Information Anatomy of Stochastic Equilibria

A stochastic nonlinear dynamical system generates information, as measured by its entropy rate. Some---the ephemeral information---is dissipated and some---the bound information---is actively stored and so affects future behavior. We derive analytic expressions for the ephemeral and bound informations in the limit of small-time discretization for two classical systems that exhibit dynamical equilibria: first-order Langevin equations (i) where the drift is the gradient of a potential function and the diffusion matrix is invertible and (ii) with a linear drift term (Ornstein-Uhlenbeck) but a noninvertible diffusion matrix. In both cases, the bound information is sensitive only to the drift, while the ephemeral information is sensitive only to the diffusion matrix and not to the drift. Notably, this information anatomy changes discontinuously as any of the diffusion coefficients vanishes, indicating that it is very sensitive to the noise structure. We then calculate the information anatomy of the stochastic cusp catastrophe and of particles diffusing in a heat bath in the overdamped limit, both examples of stochastic gradient descent on a potential landscape. Finally, we use our methods to calculate and compare approximations for the so-called time-local predictive information for adaptive agents.Comment: 35 pages, 3 figures, 1 table; http://csc.ucdavis.edu/~cmg/compmech/pubs/iase.ht

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

Informational and Causal Architecture of Continuous-time Renewal and Hidden Semi-Markov Processes

We introduce the minimal maximally predictive models ({\epsilon}-machines) of processes generated by certain hidden semi-Markov models. Their causal states are either hybrid discrete-continuous or continuous random variables and causal-state transitions are described by partial differential equations. Closed-form expressions are given for statistical complexities, excess entropies, and differential information anatomy rates. We present a complete analysis of the {\epsilon}-machines of continuous-time renewal processes and, then, extend this to processes generated by unifilar hidden semi-Markov models and semi-Markov models. Our information-theoretic analysis leads to new expressions for the entropy rate and the rates of related information measures for these very general continuous-time process classes.Comment: 16 pages, 7 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/ctrp.ht

Downright Sexy: Verticality, Implicit Power, and Perceived Physical Attractiveness

Grounded theory proposes that abstract concepts (e.g., power) are represented by perceptions of vertical space (e.g., up is powerful; down is powerless). We used this theory to examine predictions made by evolutionary psychologists who suggest that desirable males are those who have status and resources (i.e., powerful) while desirable females are those who are youthful and faithful (i.e., powerless). Using vertical position as an implicit cue for power, we found that male participants rated pictures of females as more attractive when their images were presented near the bottom of a computer screen, whereas female participants rated pictures of males as more attractive when their images were presented near the top of a computer screen. Our results support the evolutionary theory of attraction and reveal the social-judgment consequences of grounded theories of cognition

Prediction and Power in Molecular Sensors: Uncertainty and Dissipation When Conditionally Markovian Channels Are Driven by Semi-Markov Environments

Sensors often serve at least two purposes: predicting their input and minimizing dissipated heat. However, determining whether or not a particular sensor is evolved or designed to be accurate and efficient is difficult. This arises partly from the functional constraints being at cross purposes and partly since quantifying the predictive performance of even in silico sensors can require prohibitively long simulations. To circumvent these difficulties, we develop expressions for the predictive accuracy and thermodynamic costs of the broad class of conditionally Markovian sensors subject to unifilar hidden semi-Markov (memoryful) environmental inputs. Predictive metrics include the instantaneous memory and the mutual information between present sensor state and input future, while dissipative metrics include power consumption and the nonpredictive information rate. Success in deriving these formulae relies heavily on identifying the environment's causal states, the input's minimal sufficient statistics for prediction. Using these formulae, we study the simplest nontrivial biological sensor model---that of a Hill molecule, characterized by the number of ligands that bind simultaneously, the sensor's cooperativity. When energetic rewards are proportional to total predictable information, the closest cooperativity that optimizes the total energy budget generally depends on the environment's past hysteretically. In this way, the sensor gains robustness to environmental fluctuations. Given the simplicity of the Hill molecule, such hysteresis will likely be found in more complex predictive sensors as well. That is, adaptations that only locally optimize biochemical parameters for prediction and dissipation can lead to sensors that "remember" the past environment.Comment: 21 pages, 4 figures, http://csc.ucdavis.edu/~cmg/compmech/pubs/piness.ht

Optimized Bacteria are Environmental Prediction Engines

Experimentalists have observed phenotypic variability in isogenic bacteria populations. We explore the hypothesis that in fluctuating environments this variability is tuned to maximize a bacterium's expected log growth rate, potentially aided by epigenetic markers that store information about past environments. We show that, in a complex, memoryful environment, the maximal expected log growth rate is linear in the instantaneous predictive information---the mutual information between a bacterium's epigenetic markers and future environmental states. Hence, under resource constraints, optimal epigenetic markers are causal states---the minimal sufficient statistics for prediction. This is the minimal amount of information about the past needed to predict the future as well as possible. We suggest new theoretical investigations into and new experiments on bacteria phenotypic bet-hedging in fluctuating complex environments.Comment: 7 pages, 1 figure; http://csc.ucdavis.edu/~cmg/compmech/pubs/obepe.ht

Child poverty high in rural America

On August 28, 2007, new data from the U.S. Census Bureau\u27s American Community Survey show that 22 percent of rural children are living in poverty, up from 19 percent in 2000. On average, rates are highest in the nonmetropolitan South (27 percent) and have climbed the most in the nonmetropolitan Midwest (by 3.9 percentage points)

The Trans-Pacific Partnership and regulating capital flows: recommendations for strengthening proposed safeguards in the leaked TPP investment chapter

This repository item contains a policy brief from the Boston University Global Economic Governance Initiative. The Global Economic Governance Initiative (GEGI) is a research program of the Center for Finance, Law & Policy, the Frederick S. Pardee Center for the Study of the Longer-Range Future, and the Frederick S. Pardee School of Global Studies. It was founded in 2008 to advance policy-relevant knowledge about governance for financial stability, human development, and the environment.The leaked text of the Trans-Pacific Partnership (TPP) Agreement’s investment chapter reveals that negotiators are giving serious consideration to a safeguard intended to allow nations to regulate capital flows. It is critical that the safeguard be drafted in such a way that governments have sufficient policy flexibility to prevent and mitigate financial instability

Low income dynamics in 1990s Britain

This paper analyses low income dynamics in Britain using the first four waves of the British Household Panel Survey. There is much low income turnover: although there is a small group of people who are persistently poor, more striking is the relatively large number of low income escapers and entrants from one year to the next. Simulations using estimated low income exit and re-entry rates demonstrate the importance of repeated low income spells for explaining a person’s experience of low income over a given period. We also document the characteristics of low income stayers, escapers and entrants.

Depression and Anxiety in Roman Catholic Secular Clergy

A nationally selected random sample of Roman Catholic secular priests was investigated using the Center for Epidemiological Studies-Depression scale and the State-Trait Anxiety Inventory Form Y. Additionally, a Self-Report Inventory requested information regarding participants\u27 demographics as well as four categories of predictor variables (i.e., Vocational Satisfaction, Social Support, Spiritual Activities, Physical Environment) potentially associated with depression and anxiety. The study yielded a return rate of 64%. Secular clergy reported significantly greater depression and anxiety (both state and trait) than are reported in the general population. Low Vocational Satisfaction was found to be predictive of depression as well as both state and trait anxiety. Additionally, low Social Support was found to be predictive of state and trait anxiety. When the significant predictor variables were conceptually collapsed, it appeared that both people and place were significantly related to Roman Catholic secular priests\u27 experience of depression and anxiety