arXiv subjects

Cosma Shalizi

Publications and source records attributed to Cosma Shalizi.

3 recordsLinked to original sources

arXiv2014

Blind Construction of Optimal Nonlinear Recursive Predictors for Discrete Sequences

We present a new method for nonlinear prediction of discrete random sequences under minimal structural assumptions. We give a mathematical construction for optimal predictors of such processes, in the form of hidden Markov models. We then describe an algorithm, CSSR (Causal-State Splitting Reconstruction), which approximates the ideal predictor from data. We discuss the reliability of CSSR, its data requirements, and its performance in simulations. Finally, we compare our approach to existing methods using variablelength Markov models and cross-validated hidden Markov models, and show theoretically and experimentally that our method delivers results superior to the former and at least comparable to the latter.

cs.LG↗

arXiv2005

Nonlinear aspects of the EEG during sleep in children

Electroencephalograph (EEG) analysis enables the neuronal behavior of a section of the brain to be examined. If the behavior is nonlinear then nonlinear tools can be used to glean information on brain behavior, and aid in the diagnosis of sleep abnormalities such as obstructive sleep apnea syndrome (OSAS). In this paper the sleep EEGs of a set of normal and mild OSAS children are evaluated for nonlinear behaviour. We consider how the behaviour of the brain changes with sleep stage and between normal and OSAS children.

q-bio.NC↗

arXiv1999

Vortex Dynamics and Entropic Coulomb Forces in Ising and Potts Antiferromagnets and Ice Models

We study the dynamics of topological defects in the triangular Ising antiferromagnet, a related model on the square lattice equivalent to the six-vertex ice model, and the three-state antiferromagnetic Potts model on the square lattice. Since each of these models has a height representation in which defects are screw dislocations, we expect them to be attracted or repelled with an entropy-driven Coulomb force. In each case we show explicitly how this force is felt through local fields. We measure the force numerically, both by quenching the system to zero temperature and by measuring the motion of vortex pairs. For the three-state Potts model, we calculate both the force and the defect mobility, and find reasonable agreement with theory.

cond-mat.stat-mech↗