General anesthesia reduces complexity and temporal asymmetry of the informational structures derived from neural recordings in Drosophila

We apply techniques from the field of computational mechanics to evaluate the statistical complexity of neural recording data from fruit flies. First, we connect statistical complexity to the flies' level of conscious arousal, which is manipulated by general anesthesia (isoflurane). We show that the complexity of even single channel time series data decreases under anesthesia. The observed difference in complexity between the two states of conscious arousal increases as higher orders of temporal correlations are taken into account. We then go on to show that, in addition to reducing complexity, anesthesia also modulates the informational structure between the forward- and reverse-time neural signals. Specifically, using three distinct notions of temporal asymmetry we show that anesthesia reduces temporal asymmetry on information-theoretic and information-geometric grounds. In contrast to prior work, our results show that: (1) Complexity differences can emerge at very short timescales and across broad regions of the fly brain, thus heralding the macroscopic state of anesthesia in a previously unforeseen manner, and (2) that general anesthesia also modulates the temporal asymmetry of neural signals. Together, our results demonstrate that anesthetized brains become both less structured and more reversible.Comment: 14 pages, 6 figures. Comments welcome; Added time-reversal analysis, updated discussion, new figures (Fig. 5 & Fig. 6) and Tables (Tab. 1

Flexible and practical modeling of animal telemetry data: hidden Markov models and extensions

We discuss hidden Markov-type models for fitting a variety of multistate random walks to wildlife movement data. Discrete-time hidden Markov models (HMMs) achieve considerable computational gains by focusing on observations that are regularly spaced in time, and for which the measurement error is negligible. These conditions are often met, in particular for data related to terrestrial animals, so that a likelihood-based HMM approach is feasible. We describe a number of extensions of HMMs for animal movement modeling, including more flexible state transition models and individual random effects (fitted in a non-Bayesian framework). In particular we consider so-called hidden semi-Markov models, which may substantially improve the goodness of fit and provide important insights into the behavioral state switching dynamics. To showcase the expediency of these methods, we consider an application of a hierarchical hidden semi-Markov model to multiple bison movement paths

Informational and Causal Architecture of Discrete-Time Renewal Processes

Renewal processes are broadly used to model stochastic behavior consisting of isolated events separated by periods of quiescence, whose durations are specified by a given probability law. Here, we identify the minimal sufficient statistic for their prediction (the set of causal states), calculate the historical memory capacity required to store those states (statistical complexity), delineate what information is predictable (excess entropy), and decompose the entropy of a single measurement into that shared with the past, future, or both. The causal state equivalence relation defines a new subclass of renewal processes with a finite number of causal states despite having an unbounded interevent count distribution. We use these formulae to analyze the output of the parametrized Simple Nonunifilar Source, generated by a simple two-state hidden Markov model, but with an infinite-state epsilon-machine presentation. All in all, the results lay the groundwork for analyzing processes with infinite statistical complexity and infinite excess entropy.Comment: 18 pages, 9 figures, 1 table; http://csc.ucdavis.edu/~cmg/compmech/pubs/dtrp.ht

The Origins of Computational Mechanics: A Brief Intellectual History and Several Clarifications

The principle goal of computational mechanics is to define pattern and structure so that the organization of complex systems can be detected and quantified. Computational mechanics developed from efforts in the 1970s and early 1980s to identify strange attractors as the mechanism driving weak fluid turbulence via the method of reconstructing attractor geometry from measurement time series and in the mid-1980s to estimate equations of motion directly from complex time series. In providing a mathematical and operational definition of structure it addressed weaknesses of these early approaches to discovering patterns in natural systems. Since then, computational mechanics has led to a range of results from theoretical physics and nonlinear mathematics to diverse applications---from closed-form analysis of Markov and non-Markov stochastic processes that are ergodic or nonergodic and their measures of information and intrinsic computation to complex materials and deterministic chaos and intelligence in Maxwellian demons to quantum compression of classical processes and the evolution of computation and language. This brief review clarifies several misunderstandings and addresses concerns recently raised regarding early works in the field (1980s). We show that misguided evaluations of the contributions of computational mechanics are groundless and stem from a lack of familiarity with its basic goals and from a failure to consider its historical context. For all practical purposes, its modern methods and results largely supersede the early works. This not only renders recent criticism moot and shows the solid ground on which computational mechanics stands but, most importantly, shows the significant progress achieved over three decades and points to the many intriguing and outstanding challenges in understanding the computational nature of complex dynamic systems.Comment: 11 pages, 123 citations; http://csc.ucdavis.edu/~cmg/compmech/pubs/cmr.ht

Prediction, Retrodiction, and The Amount of Information Stored in the Present

We introduce an ambidextrous view of stochastic dynamical systems, comparing their forward-time and reverse-time representations and then integrating them into a single time-symmetric representation. The perspective is useful theoretically, computationally, and conceptually. Mathematically, we prove that the excess entropy--a familiar measure of organization in complex systems--is the mutual information not only between the past and future, but also between the predictive and retrodictive causal states. Practically, we exploit the connection between prediction and retrodiction to directly calculate the excess entropy. Conceptually, these lead one to discover new system invariants for stochastic dynamical systems: crypticity (information accessibility) and causal irreversibility. Ultimately, we introduce a time-symmetric representation that unifies all these quantities, compressing the two directional representations into one. The resulting compression offers a new conception of the amount of information stored in the present.Comment: 17 pages, 7 figures, 1 table; http://users.cse.ucdavis.edu/~cmg/compmech/pubs/pratisp.ht

Spectral Simplicity of Apparent Complexity, Part I: The Nondiagonalizable Metadynamics of Prediction

Virtually all questions that one can ask about the behavioral and structural complexity of a stochastic process reduce to a linear algebraic framing of a time evolution governed by an appropriate hidden-Markov process generator. Each type of question---correlation, predictability, predictive cost, observer synchronization, and the like---induces a distinct generator class. Answers are then functions of the class-appropriate transition dynamic. Unfortunately, these dynamics are generically nonnormal, nondiagonalizable, singular, and so on. Tractably analyzing these dynamics relies on adapting the recently introduced meromorphic functional calculus, which specifies the spectral decomposition of functions of nondiagonalizable linear operators, even when the function poles and zeros coincide with the operator's spectrum. Along the way, we establish special properties of the projection operators that demonstrate how they capture the organization of subprocesses within a complex system. Circumventing the spurious infinities of alternative calculi, this leads in the sequel, Part II, to the first closed-form expressions for complexity measures, couched either in terms of the Drazin inverse (negative-one power of a singular operator) or the eigenvalues and projection operators of the appropriate transition dynamic.Comment: 24 pages, 3 figures, 4 tables; current version always at http://csc.ucdavis.edu/~cmg/compmech/pubs/sdscpt1.ht