Hessian and concavity of mutual information, differential entropy, and entropy power in linear vector Gaussian channels

Within the framework of linear vector Gaussian channels with arbitrary signaling, closed-form expressions for the Jacobian of the minimum mean square error and Fisher information matrices with respect to arbitrary parameters of the system are calculated in this paper. Capitalizing on prior research where the minimum mean square error and Fisher information matrices were linked to information-theoretic quantities through differentiation, closed-form expressions for the Hessian of the mutual information and the differential entropy are derived. These expressions are then used to assess the concavity properties of mutual information and differential entropy under different channel conditions and also to derive a multivariate version of the entropy power inequality due to Costa.Comment: 33 pages, 2 figures. A shorter version of this paper is to appear in IEEE Transactions on Information Theor

Superconformal Ward Identities and their Solution

Superconformal Ward identities are derived for the the four point functions of chiral primary BPS operators for $\N=2,4$ superconformal symmetry in four dimensions. Manipulations of arbitrary tensorial fields are simplified by introducing a null vector so that the four point functions depend on two internal $R$-symmetry invariants as well as two conformal invariants. The solutions of these identities are interpreted in terms of the operator product expansion and are shown to accommodate long supermultiplets with free scale dimensions and also short and semi-short multiplets with protected dimensions. The decomposition into $R$-symmetry representations is achieved by an expansion in terms of two variable harmonic polynomials which can be expressed also in terms of Legendre polynomials. Crossing symmetry conditions on the four point functions are also discussed.Comment: 73 pages, plain Tex, uses harvmac, version 2, extra reference

The NxD-BMAP/G/1 queueing model : queue contents and delay analysis

We consider a single-server discrete-time queueing system with N sources, where each source is modelled as a correlated Markovian customer arrival process, and the customer service times are generally distributed. We focus on the analysis of the number of customers in the queue, the amount of work in the queue, and the customer delay. For each of these quantities, we will derive an expression for their steady-state probability generating function, and from these results, we derive closed-form expressions for key performance measures such as their mean value, variance, and tail distribution. A lot of emphasis is put on finding closed-form expressions for these quantities that reduce all numerical calculations to an absolute minimum

Poisson's ratio in cubic materials

Expressions are given for the maximum and minimum values of Poisson's ratio $\nu$ for materials with cubic symmetry. Values less than -1 occur if and only if the maximum shear modulus is associated with the cube axis and is at least 25 times the value of the minimum shear modulus. Large values of $|\nu|$ occur in directions at which the Young's modulus is approximately equal to one half of its 111 value. Such directions, by their nature, are very close to 111. Application to data for cubic crystals indicates that certain Indium Thallium alloys simultaneously exhibit Poisson's ratio less than -1 and greater than +2.Comment: 20 pages, 6 figure

Modeling of Protostellar Clouds and their Observational Properties

A physical model and two-dimensional numerical method for computing the evolution and spectra of protostellar clouds are described. The physical model is based on a system of magneto-gasdynamical equations, including ohmic and ambipolar diffusion, and a scheme for calculating the thermal and ionization structure of a cloud. The dust and gas temperatures are determined during the calculations of the thermal structure of the cloud. The results of computing the dynamical and thermal structure of the cloud are used to model the radiative transfer in continuum and in molecular lines. We presented the results for clouds in hydrostatic and thermal equilibrium. The evolution of a rotating magnetic protostellar cloud starting from a quasi-static state is also considered. Spectral maps for optically thick lines of linear molecules are analyzed. We have shown that the influence of the magnetic field and rotation can lead to a redistribution of angular momentum in the cloud and the formation of a characteristic rotational velocity structure. As a result, the distribution of the velocity centroid of the molecular lines can acquire an hourglass shape. We plan to use the developed program package together with a model for the chemical evolution to interpret and model observed starless and protostellar cores.Comment: Accepted to Astronomy Report

Explicit expressions for the minimum efficiency and most penetrating particle size of Nuclepore filters

Nuclepore filters are capillary pore membrane filters with an array of microscopic cylindrical holes of uniform diameters. Their structure is suitable for particle collection and ensuing offline analyses, therefore they are being widely used for exposure assessment of engineered nanoparticles, ambient PM2.5, virus, bacteria, asbestos, etc., as well as in powder manufacturing industries. However, there exists a particle size range in which all the filtration capture mechanisms are not effective. This size is the most penetrating particle size (MPPS), which corresponds to the minimum efficiency (ME) of the filter. Both MPPS and ME are important parameters for a user to select an adequate Nuclepore filter and preferred operating conditions. For rapid estimation of the MPPS and ME, we derived their explicit expressions by simplifying the formulas for the impaction, diffusion and interception deposition and differentiating the combined efficiency with respect to the particle size. The comparison between the experimental data and the prediction from the explicit expressions shows the explicit expressions can provide MPPS for a wide range of filter properties (pore radius, porosity and length) and filtration conditions (particle density, face velocity and temperature). The ME can also be estimated satisfactorily when a simplified term of filter surface diffusion deposition is further considered. By the explicit expressions of MPPS and ME, a quick screening for selecting a Nuclepore filter with the proper properties and suitable filtration conditions can be easily achieved. From the theoretical point of view, the explicit expressions facilitate better understanding of the effects of filter properties and conditions on the filtration characteristic