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Researcher profile

Randall D. Beer

Randall D. Beer contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Information Theorymath.DSmath.ITNeurons and Cognitionphysics.data-anQuantitative MethodsBiological Physicsmath-phmath.COmath.MPMolecular Networksnlin.AO

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Published work

5 published item(s)

preprint2026arXiv

Viability Space Decomposition: A geometric partition of survival outcomes in single- and multi-agent systems

What determines whether an organism or collective will survive under particular conditions? This question is asked across the life sciences when determining adaptive fit, developing efficacious treatments for diseases, and assessing the risks posed by ecological shifts. To aid their investigations, researchers employ models of agents which must respect particular constraints to remain alive. By constraining the dynamics of these agents to bounded viability regions, these models form a class of extended dynamical systems where transient dynamics can lead to death, making traditional attractors and separatrices insufficient for characterizing the global space of possible behaviors. To remedy this, we develop viability space decomposition, an analysis framework for ordinary differential equation models of agents with viability constraints. We first introduce the general theory, revealing how several new classes of manifolds (mortality, ordering, and collapse) permit a complete decomposition of state space into regions of qualitatively similar survival outcomes: a viability portrait. We then demonstrate the method by completely analyzing the global behavior of three models: a subcellular network, a behaving cell with the same physiology, and two coupled cell networks. Finally, we finish by discussing how the framework scales and future directions for its development and application.

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preprint2015arXiv

Information flow through a model of the C. elegans klinotaxis circuit

Understanding how information about external stimuli is transformed into behavior is one of the central goals of neuroscience. Here we characterize the information flow through a complete sensorimotor circuit: from stimulus, to sensory neurons, to interneurons, to motor neurons, to muscles, to motion. Specifically, we apply a recently developed framework for quantifying information flow to a previously published ensemble of models of salt klinotaxis in the nematode worm C. elegans. The models are grounded in the neuroanatomy and currently known neurophysiology of the worm. The unknown model parameters were optimized to reproduce the worm's behavior. Information flow analysis reveals several key principles underlying how the models operate: (1) Interneuron class AIY is responsible for integrating information about positive and negative changes in concentration, and exhibits a strong left/right information asymmetry. (2) Gap junctions play a crucial role in the transfer of information responsible for the information symmetry observed in interneuron class AIZ. (3) Neck motor neuron class SMB implements an information gating mechanism that underlies the circuit's state-dependent response. (4) The neck carries non-uniform distribution about changes in concentration. Thus, not all directions of movement are equally informative. Each of these findings corresponds to an experimental prediction that could be tested in the worm to greatly refine our understanding of the neural circuit underlying klinotaxis. Information flow analysis also allows us to explore how information flow relates to underlying electrophysiology. Despite large variations in the neural parameters of individual circuits, the overall information flow architecture circuit is remarkably consistent across the ensemble, suggesting that information flow analysis captures general principles of operation for the klinotaxis circuit.

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preprint2011arXiv

Generalized Measures of Information Transfer

Transfer entropy provides a general tool for analyzing the magnitudes and directions---but not the \emph{kinds}---of information transfer in a system. We extend transfer entropy in two complementary ways. First, we distinguish state-dependent from state-independent transfer, based on whether a source's influence depends on the state of the target. Second, for multiple sources, we distinguish between unique, redundant, and synergistic transfer. The new measures are demonstrated on several systems that extend examples from previous literature.

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preprint2010arXiv

Nonnegative Decomposition of Multivariate Information

Of the various attempts to generalize information theory to multiple variables, the most widely utilized, interaction information, suffers from the problem that it is sometimes negative. Here we reconsider from first principles the general structure of the information that a set of sources provides about a given variable. We begin with a new definition of redundancy as the minimum information that any source provides about each possible outcome of the variable, averaged over all possible outcomes. We then show how this measure of redundancy induces a lattice over sets of sources that clarifies the general structure of multivariate information. Finally, we use this redundancy lattice to propose a definition of partial information atoms that exhaustively decompose the Shannon information in a multivariate system in terms of the redundancy between synergies of subsets of the sources. Unlike interaction information, the atoms of our partial information decomposition are never negative and always support a clear interpretation as informational quantities. Our analysis also demonstrates how the negativity of interaction information can be explained by its confounding of redundancy and synergy.

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preprint2010arXiv

Saturation Probabilities of Continuous-Time Sigmoidal Networks

From genetic regulatory networks to nervous systems, the interactions between elements in biological networks often take a sigmoidal or S-shaped form. This paper develops a probabilistic characterization of the parameter space of continuous-time sigmoidal networks (CTSNs), a simple but dynamically-universal model of such interactions. We describe an efficient and accurate method for calculating the probability of observing effectively M-dimensional dynamics in an N-element CTSN, as well as a closed-form but approximate method. We then study the dependence of this probability on N, M, and the parameter ranges over which sampling occurs. This analysis provides insight into the overall structure of CTSN parameter space.

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