. species extinction rates in nature ([3]) or the Gutenberg Richter law of earthquakes ( 17] The main idea in SOC is that most state transitions in a component of a complex system only a#ects its neighbourhood, but once in a while entire avalanches of propagating state transitions lead to a major reconfiguration of the system. Inspired ....

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P. Bak, "How Nature Works", Copernicus, Springer-Verlag, 1. edition, 1996.

....This work was done to investigate one way of enhancing the PSO. Complex system behaviour is neither linear (stable) nor uncorrelated (chaos) but formed by self organisation in a long transient period and found at the border of stability and chaos a state known as Self Organized Criti cality [2]. Typically, in complex systems the strength of an emergent property is inversely proportional to its frequency with the functional relationship of a power law: x x . When plotted on a log log scale, power law data can be described by a linear fit with a negative slope. Various complex systems ....

....is inversely proportional to its frequency with the functional relationship of a power law: x x . When plotted on a log log scale, power law data can be described by a linear fit with a negative slope. Various complex systems follow these power laws e.g. species extinction rates in nature [2]. The main idea in SOC is that most state transitions in a component of a complex system only affects its neighbourhood, but once in a while entire avalanches of propagating state transitions can lead to a major reconfiguration of the system. This study was motivated by the successful application ....

P. Bak, "How Nature Works", 1996, Copernicus, Springer-Verlag, 1. edition.

....of the interactions and dependencies among animals, such as symbiotic mutualism or food web interactions. Here, the extinction of a specific group of animals can cause the extinction of others. Interestingly, mass extinction has been suggested to be a key mechanism for evolutionary progress [2]. Extinction allows the repopulation of niches and gives room for new experimentation and adaptations. In the field of evolutionary algorithms (EAs) this idea has been the motivation for socalled (mass ) extinction models, which have been introduced recently [6] 9] 10] 5] 8] In mass ....

....model of species dependencies. In their approach, all individuals of a species die if the majority of the neighbored species had a better fitness. Thus mass extinction is induced when a new and very good solution is found. This model partly resembles aspects of the Bak Sneppen extinction model [2], where species are arranged in a circle and represented by random numbers. At each time step, the lowest number, and the numbers at its two neighbors, are each replaced by new random numbers. The drawback of the MA approach is that neither crossover nor mutation is applied in the background. The ....

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BAK, P. How Nature Works, 1 ed. Copernicus, Springer-Verlag, New York, 1996.

.... terms of a complex adaptive system with interactions among di erent species was introduced by Kau man and Johnsen [25] who used previous theoretical work on tness landscapes [26] The model is inspired in previous theoretical work by Per Bak and co workers on self organized criticality [3] 5] [6]. The basic idea of Fig. 4. Wavelet transform obtained from the extinction dynamics shown in gure 2. The horizontal axis indicates time and the vertical indicates the analysis scale, withlarge scales at the bottom. Brighter areas indicate larger extinction events. This picture displays some of ....

Bak, P.How Nature Works, Springer (1996)

....In a critical state, the elements become connected, propagating order throughout the system in the sense that the statistical characteristics of the system are self ane with system wide correlations. This is more to do with the connectivity of the elements than the elements themselves [8]. Critical states can of course be stable in the dynamical sense. Moreover, critical states appear to be governed by the universal power law J.M. Blackledge et al. 191 System(size) 1 size q where q is a non integer value. Here, the term System is a generic term representative of some de ....

....fossil records) is starting to indicate that the pattern of tness for survival is statistically self ane. This result can be simulated by relatively simple iteration function systems such as in the Bak Sneppen model which yields self ane distributions for the tness of di erent species over time [8]. The distribution of base pairs in DNA is statistically self ane, i.e. the frequency of occurrence of Adenine Thymine and Cytosine Guanine in a DNA molecule is the same at di erent scales. DNA is in e ect, a self ane bit stream. Conventional RSF models are based on stationary processes in which ....

Bak P, How Nature Works, Oxford University Press, 1997

....Optimized Configurations Natural systems are complex structures, and often optimize efficiency in surprisingly sophisticated ways. Biological evolution has resulted in a plethora of interdependent species, collectively competing for resources in such a way that these resources rarely go to waste [Bak96]. Geographic landscapes, in their minute intricacy, can serve a valuable purpose such as efficient drainage of water [Ro97] Yet in spite of the complexity of the outcome, nature s mechanisms are in general exceedingly simple. Evolution is driven merely by sunlight. Amazing as it may seem from an ....

Bak, P. How Nature Works. Springer, New York, 1996.

.... example, progresses by selecting against the few most poorly adapted species, rather than by expressly breeding those species best adapted to their environment [13] To describe the dynamics of systems with emergent complexity, the concept of self organized criticality (SOC) has been proposed [2,4]. Models of SOC often rely on extremal processes [30] where the least fit variables are progressively eliminated. This principle has been applied successfully in the Bak Sneppen model of evolution [3,33] where a species i is characterized by a fitness value # i #[0,1] and the weakest ....

P. Bak, How Nature Works, Springer, New York, 1996.

....1998 slow decaying power law. Many systems evolve, spontaneously, to the critical state. The name self organized criticality has been coined for them by Bak, whose seminal papers (Bak et al. 1987; Bak et al. 1988) have triggered a major comprehension of how a broad class of such systems work (Bak, 1997). In DNA sequences, not only the existence of this long ranged correlation is surprising, but also the peculiar form of it. Indeed, it was found a 1=f spectrum in the Fourier transform of some sequences (Li et al. 1994) that implies a corresponding slow decay in space. This behavior is ....

Bak, Per. 1997. How Nature works. Oxford: Oxford University Press.

