arXiv subjects

James P. Crutchfield

Publications and source records attributed to James P. Crutchfield.

At least 145 records · Page 8Linked to original sources

arXiv2006

Insects, Trees, and Climate: The Bioacoustic Ecology of Deforestation and Entomogenic Climate Change

Accumulating observational evidence suggests an intimate connection between rapidly expanding insect populations, deforestation, and global climate change. We review the evidence, emphasizing the vulnerability of key planetary carbon pools, especially the Earth's forests that link the micro-ecology of insect infestation to climate. We survey current research regimes and insect control strategies, concluding that at present they are insufficient to cope with the problem's present regional scale and its likely future global scale. We propose novel bioacoustic interactions between insects and trees as key drivers of infestation population dynamics and the resulting wide-scale deforestation. The bioacoustic mechanisms suggest new, nontoxic control interventions and detection strategies.

q-bio.PE↗

arXiv2006

Language Diversity of Measured Quantum Processes

The behavior of a quantum system depends on how it is measured. How much of what is observed comes from the structure of the quantum system itself and how much from the observer's choice of measurement? We explore these questions by analyzing the \emph{language diversity} of quantum finite-state generators. One result is a new way to distinguish quantum devices from their classical (stochastic) counterparts. While the diversity of languages generated by these two computational classes is the same in the case of periodic processes, quantum systems generally generate a wider range of languages than classical systems.

quant-ph↗

arXiv2006

Infinite Correlation in Measured Quantum Processes

We show that quantum dynamical systems can exhibit infinite correlations in their behavior when repeatedly measured. We model quantum processes using quantum finite-state generators and take the stochastic language they generate as a representation of their behavior. We analyze two spin-1 quantum systems that differ only in how they are observed. The corresponding language generated has short-range correlation in one case and infinite correlation in the other.

quant-ph↗

arXiv2006

How Random is a Coin Toss? Bayesian Inference and the Symbolic Dynamics of Deterministic Chaos

Symbolic dynamics has proven to be an invaluable tool in analyzing the mechanisms that lead to unpredictability and random behavior in nonlinear dynamical systems. Surprisingly, a discrete partition of continuous state space can produce a coarse-grained description of the behavior that accurately describes the invariant properties of an underlying chaotic attractor. In particular, measures of the rate of information production--the topological and metric entropy rates--can be estimated from the outputs of Markov or generating partitions. Here we develop Bayesian inference for k-th order Markov chains as a method to finding generating partitions and estimating entropy rates from finite samples of discretized data produced by coarse-grained dynamical systems.

cs.LG↗

arXiv2006

Hierarchical Self-Organization in the Finitary Process Soup

Current analyses of genomes from numerous species show that the diversity of organism's functional and behavioral characters is not proportional to the number of genes that encode the organism. We investigate the hypothesis that the diversity of organismal character is due to hierarchical organization. We do this with the recently introduced model of the finitary process soup, which allows for a detailed mathematical and quantitative analysis of the population dynamics of structural complexity. Here we show that global complexity in the finitary process soup is due to the emergence of successively higher levels of organization, that the hierarchical structure appears spontaneously, and that the process of structural innovation is facilitated by the discovery and maintenance of relatively noncomplex, but general individuals in a population.

nlin.AO↗

arXiv2004

Stability and Diversity in Collective Adaptation

We derive a class of macroscopic differential equations that describe collective adaptation, starting from a discrete-time stochastic microscopic model. The behavior of each agent is a dynamic balance between adaptation that locally achieves the best action and memory loss that leads to randomized behavior. We show that, although individual agents interact with their environment and other agents in a purely self-interested way, macroscopic behavior can be interpreted as game dynamics. Application to several familiar, explicit game interactions shows that the adaptation dynamics exhibits a diversity of collective behaviors. The simplicity of the assumptions underlying the macroscopic equations suggests that these behaviors should be expected broadly in collective adaptation. We also analyze the adaptation dynamics from an information-theoretic viewpoint and discuss self-organization induced by information flux between agents, giving a novel view of collective adaptation.

nlin.AO↗

arXiv2004

Automated Pattern Detection--An Algorithm for Constructing Optimally Synchronizing Multi-Regular Language Filters

