Understanding the Constraints in Maximum Entropy Methods for Modeling and Inference.

The principle of maximum entropy, developed more than six decades ago, provides a systematic approach to modeling inference, and data analysis grounded in the principles of information theory, Bayesian probability and constrained optimization. Since its formulation, criticisms about the consistency of that method and the role of constraints have been raised. Among these, the chief criticism is that maximum entropy does not satisfy the principle of causation, or similarly, that maximum entropy updating is inconsistent due to an inadequate representation of causal information.

Phase Gradients and Anisotropy of the Suprachiasmatic Network: Discovery of Phaseoids.

Biological neural networks operate at several levels of granularity, from the individual neuron to local neural circuits to networks of thousands of cells. The daily oscillation of the brain's master clock in the suprachiasmatic nucleus (SCN) rests on a yet to be identified network of connectivity among its ∼20,000 neurons. The SCN provides an accessible model to explore neural organization at several levels of organization.

Differential localization of PER1 and PER2 in the brain master circadian clock.

The hypothalamic suprachiasmatic nucleus (SCN), locus of the master circadian clock, bears many neuronal types. At the cellular-molecular level, the clock is comprised of feedback loops involving 'clock' genes including Period1 and Period2, and their protein products, PERIOD1 and PERIOD2 (PER1/2). In the canonical model of circadian oscillation, the PER1/2 proteins oscillate together.

Characterization of orderly spatiotemporal patterns of clock gene activation in mammalian suprachiasmatic nucleus.

Because we can observe oscillation within individual cells and in the tissue as a whole, the suprachiasmatic nucleus (SCN) presents a unique system in the mammalian brain for the analysis of individual cells and the networks of which they are a part. While dispersed cells of the SCN sustain circadian oscillations in isolation, they are unstable oscillators that require network interactions for robust cycling. Using cluster analysis to assess bioluminescence in acute brain slices from PERIOD2::Luciferase (PER2::LUC) knockin mice, and immunochemistry of SCN from animals harvested at various circadian times, we assessed the spatiotemporal activation patterns of PER2 to explore the emergence of a coherent oscillation at the tissue level.

Gates and oscillators II: zeitgebers and the network model of the brain clock.

Circadian rhythms in physiology and behavior are regulated by the SCN. When assessed by expression of clock genes, at least 2 distinct functional cell types are discernible within the SCN: nonrhythmic, light-inducible, retinorecipient cells and rhythmic autonomous oscillator cells that are not directly retinorecipient. To predict the responses of the circadian system, the authors have proposed a model based on these biological properties.

Gates and oscillators: a network model of the brain clock.

The suprachiasmatic nuclei (SCN) control circadian oscillations of physiology and behavior. Measurements of electrical activity and of gene expression indicate that these heterogeneous structures are composed of both rhythmic and nonrhythmic cells. A fundamental question with regard to the organization of the circadian system is how the SCN achieve a coherent output while their constituent independent cellular oscillators express a wide range of periods.