Optical/Infrared Observations of the Anomalous X-ray Pulsar 1E 1048.1-5937 During Its 2007 X-Ray Flare

We report on optical and infrared observations of the anomalous X-ray pulsar (AXP) 1E 1048.1-5937, made during its ongoing X-ray flare which started in 2007 March. We detected the source in the optical I and near-infrared Ks bands in two ground-based observations and obtained deep flux upper limits from four observations, including one with the Spitzer Space Telescope at 4.5 and 8.0 microns. The detections indicate that the source was approximately 1.3--1.6 magnitudes brighter than in 2003--2006, when it was at the tail of a previous similar X-ray flare. Similar related flux variations have been seen in two other AXPs during their X-ray outbursts, suggesting common behavior for large X-ray flux variation events in AXPs. The Spitzer flux 1E 1048.1-5937 limits are sufficiently deep that we can exclude mid-infrared emission similar to that from the AXP 4U 0142+61, which has been interpreted as arising from a dust disk around the AXP. The optical/near-infrared emission from probably has a magnetospheric origin. The similarity in the flux spectra of 4U 0142+61 and 1E 1048.1-5937 challenges the dust disk model proposed for the latter.Comment: 5 pages, 1 figure, accepted by Ap

The Maximal Denumerant of a Numerical Semigroup

Given a numerical semigroup S = and n in S, we consider the factorization n = c_0 a_0 + c_1 a_1 + ... + c_t a_t where c_i >= 0. Such a factorization is maximal if c_0 + c_1 + ... + c_t is a maximum over all such factorizations of n. We provide an algorithm for computing the maximum number of maximal factorizations possible for an element in S, which is called the maximal denumerant of S. We also consider various cases that have connections to the Cohen-Macualay and Gorenstein properties of associated graded rings for which this algorithm simplifies.Comment: 13 Page

Towards Verifying Nonlinear Integer Arithmetic

We eliminate a key roadblock to efficient verification of nonlinear integer arithmetic using CDCL SAT solvers, by showing how to construct short resolution proofs for many properties of the most widely used multiplier circuits. Such short proofs were conjectured not to exist. More precisely, we give n^{O(1)} size regular resolution proofs for arbitrary degree 2 identities on array, diagonal, and Booth multipliers and quasipolynomial- n^{O(\log n)} size proofs for these identities on Wallace tree multipliers.Comment: Expanded and simplified with improved result

When B cells break bad:development of pathogenic B cells in Sjögren’s syndrome

Primary Sjögren's syndrome (pSS) is often considered a B cell-mediated disease, yet the precise role of B cells in the pathogenesis is not fully understood. This is exemplified by the failure of multiple clinical trials directed at B cell depletion or inhibition. To date, most prognostic markers for severe disease outcomes are autoantibodies, but the underlying mechanisms by which B cells drive diverse disease presentations in pSS likely extend beyond autoantibody production. Here we outline an expanded role of B cells in disease pathogenesis drawing on examples from animal models of SS, and from other autoimmune diseases that share similar clinical or immunological abnormalities. We focus on recent findings from the detailed analysis of pathogenic B cells in patients with pSS to propose strategies for patient stratification to improve clinical trial outcomes. We conclude that an integrated cellular, molecular and genetic analysis of patients with pSS will reveal the underlying pathogenic mechanisms and guide precision medicine.J.H. Reed, G.M. Verstappen, M. Rischmueller, V.L. Bryan

Conservation laws for multidimensional systems and related linear algebra problems

We consider multidimensional systems of PDEs of generalized evolution form with t-derivatives of arbitrary order on the left-hand side and with the right-hand side dependent on lower order t-derivatives and arbitrary space derivatives. For such systems we find an explicit necessary condition for existence of higher conservation laws in terms of the system's symbol. For systems that violate this condition we give an effective upper bound on the order of conservation laws. Using this result, we completely describe conservation laws for viscous transonic equations, for the Brusselator model, and the Belousov-Zhabotinskii system. To achieve this, we solve over an arbitrary field the matrix equations SA=A^tS and SA=-A^tS for a quadratic matrix A and its transpose A^t, which may be of independent interest.Comment: 12 pages; proof of Theorem 1 clarified; misprints correcte

Coexistence of orbital and quantum critical magnetoresistance in FeSe1−x_{1-x}Sx_{x}

The recent discovery of a non-magnetic nematic quantum critical point (QCP) in the iron chalcogenide family FeSe$_{1-x}$S$_{x}$ has raised the prospect of investigating, in isolation, the role of nematicity on the electronic properties of correlated metals. Here we report a detailed study of the normal state transverse magnetoresistance (MR) in FeSe$_{1-x}$S$_{x}$ for a series of S concentrations spanning the nematic QCP. For all temperatures and \textit{x}-values studied, the MR can be decomposed into two distinct components: one that varies quadratically in magnetic field strength $\mu_{0}\textit{H}$ and one that follows precisely the quadrature scaling form recently reported in metals at or close to a QCP and characterized by a \textit{H}-linear MR over an extended field range. The two components evolve systematically with both temperature and S-substitution in a manner that is determined by their proximity to the nematic QCP. This study thus reveals unambiguously the coexistence of two independent charge sectors in a quantum critical system. Moreover, the quantum critical component of the MR is found to be less sensitive to disorder than the quadratic (orbital) MR, suggesting that detection of the latter in previous MR studies of metals near a QCP may have been obscured.Comment: 19 pages (including Supplemental Material), 12 figure

Asymptotic conservation laws in field theory

A new, general, field theoretic approach to the derivation of asymptotic conservation laws is presented. In this approach asymptotic conservation laws are constructed directly from the field equations according to a universal prescription which does not rely upon the existence of Noether identities or any Lagrangian or Hamiltonian formalisms. The resulting general expressions of the conservation laws enjoy important invariance properties and synthesize all known asymptotic conservation laws, such as the ADM energy in general relativity.Comment: 13 pages, AMS-TeX, amsppt.sty, revised to give a better exposition (we hope), and to correct some typesetting error