Efficient algorithms for domination and Hamilton circuit problems on permutation graphs

The domination and Hamilton circuit problems are of interest both in algorithm design and complexity theory. The domination problem has applications in facility location and the Hamilton circuit problem has applications in routing problems in communications and operations research.The problem of deciding if G has a dominating set of cardinality at most k, and the problem of determining if G has a Hamilton circuit are NP-Complete. Polynomial time algorithms are, however, available for a large number of restricted classes. A motivation for the study of these algorithms is that they not only give insight into the characterization of these classes but also require a variety of algorithmic techniques and data structures. So the search for efficient algorithms, for these problems in many classes still continues.A class of perfect graphs which is practically important and mathematically interesting is the class of permutation graphs. The domination problem is polynomial time solvable on permutation graphs. Algorithms that are already available are of time complexity O(n2) or more, and space complexity O(n2) on these graphs. The Hamilton circuit problem is open for this class.We present a simple O(n) time and O(n) space algorithm for the domination problem on permutation graphs. Unlike the existing algorithms, we use the concept of geometric representation of permutation graphs. Further, exploiting this geometric notion, we develop an O(n2) time and O(n) space algorithm for the Hamilton circuit problem.

The complexity of certain incremental code generation problems

This paper looks at the complexity of four different incremental problems. The following are the problems considered: (1) Interval partitioning of a flow graph (2) Breadth first search (BFS) of a directed graph (3) Lexicographic depth first search (DFS) of a directed graph (4) Constructing the postorder listing of the nodes of a binary tree. The last problem arises out of the need for incrementally computing the Sethi-Ullman (SU) ordering [1] of the subtrees of a tree after it has undergone changes of a given type. These problems are among those that claimed our attention in the process of our designing algorithmic techniques for incremental code generation. BFS and DFS have certainly numerous other applications, but as far as our work is concerned, incremental code generation is the common thread linking these problems. The study of the complexity of these problems is done from two different perspectives. In [2] is given the theory of incremental relative lower bounds (IRLB). We use this theory to derive the IRLBs of the first three problems. Then we use the notion of a bounded incremental algorithm [4] to prove the unboundedness of the fourth problem with respect to the locally persistent model of computation. Possibly, the lower bound result for lexicographic DFS is the most interesting. In [5] the author considers lexicographic DFS to be a problem for which the incremental version may require the recomputation of the entire solution from scratch. In that sense, our IRLB result provides further evidence for this possibility with the proviso that the incremental DFS algorithms considered be ones that do not require too much of preprocessing.

No-reference image quality assessment using modified extreme learning machine classifier

In this paper, we present a machine learning approach to measure the visual quality of JPEG-coded images. The features for predicting the perceived image quality are extracted by considering key human visual sensitivity (HVS) factors such as edge amplitude, edge length, background activity and background luminance. Image quality assessment involves estimating the functional relationship between HVS features and subjective test scores. The quality of the compressed images are obtained without referring to their original images ('No Reference' metric). Here, the problem of quality estimation is transformed to a classification problem and solved using extreme learning machine (ELM) algorithm. In ELM, the input weights and the bias values are randomly chosen and the output weights are analytically calculated. The generalization performance of the ELM algorithm for classification problems with imbalance in the number of samples per quality class depends critically on the input weights and the bias values. Hence, we propose two schemes, namely the k-fold selection scheme (KS-ELM) and the real-coded genetic algorithm (RCGA-ELM) to select the input weights and the bias values such that the generalization performance of the classifier is a maximum. Results indicate that the proposed schemes significantly improve the performance of ELM classifier under imbalance condition for image quality assessment. The experimental results prove that the estimated visual quality of the proposed RCGA-ELM emulates the mean opinion score very well. The experimental results are compared with the existing JPEG no-reference image quality metric and full-reference structural similarity image quality metric.

Steam-cured stabilised soil blocks for masonry construction

Energy-efficient, economical and durable building materials are essential for sustainable construction practices. The paper deals with production and properties of energy-efficient steam-cured stabilised soil blocks used fbr masonry construction. Problems of mixing expansive soil and lime, and production of blocks using soil-lime mixtures have been discussed briefly. Details of steam curing of stabilised soil blocks and properties of such blocks are given. A comparison of energy content of steam-cured soil blocks and burnt bricks is presented. It has been shown that energy-efficient steam cured soil blocks (consuming 35% less thermal energy compared to burnt clay bricks) having high compressive strength can be easily produced in a decentralised manner.

