Density matrix renormalization group algorithm for Bethe lattices of spin-1/2 or spin-1 sites with Heisenberg antiferromagnetic exchange

A density matrix renormalization group (DMRG) algorithm is presented for the Bethe lattice with connectivity Z = 3 and antiferromagnetic exchange between nearest-neighbor spins s = 1/2 or 1 sites in successive generations g. The algorithm is accurate for s = 1 sites. The ground states are magnetic with spin S(g) = 2(g)s, staggered magnetization that persists for large g > 20, and short-range spin correlation functions that decrease exponentially. A finite energy gap to S > S(g) leads to a magnetization plateau in the extended lattice. Closely similar DMRG results for s = 1/2 and 1 are interpreted in terms of an analytical three-site model.

Construction of Equivalent Circuit of a Single and Isolated Transformer Winding From FRA Data Using the ABC Algorithm

This paper reports the results of employing an artificial bee colony search algorithm for synthesizing a mutually coupled lumped-parameter ladder-network representation of a transformer winding, starting from its measured magnitude frequency response. The existing bee colony algorithm is suitably adopted by appropriately defining constraints, inequalities, and bounds to restrict the search space and thereby ensure synthesis of a nearly unique ladder network corresponding to each frequency response. Ensuring near-uniqueness while constructing the reference circuit (i.e., representation of healthy winding) is the objective. Furthermore, the synthesized circuits must exhibit physical realizability. The proposed method is easy to implement, time efficient, and problems associated with the supply of initial guess in existing methods are circumvented. Experimental results are reported on two types of actual, single, and isolated transformer windings (continuous disc and interleaved disc).

Incremental Cycle Detection, Topological Ordering, and Strong Component Maintenance

We present two online algorithms for maintaining a topological order of a directed n-vertex acyclic graph as arcs are added, and detecting a cycle when one is created. Our first algorithm handles m arc additions in O(m(3/2)) time. For sparse graphs (m/n = O(1)), this bound improves the best previous bound by a logarithmic factor, and is tight to within a constant factor among algorithms satisfying a natural locality property. Our second algorithm handles an arbitrary sequence of arc additions in O(n(5/2)) time. For sufficiently dense graphs, this bound improves the best previous bound by a polynomial factor. Our bound may be far from tight: we show that the algorithm can take Omega(n(2)2 root(2lgn)) time by relating its performance to a generalization of the k-levels problem of combinatorial geometry. A completely different algorithm running in Theta (n(2) log n) time was given recently by Bender, Fineman, and Gilbert. We extend both of our algorithms to the maintenance of strong components, without affecting the asymptotic time bounds.

An Online Actor-Critic Algorithm with Function Approximation for Constrained Markov Decision Processes

We develop an online actor-critic reinforcement learning algorithm with function approximation for a problem of control under inequality constraints. We consider the long-run average cost Markov decision process (MDP) framework in which both the objective and the constraint functions are suitable policy-dependent long-run averages of certain sample path functions. The Lagrange multiplier method is used to handle the inequality constraints. We prove the asymptotic almost sure convergence of our algorithm to a locally optimal solution. We also provide the results of numerical experiments on a problem of routing in a multi-stage queueing network with constraints on long-run average queue lengths. We observe that our algorithm exhibits good performance on this setting and converges to a feasible point.

Damage-tolerant design optimization of laminated composite structures using dispersion of ply angles by genetic algorithm

This article aims to obtain damage-tolerant designs with minimum weight for a laminated composite structure using genetic algorithm. Damage tolerance due to impacts in a laminated composite structure is enhanced by dispersing the plies such that too many adjacent plies do not have the same angle. Weight of the structure is minimized and the Tsai-Wu failure criterion is considered for the safe design. Design variables considered are the number of plies and ply orientation. The influence of dispersed ply angles on the weight of the structure for a given loading conditions is studied by varying the angles in the range of 0 degrees-45 degrees, 0 degrees-60 degrees and 0 degrees-90 degrees at intervals of 5 degrees and by using specific ply angles tailored to loading conditions. A comparison study is carried out between the conventional stacking sequence and the stacking sequence with dispersed ply angles for damage-tolerant weight minimization and some useful designs are obtained. Unconventional stacking sequence is more damage tolerant than the conventional stacking sequence is demonstrated by performing a finite element analysis under both tensile as well as compressive loading conditions. Moreover, a new mathematical function called the dispersion function is proposed to measure the dispersion of ply angles in a laminate. The approach for dispersing ply angles to achieve damage tolerance is especially suited for composite material design space which has multiple local minima.

