Searcharxiv⌕ Search

SEARCH · Searcharxiv

Results for “adap-org”

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

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 181 records · Page 10Linked to original sources
arXiv1999

Pfaff tau-functions

Consider the evolution $$ \frac{\pl m_\iy}{\pl t_n}=\Lb^n m_\iy, \frac{\pl m_\iy}{\pl s_n}=-m_\iy(\Lb^\top)^n, $$ on bi- or semi-infinite matrices $m_\iy=m_\iy(t,s)$, with skew-symmetric initial data $m_{\iy}(0,0)$. Then, $m_\iy(t,-t)$ is skew-symmetric, and so the determinants of the successive "upper-left corners" vanish or are squares of Pfaffians. In this paper, we investigate the rich nature of these Pfaffians, as functions of t. This problem is motivated by questions concerning the spectrum of symmetric and symplectic random matrix ensembles.

solv-int↗
arXiv2001

Matrix integrals and the geometry of spinors

We obtain the collection of symmetric and symplectic matrix integrals and the collection of Pfaffian tau-functions, recently described by Peng and Adler and van Moerbeke, as specific elements in the Spin-group orbit of the vacuum vector of a fermionic Fock space. This fermionic Fock space is the same space as one constructs to obtain the KP and 1-Toda lattice hierarchy.

solv-int↗
arXiv1998

Brownian motion in fluctuating periodic potentials

This work deals with the overdamped motion of a particle in a fluctuating one-dimensional periodic potential. If the potential has no inversion symmetry and its fluctuations are asymmetric and correlated in time, a net flow can be generated at finite temperatures. We present results for the stationary current for the case of a piecewise linear potential, especially for potentials being close to the case with inversion symmetry. The aim is to study the stationary current as a function of the potential. Depending on the form of the potential, the current changes sign once or even twice as a function of the correlation time of the potential fluctuations. To explain these current reversals, several mechanisms are proposed. Finally, we discuss to what extent the model is useful to understand the motion of biomolecular motors.

cond-mat↗
arXiv1996

Mass Extinctions vs. Uniformitarianism in Biological Evolution

It is usually believed that Darwin's theory leads to a smooth gradual evolution, so that mass extinctions must be caused by external shocks. However, it has recently been argued that mass extinctions arise from the intrinsic dynamics of Darwinian evolution. Species become extinct when swept by intermittent avalanches propagating through the global ecology. These ideas are made concrete through studies of simple mathematical models of coevolving species. The models exhibit self-organized criticality and describe some general features of the extinction pattern in the fossil record.

cond-mat↗
arXiv1997

Modeling diffusion of innovations with probabilistic cellular automata

We present a family of one-dimensional cellular automata modeling the diffusion of an innovation in a population. Starting from simple deterministic rules, we construct models parameterized by the interaction range and exhibiting a second-order phase transition. We show that the number of individuals who eventually keep adopting the innovation strongly depends on connectivity between individuals.

adap-org↗
arXiv1994

Nonlinear Dynamics in Distributed Systems

We build on a previous statistical model for distributed systems and formulate it in a way that the deterministic and stochastic processes within the system are clearly separable. We show how internal fluctuations can be analysed in a systematic way using Van Kanpen's expansion method for Markov processes. We present some results for both stationary and time-dependent states. Our approach allows the effect of fluctuations to be explored, particularly in finite systems where such processes assume increasing importance.

adap-org↗
arXiv1995

Scaling, Propagation, and Kinetic Roughening of Flame Fronts in Random Media

We introduce a model of two coupled reaction-diffusion equations to describe the dynamics and propagation of flame fronts in random media. The model incorporates heat diffusion, its dissipation, and its production through coupling to the background reactant density. We first show analytically and numerically that there is a finite critical value of the background density, below which the front associated with the temperature field stops propagating. The critical exponents associated with this transition are shown to be consistent with mean field theory of percolation. Second, we study the kinetic roughening associated with a moving planar flame front above the critical density. By numerically calculating the time dependent width and equal time height correlation function of the front, we demonstrate that the roughening process belongs to the universality class of the Kardar-Parisi-Zhang interface equation. Finally, we show how this interface equation can be analytically derived from our model in the limit of almost uniform background density.

