Outage Capacity for the Optical MIMO Channel

MIMO processing techniques in fiber optical communications have been proposed as a promising approach to meet increasing demand for information throughput. In this context, the multiple channels correspond to the multiple modes and/or multiple cores in the fiber. In this paper we characterize the distribution of the mutual information with Gaussian input in a simple channel model for this system. Assuming significant cross talk between cores, negligible backscattering and near-lossless propagation in the fiber, we model the transmission channel as a random complex unitary matrix. The loss in the transmission may be parameterized by a number of unutilized channels in the fiber. We analyze the system in a dual fashion. First, we evaluate a closed-form expression for the outage probability, which is handy for small matrices. We also apply the asymptotic approach, in particular the Coulomb gas method from statistical mechanics, to obtain closed-form results for the ergodic mutual information, its variance as well as the outage probability for Gaussian input in the limit of large number of cores/modes. By comparing our analytic results to simulations, we see that, despite the fact that this method is nominally valid for large number of modes, our method is quite accurate even for small to modest number of channels.Comment: Revised version includes more details, proofs and a closed-form expression for the outage probabilit

The Bernstein-Von Mises Theorem in Semiparametric Competing Risks Models

Semiparametric Bayesian models are nowadays a popular tool in survival analysis. An important area of research concerns the investigation of frequentist properties of these models. In this paper, a Bernstein-von Mises theorem is derived for semiparametric Bayesian models of competing risks data. The cause-specific hazard is taken as the product of the conditional probability of a failure type and the overall hazard rate. We model the conditional probability as a smooth function of time and leave the cumulative overall hazard unspecified. A prior distribution is defined on the joint parameter space, which includes a beta process prior for the cumulative overall hazard. We show that the posterior distribution for any differentiable functional of interest is asymptotically equivalent to the sampling distribution derived from maximum likelihood estimation. A simulation study is provided to illustrate the coverage properties of credible intervals on cumulative incidence functions.Bayesian nonparametrics, Bernstein-von Mises theorem, beta process, competing risks, conditional probability of a failure type, semiparametric inference.

Interatrial shunt devices for heart failure with normal ejection fraction: a technology update

Heart failure with normal ejection fraction (HeFNEF) accounts for ~50% of heart failure admissions. Its pathophysiology and diagnostic criteria are yet to be defined clearly which may hinder the search for effective treatments. The clinical hallmark of HeFNEF is exertional breathlessness, often due to an abnormal increase in left atrial pressure during exercise. Creation of an interatrial communication to offload the left atrium is a possible therapeutic approach. There are two percutaneously delivered devices currently under investigation which are discussed in this review

Random Matrix approach to collective behavior and bulk universality in protein dynamics

Covariance matrices of amino acid displacements, commonly used to characterize the large-scale movements of proteins, are investigated through the prism of Random Matrix Theory. Bulk universality is detected in the local spacing statistics of noise-dressed eigenmodes, which is well described by a Brody distribution with parameter $\beta\simeq 0.8$. This finding, supported by other consistent indicators, implies a novel quantitative criterion to single out the collective degrees of freedom of the protein from the majority of high-energy, localized vibrations.Comment: 4 pages, 7 figure

Twistor-Inspired Construction of Electroweak Vector Boson Currents

We present an extension of the twistor-motivated MHV vertices and accompanying rules presented by Cachazo, Svrvcek and Witten to the construction of vector-boson currents coupling to an arbitrary source. In particular, we give rules for constructing off-shell vector-boson currents with one fermion pair and n gluons of arbitrary helicity. These currents may be employed directly in the computation of electroweak amplitudes. The rules yield expressions in agreement with previously-obtained results for Z,W,\gamma^* --> qbar q + n gluons (analytically up to n=3, beyond via the Berends--Giele recursion relations). We also confirm that the contribution to a seven-point amplitude containing the non-abelian triple vector-boson coupling obtained using the next-to-MHV currents matches the previous result in the literature.Comment: 22 pages, 4 figures, v2 minor corrections and added commentary on multiple vector boson

Intersection Numbers in Quantum Mechanics and Field Theory

By elaborating on the recent progress made in the area of Feynman integrals, we apply the intersection theory for twisted de Rham cohomologies to simple integrals involving orthogonal polynomials, matrix elements of operators in Quantum Mechanics and Green's functions in Field Theory, showing that the algebraic identities they obey are related to the decomposition of twisted cocycles within cohomology groups, and which, therefore, can be derived by means of intersection numbers. Our investigation suggests an algebraic approach generically applicable to the study of higher-order moments of probability distributions, where the dimension of the cohomology groups corresponds to the number of independent moments; the intersection numbers for twisted cocycles can be used to derive linear and quadratic relations among them. Our study offers additional evidence of the intertwinement between physics, geometry, and statistics

The Index Distribution of Gaussian Random Matrices

We compute analytically, for large N, the probability distribution of the number of positive eigenvalues (the index N_{+}) of a random NxN matrix belonging to Gaussian orthogonal (\beta=1), unitary (\beta=2) or symplectic (\beta=4) ensembles. The distribution of the fraction of positive eigenvalues c=N_{+}/N scales, for large N, as Prob(c,N)\simeq\exp[-\beta N^2 \Phi(c)] where the rate function \Phi(c), symmetric around c=1/2 and universal (independent of $\beta$), is calculated exactly. The distribution has non-Gaussian tails, but even near its peak at c=1/2 it is not strictly Gaussian due to an unusual logarithmic singularity in the rate function.Comment: 4 pages Revtex, 4 .eps figures include

Number statistics for β\beta-ensembles of random matrices: applications to trapped fermions at zero temperature

Let $\mathcal{P}_{\beta}^{(V)} (N_{\cal I})$ be the probability that a $N\times N$ $\beta$-ensemble of random matrices with confining potential $V(x)$ has $N_{\cal I}$ eigenvalues inside an interval ${\cal I}=[a,b]$ of the real line. We introduce a general formalism, based on the Coulomb gas technique and the resolvent method, to compute analytically $\mathcal{P}_{\beta}^{(V)} (N_{\cal I})$ for large $N$. We show that this probability scales for large $N$ as $\mathcal{P}_{\beta}^{(V)} (N_{\cal I})\approx \exp\left(-\beta N^2 \psi^{(V)}(N_{\cal I} /N)\right)$, where $\beta$ is the Dyson index of the ensemble. The rate function $\psi^{(V)}(k_{\cal I})$, independent of $\beta$, is computed in terms of single integrals that can be easily evaluated numerically. The general formalism is then applied to the classical $\beta$-Gaussian (${\cal I}=[-L,L]$), $\beta$-Wishart (${\cal I}=[1,L]$) and $\beta$-Cauchy (${\cal I}=[-L,L]$) ensembles. Expanding the rate function around its minimum, we find that generically the number variance ${\rm Var}(N_{\cal I})$ exhibits a non-monotonic behavior as a function of the size of the interval, with a maximum that can be precisely characterized. These analytical results, corroborated by numerical simulations, provide the full counting statistics of many systems where random matrix models apply. In particular, we present results for the full counting statistics of zero temperature one-dimensional spinless fermions in a harmonic trap.Comment: 34 pages, 19 figure

Prevention or procrastination for heart failure?: Why we need a universal definition of heart failure

No abstract available