Landau-Zener problem with waiting at the minimum gap and related quench dynamics of a many-body system

We discuss a technique for solving the Landau-Zener (LZ) problem of finding the probability of excitation in a two-level system. The idea of time reversal for the Schrodinger equation is employed to obtain the state reached at the final time and hence the excitation probability. Using this method, which can reproduce the well-known expression for the LZ transition probability, we solve a variant of the LZ problem, which involves waiting at the minimum gap for a time t(w); we find an exact expression for the excitation probability as a function of t(w). We provide numerical results to support our analytical expressions. We then discuss the problem of waiting at the quantum critical point of a many-body system and calculate the residual energy generated by the time-dependent Hamiltonian. Finally, we discuss possible experimental realizations of this work.

Interactive Distributed Source Coding in Asymmetric Communication Scenarios

We provide a new unified framework, called "multiple correlated informants - single recipient" communication, to address the variations of the traditional Distributed Source Coding (DSC) problem. Different combinations of the assumptions about the communication scenarios and the objectives of communication result in different variations of the DSC problem. For each of these variations, the complexities of communication and computation of the optimal solution is determined by the combination of the underlying assumptions. In the proposed framework, we address the asymmetric, interactive, and lossless variant of the DSC problem, with various objectives of communication and provide optimal solutions for those. Also, we consider both, the worst-case and average-case scenarios.

Single-resolution and multiresolution extended-Kalman-filter-based reconstruction approaches to optical refraction tomography

The problem of reconstruction of a refractive-index distribution (RID) in optical refraction tomography (ORT) with optical path-length difference (OPD) data is solved using two adaptive-estimation-based extended-Kalman-filter (EKF) approaches. First, a basic single-resolution EKF (SR-EKF) is applied to a state variable model describing the tomographic process, to estimate the RID of an optically transparent refracting object from noisy OPD data. The initialization of the biases and covariances corresponding to the state and measurement noise is discussed. The state and measurement noise biases and covariances are adaptively estimated. An EKF is then applied to the wavelet-transformed state variable model to yield a wavelet-based multiresolution EKF (MR-EKF) solution approach. To numerically validate the adaptive EKF approaches, we evaluate them with benchmark studies of standard stationary cases, where comparative results with commonly used efficient deterministic approaches can be obtained. Detailed reconstruction studies for the SR-EKF and two versions of the MR-EKF (with Haar and Daubechies-4 wavelets) compare well with those obtained from a typically used variant of the (deterministic) algebraic reconstruction technique, the average correction per projection method, thus establishing the capability of the EKF for ORT. To the best of our knowledge, the present work contains unique reconstruction studies encompassing the use of EKF for ORT in single-resolution and multiresolution formulations, and also in the use of adaptive estimation of the EKF's noise covariances. (C) 2010 Optical Society of America

Vector evaluated particle swarm optimization (VEPSO) for multi-objective design optimization of composite structures

We present a generic method/model for multi-objective design optimization of laminated composite components, based on vector evaluated particle swarm optimization (VEPSO) algorithm. VEPSO is a novel, co-evolutionary multi-objective variant of the popular particle swarm optimization algorithm (PSO). In the current work a modified version of VEPSO algorithm for discrete variables has been developed and implemented successfully for the, multi-objective design optimization of composites. The problem is formulated with multiple objectives of minimizing weight and the total cost of the composite component to achieve a specified strength. The primary optimization variables are - the number of layers, its stacking sequence (the orientation of the layers) and thickness of each layer. The classical lamination theory is utilized to determine the stresses in the component and the design is evaluated based on three failure criteria; failure mechanism based failure criteria, Maximum stress failure criteria and the Tsai-Wu failure criteria. The optimization method is validated for a number of different loading configurations - uniaxial, biaxial and bending loads. The design optimization has been carried for both variable stacking sequences, as well fixed standard stacking schemes and a comparative study of the different design configurations evolved has been presented. (C) 2007 Elsevier Ltd. All rights reserved.

