Rainbow connection number and connected dominating sets

The rainbow connection number of a connected graph is the minimum number of colors needed to color its edges, so that every pair of its vertices is connected by at least one path in which no two edges are colored the same. In this article we show that for every connected graph on n vertices with minimum degree delta, the rainbow connection number is upper bounded by 3n/(delta + 1) + 3. This solves an open problem from Schiermeyer (Combinatorial Algorithms, Springer, Berlin/Hiedelberg, 2009, pp. 432437), improving the previously best known bound of 20n/delta (J Graph Theory 63 (2010), 185191). This bound is tight up to additive factors by a construction mentioned in Caro et al. (Electr J Combin 15(R57) (2008), 1). As an intermediate step we obtain an upper bound of 3n/(delta + 1) - 2 on the size of a connected two-step dominating set in a connected graph of order n and minimum degree d. This bound is tight up to an additive constant of 2. This result may be of independent interest. We also show that for every connected graph G with minimum degree at least 2, the rainbow connection number, rc(G), is upper bounded by Gc(G) + 2, where Gc(G) is the connected domination number of G. Bounds of the form diameter(G)?rc(G)?diameter(G) + c, 1?c?4, for many special graph classes follow as easy corollaries from this result. This includes interval graphs, asteroidal triple-free graphs, circular arc graphs, threshold graphs, and chain graphs all with minimum degree delta at least 2 and connected. We also show that every bridge-less chordal graph G has rc(G)?3.radius(G). In most of these cases, we also demonstrate the tightness of the bounds.

Two-User Gaussian Interference Channel with Finite Constellation Input and FDMA

In the two-user Gaussian Strong Interference Channel (GSIC) with finite constellation inputs, it is known that relative rotation between the constellations of the two users enlarges the Constellation Constrained (CC) capacity region. In this paper, a metric for finding the approximate angle of rotation to maximally enlarge the CC capacity is presented. It is shown that for some portion of the Strong Interference (SI) regime, with Gaussian input alphabets, the FDMA rate curve touches the capacity curve of the GSIC. Even as the Gaussian alphabet FDMA rate curve touches the capacity curve of the GSIC, at high powers, with both the users using the same finite constellation, we show that the CC FDMA rate curve lies strictly inside the CC capacity curve for the constellations BPSK, QPSK, 8-PSK, 16-QAM and 64-QAM. It is known that, with Gaussian input alphabets, the FDMA inner-bound at the optimum sum-rate point is always better than the simultaneous-decoding inner-bound throughout the Weak Interference (WI) regime. For a portion of the WI regime, it is shown that, with identical finite constellation inputs for both the users, the simultaneous-decoding inner-bound enlarged by relative rotation between the constellations can be strictly better than the FDMA inner-bound.

Maximum weight independent sets in hole- and dart-free graphs

The Maximum Weight Independent Set (MWIS) problem on graphs with vertex weights asks for a set of pairwise nonadjacent vertices of maximum total weight. The complexity of the MWIS problem for hole-free graphs is unknown. In this paper, we first prove that the MWIS problem for (hole, dart, gem)-free graphs can be solved in O(n(3))-time. By using this result, we prove that the MWIS problem for (hole, dart)-free graphs can be solved in O(n(4))-time. Though the MWIS problem for (hole, dart, gem)-free graphs is used as a subroutine, we also give the best known time bound for the solvability of the MWIS problem in (hole, dart, gem)-free graphs. (C) 2012 Elsevier B.V. All rights reserved.

A finite population model of mlecular evolution: theory and computation

This article is concerned with the evolution of haploid organisms that reproduce asexually. In a seminal piece of work, Eigen and coauthors proposed the quasispecies model in an attempt to understand such an evolutionary process. Their work has impacted antiviral treatment and vaccine design strategies. Yet, predictions of the quasispecies model are at best viewed as a guideline, primarily because it assumes an infinite population size, whereas realistic population sizes can be quite small. In this paper we consider a population genetics-based model aimed at understanding the evolution of such organisms with finite population sizes and present a rigorous study of the convergence and computational issues that arise therein. Our first result is structural and shows that, at any time during the evolution, as the population size tends to infinity, the distribution of genomes predicted by our model converges to that predicted by the quasispecies model. This justifies the continued use of the quasispecies model to derive guidelines for intervention. While the stationary state in the quasispecies model is readily obtained, due to the explosion of the state space in our model, exact computations are prohibitive. Our second set of results are computational in nature and address this issue. We derive conditions on the parameters of evolution under which our stochastic model mixes rapidly. Further, for a class of widely used fitness landscapes we give a fast deterministic algorithm which computes the stationary distribution of our model. These computational tools are expected to serve as a framework for the modeling of strategies for the deployment of mutagenic drugs.