In the computational-mechanics structural analysis of one-dimensional cellular automata the following automata-theoretic analogue of the \emph{change-point problem} from time series analysis arises: \emph{Given a string $σ$ and a collection $\{\mc{D}_i\}$ of finite automata, identify the regions of $σ$ that belong to each $\mc{D}_i$ and, in particular, the boundaries separating them.} We present two methods for solving this \emph{multi-regular language filtering problem}. The first, although providing the ideal solution, requires a stack, has a worst-case compute time that grows quadratically in $σ$'s length and conditions its output at any point on arbitrarily long windows of future input. The second method is to algorithmically construct a transducer that approximates the first algorithm. In contrast to the stack-based algorithm, however, the transducer requires only a finite amount of memory, runs in linear time, and gives immediate output for each letter read; it is, moreover, the best possible finite-state approximation with these three features.

cs.CV↗

arXiv2004

Objects That Make Objects: The Population Dynamics of Structural Complexity

To analyze the evolutionary emergence of structural complexity in physical processes we introduce a general, but tractable, model of objects that interact to produce new objects. Since the objects--\emph{$epsilon$-machines}--have well defined structural properties, we demonstrate that complexity in the resulting population dynamical system emerges on several distinct organizational scales during evolution--from individuals to nested levels of mutually self-sustaining interaction. The evolution to increased organization is dominated by the spontaneous creation of structural hierarchies and this, in turn, is facilitated by the innovation and maintenance of relatively low-complexity, but general individuals.

nlin.AO↗

arXiv2004

Reductions of Hidden Information Sources

In all but special circumstances, measurements of time-dependent processes reflect internal structures and correlations only indirectly. Building predictive models of such hidden information sources requires discovering, in some way, the internal states and mechanisms. Unfortunately, there are often many possible models that are observationally equivalent. Here we show that the situation is not as arbitrary as one would think. We show that generators of hidden stochastic processes can be reduced to a minimal form and compare this reduced representation to that provided by computational mechanics--the epsilon-machine. On the way to developing deeper, measure-theoretic foundations for the latter, we introduce a new two-step reduction process. The first step (internal-event reduction) produces the smallest observationally equivalent sigma-algebra and the second (internal-state reduction) removes sigma-algebra components that are redundant for optimal prediction. For several classes of stochastic dynamical systems these reductions produce representations that are equivalent to epsilon-machines.

math.PR↗

arXiv2002

Structural Information in Two-Dimensional Patterns: Entropy Convergence and Excess Entropy

We develop information-theoretic measures of spatial structure and pattern in more than one dimension. As is well known, the entropy density of a two-dimensional configuration can be efficiently and accurately estimated via a converging sequence of conditional entropies. We show that the manner in which these conditional entropies converge to their asymptotic value serves as a measure of global correlation and structure for spatial systems in any dimension. We compare and contrast entropy-convergence with mutual-information and structure-factor techniques for quantifying and detecting spatial structure.

cond-mat.stat-mech↗

arXiv2002

An Algorithm for Pattern Discovery in Time Series

We present a new algorithm for discovering patterns in time series and other sequential data. We exhibit a reliable procedure for building the minimal set of hidden, Markovian states that is statistically capable of producing the behavior exhibited in the data -- the underlying process's causal states. Unlike conventional methods for fitting hidden Markov models (HMMs) to data, our algorithm makes no assumptions about the process's causal architecture (the number of hidden states and their transition structure), but rather infers it from the data. It starts with assumptions of minimal structure and introduces complexity only when the data demand it. Moreover, the causal states it infers have important predictive optimality properties that conventional HMM states lack. We introduce the algorithm, review the theory behind it, prove its asymptotic reliability, use large deviation theory to estimate its rate of convergence, and compare it to other algorithms which also construct HMMs from data. We also illustrate its behavior on an example process, and report selected numerical results from an implementation.

cs.LG↗

arXiv2002

Synchronizing to Periodicity: The Transient Information and Synchronization Time of Periodic Sequences