Hierarchical Clustering Algorithm for Land Cover Mapping Using Satellite Images

This paper presents hierarchical clustering algorithms for land cover mapping problem using multi-spectral satellite images. In unsupervised techniques, the automatic generation of number of clusters and its centers for a huge database is not exploited to their full potential. Hence, a hierarchical clustering algorithm that uses splitting and merging techniques is proposed. Initially, the splitting method is used to search for the best possible number of clusters and its centers using Mean Shift Clustering (MSC), Niche Particle Swarm Optimization (NPSO) and Glowworm Swarm Optimization (GSO). Using these clusters and its centers, the merging method is used to group the data points based on a parametric method (k-means algorithm). A performance comparison of the proposed hierarchical clustering algorithms (MSC, NPSO and GSO) is presented using two typical multi-spectral satellite images - Landsat 7 thematic mapper and QuickBird. From the results obtained, we conclude that the proposed GSO based hierarchical clustering algorithm is more accurate and robust.

The local polynomial hull near a degenerate CR singularity: Bishop discs revisited

Let be a smooth real surface in and let be a point at which the tangent plane is a complex line. How does one determine whether or not is locally polynomially convex at such a p-i.e. at a CR singularity? Even when the order of contact of with at p equals 2, no clean characterisation exists; difficulties are posed by parabolic points. Hence, we study non-parabolic CR singularities. We show that the presence or absence of Bishop discs around certain non-parabolic CR singularities is completely determined by a Maslov-type index. This result subsumes all known facts about Bishop discs around order-two, non-parabolic CR singularities. Sufficient conditions for Bishop discs have earlier been investigated at CR singularities having high order of contact with . These results relied upon a subharmonicity condition, which fails in many simple cases. Hence, we look beyond potential theory and refine certain ideas going back to Bishop.

Singlet-state creation and universal quantum computation in NMR using a genetic algorithm

The experimental implementation of a quantum algorithm requires the decomposition of unitary operators. Here we treat unitary-operator decomposition as an optimization problem, and use a genetic algorithm-a global-optimization method inspired by nature's evolutionary process-for operator decomposition. We apply this method to NMR quantum information processing, and find a probabilistic way of performing universal quantum computation using global hard pulses. We also demonstrate the efficient creation of the singlet state (a special type of Bell state) directly from thermal equilibrium, using an optimum sequence of pulses. © 2012 American Physical Society.

Singlet-state creation and universal quantum computation in NMR using a genetic algorithm

The experimental implementation of a quantum algorithm requires the decomposition of unitary operators. Here we treat unitary-operator decomposition as an optimization problem, and use a genetic algorithm-a global-optimization method inspired by nature's evolutionary process-for operator decomposition. We apply this method to NMR quantum information processing, and find a probabilistic way of performing universal quantum computation using global hard pulses. We also demonstrate the efficient creation of the singlet state (a special type of Bell state) directly from thermal equilibrium, using an optimum sequence of pulses.

Surrogate based design optimisation of composite aerofoil cross-section for helicopter vibration reduction

Design optimisation of a helicopter rotor blade is performed. The objective is to reduce helicopter vibration and constraints are put on frequencies and aeroelastic stability. The ply angles of the D-spar and skin of the composite rotor blade with NACA 0015 aerofoil section are considered as design variables. Polynomial response surfaces and space filling experimental designs are used to generate surrogate models of the objective function with respect to cross-section properties. The stacking sequence corresponding to the optimal cross-section is found using a real-coded genetic algorithm. Ply angle discretisation of 1 degrees, 15 degrees, 30 degrees and 45 degrees are used. The mean value of the objective function is used to find the optimal blade designs and the resulting designs are tested for variance. The optimal designs show a vibration reduction of 26% to 33% from the baseline design. A substantial reduction in vibration and an aeroelastically stable blade is obtained even after accounting for composite material uncertainty.

As(3)p: A Fast Algorithm to Search Structurally Similar Protiens

Protein structure comparison is essential for understanding various aspects of protein structure, function and evolution. It can be used to explore the structural diversity and evolutionary patterns of protein families. In view of the above, a new algorithm is proposed which performs faster protein structure comparison using the peptide backbone torsional angles. It is fast, robust, computationally less expensive and efficient in finding structural similarities between two different protein structures and is also capable of identifying structural repeats within the same protein molecule.