....from di erent cities and very few are from di erent countries. This exponential (power law) relationship between the frequency of an event and the size of its impact (here: the distance between mates) is a typical property of complex systems, which operate in a state of self organized criticality (Bak, 1996). In the study that we present in this paper, we took the concept of mate choice dispersal as an inspiration for a re nement of the di usion model. Our main motivation was the idea that occasional outbreeding could improve the performance of the di usion model by counterbalancing the e ect of the ....

....of this study in section 6. 2 SELF ORGANIZED CRITICALITY Complex system behavior is neither linear (stable systems) nor uncorrelated (chaos) but formed by selforganization in a long transient period and found at the border of stability and chaos a state known as self organized criticality (Bak, 1996). Typically, in complex systems the strength of an emergent property is inversely proportional to its frequency f (also known as 1=f noise) with the functional relationship of a power law: x x . When plotted on a log log scale, power law data can be described by a linear t with a negative ....

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Bak, P. (1996). How Nature Works. Copernicus, Springer-Verlag, 1 edition.

....the model is quite complicated to implement and it requires substantial additional computation time. Furthermore, this model produces only better results when compared to a standard EA in one out of three test cases [10] This model partly resembles aspects of Per Bak s species extinction model [1]. Here, species represented by random numbers are arranged in a circle. At each time step, the lowest number, and the numbers at its two neighbours, are each replaced by new random numbers. Greenwood et al. 6] presented a simpler, but very e ective mass extinction model where the mortality of ....

.... time, since parameter values are gradually tuned towards optimal values [5] In this paper, we present an approach which tries to overcome the classical problem of premature convergence on local hills by application of self organised criticality (SOC) a theory based on complexity research [1]. The key idea is to control the variance of Gaussian mutation and the extinction size during selection by a power law function, which re ects typical dynamics found in complex systems such as Darwinian evolution. 2 Self Organised Criticality Complex system behaviour is neither linear (stable ....

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Bak, P. How Nature Works, 1 ed. Copernicus, Springer-Verlag, New York, 1996.

....that many models produce polo distributions starting from many different explanations (e.g. Zipf 1949; John Conway s Game of Life, Berlekamp et al. 1982; Barlow 1994; Pahl Wostl 1995) as the trend results from similar fundamentals such as neighbourhood interaction or competition for resources. Bak (1997) suggested that such models evolve to criticality, as do natural systems (e.g. Lockwood and Lockwood 1997) Whatever the underlying principles, there is a need to describe these in a way valid for all systems. For example, the analogies with fundamental quantum theory are intriguing ( quanta of ....

Bak, P. (1997) How nature works. The science of self-organized criticality, Oxford University Press, Oxford.

....acyclic graph (look at the figure 1) Moreover a tree is balanced if approximately all the leaves are at the same distance from the root. There are different kinds of balanced trees (AVL, 2 3 trees, RedBlack, Here we study efficient dictionaries as a selforganized critical structure [3]. Good tree structures require sophisticated update algorithms in order to maintain the performance. More precisely, while evolving the tree needs to maintain the general shape ever if the concrete details change continuously. Therefore along its evolution a balanced tree behaves as ....

P. Bak. How nature works. Copernicus, 1996.

....state. In economy stock market prices are an example of a possibly very pro table prediction task. It should be pointed out, however, that there exists the question whether a process is predictable or not. In nature and in economy one can nd complex processes that show self organizing criticality [1]. In this case the answer to the question is not obvious. We have, however, passed by this question by taking here the view that a process is somehow predictable or in fact modelable accurately or not as long as there is statistical data available. A time series can be nonstationary but still ....

....dx dt = fix(t) ffx(t Gamma fl) 1 x(t Gamma fl) 10 (15) where x(t) is the value of the time series at time t. This system is chaotic for fl 16:8. In the present test the time series was constructed with parameter values ff = 0:2, fi = Gamma0:1 and fl = 17 and it was scaled between [ 1,1]. From the beginning of the series shown in Fig. 3 3000 samples was selected for training, and the rest 1000 samples were used for testing. For RSOM and MLP models length of the input vector was varied as p 2 f3; 5; 7g. 0 500 1000 1500 2000 2500 3000 3500 4000 1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 ....

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P. Bak. How Nature Works. Springer Verlag, New York, 1996.

....enough of the stochastically determined winners. Brian Arthur s (1994a) example of growth following a Polya process tells us of the fundamental unpredictability of what happens to a single innovating firm. It does not argue against what happens to the mean performance of the universe of firms. Per Bak s (1996) example of avalanches on a sand pile or of the Gutenberg Richter law on the frequency (but not the timing) of the occurrence of earthquakes argue in favor of science with prediction of global but not individual properties. Ralph Gomory s (1995) observations on the unknowable are consistent with ....

....are under constant revision 5. Perpetual novelty: Niches are constantly being created by new markets, institutions, technologies and behavior 6. the economy operates far from any equilibrium. The incessant bombardment of change from technology, society, the polity The models of Kaufmann (1993) Bak (1996), Conway (see Sigmund, 1993) and others together with this perceptive list should be regarded as a challenge to the economist, biologist, other behavioral scientists and game theorists in particular. A central element is the study of coevolution in nonconservative, nonequilibrium systems. A new ....

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Bak, P. 1996. How Nature works. New York: Springer Verlag.

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Per Bak. How Nature Works. Oxford University Press, 1997.

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Bak, P. (1996) How Nature Works, Springer-Verlag

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P. Bak. How Nature Works. Springer-Verlag, 1996.

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Bak, P., 1996, How Nature Works,(Springer-Verlag)

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P. Bak, How Nature Works, Springer-Verlag, New York, 1996.

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P. Bak (1996), How Nature Works, Springer.

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Bak, P., How Nature Works, Oxford Univ. Press, London, 1996.

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