Towards Theory of Massive-Parallel Proofs. Cellular Automata Approach

In the paper I sketch a theory of massively parallel proofs using cellular automata presentation of deduction. In this presentation inference rules play the role of cellular-automatic local transition functions. In this approach we completely avoid axioms as necessary notion of deduction theory and therefore we can use cyclic proofs without additional problems. As a result, a theory of massive-parallel proofs within unconventional computing is proposed for the first time.Comment: 13 page

Spatial moment analysis of transport of nonlinearly absorbing pesticides using analytical approximations

Analytical approximations were derived for solute transport of pesticides subject to Freundlich sorption, and first-order degradation restricted to the liquid phase. Solute transport was based on the convection-dispersion equation (CDE) assuming steady flow. The center of mass (first spatial moment) was approximated both for a non-degraded solute pulse and for a pulse degraded in the liquid phase. The remaining mass (zeroth spatial moment) of a linearly sorbing solute degraded in the liquid phase was found to be a function of only the center of mass (first spatial moment) and the Damköhler number (i.e., the product of degradation rate coefficient and dispersivity divided by flow velocity). This relationship between the zeroth and first spatial moments was shown to apply to nonlinearly sorbing pulses as well. The mass fraction leached of a pesticide subject to Freundlich sorption and first-order degradation in the solution phase only was found to be a function of the Damköhler number and of the dispersivity, so independent of sorption. Hence perceptions of the effects of sorption on pesticide leaching should be reconsidered. These conclusions equally hold for other micropollutants that degrade in the solution phase onl

A Nonparametric Bayesian Approach to Uncovering Rat Hippocampal Population Codes During Spatial Navigation

Rodent hippocampal population codes represent important spatial information about the environment during navigation. Several computational methods have been developed to uncover the neural representation of spatial topology embedded in rodent hippocampal ensemble spike activity. Here we extend our previous work and propose a nonparametric Bayesian approach to infer rat hippocampal population codes during spatial navigation. To tackle the model selection problem, we leverage a nonparametric Bayesian model. Specifically, to analyze rat hippocampal ensemble spiking activity, we apply a hierarchical Dirichlet process-hidden Markov model (HDP-HMM) using two Bayesian inference methods, one based on Markov chain Monte Carlo (MCMC) and the other based on variational Bayes (VB). We demonstrate the effectiveness of our Bayesian approaches on recordings from a freely-behaving rat navigating in an open field environment. We find that MCMC-based inference with Hamiltonian Monte Carlo (HMC) hyperparameter sampling is flexible and efficient, and outperforms VB and MCMC approaches with hyperparameters set by empirical Bayes

The Random-Diluted Triangular Plaquette Model: study of phase transitions in a Kinetically Constrained Model

We study how the thermodynamic properties of the Triangular Plaquette Model (TPM) are influenced by the addition of extra interactions. The thermodynamics of the original TPM is trivial, while its dynamics is glassy, as usual in Kinetically Constrained Models. As soon as we generalize the model to include additional interactions, a thermodynamic phase transition appears in the system. The additional interactions we consider are either short ranged, forming a regular lattice in the plane, or long ranged of the small-world kind. In the case of long-range interactions we call the new model Random-Diluted TPM. We provide arguments that the model so modified should undergo a thermodynamic phase transition, and that in the long-range case this is a glass transition of the "Random First-Order" kind. Finally, we give support to our conjectures studying the finite temperature phase diagram of the Random-Diluted TPM in the Bethe approximation. This corresponds to the exact calculation on the random regular graph, where free-energy and configurational entropy can be computed by means of the cavity equations.Comment: 20 pages, 7 figures; final version to appear on PR