Evolution of polyandry by reduction in progeny number variance in structured populations

When there is a variation in the quality of males in a population, multiple mating can lead to an increase in the genetic fitness of a female by reducing the variance of the progeny number. The extent of selective advantage obtainable by this process is investigated for a population subdivided into structured demes. It is seen that for a wide range of model parameters (deme size, distribution of male quality, local resource level), multiple mating leads to a considerable increase in the fitness. Frequency-dependent selection or a stable coexistence between polyandry and monandry can also result when the possible costs involved in multiple mating are taken into account.

On Finding the Natural Number of Topics with Latent Dirichlet Allocation: Some Observations

It is important to identify the ``correct'' number of topics in mechanisms like Latent Dirichlet Allocation(LDA) as they determine the quality of features that are presented as features for classifiers like SVM. In this work we propose a measure to identify the correct number of topics and offer empirical evidence in its favor in terms of classification accuracy and the number of topics that are naturally present in the corpus. We show the merit of the measure by applying it on real-world as well as synthetic data sets(both text and images). In proposing this measure, we view LDA as a matrix factorization mechanism, wherein a given corpus C is split into two matrix factors M-1 and M-2 as given by C-d*w = M1(d*t) x Q(t*w).Where d is the number of documents present in the corpus anti w is the size of the vocabulary. The quality of the split depends on ``t'', the right number of topics chosen. The measure is computed in terms of symmetric KL-Divergence of salient distributions that are derived from these matrix factors. We observe that the divergence values are higher for non-optimal number of topics - this is shown by a `dip' at the right value for `t'.

Design of speaker identification schemes for large number of speakers (A)

Design of speaker identification schemes for a small number of speakers (around 10) with a high degree of accuracy in controlled environment is a practical proposition today. When the number of speakers is large (say 50–100), many of these schemes cannot be directly extended, as both recognition error and computation time increase monotonically with population size. The feature selection problem is also complex for such schemes. Though there were earlier attempts to rank order features based on statistical distance measures, it has been observed only recently that the best two independent measurements are not the same as the combination in two's for pattern classification. We propose here a systematic approach to the problem using the decision tree or hierarchical classifier with the following objectives: (1) Design of optimal policy at each node of the tree given the tree structure i.e., the tree skeleton and the features to be used at each node. (2) Determination of the optimal feature measurement and decision policy given only the tree skeleton. Applicability of optimization procedures such as dynamic programming in the design of such trees is studied. The experimental results deal with the design of a 50 speaker identification scheme based on this approach.

Low reynolds number flow of a dilute suspension in slowly varying tubes

We have discussed here the flow of a dilute suspension of rigid particles in Newtonian fluid in slowly varying tubes characterized by a small parameter ε. Solutions are presented in the form of asymptotic expansions in powers of ε. The effect of the suspension on the fluid is described by two parameters β and γ which depend on the volume fraction of the particles which we assume to be small. It is found that the presence of the particles accelerate the process of eddy formation near the constriction and shifts the point of separation.

Cubicity of Interval Graphs and the Claw Number

Let G(V, E) be a simple, undirected graph where V is the set of vertices and E is the set of edges. A b-dimensional cube is a Cartesian product l(1) x l(2) x ... x l(b), where each l(i) is a closed interval of unit length on the real line. The cub/city of G, denoted by cub(G), is the minimum positive integer b such that the vertices in G can be mapped to axis parallel b-dimensional cubes in such a way that two vertices are adjacent in G if and only if their assigned cubes intersect. An interval graph is a graph that can be represented as the intersection of intervals on the real line-i.e. the vertices of an interval graph can be mapped to intervals on the real line such that two vertices are adjacent if and only if their corresponding intervals overlap. Suppose S(m) denotes a star graph on m+1 nodes. We define claw number psi(G) of the graph to be the largest positive integer m such that S(m) is an induced subgraph of G. It can be easily shown that the cubicity of any graph is at least log(2) psi(G)]. In this article, we show that for an interval graph G log(2) psi(G)-]<= cub(G)<=log(2) psi(G)]+2. It is not clear whether the upper bound of log(2) psi(G)]+2 is tight: till now we are unable to find any interval graph with cub(G)> (log(2)psi(G)]. We also show that for an interval graph G, cub(G) <= log(2) alpha], where alpha is the independence number of G. Therefore, in the special case of psi(G)=alpha, cub(G) is exactly log(2) alpha(2)]. The concept of cubicity can be generalized by considering boxes instead of cubes. A b-dimensional box is a Cartesian product l(1) x l(2) x ... x l(b), where each I is a closed interval on the real line. The boxicity of a graph, denoted box(G), is the minimum k such that G is the intersection graph of k-dimensional boxes. It is clear that box(G)<= cub(G). From the above result, it follows that for any graph G, cub(G) <= box(G)log(2) alpha]. (C) 2010 Wiley Periodicals, Inc. J Graph Theory 65: 323-333, 2010

On numerical implementation of an isotropic elastic-viscoplastic constitutive model for bulk metallic glasses

An efficient algorithm within the finite deformation framework is developed for finite element implementation of a recently proposed isotropic, Mohr-Coulomb type material model, which captures the elastic-viscoplastic, pressure sensitive and plastically dilatant response of bulk metallic glasses. The constitutive equations are first reformulated and implemented using an implicit numerical integration procedure based on the backward Euler method. The resulting system of nonlinear algebraic equations is solved by the Newton-Raphson procedure. This is achieved by developing the principal space return mapping technique for the present model which involves simultaneous shearing and dilatation on multiple potential slip systems. The complete stress update algorithm is presented and the expressions for viscoplastic consistent tangent moduli are derived. The stress update scheme and the viscoplastic consistent tangent are implemented in the commercial finite element code ABAQUS/Standard. The accuracy and performance of the numerical implementation are verified by considering several benchmark examples, which includes a simulation of multiple shear bands in a 3D prismatic bar under uniaxial compression.