cond-mat↗
arXiv1994

Reaction-Diffusion Processes of Hard-Core Particles

We study a 12-parameter stochastic process involving particles with two-site interaction and hard-core repulsion on a $d$-dimensional lattice. In this model, which includes the asymmetric exclusion process, contact processes and other processes, the stochastic variables are particle occupation numbers taking values $n_{\vec{x}}=0,1$. We show that on a 10-parameter submanifold the $k$-point equal-time correlation functions $\exval{n_{\vec{x}_1} \cdots n_{\vec{x}_k}}$ satisfy linear differential- difference equations involving no higher correlators. In particular, the average density $\exval{n_{\vec{x}}} $ satisfies an integrable diffusion-type equation. These properties are explained in terms of dual processes and various duality relations are derived. By defining the time evolution of the stochastic process in terms of a quantum Hamiltonian $H$, the model becomes equivalent to a lattice model in thermal equilibrium in $d+1$ dimensions. We show that the spectrum of $H$ is identical to the spectrum of the quantum Hamiltonian of a $d$-dimensional, anisotropic spin-1/2 Heisenberg model. In one dimension our results hint at some new algebraic structure behind the integrability of the system.

cond-mat↗
arXiv1995

Ground State Structure in a Highly Disordered Spin Glass Model

We propose a new Ising spin glass model on $Z^d$ of Edwards-Anderson type, but with highly disordered coupling magnitudes, in which a greedy algorithm for producing ground states is exact. We find that the procedure for determining (infinite volume) ground states for this model can be related to invasion percolation with the number of ground states identified as $2^{\cal N}$, where ${\cal N} = {\cal N}(d)$ is the number of distinct global components in the ``invasion forest''. We prove that ${\cal N}(d) = \infty$ if the invasion connectivity function is square summable. We argue that the critical dimension separating ${\cal N} = 1$ and ${\cal N} = \infty$ is $d_c = 8$. When ${\cal N}(d) = \infty$, we consider free or periodic boundary conditions on cubes of side length $L$ and show that frustration leads to chaotic $L$ dependence with {\it all} pairs of ground states occuring as subsequence limits. We briefly discuss applications of our results to random walk problems on rugged landscapes.

adap-org↗
arXiv1998

Effect of noise on coupled chaotic systems

Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by identical noise, show synchronization phenomena where chaotic trajectories exponentially converge towards a single noisy trajectory, independent of the initial conditions. In a random neural network, with infinite range coupling, chaos is suppressed due to noise and the system evolves towards a fixed point. Spatiotemporal stochastic resonance phenomenon has been observed in a square array of coupled threshold devices where a temporal characteristic of the system resonates at a given noise strength. In a chaotically evolving coupled map lattice with logistic map as local dynamics and driven by identical noise at each site, we report that the number of structures (a structure is a group of neighbouring lattice sites for whom values of the variable follow certain predefined pattern) follow a power-law decay with the length of the structure. An interesting phenomenon, which we call stochastic coherence, is also reported in which the abundance and lifetimes of these structures show characteristic peaks at some intermediate noise strength.

chao-dyn↗
arXiv1998

Competing Species Dynamics: Qualitative Advantage versus Geography

A simple cellular automata model for a two-group war over the same territory is presented. It is shown that a qualitative advantage is not enough for a minority to win. A spatial organization as well a definite degree of aggressiveness are instrumental to overcome a less fitted majority. The model applies to a large spectrum of competing groups: smoker-non smoker war, epidemic spreading, opinion formation, competition for industrial standards and species evolution. In the last case, it provides a new explanation for punctuated equilibria.

