Parameterized Algorithms for MAX COLORABLE INDUCED SUBGRAPH Problem on Perfect Graphs

We address the parameterized complexity ofMaxColorable Induced Subgraph on perfect graphs. The problem asks for a maximum sized q-colorable induced subgraph of an input graph G. Yannakakis and Gavril IPL 1987] showed that this problem is NP-complete even on split graphs if q is part of input, but gave a n(O(q)) algorithm on chordal graphs. We first observe that the problem is W2]-hard parameterized by q, even on split graphs. However, when parameterized by l, the number of vertices in the solution, we give two fixed-parameter tractable algorithms. The first algorithm runs in time 5.44(l) (n+#alpha(G))(O(1)) where #alpha(G) is the number of maximal independent sets of the input graph. The second algorithm runs in time q(l+o()l())n(O(1))T(alpha) where T-alpha is the time required to find a maximum independent set in any induced subgraph of G. The first algorithm is efficient when the input graph contains only polynomially many maximal independent sets; for example split graphs and co-chordal graphs. The running time of the second algorithm is FPT in l alone (whenever T-alpha is a polynomial in n), since q <= l for all non-trivial situations. Finally, we show that (under standard complexitytheoretic assumptions) the problem does not admit a polynomial kernel on split and perfect graphs in the following sense: (a) On split graphs, we do not expect a polynomial kernel if q is a part of the input. (b) On perfect graphs, we do not expect a polynomial kernel even for fixed values of q >= 2.

Ecology of acoustic signalling and the problem of masking interference in insects

The efficiency of long-distance acoustic signalling of insects in their natural habitat is constrained in several ways. Acoustic signals are not only subjected to changes imposed by the physical structure of the habitat such as attenuation and degradation but also to masking interference from co-occurring signals of other acoustically communicating species. Masking interference is likely to be a ubiquitous problem in multi-species assemblages, but successful communication in natural environments under noisy conditions suggests powerful strategies to deal with the detection and recognition of relevant signals. In this review we present recent work on the role of the habitat as a driving force in shaping insect signal structures. In the context of acoustic masking interference, we discuss the ecological niche concept and examine the role of acoustic resource partitioning in the temporal, spatial and spectral domains as sender strategies to counter masking. We then examine the efficacy of different receiver strategies: physiological mechanisms such as frequency tuning, spatial release from masking and gain control as useful strategies to counteract acoustic masking. We also review recent work on the effects of anthropogenic noise on insect acoustic communication and the importance of insect sounds as indicators of biodiversity and ecosystem health.

Optimality Conditions and Duality for Semi-Infinite Mathematical Programming Problem with Equilibrium Constraints

This article considers a semi-infinite mathematical programming problem with equilibrium constraints (SIMPEC) defined as a semi-infinite mathematical programming problem with complementarity constraints. We establish necessary and sufficient optimality conditions for the (SIMPEC). We also formulate Wolfe- and Mond-Weir-type dual models for (SIMPEC) and establish weak, strong and strict converse duality theorems for (SIMPEC) and the corresponding dual problems under invexity assumptions.

COMPUTATIONAL MODELING OF A MULTI-LAYERED PIEZO-COMPOSITE BEAM MADE UP OF MFC

The Variational Asymptotic Method (VAM) is used for modeling a coupled non-linear electromechanical problem finding applications in aircrafts and Micro Aerial Vehicle (MAV) development. VAM coupled with geometrically exact kinematics forms a powerful tool for analyzing a complex nonlinear phenomena as shown previously by many in the literature 3 - 7] for various challenging problems like modeling of an initially twisted helicopter rotor blades, matrix crack propagation in a composite, modeling of hyper elastic plates and various multi-physics problems. The problem consists of design and analysis of a piezocomposite laminate applied with electrical voltage(s) which can induce direct and planar distributed shear stresses and strains in the structure. The deformations are large and conventional beam theories are inappropriate for the analysis. The behavior of an elastic body is completely understood by its energy. This energy must be integrated over the cross-sectional area to obtain the 1-D behavior as is typical in a beam analysis. VAM can be used efficiently to approximate 3-D strain energy as closely as possible. To perform this simplification, VAM makes use of thickness to width, width to length, width multiplied by initial twist and strain as small parameters embedded in the problem definition and provides a way to approach the exact solution asymptotically. In this work, above mentioned electromechanical problem is modeled using VAM which breaks down the 3-D elasticity problem into two parts, namely a 2-D non-linear cross-sectional analysis and a 1-D non-linear analysis, along the reference curve. The recovery relations obtained as a by-product in the cross-sectional analysis earlier are used to obtain 3-D stresses, displacements and velocity contours. The piezo-composite laminate which is chosen for an initial phase of computational modeling is made up of commercially available Macro Fiber Composites (MFCs) stacked together in an arbitrary lay-up and applied with electrical voltages for actuation. The expressions of sectional forces and moments as obtained from cross-sectional analysis in closed-form show the electro-mechanical coupling and relative contribution of electric field in individual layers of the piezo-composite laminate. The spatial and temporal constitutive law as obtained from the cross-sectional analysis are substituted into 1-D fully intrinsic, geometrically exact equilibrium equations of motion and 1-D intrinsic kinematical equations to solve for all 1-D generalized variables as function of time and an along the reference curve co-ordinate, x(1).