Some new results regarding spikes and a heuristic for spike construction

his paper addresses the problem of minimizing the number of columns with superdiagonal nonzeroes (viz., spiked columns) in a square, nonsingular linear system of equations which is to be solved by Gaussian elimination. The exact focus is on a class of min-spike heuristics in which the rows and columns of the coefficient matrix are first permuted to block lower-triangular form. Subsequently, the number of spiked columns in each irreducible block and their heights above the diagonal are minimized heuristically. We show that ifevery column in an irreducible block has exactly two nonzeroes, i.e., is a doubleton, then there is exactly one spiked column. Further, if there is at least one non-doubleton column, there isalways an optimal permutation of rows and columns under whichnone of the doubleton columns are spiked. An analysis of a few benchmark linear programs suggests that singleton and doubleton columns can abound in practice. Hence, it appears that the results of this paper can be practically useful. In the rest of the paper, we develop a polynomial-time min-spike heuristic based on the above results and on a graph-theoretic interpretation of doubleton columns.

Squeezed states, photon-number distributions, and U(l) invariance

We study the photon-number distribution in squeezed states of a single-mode radiation field. A U(l)-invariant squeezing criterion is compared and contrasted with a more restrictive criterion, with the help of suggestive geometric representations. The U(l) invariance of the photon-number distribution in a squeezed coherent state, with arbitrary complex squeeze and displacement parameters, is explicitly demonstrated. The behavior of the photon-number distribution for a representative value of the displacement and various values of the squeeze parameter is numerically investigated. A new kind of giant oscillation riding as an envelope over more rapid oscillations in this distribution is demonstrated.

Improved mechanical properties of polymer nanocomposites incorporating graphene-like BN: Dependence on the number of BN layers

The mechanical properties of composites of polymethylmethacrylate (PMMA) with two-dimensional graphene-like boron nitride (BN) have been investigated to explore the dependence of the properties on the number of BN layers. This study demonstrates that significantly improved mechanical properties are exhibited by the composite with the fewest number of BN layers. Thus, with incorporation of three BN layers, the hardness and elastic modulus of the composite showed an increase of 125% and 130%, respectively, relative to pure PMMA. (C) 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Flat connections, geometric invariants and the symplectic nature of the fundamental group of surfaces

In this paper we associate a new geometric invariant to the space of fiat connections on a G (= SU(2))-bundle on a compact Riemann surface M and relate it tcr the symplectic structure on the space Hom(pi(1)(M), G)/G consisting of representations of the fundamental group pi(1)(M) Of M into G module the conjugate action of G on representations.

Five-level inverter scheme for an open-end winding induction machine with less number of switches

Higher level of inversion is achieved with a less number of switches in the proposed scheme. The scheme proposes a five-level inverter for an open-end winding induction motor which uses only two DC-link rectifiers of voltage rating of Vdc/4, a neutral-point clamped (NPC) three-level inverter and a two-level inverter. Even though the two-level inverter is connected to the high-voltage side, it is always in square-wave operation. Since the two-level inverter is not switching in a pulse width modulated fashion and the magnitude of switching transient is only half compared to the convention three-level NPC inverter, the switching losses and electromagnetic interference is not so high. The scheme is experimentally verified on a 2.5 kW induction machine.

PVU and wave-particle splitting schemes for Euler equations of gas dynamics

A new way of flux-splitting, termed as the wave-particle splitting is presented for developing upwind methods for solving Euler equations of gas dynamics. Based on this splitting, two new upwind methods termed as Acoustic Flux Vector Splitting (AFVS) and Acoustic Flux Difference Splitting (AFDS) methods are developed. A new Boltzmann scheme, which closely resembles the wave-particle splitting, is developed using the kinetic theory of gases. This method, termed as Peculiar Velocity based Upwind (PVU) method, uses the concept of peculiar velocity for upwinding. A special feature of all these methods that the unidirectional and multidirectional parts of the flux vector are treated separately. Extensive computations done using these schemes demonstrate the soundness of the ideas.

Squeezed states, metaplectic group, and operator möbius transformations

We present an analysis, based on the metaplectic group Mp(2), of the recently introduced single-mode inverse creation and annihilation operators and of the associated eigenstates of different two-photon annihilation operators. We motivate and obtain a quantum operator form of the classical Mobius or fractional linear transformation. The subtle relation to the two unitary irreducible representations of Mp(2) is brought out. For problems involving inverse operators the usefulness of the Bargmann analytic function representation of quantum mechanics is demonstrated. Squeezing, bunching, and photon-number distributions of the four families of states that arise in this context are studied both analytically and numerically