cond-mat.dis-nn↗
arXiv1999

Stochastic group selection model for the evolution of altruism

We study numerically and analytically a stochastic group selection model in which a population of asexually reproducing individuals, each of which can be either altruist or non-altruist, is subdivided into $M$ reproductively isolated groups (demes) of size $N$. The cost associated with being altruistic is modelled by assigning the fitness $1- τ$, with $τ\in [0,1]$, to the altruists and the fitness 1 to the non-altruists. In the case that the altruistic disadvantage $τ$ is not too large, we show that the finite $M$ fluctuations are small and practically do not alter the deterministic results obtained for $M \to \infty$. However, for large $τ$ these fluctuations greatly increase the instability of the altruistic demes to mutations. These results may be relevant to the dynamics of parasite-host systems and, in particular, to explain the importance of mutation in the evolution of parasite virulence.

adap-org↗
arXiv2000

Modelling Collective Opinion Formation by Means of Active Brownian Particles

The concept of active Brownian particles is used to model a collective opinion formation process. It is assumed that individuals in community create a two-component communication field that influences the change of opinions of other persons and/or can induce their migration. The communication field is described by a reaction-diffusion equation, the opinion change of the individuals is given by a master equation, while the migration is described by a set of Langevin equations, coupled by the communication field. In the mean-field limit holding for fast communication we derive a critical population size, above which the community separates into a majority and a minority with opposite opinions. The existence of external support (e.g. from mass media) changes the ratio between minority and majority, until above a critical external support the supported subpopulation exists always as a majority. Spatial effects lead to two critical ``social'' temperatures, between which the community exists in a metastable state, thus fluctuations below a certain critical wave number may result in a spatial opinion separation. The range of metastability is particularly determined by a parameter characterizing the individual response to the communication field. In our discussion, we draw analogies to phase transitions in physical systems.

adap-org↗
arXiv2000

Temperature scaling, glassiness and stationarity in the Bak-Sneppen model

We show that the emergence of criticality in the locally-defined Bak-Sneppen model corresponds to separation over a hierarchy of timescales. Near to the critical point the model obeys scaling relations, with exponents which we derive numerically for a one-dimensional system. We further describe how the model can be related to the glass model of Bouchaud [{\em J. Phys. I France {\bf 2}, 1705 (1992)}], and we use this insight to comment on the usual assumption of stationarity in the Bak-Sneppen model. Finally, we propose a general definition of self-organised criticality which is in partial agreement with other recent definitions.

cond-mat.stat-mech↗
arXiv1999

Colective Effects from Induced Behaviour

We present a solvable model for describing quantitatively situations where the individual behaviour of agents in a group "percolates" to collective behaviour of the group as a whole as a result of mutual influence between the agents.

adap-org↗
arXiv1993

Antichaos in a Class of Random Boolean Cellular Automata

A variant of Kauffman's model of cellular metabolism is presented. It is a randomly generated network of boolean gates, identical to Kauffman's except for a small bias in favor of boolean gates that depend on at most one input. The bias is asymptotic to 0 as the number of gates increases. Upper bounds on the time until the network reaches a state cycle and the size of the state cycle, as functions of the number of gates $n$, are derived. If the bias approaches 0 slowly enough, the state cycles will be smaller than $n^c$ for some $c<1$. This lends support to Kauffman's claim that in his version of random network the average size of the state cycles is approximately $n^{1/2}$.

adap-org↗
arXiv1994

Pattern Dynamics of a Coupled Map Lattice for Open Flow

The pattern dynamics of the one-way coupled logistic lattice which can serve as a phenomenological model for open flow is investigated and shown to be extremely rich. For medium and large coupling strengths, we find spatially periodic, quasiperiodic and chaotic patterns with temporal periodicity and analyze their stability with the help of a newly introduced spatial map. Criteria are established for predicting the down-flow bifurcation behavior of the coupled map lattice, and for selecting attractors through modulation of the boundary. For smaller coupling strengths we find a novel regime in which chaotic defects form a periodic lattice that is shown to be the result of a boundary crisis.

chao-dyn↗