Arrangements of hyperplanes II: Szenes formula and Eisenstein series

The aim of this article is to generalize in several variables some formulae for Eisenstein series in one variable. For example the formula $2\zeta(2k) = (2\pi)^{2k} \frac{B_{2k}}{(2k)!} = Res_{z=0}(\frac{1}{z^{2k}(1-e^z)})$ for the values of zeta functions at even integers in functions of Bernoulli numbers. A. Szenes proved in several variables a similar residue formula for the values of the zeta function introduced by Witten. We introduce some Eisenstein series by averaging over a lattice rational functions with poles in an arrangement of hyperplanes. We give another proof of Szenes residue formula by relating it to the constant term of these Eisenstein series.Comment: revised version (introduction rewritten, references added, minor changes made), 28 pages, LaTEX2

Collisions in shape memory alloys

We present here a model for instantaneous collisions in a solid made of shape memory alloys (SMA) by means of a predictive theory which is based on the introduction not only of macroscopic velocities and temperature, but also of microscopic velocities responsible of the austenite-martensites phase changes. Assuming time discontinuities for velocities, volume fractions and temperature, and applying the principles of thermodynamics for non-smooth evolutions together with constitutive laws typical of SMA, we end up with a system of nonlinearly coupled elliptic equations for which we prove an existence and uniqueness result in the 2 and 3 D cases. Finally, we also present numerical results for a SMA 2D solid subject to an external percussion by an hammer stroke

Dynamical behavior across the Mott transition of two bands with different bandwidths

We investigate the role of the bandwidth difference in the Mott metal-insulator transition of a two-band Hubbard model in the limit of infinite dimensions, by means of a Gutzwiller variational wave function as well as by dynamical mean-field theory. The variational calculation predicts a two-stage quenching of the charge degrees of freedom, in which the narrower band undergoes a Mott transition before the wider one, both in the presence and in the absence of a Hund's exchange coupling. However, this scenario is not fully confirmed by the dynamical mean-field theory calculation, which shows that, although the quasiparticle residue of the narrower band is zero within our numerical accuracy, low-energy spectral weight still exists inside the Mott-Hubbard gap, concentrated into two peaks symmetric around the chemical potential. This spectral weight vanishes only when the wider band ceases to conduct too. Although our results are compatible with several scenarios, e.g., a narrow gap semiconductor or a semimetal, we argue that the most plausible one is that the two peaks coexist with a narrow resonance tied at the chemical potential, with a spectral weight below our numerical accuracy. This quasiparticle resonance is expected to vanish when the wider band undergoes the Mott transition.Comment: 11 pages, 12 figure

Niche Markets for Fresh Canadian Pork in the Pacific Northwest: A Case Study

Livestock Production/Industries, Marketing,

Top ten risk factors for morbidity and mortality in patients with chronic systolic heart failure and elevated heart rate: the SHIFT risk model

Aims We identified easily obtained baseline characteristics associated with outcomes in patients with chronic heart failure (HF) and elevated heart rate (HR) receiving contemporary guideline-recommended therapy in the SHIFT trial, and used them to develop a prognostic model. Methods We selected the 10 best predictors for each of four outcomes (cardiovascular death or HF hospitalisation; all-cause mortality; cardiovascular mortality; and HF hospitalisation). All variables with p &#60; 0.05 for association were entered into a forward stepwise Cox regression model. Our initial analysis excluded baseline therapies, though randomisation to ivabradine or placebo was forced into the model for the composite endpoint and HF hospitalisation. Results Increased resting HR, low ejection fraction, raised creatinine, New York Heart Association class III/IV, longer duration of HF, history of left bundle branch block, low systolic blood pressure and, for three models, age were strong predictors of all outcomes. Additional predictors were low body mass index, male gender, ischaemic HF, low total cholesterol, no history of hyperlipidaemia or dyslipidaemia and presence of atrial fibrillation/flutter. The c-statistics for the four outcomes ranged from 67.6% to 69.5%. There was no evidence for lack of fit of the models with the exception of all-cause mortality (p = 0.017). Similar results were found including baseline therapies. Conclusion The SHIFT Risk Model includes simple, readily obtainable clinical characteristics to produce important prognostic information in patients with chronic HF, systolic dysfunction, and elevated HR. This may help better calibrate management to individual patient risk.</p