A Reliable Residual Based A Posteriori Error Estimator for a Quadratic Finite Element Method for the Elliptic Obstacle Problem

A residual based a posteriori error estimator is derived for a quadratic finite element method (FEM) for the elliptic obstacle problem. The error estimator involves various residuals consisting of the data of the problem, discrete solution and a Lagrange multiplier related to the obstacle constraint. The choice of the discrete Lagrange multiplier yields an error estimator that is comparable with the error estimator in the case of linear FEM. Further, an a priori error estimate is derived to show that the discrete Lagrange multiplier converges at the same rate as that of the discrete solution of the obstacle problem. The numerical experiments of adaptive FEM show optimal order convergence. This demonstrates that the quadratic FEM for obstacle problem exhibits optimal performance.

A Remark on the A Posteriori Error Analysis of Discontinuous Galerkin Methods for the Obstacle Problem

We revisit the a posteriori error analysis of discontinuous Galerkin methods for the obstacle problem derived in 25]. Under a mild assumption on the trace of obstacle, we derive a reliable a posteriori error estimator which does not involve min/max functions. A key in this approach is an auxiliary problem with discrete obstacle. Applications to various discontinuous Galerkin finite element methods are presented. Numerical experiments show that the new estimator obtained in this article performs better.

Two player game variant of the Erdos-Szekeres problem

The classical Erdos-Szekeres theorem states that a convex k-gon exists in every sufficiently large point set. This problem has been well studied and finding tight asymptotic bounds is considered a challenging open problem. Several variants of the Erdos-Szekeres problem have been posed and studied in the last two decades. The well studied variants include the empty convex k-gon problem, convex k-gon with specified number of interior points and the chromatic variant. In this paper, we introduce the following two player game variant of the Erdos-Szekeres problem: Consider a two player game where each player playing in alternate turns, place points in the plane. The objective of the game is to avoid the formation of the convex k-gon among the placed points. The game ends when a convex k-gon is formed and the player who placed the last point loses the game. In our paper we show a winning strategy for the player who plays second in the convex 5-gon game and the empty convex 5-gon game by considering convex layer configurations at each step. We prove that the game always ends in the 9th step by showing that the game reaches a specific set of configurations.

A Variant of the Hadwiger-Debrunner (p, q)-Problem in the Plane

Let X be a convex curve in the plane (say, the unit circle), and let be a family of planar convex bodies such that every two of them meet at a point of X. Then has a transversal of size at most . Suppose instead that only satisfies the following ``(p, 2)-condition'': Among every p elements of , there are two that meet at a common point of X. Then has a transversal of size . For comparison, the best known bound for the Hadwiger-Debrunner (p, q)-problem in the plane, with , is . Our result generalizes appropriately for if is, for example, the moment curve.

A posteriori error estimates of discontinuous Galerkin methods for the Signorini problem

A reliable and efficient a posteriori error estimator is derived for a class of discontinuous Galerkin (DG) methods for the Signorini problem. A common property shared by many DG methods leads to a unified error analysis with the help of a constraint preserving enriching map. The error estimator of DG methods is comparable with the error estimator of the conforming methods. Numerical experiments illustrate the performance of the error estimator. (C) 2015 Elsevier B.V. All rights reserved.