A Quasi-Newton Adaptive Algorithm for Generalized Symmetric Eigenvalue Problem

In this paper, we first recast the generalized symmetric eigenvalue problem, where the underlying matrix pencil consists of symmetric positive definite matrices, into an unconstrained minimization problem by constructing an appropriate cost function, We then extend it to the case of multiple eigenvectors using an inflation technique, Based on this asymptotic formulation, we derive a quasi-Newton-based adaptive algorithm for estimating the required generalized eigenvectors in the data case. The resulting algorithm is modular and parallel, and it is globally convergent with probability one, We also analyze the effect of inexact inflation on the convergence of this algorithm and that of inexact knowledge of one of the matrices (in the pencil) on the resulting eigenstructure. Simulation results demonstrate that the performance of this algorithm is almost identical to that of the rank-one updating algorithm of Karasalo. Further, the performance of the proposed algorithm has been found to remain stable even over 1 million updates without suffering from any error accumulation problems.

The effect of surface tension in porous wave maker problems

Using a mixed-type Fourier transform of a general form in the case of water of infinite depth and the method of eigenfunction expansion in the case of water of finite depth, several boundary-value problems involving the propagation and scattering of time harmonic surface water waves by vertical porous walls have been fully investigated, taking into account the effect of surface tension also. Known results are recovered either directly or as particular cases of the general problems under consideration.

Problems with geoengineering schemes to combat climate change

The accelerated rate of increase in atmospheric CO2 concentration in recent years has revived the idea of stabilizing the global climate through geoengineering schemes. Majority of the proposed geoengineering schemes will attempt to reduce the amount of solar radiation absorbed by our planet. Climate modelling studies of these so called 'sunshade geoengineering schemes' show that global warming from increasing concentrations of CO2 can be mitigated by intentionally manipulating the amount of sunlight absorbed by the climate system. These studies also suggest that the residual changes could be large on regional scales, so that climate change may not be mitigated on a local basis. More recent modelling studies have shown that these schemes could lead to a slow-down in the global hydrological cycle. Other problems such as changes in the terrestrial carbon cycle and ocean acidification remain unsolved by sunshade geoengineering schemes. In this article, I review the proposed geoengineering schemes, results from climate models and discuss why geoengineering is not the best option to deal with climate change.

Solution of a System of Generalized Abel Integral Equations Using Fractional Calculus

A method is presented for obtaining useful closed form solution of a system of generalized Abel integral equations by using the ideas of fractional integral operators and their applications. This system appears in solving certain mixed boundary value problems arising in the classical theory of elasticity.

Finite Element Solution Of Surface-Tension Driven Flows In Laser Surface-Melting

Lasers are very efficient in heating localized regions and hence they find a wide application in surface treatment processes. The surface of a material can be selectively modified to give superior wear and corrosion resistance. In laser surface-melting and welding problems, the high temperature gradient prevailing in the free surface induces a surface-tension gradient which is the dominant driving force for convection (known as thermo-capillary or Marangoni convection). It has been reported that the surface-tension driven convection plays a dominant role in determining the melt pool shape. In most of the earlier works on laser-melting and related problems, the finite difference method (FDM) has been used to solve the Navier Stokes equations [1]. Since the Reynolds number is quite high in these cases, upwinding has been used. Though upwinding gives physically realistic solutions even on a coarse grid, the results are inaccurate. McLay and Carey have solved the thermo-capillary flow in welding problems by an implicit finite element method [2]. They used the conventional Galerkin finite element method (FEM) which requires that the pressure be interpolated by one order lower than velocity (mixed interpolation). This restricts the choice of elements to certain higher order elements which need numerical integration for evaluation of element matrices. The implicit algorithm yields a system of nonlinear, unsymmetric equations which are not positive definite. Computations would be possible only with large mainframe computers.Sluzalec [3] has modeled the pulsed laser-melting problem by an explicit method (FEM). He has used the six-node triangular element with mixed interpolation. Since he has considered the buoyancy induced flow only, the velocity values are small. In the present work, an equal order explicit FEM is used to compute the thermo-capillary flow in the laser surface-melting problem. As this method permits equal order interpolation, there is no restriction in the choice of elements. Even linear elements such as the three-node triangular elements can be used. As the governing equations are solved in a sequential manner, the computer memory requirement is less. The finite element formulation is discussed in this paper along with typical numerical results.

Processing and compressive strength of Al-Li-SiCp composites fabricated by a compound billet technique

Al-Li-SiCp composites were fabricated by a simple and cost effective stir casting technique. A compound billet technique has been developed to overcome the problems encountered during hot extrusion of these composites. After successful fabrication hardness measurement and room temperature compressive test were carried out on 8090 Al and its composites reinforced with 8, 12 and 18vol.% SiC particles in as extruded and peak aged conditions. The addition of SiC increases the hardness. 0.2% proof stress and compressive strength of Al-Li-8%SiC and Al-Li-12%SiC composites are higher than the unreinforced alloy. in case of the Al-Li-18%SiC composite, the 0.2% proof stress and compressive strength were higher than the unreinforced alloy but lower than those of Al-Li-8%SiC and Al-Li-12%SiC composites. This is attributed to clustering of particles and poor interfacial bonding.