Into the Square: On the Complexity of Some Quadratic-time Solvable Problems

International audienceWe analyze several quadratic-time solvable problems, and we show that these problems are not solvable in truly subquadratic time (that is, in time O(n2−ϵ) for some ϵ>0), unless the well known Strong Exponential Time Hypothesis (in short, SETH) is false. In particular, we start from an artificial quadratic-time solvable variation of the k-Sat problem (already introduced and used in the literature) and we will construct a web of Karp reductions, proving that a truly subquadratic-time algorithm for any of the problems in the web falsifies SETH. Some of these results were already known, while others are, as far as we know, new. The new problems considered are: computing the betweenness centrality of a vertex (the same result was proved independently by Abboud et al.), computing the minimum closeness centrality in a graph, computing the hyperbolicity of a graph, and computing the subset graph of a collection of sets. On the other hand, we will show that testing if a directed graph is transitive and testing if a graph is a comparability graph are subquadratic-time solvable (our algorithm is practical, since it is not based on intricate matrix multiplication algorithms)

Effect of visit-to-visit variation of heart rate and systolic blood pressure on outcomes in chronic systolic heart failure: results from the Systolic Heart Failure Treatment With the If Inhibitor Ivabradine Trial (SHIFT) trial

Background: Elevated resting heart rate (HR) and low systolic blood pressure (SBP) are related to poor outcomes in heart failure (HF). The association between visit-to-visit variation in SBP and HR and risk in HF is unknown. Methods and Results: In Systolic Heart Failure Treatment with the If inhibitor ivabradine Trial (SHIFT) patients, we evaluated relationships between mean HR, mean SBP, and visit-to-visit variations (coefficient of variation [CV]=SD/mean×100%) in SBP and HR (SBP-CV and HR-CV, respectively) and primary composite endpoint (cardiovascular mortality or HF hospitalization), its components, all-cause mortality, and all-cause hospitalization. High HR and low SBP were closely associated with risk for primary endpoint, all-cause mortality, and HF hospitalization. The highest number of primary endpoint events occurred in the highest HR tertile (38.8% vs 16.4% lowest tertile; P&lt;0.001). For HR-CV, patients at highest risk were those in the lowest tertile. Patients in the lowest thirds of mean SBP and SBP-CV had the highest risk. The combination of high HR and low HR-CV had an additive deleterious effect on risk, as did that of low SBP and low SBP-CV. Ivabradine reduced mean HR and increased HR-CV, and increased SBP and SBP-CV slightly. Conclusions: Beyond high HR and low SBP, low HR-CV and low SBP-CV are predictors of cardiovascular outcomes with additive effects on risk in HF, but with an unknown effect size. Beyond HR reduction, ivabradine increases HR-CV. Low visit-to-visit variation of HR and SBP might signal risk of cardiovascular outcomes in systolic HF. Clinical Trial Registration: URL: http://www.isrctn.com/. Unique identifier: ISRCTN70429960

Odd elasticity and topological waves in active surfaces

Odd elasticity encompasses active elastic systems whose stress-strain relationship is not compatible with a potential energy. As the requirement of energy conservation is lifted from linear elasticity, new anti-symmetric (odd) components appear in the elastic tensor. In this work, we study the odd elasticity and non-Hermitian wave dynamics of active surfaces, specifically plates of moderate thickness. We find that a free-standing moderately thick, isotropic plate can exhibit two odd-elastic moduli, both of which are related to shear deformations of the plate. These odd moduli can endow the vibrational modes of the plate with a nonzero topological invariant known as the first Chern number. Within continuum elastic theory, we show that the Chern number is related to the presence of unidirectional shearing waves that are hosted at the plate's boundary. We show that the existence of these chiral edge waves hinges on a distinctive two-step mechanism: the finite thickness of the sample gaps the shear modes and the odd elasticity endows them with chirality.Comment: 13 pages, 6 figure

Dynamical correlations and screened exchange on the experimental bench: spectral properties of the cobalt pnictide BaCo2As2

Understanding the Fermi surface and low-energy excitations of iron or cobalt pnictides is crucial for assessing electronic instabilities such as magnetic or superconducting states. Here, we propose and implement a new approach to compute the low-energy properties of correlated electron materials, taking into account both screened exchange beyond the local density approximation and local dynamical correlations. The scheme allows us to resolve the puzzle of BaCo2As2, for which standard electronic structure techniques predict a ferromagnetic instability not observed in nature.Comment: 6 pages, 4 figures + Supplementary materia