Cohomology for Anyone

Crystallography has proven a rich source of ideas over several centuries. Among the many ways of looking at space groups, N. David Mermin has pioneered the Fourier-space approach. Recently, we have supplemented this approach with methods borrowed from algebraic topology. We now show what topology, which studies global properties of manifolds, has to do with crystallography. No mathematics is assumed beyond what the typical physics or crystallography student will have seen of group theory; in particular, the reader need not have any prior exposure to topology or to cohomology of groups.Comment: 21 pages + figures, bibliography, Mathematica code homology.

Fluctuation Induced Instabilities in Front Propagation up a Co-Moving Reaction Gradient in Two Dimensions

We study 2D fronts propagating up a co-moving reaction rate gradient in finite number reaction-diffusion systems. We show that in a 2D rectangular channel, planar solutions to the deterministic mean-field equation are stable with respect to deviations from planarity. We argue that planar fronts in the corresponding stochastic system, on the other hand, are unstable if the channel width exceeds a critical value. Furthermore, the velocity of the stochastic fronts is shown to depend on the channel width in a simple and interesting way, in contrast to fronts in the deterministic MFE. Thus, fluctuations alter the behavior of these fronts in an essential way. These affects are shown to be partially captured by introducing a density cutoff in the reaction rate. Some of the predictions of the cutoff mean-field approach are shown to be in quantitative accord with the stochastic results

Permutation-Symmetric Multicritical Points in Random Antiferromagnetic Spin Chains

The low-energy properties of a system at a critical point may have additional symmetries not present in the microscopic Hamiltonian. This letter presents the theory of a class of multicritical points that provide an interesting example of this in the phase diagrams of random antiferromagnetic spin chains. One case provides an analytic theory of the quantum critical point in the random spin-3/2 chain, studied in recent work by Refael, Kehrein and Fisher (cond-mat/0111295).Comment: Revtex, 4 pages (2 column format), 2 eps figure

Heuristic Spike Sorting Tuner (HSST), a framework to determine optimal parameter selection for a generic spike sorting algorithm

Extracellular microelectrodes frequently record neural activity from more than one neuron in the vicinity of the electrode. The process of labeling each recorded spike waveform with the identity of its source neuron is called spike sorting and is often approached from an abstracted statistical perspective. However, these approaches do not consider neurophysiological realities and may ignore important features that could improve the accuracy of these methods. Further, standard algorithms typically require selection of at least one free parameter, which can have significant effects on the quality of the output. We describe a Heuristic Spike Sorting Tuner (HSST) that determines the optimal choice of the free parameters for a given spike sorting algorithm based on the neurophysiological qualification of unit isolation and signal discrimination. A set of heuristic metrics are used to score the output of a spike sorting algorithm over a range of free parameters resulting in optimal sorting quality. We demonstrate that these metrics can be used to tune parameters in several spike sorting algorithms. The HSST algorithm shows robustness to variations in signal to noise ratio, number and relative size of units per channel. Moreover, the HSST algorithm is computationally efficient, operates unsupervised, and is parallelizable for batch processing

A Jewish Family of Thirteenth Century England

There is a wealth of material on medieval Anglo-Jewry in the public records (rolls) of twelfth and thirteenth century England. These documents refer primarily to the financial transactions of the English Jews. Usury was forbidden to Christians by both the Church and the laws of the realm. The injunctions against usury, however, did not apply to the Jews.The Jews of this period were considered to be the private property of the king and were forbidden from engaging in all economic pursuits with the exception of money-lending. The crown benefited from the arrangement by applying heavy taxes on the Jews