Adsorbed self-avoiding walks subject to a force

We consider a self-avoiding walk model of polymer adsorption where the adsorbed polymer can be desorbed by the application of a force. In this paper the force is applied normal to the surface at the last vertex of the walk. We prove that the appropriate limiting free energy exists where there is an applied force and a surface potential term, and prove that this free energy is convex in appropriate variables. We then derive an expression for the limiting free energy in terms of the free energy without a force and the free energy with no surface interaction. Finally we show that there is a phase boundary between the adsorbed phase and the desorbed phase in the presence of a force, prove some qualitative properties of this boundary and derive bounds on the location of the boundary

Self-avoiding walks and polygons confined to a square

We prove several rigorous results about the asymptotic behaviour of the numbers of polygons and self-avoiding walks confined to a square on the square lattice. Specifically we prove that the dominant asymptotic behaviour of polygons confined to an LxL square is identical to that of self-avoiding walks that cross an LxL square from one corner vertex to the opposite corner vertex. We also prove a result about the subdominant asymptotic behaviour of self-avoiding walks crossing a square and extend this result to polygons confined to a square. In addition, we investigate the problems of self-avoiding walks and polygons in a hypercube in the d-dimensional hypercubic lattice.Comment: Minor errors corrected and some additional results adde

Rapid identification of some Leptospira isolates from cattle by random amplified polymorphic DNA fingerprinting

We compared random amplified polymorphic DNA (RAPD) fingerprinting with cross-absorption agglutination and restriction enzyme analysis for typing bovine leptospires. Using RAPD fingerprinting, we examined a number of Leptospira serovars, namely, hardjo genotypes bovis and prajitno, pomona, balcanica, tarassovi, swajizak, kremastos, australis, and zanoni, which are likely to be isolated from Australian cattle. Each serovar and genotype had a unique RAPD profile. Of 26 field isolates of Leptospira, 23 were identified as hardjo genotype bovis subtype A, 2 were identified as zanoni, and 1 was identified as pomona by RAPD fingerprinting, and their types were confirmed by cross-absorption agglutination and restriction enzyme analysis

Statistics of nested spiral self-avoiding loops: exact results on the square and triangular lattices

The statistics of nested spiral self-avoiding loops, which is closely related to the partition of integers into decreasing parts, is studied on the square and triangular lattices.Comment: Old paper, for archiving. 7 pages, 2 figures, epsf, IOP macr

The Tolman-Eichenbaum Machine: Unifying Space and Relational Memory through Generalization in the Hippocampal Formation

The hippocampal-entorhinal system is important for spatial and relational memory tasks. We formally link these domains, provide a mechanistic understanding of the hippocampal role in generalization, and offer unifying principles underlying many entorhinal and hippocampal cell types. We propose medial entorhinal cells form a basis describing structural knowledge, and hippocampal cells link this basis with sensory representations. Adopting these principles, we introduce the Tolman-Eichenbaum machine (TEM). After learning, TEM entorhinal cells display diverse properties resembling apparently bespoke spatial responses, such as grid, band, border, and object-vector cells. TEM hippocampal cells include place and landmark cells that remap between environments. Crucially, TEM also aligns with empirically recorded representations in complex non-spatial tasks. TEM also generates predictions that hippocampal remapping is not random as previously believed; rather, structural knowledge is preserved across environments. We confirm this structural transfer over remapping in simultaneously recorded place and grid cells

Dynamically-Coupled Oscillators -- Cooperative Behavior via Dynamical Interaction --

We propose a theoretical framework to study the cooperative behavior of dynamically coupled oscillators (DCOs) that possess dynamical interactions. Then, to understand synchronization phenomena in networks of interneurons which possess inhibitory interactions, we propose a DCO model with dynamics of interactions that tend to cause 180-degree phase lags. Employing an approach developed here, we demonstrate that although our model displays synchronization at high frequencies, it does not exhibit synchronization at low frequencies because this dynamical interaction does not cause a phase lag sufficiently large to cancel the effect of the inhibition. We interpret the disappearance of synchronization in our model with decreasing frequency as describing the breakdown of synchronization in the interneuron network of the CA1 area below the critical frequency of 20 Hz.Comment: 10 pages, 3 figure