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Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.

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At least 541 records · Page 30Linked to original sources

arXiv1997

Solvable dynamics in a system of interacting random tops

In this letter a new solvable model of synchronization dynamics is introduced. It consists of a system of long range interacting tops with random precession frequencies. The model allows for an explicit study of orientational effects in synchronized phenomena. A stability analysis of the incoherent solution is performed for different types of orientational disorder. A system with only orientational disorder always synchronizes in the absence of external noise.

cond-mat.dis-nn↗

arXiv1999

Neutral Mutations and Punctuated Equilibrium in Evolving Genetic Networks

Boolean networks may be viewed as idealizations of biological genetic networks, where each node is represented by an on-off switch which is a function of the binary output from some other nodes. We evolve connectivity in a single Boolean network, and demonstrate how the sole requirement of sequential matching of attractors may open for an evolution that exhibits punctuated equilibrium.

physics.bio-ph↗

arXiv1998

A Simple Model of Superconducting Vortex Avalanches

We introduce a simple lattice model of superconducting vortices driven by repulsive interactions through a random pinning potential. The model describes the behavior at the scale of the London length lambda or larger. It self-organizes to a critical state, characterized by a constant flux density gradient, where the activity takes place in terms of avalanches spanning all length scales up to the system size. We determine scaling relations as well as four universal critical exponents for avalanche moments and durations: tau = 1.63 +/- 0.02, D = 2.7 +/- 0.1, z = 1.5 +/- 0.1, and tau_t = 2.13 +/- 0.14, for the system driven at the boundary.

cond-mat.stat-mech↗

arXiv1998

Phase Transition in the Number Partitioning Problem

Number partitioning is an NP-complete problem of combinatorial optimization. A statistical mechanics analysis reveals the existence of a phase transition that separates the easy from the hard to solve instances and that reflects the pseudo-polynomiality of number partitioning. The phase diagram and the value of the typical ground state energy are calculated.

cond-mat↗

arXiv1998

Matrix Games, Mixed Strategies, and Statistical Mechanics

Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties of optimal mixed strategies of large matrix games with random payoff matrices and derive analytical expressions for the value of the game and the distribution of strategy strengths. In particular the fraction of pure strategies not contributing to the optimal mixed strategy of a player is calculated. Both independently distributed as well as correlated elements of the payoff matrix are considered and the results compared with numerical simulations.

cond-mat.dis-nn↗

arXiv1998

Extinction events and species lifetimes in a simple ecological model

A model for large-scale evolution recently introduced by Amaral and Meyer is studied analytically and numerically. Species are located at different trophic levels and become extinct if their prey becomes extinct. It is proved that this model is self-organized critical in the thermodynamic limit, with an exponent 2 characterizing the size distribution of extinction events. The lifetime distribution of species, cutoffs due to finite-size effects, and other quantities are evaluated. The relevance of this model to biological evolution is critically assessed.

adap-org↗

arXiv1998

Autocatalytic Sets and the Growth of Complexity in an Evolutionary Model

A model of $s$ interacting species is considered with two types of dynamical variables. The fast variables are the populations of the species and slow variables the links of a directed graph that defines the catalytic interactions among them. The graph evolves via mutations of the least fit species. Starting from a sparse random graph, we find that an autocatalytic set (ACS) inevitably appears and triggers a cascade of exponentially increasing connectivity until it spans the whole graph. The connectivity subsequently saturates in a statistical steady state. The time scales for the appearance of an ACS in the graph and its growth have a power law dependence on $s$ and the catalytic probability. At the end of the growth period the network is highly non-random, being localized on an exponentially small region of graph space for large $s$.

adap-org↗

arXiv1999

Noise-correlation-time-mediated localization in random nonlinear dynamical systems

We investigate the behavior of the residence times density function for different nonlinear dynamical systems with limit cycle behavior and perturbed parametrically with a colored noise. We present evidence that underlying the stochastic resonancelike behavior with the noise correlation time, there is an effect of optimal localization of the system trajectories in the phase space. This phenomenon is observed in systems with different nonlinearities, suggesting a degree of universality.

chao-dyn↗

arXiv1999

Small-world networks: Evidence for a crossover picture

Watts and Strogatz [Nature 393, 440 (1998)] have recently introduced a model for disordered networks and reported that, even for very small values of the disorder $p$ in the links, the network behaves as a small-world. Here, we test the hypothesis that the appearance of small-world behavior is not a phase-transition but a crossover phenomenon which depends both on the network size $n$ and on the degree of disorder $p$. We propose that the average distance $\ell$ between any two vertices of the network is a scaling function of $n / n^*$. The crossover size $n^*$ above which the network behaves as a small-world is shown to scale as $n^*(p \ll 1) \sim p^{-τ}$ with $τ\approx 2/3$.