Maximal regularity for second order non-autonomous Cauchy problems

We consider some non-autonomous second order Cauchy problems of the form u + B(t)(u) over dot + A(t)u = f (t is an element of [0, T]), u(0) = (u) over dot(0) = 0. We assume that the first order problem (u) over dot + B(t)u = f (t is an element of [0, T]), u(0) = 0, has L-p-maximal regularity. Then we establish L-p-maximal regularity of the second order problem in situations when the domains of B(t(1)) and A(t(2)) always coincide, or when A(t) = kappa B(t).

In search of inorganic nonlinear optical materials for second harmonic generation

In a search for inorganic oxide materials showing second-order nonlinear optical (NLO) susceptibility, we investigated several berates, silicates, and a phosphate containing trans-connected MO6, octahedral chains or MO5 square pyramids, where, M = d(0): Ti(IV), Nb(V), or Ta(V), Our investigations identified two new NLO structures: batisite, Na2Ba(TiO)(2)Si4O12, containing trans-connected TiO5 octahedral chains, and fresnoite, Ba2TiOSi2O7, containing square-pyramidal TiO5. Investigation of two other materials containing square-pyramidal TiO5 viz,, Cs2TiOP2O7 and Na4Ti2Si8O22. 4H(2)O, revealed that isolated TiO5, square pyramids alone do not cause a second harmonic generation (SHG) response; rather, the orientation of TiO5 units to produce -Ti-O-Ti-O- chains with alternating long and short Ti-O distances in the fresnoite structure is most likely the origin of a strong SHG response in fresnoite,

Lopsided spiral galaxies

The light distribution in the disks of many galaxies is ‘lopsided’ with a spatial extent much larger along one half of a galaxy than the other, as seen in M101. Recent observations show that the stellar disk in a typical spiral galaxy is significantly lopsided, indicating asymmetry in the disk mass distribution. The mean amplitude of lopsidedness is 0.1, measured as the Fourier amplitude of the m=1 component normalized to the average value. Thus, lopsidedness is common, and hence it is important to understand its origin and dynamics. This is a new and exciting area in galactic structure and dynamics, in contrast to the topic of bars and two-armed spirals (m=2) which has been extensively studied in the literature. Lopsidedness is ubiquitous and occurs in a variety of settings and tracers. It is seen in both stars and gas, in the outer disk and the central region, in the field and the group galaxies. The lopsided amplitude is higher by a factor of two for galaxies in a group. The lopsidedness has a strong impact on the dynamics of the galaxy, its evolution, the star formation in it, and on the growth of the central black hole and on the nuclear fuelling. We present here an overview of the observations that measure the lopsided distribution, as well as the theoretical progress made so far to understand its origin and properties. The physical mechanisms studied for its origin include tidal encounters, gas accretion and a global gravitational instability. The related open, challenging problems in this emerging area are discussed.

On the cubicity of bipartite graphs

A unit cube in k-dimension (or a k-cube) is defined as the Cartesian product R-1 x R-2 x ... x R-k, where each R-i is a closed interval on the real line of the form [a(j), a(i), + 1]. The cubicity of G, denoted as cub(G), is the minimum k such that G is the intersection graph of a collection of k-cubes. Many NP-complete graph problems can be solved efficiently or have good approximation ratios in graphs of low cubicity. In most of these cases the first step is to get a low dimensional cube representation of the given graph. It is known that for graph G, cub(G) <= left perpendicular2n/3right perpendicular. Recently it has been shown that for a graph G, cub(G) >= 4(Delta + 1) In n, where n and Delta are the number of vertices and maximum degree of G, respectively. In this paper, we show that for a bipartite graph G = (A boolean OR B, E) with |A| = n(1), |B| = n2, n(1) <= n(2), and Delta' = min {Delta(A),Delta(B)}, where Delta(A) = max(a is an element of A)d(a) and Delta(B) = max(b is an element of B) d(b), d(a) and d(b) being the degree of a and b in G, respectively , cub(G) <= 2(Delta' + 2) bar left rightln n(2)bar left arrow. We also give an efficient randomized algorithm to construct the cube representation of G in 3 (Delta' + 2) bar right arrowIn n(2)bar left arrow dimension. The reader may note that in general Delta' can be much smaller than Delta.

A pseudo-dynamical systems approach to a class of inverse problems in engineering

A pseudo-dynamical approach for a class of inverse problems involving static measurements is proposed and explored. Following linearization of the minimizing functional associated with the underlying optimization problem, the new strategy results in a system of linearized ordinary differential equations (ODEs) whose steady-state solutions yield the desired reconstruction. We consider some explicit and implicit schemes for integrating the ODEs and thus establish a deterministic reconstruction strategy without an explicit use of regularization. A stochastic reconstruction strategy is then developed making use of an ensemble Kalman filter wherein these ODEs serve as the measurement model. Finally, we assess the numerical efficacy of the developed tools against a few linear and nonlinear inverse problems of engineering interest.