Random matrices and the New York City subway system

We analyze subway arrival times in the New York City subway system. We find regimes where the gaps between trains exhibit both (unitarily invariant) random matrix statistics and Poisson statistics. The departure from random matrix statistics is captured by the value of the Coulomb potential along the subway route. This departure becomes more pronounced as trains make more stops

Low Temperature Asymptotics in Spherical Mean Field Spin Glasses

In this paper, we study the low temperature limit of the spherical Crisanti-Sommers variational problem. We identify the $\Gamma$-limit of the Crisanti-Sommers functionals, thereby establishing a rigorous variational problem for the ground state energy of spherical mixed $p$-spin glasses. As an application, we compute moderate deviations of the corresponding minimizers in the low temperature limit. In particular, for a large class of models this yields moderate deviations for the overlap distribution. We then analyze the ground state energy problem. We show that this variational problem is dual to an obstacle-type problem. This duality is at the heart of our analysis. We present the regularity theory of the optimizers of the primal and dual problems. This culminates in a simple method for constructing a finite dimensional space in which these optimizers live for any model. As a consequence of these results, we unify independent predictions of Crisanti-Leuzzi and Auffinger-Ben Arous regarding the 1RSB phase in this limit. We find that the "positive replicon eigenvalue" and "pure-like" conditions are together necessary for optimality, but that neither are themselves sufficient, answering a question of Auffinger and Ben Arous in the negative. We end by proving that these conditions completely characterize the 1RSB phase in $2+p$-spin models

An examination of walking track analysis footprints of right-side unoperated limbs in rats prior to and following peripheral nerve injury and PEG fusion repair

Peripheral nerve injury can result in long-lasting functional deficits in humans due to mammals’ limited axon regenerative capacity. PEG fusion is a defined technique that fuses injured axons, resulting in morphological and electrophysiological continuity. The technology has been shown to restore lost behaviors due to peripheral nerve injury. The process involves an invasive surgical procedure on the left hind limb of female Sprague-Dawley rats that results in the severance of the sciatic nerve. Assessing behavioral recovery is perhaps the most important metric by which to quantify PEG fusion’s success. Recovery is most accurately and best assessed using the Sciatic Functional Index walking track analysis, or SFI. This procedure involves having a rat run up a path with its paws inked, and subsequent analysis compares the print length, toe spread, and intermediate toe spread of the “normal” and unoperated side (right) with the “experimental” and operated side (left). In this paper, we examine if surgical intervention and sciatic nerve transection on the left, experimental limb in rats results in significantly altered measurements on the right, unoperated side compared to pre-op, baseline measurements. Comparisons are made between baseline normal prints, normal prints three days post-op, and normal prints 42 days post-op for PEG-fused animals. Differences may exist due to altered gait after operation, physiological effects of surgical intervention, or random variation in the SFI testing paradigm. Regardless, attempting to highlight such discrepancies can contribute to developing better models for measuring recovery following peripheral nerve injury in mammals. Such models would more accurately be able to predict the clinical translatability of potential treatments for these nerve injuries. Analysis of SFI measurements pre- and post-op suggests that surgical intervention on the left experimental hind limb of rats does result in statistically significant differences in measured print length, toe spread, and intermediate toe spread post-op. In addition, we found that the differences between baseline and post-op measurements seem to become mitigated over time.Neuroscienc