cond-mat.stat-mech↗

arXiv1999

Self-Organized Segregation within an Evolving Population

An evolving population, in which individual members (`agents') adapt their behaviour according to past experience, is of central importance to many disciplines. Because of their limited knowledge and capabilities, agents are forced to make decisions based on inductive, rather than deductive, thinking. We show that a population of competing agents with similar capabilities and knowledge will tend to self-segregate into opposing groups characterized by extreme behavior. Cautious agents perform poorly and tend to become rare.

cond-mat↗

arXiv1999

A simple model for the formation of a complex organism

A simple model for the formation of a complex organism is introduced. Individuals can communicate and specialize, leading to an increase in productivity. If there are limits to the capacity of individuals to communicate with other individuals, the individuals form groups that interact with each other, leading to a complex organism that has interacting units on all scales.

adap-org↗

arXiv1999

1/f Noise and Long Configuration Memory in Bak-Tang-Wiesenfeld Models on Narrow Stripes

We report our findings of an 1/f power spectrum for the total amount of sand in directed and undirected Bak-Tang-Wiesenfeld models confined on narrow stripes and driven locally. The underlying mechanism for the 1/f noise in these systems is an exponentially long configuration memory giving rise to a very broad distribution of time scales. Both models are solved analytically with the help of an operator algebra to explicitly show the appearance of the long configuration memory.

cond-mat.stat-mech↗

arXiv1999

Field Theoretical Analysis of On-line Learning of Probability Distributions

On-line learning of probability distributions is analyzed from the field theoretical point of view. We can obtain an optimal on-line learning algorithm, since renormalization group enables us to control the number of degrees of freedom of a system according to the number of examples. We do not learn parameters of a model, but probability distributions themselves. Therefore, the algorithm requires no a priori knowledge of a model.

cond-mat.dis-nn↗

arXiv1999

Thermodynamic limit from small lattices of coupled maps

We compare the behaviour of a small truncated coupled map lattice with random inputs at the boundaries with that of a large deterministic lattice essentially at the thermodynamic limit. We find exponential convergence for the probability density, predictability, power spectrum, and two-point correlation with increasing truncated lattice size. This suggests that spatio-temporal embedding techniques using local observations cannot detect the presence of spatial extent in such systems and hence they may equally well be modelled by a local low dimensional stochastically driven system.

chao-dyn↗

arXiv1999

Braided Rivers and Superconducting Vortex Avalanches

Magnetic vortices intermittently flow through preferred channels when they are forced in or out of a superconductor. We study this behavior using a cellular model, and find that the vortex flow can make braided rivers strikingly similar to aerial photographs of braided fluvial rivers, such as the Brahmaputra. By developing an analysis technique suitable for characterizing a self-affine (multi)fractal, the scaling properties of the braided vortex rivers in the model are compared with those of braided fluvial rivers. We suggest that avalanche dynamics leads to braiding in both cases.

cond-mat.stat-mech↗

arXiv1999

A thermal model for adaptive competition in a market

New continuous and stochastic extensions of the minority game, devised as a fundamental model for a market of competitive agents, are introduced and studied in the context of statistical physics. The new formulation reproduces the key features of the original model, without the need for some of its special assumptions and, most importantly, it demonstrates the crucial role of stochastic decision-making. Furthermore, this formulation provides the exact but novel non-linear equations for the dynamics of the system.

cond-mat.stat-mech↗

arXiv1999

Avalanche Merging and Continuous Flow in a Sandpile Model

A dynamical transition separating intermittent and continuous flow is observed in a sandpile model, with scaling functions relating the transport behaviors between both regimes. The width of the active zone diverges with system size in the avalanche regime but becomes very narrow for continuous flow. The change of the mean slope, Delta z, on increasing the driving rate, r, obeys Delta z ~ r^{1/theta}. It has nontrivial scaling behavior in the continuous flow phase with an exponent theta given, paradoxically, only in terms of exponents characterizing the avalanches theta = (1+z-D)/(3-D).

cond-mat.stat-mech↗

arXiv2000

Beyond Hebb: Exclusive-OR and Biological Learning

A learning algorithm for multilayer neural networks based on biologically plausible mechanisms is studied. Motivated by findings in experimental neurobiology, we consider synaptic averaging in the induction of plasticity changes, which happen on a slower time scale than firing dynamics. This mechanism is shown to enable learning of the exclusive-OR (XOR) problem without the aid of error back-propagation, as well as to increase robustness of learning in the presence of noise.

adap-org↗