Fracture Analysis of High strength and Ultra high strength Concrete beams by using Finite Element Method

This paper presents the details of nonlinear finite element analysis (FEA) of three point bending specimens made up of high strength concrete (HSC, HSC1) and ultra high strength concrete (UHSC). Brief details about characterization and experimentation of HSC, HSC1 and UHSC have been provided. Cracking strength criterion has been used for simulation of crack propagation by conducting nonlinear FEA. The description about FEA using crack strength criterion has been outlined. Bi-linear tension softening relation has been used for modeling the cohesive stresses ahead of the crack tip. Numerical studies have been carried out on fracture analysis of three point bending specimens. It is observed from the studies that the computed values from FEA are in very good agreement with the corresponding experimental values. The computed values of stress vs crack width will be useful for evaluation of fracture energy, crack tip opening displacement and fracture toughness. Further, these values can also be used for crack growth study, remaining life assessment and residual strength evaluation of concrete structural components.

Non-Stationary Semi-Markov Decision Processes on a Finite Horizon

We introduce and study a class of non-stationary semi-Markov decision processes on a finite horizon. By constructing an equivalent Markov decision process, we establish the existence of a piecewise open loop relaxed control which is optimal for the finite horizon problem.

Distributed Space Time Coding for Wireless Two-Way Relaying

We consider the wireless two-way relay channel, in which two-way data transfer takes place between the end nodes with the help of a relay. For the Denoise-And-Forward (DNF) protocol, it was shown by Koike-Akino et al. that adaptively changing the network coding map used at the relay greatly reduces the impact of Multiple Access Interference at the relay. The harmful effect of the deep channel fade conditions can be effectively mitigated by proper choice of these network coding maps at the relay. Alternatively, in this paper we propose a Distributed Space Time Coding (DSTC) scheme, which effectively removes most of the deep fade channel conditions at the transmitting nodes itself without any CSIT and without any need to adaptively change the network coding map used at the relay. It is shown that the deep fades occur when the channel fade coefficient vector falls in a finite number of vector subspaces of, which are referred to as the singular fade subspaces. DSTC design criterion referred to as the singularity minimization criterion under which the number of such vector subspaces are minimized is obtained. Also, a criterion to maximize the coding gain of the DSTC is obtained. Explicit low decoding complexity DSTC designs which satisfy the singularity minimization criterion and maximize the coding gain for QAM and PSK signal sets are provided. Simulation results show that at high Signal to Noise Ratio, the DSTC scheme provides large gains when compared to the conventional Exclusive OR network code and performs better than the adaptive network coding scheme.

Operator-splitting finite element algorithms for computations of high-dimensional parabolic problems

An operator-splitting finite element method for solving high-dimensional parabolic equations is presented. The stability and the error estimates are derived for the proposed numerical scheme. Furthermore, two variants of fully-practical operator-splitting finite element algorithms based on the quadrature points and the nodal points, respectively, are presented. Both the quadrature and the nodal point based operator-splitting algorithms are validated using a three-dimensional (3D) test problem. The numerical results obtained with the full 3D computations and the operator-split 2D + 1D computations are found to be in a good agreement with the analytical solution. Further, the optimal order of convergence is obtained in both variants of the operator-splitting algorithms. (C) 2012 Elsevier Inc. All rights reserved.

Further results on geometric properties of a family of relative entropies

This paper extends some geometric properties of a one-parameter family of relative entropies. These arise as redundancies when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the Kullback-Leibler divergence. They satisfy the Pythagorean property and behave like squared distances. This property, which was known for finite alphabet spaces, is now extended for general measure spaces. Existence of projections onto convex and certain closed sets is also established. Our results may have applications in the Rényi entropy maximization rule of statistical physics.

On the capacity of quantized gaussian MAC channels with finite input alphabet

In this paper, we investigate the achievable rate region of Gaussian multiple access channels (MAC) with finite input alphabet and quantized output. With finite input alphabet and an unquantized receiver, the two-user Gaussian MAC rate region was studied. In most high throughput communication systems based on digital signal processing, the analog received signal is quantized using a low precision quantizer. In this paper, we first derive the expressions for the achievable rate region of a two-user Gaussian MAC with finite input alphabet and quantized output. We show that, with finite input alphabet, the achievable rate region with the commonly used uniform receiver quantizer has a significant loss in the rate region compared. It is observed that this degradation is due to the fact that the received analog signal is densely distributed around the origin, and is therefore not efficiently quantized with a uniform quantizer which has equally spaced quantization intervals. It is also observed that the density of the received analog signal around the origin increases with increasing number of users. Hence, the loss in the achievable rate region due to uniform receiver quantization is expected to increase with increasing number of users. We, therefore, propose a novel non-uniform quantizer with finely spaced quantization intervals near the origin. For a two-user Gaussian MAC with a given finite input alphabet and low precision receiver quantization, we show that the proposed non-uniform quantizer has a significantly larger rate region compared to what is achieved with a uniform quantizer.