We analyze how difficult it is to synchronize to a periodic sequence whose structure is known, when an observer is initially unaware of the sequence's phase. We examine the transient information T, a recently introduced information-theoretic quantity that measures the uncertainty an observer experiences while synchronizing to a sequence. We also consider the synchronization time tau, which is the average number of measurements required to infer the phase of a periodic signal. We calculate T and tau for all periodic sequences up to and including period 23. We show which sequences of a given period have the maximum and minimum possible T and tau values, develop analytic expressions for the extreme values, and show that in these cases the transient information is the product of the total phase information and the synchronization time. Despite the latter result, our analyses demonstrate that the transient information and synchronization time capture different and complementary structural properties of individual periodic sequences -- properties, moreover, that are distinct from source entropy rate and mutual information measures, such as the excess entropy.

nlin.AO↗

arXiv2002

Coupled Replicator Equations for the Dynamics of Learning in Multiagent Systems

Starting with a group of reinforcement-learning agents we derive coupled replicator equations that describe the dynamics of collective learning in multiagent systems. We show that, although agents model their environment in a self-interested way without sharing knowledge, a game dynamics emerges naturally through environment-mediated interactions. An application to rock-scissors-paper game interactions shows that the collective learning dynamics exhibits a diversity of competitive and cooperative behaviors. These include quasiperiodicity, stable limit cycles, intermittency, and deterministic chaos--behaviors that should be expected in heterogeneous multiagent systems described by the general replicator equations we derive.

nlin.AO↗

arXiv2001

Synchronizing to the Environment: Information Theoretic Constraints on Agent Learning

We show that the way in which the Shannon entropy of sequences produced by an information source converges to the source's entropy rate can be used to monitor how an intelligent agent builds and effectively uses a predictive model of its environment. We introduce natural measures of the environment's apparent memory and the amounts of information that must be (i) extracted from observations for an agent to synchronize to the environment and (ii) stored by an agent for optimal prediction. If structural properties are ignored, the missed regularities are converted to apparent randomness. Conversely, using representations that assume too much memory results in false predictability.

nlin.AO↗

arXiv2001

Regularities Unseen, Randomness Observed: Levels of Entropy Convergence

We study how the Shannon entropy of sequences produced by an information source converges to the source's entropy rate. We synthesize several phenomenological approaches to applying information theoretic measures of randomness and memory to stochastic and deterministic processes by using successive derivatives of the Shannon entropy growth curve. This leads, in turn, to natural measures of apparent memory stored in a source and the amounts of information that must be extracted from observations of a source in order for it to be optimally predicted and for an observer to synchronize to it. One consequence of ignoring these structural properties is that the missed regularities are converted to apparent randomness. We demonstrate that this problem arises particularly for small data sets; e.g., in settings where one has access only to short measurement sequences.

cond-mat.stat-mech↗

arXiv2001

Upper Bound on the Products of Particle Interactions in Cellular Automata

Particle-like objects are observed to propagate and interact in many spatially extended dynamical systems. For one of the simplest classes of such systems, one-dimensional cellular automata, we establish a rigorous upper bound on the number of distinct products that these interactions can generate. The upper bound is controlled by the structural complexity of the interacting particles---a quantity which is defined here and which measures the amount of spatio-temporal information that a particle stores. Along the way we establish a number of properties of domains and particles that follow from the computational mechanics analysis of cellular automata; thereby elucidating why that approach is of general utility. The upper bound is tested against several relatively complex domain-particle cellular automata and found to be tight.

nlin.CG↗

arXiv2000

Computational Mechanics: Pattern and Prediction, Structure and Simplicity

Computational mechanics, an approach to structural complexity, defines a process's causal states and gives a procedure for finding them. We show that the causal-state representation--an $ε$-machine--is the minimal one consistent with accurate prediction. We establish several results on $ε$-machine optimality and uniqueness and on how $ε$-machines compare to alternative representations. Further results relate measures of randomness and structural complexity obtained from $ε$-machines to those from ergodic and information theories.

cond-mat.stat-mech↗

arXiv2000

Information Bottlenecks, Causal States, and Statistical Relevance Bases: How to Represent Relevant Information in Memoryless Transduction

Discovering relevant, but possibly hidden, variables is a key step in constructing useful and predictive theories about the natural world. This brief note explains the connections between three approaches to this problem: the recently introduced information-bottleneck method, the computational mechanics approach to inferring optimal models, and Salmon's statistical relevance basis.

nlin.AO↗