On the critical pair theory in abelian groups : Beyond Chowla's Theorem

We obtain critical pair theorems for subsets S and T of an abelian group such that |S+T| < |S|+|T|+1. We generalize some results of Chowla, Vosper, Kemperman and a more recent result due to Rodseth and one of the authors.Comment: Submitted to Combinatorica, 23 pages, revised versio

Estimation in high dimensions: a geometric perspective

This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of asymptotic convex geometry, and demonstrates connections between geometric results and estimation problems. The theory is illustrated with applications to sparse recovery, matrix completion, quantization, linear and logistic regression and generalized linear models.Comment: 56 pages, 9 figures. Multiple minor change

A Method to Tackle First Order Differential Equations with Liouvillian Functions in the Solution - II

We present a semi-decision procedure to tackle first order differential equations, with Liouvillian functions in the solution (LFOODEs). As in the case of the Prelle-Singer procedure, this method is based on the knowledge of the integrating factor structure.Comment: 11 pages, late

Mesoscopic motion of atomic ions in magnetic fields

We introduce a semiclassical model for moving highly excited atomic ions in a magnetic field which allows us to describe the mixing of the Landau orbitals of the center of mass in terms of the electronic excitation and magnetic field. The extent of quantum energy flow in the ion is investigated and a crossover from localization to delocalization with increasing center of mass energy is detected. It turns out that our model of the moving ion in a magnetic field is closely connected to models for transport in disordered finite-size wires.Comment: 4 pages, 2 figures, subm. to Phys.Rev.A, Rap.Co

A framework for the successful implementation of food traceability systems in China

Implementation of food traceability systems in China faces many challenges due to the scale, diversity and complexity of China’s food supply chains. This study aims to identify critical success factors specific to the implementation of traceability systems in China. Twenty-seven critical success factors were identified in the literature. Interviews with managers at four food enterprises in a pre-study helped identify success criteria and five additional critical success factors. These critical success factors were tested through a survey of managers in eighty-three food companies. This study identifies six dimensions for critical success factors: laws, regulations and standards; government support; consumer knowledge and support; effective management and communication; top management and vendor support; and information and system quality

Spin Lifetime in Small Electron Spin Ensembles Measured by Magnetic Resonance Force Microscopy

Magnetic Resonance Force Microscopy can enable nanoscale imaging of spin lifetime. We report temperature dependent measurements of the spin correlation time $\tau_m$ of the statistical fluctuations of the spin polarization---the spin noise---of ensembles containing $\sim 100$ electron spins by this technique. Magneto-mechanical relaxation due to spin-cantilever coupling was controlled and spurious mechanisms that can affect the spin correlation time of the microscopic signal were characterized. These measurements have ramifications for optimizing spin sensitivity, understanding local spin dynamics and for nanoscale imaging.Comment: 5 pages, 5 figures, accepted in Phys. Rev. B (Rapid Comm.

Small doubling in groups

Let A be a subset of a group G = (G,.). We will survey the theory of sets A with the property that |A.A| <= K|A|, where A.A = {a_1 a_2 : a_1, a_2 in A}. The case G = (Z,+) is the famous Freiman--Ruzsa theorem.Comment: 23 pages, survey article submitted to Proceedings of the Erdos Centenary conferenc

Beyond series expansions: mathematical structures for the susceptibility of the square lattice Ising model

We first study the properties of the Fuchsian ordinary differential equations for the three and four-particle contributions $\chi^{(3)}$ and $\chi^{(4)}$ of the square lattice Ising model susceptibility. An analysis of some mathematical properties of these Fuchsian differential equations is sketched. For instance, we study the factorization properties of the corresponding linear differential operators, and consider the singularities of the three and four-particle contributions $\chi^{(3)}$ and $\chi^{(4)}$, versus the singularities of the associated Fuchsian ordinary differential equations, which actually exhibit new ``Landau-like'' singularities. We sketch the analysis of the corresponding differential Galois groups. In particular we provide a simple, but efficient, method to calculate the so-called ``connection matrices'' (between two neighboring singularities) and deduce the singular behaviors of $\chi^{(3)}$ and $\chi^{(4)}$. We provide a set of comments and speculations on the Fuchsian ordinary differential equations associated with the $n$-particle contributions $\chi^{(n)}$ and address the problem of the apparent discrepancy between such a holonomic approach and some scaling results deduced from a Painlev\'e oriented approach.Comment: 21 pages Proceedings of the Counting Complexity conferenc

iPTF Archival Search for Fast Optical Transients

There has been speculation about a class of relativistic explosions with an initial Lorentz factor Γ_init smaller than that of classical gamma-ray bursts (GRBs). These “dirty fireballs” would lack prompt GRB emission but could be pursued via their optical afterglow, appearing as transients that fade overnight. Here we report a search for such transients (that fade by 5-σ in magnitude overnight) in four years of archival photometric data from the intermediate Palomar Transient Factory (iPTF). Our search criteria yielded 50 candidates. Of these, two were afterglows to GRBs that had been found in dedicated follow-up observations to triggers from the Fermi GRB Monitor. Another (iPTF14yb) was a GRB afterglow discovered serendipitously. Eight were spurious artifacts of reference image subtraction, and one was an asteroid. The remaining 38 candidates have red stellar counterparts in external catalogs. The photometric and spectroscopic properties of the counterparts identify these transients as strong flares from M dwarfs of spectral type M3–M7 at distances of d ≈ 0.15–2.1 kpc; three counterparts were already spectroscopically classified as late-type M stars. With iPTF14yb as the only confirmed relativistic outflow discovered independently of a high-energy trigger, we constrain the all-sky rate of transients that peak at m = 18 and fade by Δm = 2 mag in Δt = 3 hr to be 680 yr-1, with a 68% confidence interval of 119-2236 {{yr}}-1. This implies that the rate of visible dirty fireballs is at most comparable to that of the known population of long-duration GRBs