A finite-rate-of-innovation signal sampling perspective of the source-filter model of speech production

We consider the speech production mechanism and the asso- ciated linear source-filter model. For voiced speech sounds in particular, the source/glottal excitation is modeled as a stream of impulses and the filter as a cascade of second-order resonators. We show that the process of sampling speech signals can be modeled as filtering a stream of Dirac impulses (a model for the excitation) with a kernel function (the vocal tract response),and then sampling uniformly. We show that the problem of esti- mating the excitation is equivalent to the problem of recovering a stream of Dirac impulses from samples of a filtered version. We present associated algorithms based on the annihilating filter and also make a comparison with the classical linear prediction technique, which is well known in speech analysis. Results on synthesized as well as natural speech data are presented.

A Novel Power Allocation Scheme for Two-User GMAC with Finite Input Constellations

Constellation Constrained (CC) capacity regions of two-user Gaussian Multiple Access Channels (GMAC) have been recently reported, wherein an appropriate angle of rotation between the constellations of the two users is shown to enlarge the CC capacity region. We refer to such a scheme as the Constellation Rotation (CR) scheme. In this paper, we propose a novel scheme called the Constellation Power Allocation (CPA) scheme, wherein the instantaneous transmit power of the two users are varied by maintaining their average power constraints. We show that the CPA scheme offers CC sum capacities equal (at low SNR values) or close (at high SNR values) to those offered by the CR scheme with reduced decoding complexity for QAM constellations. We study the robustness of the CPA scheme for random phase offsets in the channel and unequal average power constraints for the two users. With random phase offsets in the channel, we show that the CC sum capacity offered by the CPA scheme is more than the CR scheme at high SNR values. With unequal average power constraints, we show that the CPA scheme provides maximum gain when the power levels are close, and the advantage diminishes with the increase in the power difference.

A Finite Element Method Based Approach for Evaluating the Sensitivity of Faraday-Type Electromagnetic Flow Meter for Liquid Sodium Flow

Faraday-type electromagnetic flow meters are employed for measuring the flow rate of liquid sodium in fast breeder reactors. The calibration of such flow meters, owing to the required elaborative arrangements is rather difficult. On the other hand, theoretical approach requires solution of two coupled electromagnetic partial differential equation with profile of the flow and applied magnetic field as the inputs. This is also quite involved due to the 3D nature of the problem. Alternatively, Galerkin finite element method based numerical solution is suggested in the literature as an attractive option for the required calibration. Based on the same, a computer code in Matlab platform has been developed in this work with both 20 and 27 node brick elements. The boundary conditions are correctly defined and several intermediate validation exercises are carried out. Finally it is shown that the sensitivities predicted by the code for flow meters of four different dimensions agrees well with the results given by analytical expression, thereby providing strong validation. Sensitivity for higher flow rates, for which analytical approach does not exist, is shown to decrease with increase in flow velocity.

Bearing capacity of two interfering strip footings from lower bound finite elements limit analysis

A rigorous lower bound solution, with the usage of the finite elements limit analysis, has been obtained for finding the ultimate bearing capacity of two interfering strip footings placed on a sandy medium. Smooth as well as rough footingsoil interfaces are considered in the analysis. The failure load for an interfering footing becomes always greater than that for a single isolated footing. The effect of the interference on the failure load (i) for rough footings becomes greater than that for smooth footings, (ii) increases with an increase in phi, and (iii) becomes almost negligible beyond S/B>3. Compared with various theoretical and experimental results reported in literature, the present analysis generally provides the lowest magnitude of the collapse load. Copyright (c) 2011 John Wiley & Sons, Ltd.

An Outward-Wave-Favouring Finite Element-Based Strategy for Exterior Acoustical Problems

This work presents a finite element-based strategy for exterior acoustical problems based on an assumed pressure form that favours outgoing waves. The resulting governing equation, weak formulation, and finite element formulation are developed both for coupled and uncoupled problems. The developed elements are very similar to conventional elements in that they are based on the standard Galerkin variational formulation and use standard Lagrange interpolation functions and standard Gaussian quadrature. In addition and in contrast to wave envelope formulations and their extensions, the developed elements can be used in the immediate vicinity of the radiator/scatterer. The method is similar to the perfectly matched layer (PML) method in the sense that each layer of elements added around the radiator absorbs acoustical waves so that no boundary condition needs to be applied at the outermost boundary where the domain is truncated. By comparing against strategies such as the PML and wave-envelope methods, we show that the relative accuracy, both in the near and far-field results, is considerably higher.