Cubicity and Bandwidth

A unit cube in (or a k-cube in short) is defined as the Cartesian product R (1) x R (2) x ... x R (k) where R (i) (for 1 a parts per thousand currency sign i a parts per thousand currency sign k) is a closed interval of the form a (i) , a (i) + 1] on the real line. A k-cube representation of a graph G is a mapping of the vertices of G to k-cubes such that two vertices in G are adjacent if and only if their corresponding k-cubes have a non-empty intersection. The cubicity of G is the minimum k such that G has a k-cube representation. From a geometric embedding point of view, a k-cube representation of G = (V, E) yields an embedding such that for any two vertices u and v, ||f(u) - f(v)||(a) a parts per thousand currency sign 1 if and only if . We first present a randomized algorithm that constructs the cube representation of any graph on n vertices with maximum degree Delta in O(Delta ln n) dimensions. This algorithm is then derandomized to obtain a polynomial time deterministic algorithm that also produces the cube representation of the input graph in the same number of dimensions. The bandwidth ordering of the graph is studied next and it is shown that our algorithm can be improved to produce a cube representation of the input graph G in O(Delta ln b) dimensions, where b is the bandwidth of G, given a bandwidth ordering of G. Note that b a parts per thousand currency sign n and b is much smaller than n for many well-known graph classes. Another upper bound of b + 1 on the cubicity of any graph with bandwidth b is also shown. Together, these results imply that for any graph G with maximum degree Delta and bandwidth b, the cubicity is O(min{b, Delta ln b}). The upper bound of b + 1 is used to derive upper bounds for the cubicity of circular-arc graphs, cocomparability graphs and AT-free graphs in terms of the maximum degree Delta.

Coupled polynomial field approach for elimination of flexure and torsion locking phenomena in the Timoshenko and Euler-Bernoulli curved beam elements

The curvature related locking phenomena in the out-of-plane deformation of Timoshenko and Euler-Bernoulli curved beam elements are demonstrated and a novel approach is proposed to circumvent them. Both flexure and Torsion locking phenomena are noticed in Timoshenko beam and torsion locking phenomenon alone in Euler-Bernoulli beam. Two locking-free curved beam finite element models are developed using coupled polynomial displacement field interpolations to eliminate these locking effects. The coupled polynomial interpolation fields are derived independently for Timoshenko and Euler-Bernoulli beam elements using the governing equations. The presented of penalty terms in the couple displacement fields incorporates the flexure-torsion coupling and flexure-shear coupling effects in an approximate manner and produce no spurious constraints in the extreme geometric limits of flexure, torsion and shear stiffness. the proposed couple polynomial finite element models, as special cases, reduce to the conventional Timoshenko beam element and Euler-Bernoulli beam element, respectively. These models are shown to perform consistently over a wide range of flexure-to-shear (EI/GA) and flexure-to-torsion (EI/GJ) stiffness ratios and are inherently devoid of flexure, torsion and shear locking phenomena. The efficacy, accuracy and reliability of the proposed models to straight and curved beam applications are demonstrated through numerical examples. (C) 2012 Elsevier B.V. All rights reserved.

Efficient Methods for Robust Classification Under Uncertainty in Kernel Matrices

In this paper we study the problem of designing SVM classifiers when the kernel matrix, K, is affected by uncertainty. Specifically K is modeled as a positive affine combination of given positive semi definite kernels, with the coefficients ranging in a norm-bounded uncertainty set. We treat the problem using the Robust Optimization methodology. This reduces the uncertain SVM problem into a deterministic conic quadratic problem which can be solved in principle by a polynomial time Interior Point (IP) algorithm. However, for large-scale classification problems, IP methods become intractable and one has to resort to first-order gradient type methods. The strategy we use here is to reformulate the robust counterpart of the uncertain SVM problem as a saddle point problem and employ a special gradient scheme which works directly on the convex-concave saddle function. The algorithm is a simplified version of a general scheme due to Juditski and Nemirovski (2011). It achieves an O(1/T-2) reduction of the initial error after T iterations. A comprehensive empirical study on both synthetic data and real-world protein structure data sets show that the proposed formulations achieve the desired robustness, and the saddle point based algorithm outperforms the IP method significantly.

AN ITERATIVE ALGORITHM FOR PHASE RETRIEVAL WITH SPARSITY CONSTRAINTS: APPLICATION TO FREQUENCY DOMAIN OPTICAL COHERENCE TOMOGRAPHY

We address the problem of phase retrieval, which is frequently encountered in optical imaging. The measured quantity is the magnitude of the Fourier spectrum of a function (in optics, the function is also referred to as an object). The goal is to recover the object based on the magnitude measurements. In doing so, the standard assumptions are that the object is compactly supported and positive. In this paper, we consider objects that admit a sparse representation in some orthonormal basis. We develop a variant of the Fienup algorithm to incorporate the condition of sparsity and to successively estimate and refine the phase starting from the magnitude measurements. We show that the proposed iterative algorithm possesses Cauchy convergence properties. As far as the modality is concerned, we work with measurements obtained using a frequency-domain optical-coherence tomography experimental setup. The experimental results on real measured data show that the proposed technique exhibits good reconstruction performance even with fewer coefficients taken into account for reconstruction. It also suppresses the autocorrelation artifacts to a significant extent since it estimates the phase accurately.