Evidence for an association with type 2 diabetes mellitus at the PPARG locus in a South Indian population

Peroxisome proliferator activated receptor-gamma 2 (PPARG2) is a nuclear hormone receptor of ligand-dependent ranscription factor involved in adipogenesis and a molecular target of the insulin sensitizers thiazolidinediones. We addressed the question of whether the 3 variants (-1279G/A, Pro12Ala, and His478His) in the PPARG2 gene are associated with type 2 diabetes mellitus and its related traits in a South Indian population. The study subjects (1000 type 2 diabetes mellitus and 1000 normal glucose-tolerant subjects) were chosen randomly from the Chennai Urban Rural Epidemiology Study, an ongoing population-based study in southern India. The variants were screened by single-stranded conformational variant, direct sequencing, and restriction fragment length polymorphism. Linkage disequilibrium was estimated from the estimates of haplotypic frequencies. The -1279G/A, Pro12Ala, and His478His variants of the PPARG2 gene were not associated with type 2 diabetes mellitus. However, the 2-loci analyses showed that, in the presence of Pro/Pro genotype of the Pro12Ala variant, the -1279G/A promoter variant showed increased susceptibility to type 2 diabetes mellitus (odds ratio, 2.092; 95% confidence interval, 1.22-3.59; P = .008), whereas in the presence of 12Ala allele, the -1279G/A showed a protective effect against type 2 diabetes mellitus (odds ratio, 0.270; 95% confidence interval, 0.15-0.49; P < .0001). The 3-loci haplotype analysis showed that the A-Ala-T (-1279G/A-Pro12Ala-His478His) haplotype was associated with a reduced risk of type 2 diabetes mellitus (P < .0001). Although our data indicate that the PPARG2 gene variants, independently, have no association with type 2 diabetes mellitus, the 2-loci genotype analysis involving -1279G/A and Pro12Ala variants and the 3-loci haplotype analysis have shown a significant association with type 2 diabetes mellitus in this South Indian population. (C) 2010 Elsevier Inc. All rights reserved.

Solution of MDPS using simulation-based value iteration

This article proposes a three-timescale simulation based algorithm for solution of infinite horizon Markov Decision Processes (MDPs). We assume a finite state space and discounted cost criterion and adopt the value iteration approach. An approximation of the Dynamic Programming operator T is applied to the value function iterates. This 'approximate' operator is implemented using three timescales, the slowest of which updates the value function iterates. On the middle timescale we perform a gradient search over the feasible action set of each state using Simultaneous Perturbation Stochastic Approximation (SPSA) gradient estimates, thus finding the minimizing action in T. On the fastest timescale, the 'critic' estimates, over which the gradient search is performed, are obtained. A sketch of convergence explaining the dynamics of the algorithm using associated ODEs is also presented. Numerical experiments on rate based flow control on a bottleneck node using a continuous-time queueing model are performed using the proposed algorithm. The results obtained are verified against classical value iteration where the feasible set is suitably discretized. Over such a discretized setting, a variant of the algorithm of [12] is compared and the proposed algorithm is found to converge faster.

Optimal threshold policies for admission control in communication networks via discrete parameter stochastic approximation

The problem of admission control of packets in communication networks is studied in the continuous time queueing framework under different classes of service and delayed information feedback. We develop and use a variant of a simulation based two timescale simultaneous perturbation stochastic approximation (SPSA) algorithm for finding an optimal feedback policy within the class of threshold type policies. Even though SPSA has originally been designed for continuous parameter optimization, its variant for the discrete parameter case is seen to work well. We give a proof of the hypothesis needed to show convergence of the algorithm on our setting along with a sketch of the convergence analysis. Extensive numerical experiments with the algorithm are illustrated for different parameter specifications. In particular, we study the effect of feedback delays on the system performance.

Detection of multiple source locations using a glowworm metaphor with applications to collective robotics

This paper presents a glowworm swarm based algorithm that finds solutions to optimization of multiple optima continuous functions. The algorithm is a variant of a well known ant-colony optimization (ACO) technique, but with several significant modifications. Similar to how each moving region in the ACO technique is associated with a pheromone value, the agents in our algorithm carry a luminescence quantity along with them. Agents are thought of as glowworms that emit a light whose intensity is proportional to the associated luminescence and have a circular sensor range. The glowworms depend on a local-decision domain to compute their movements. Simulations demonstrate the efficacy of the proposed glowworm based algorithm in capturing multiple optima of a multimodal function. The above optimization scenario solves problems where a collection of autonomous robots is used to form a mobile sensor network. In particular, we address the problem of detecting multiple sources of a general nutrient profile that is distributed spatially on a two dimensional workspace using multiple robots.

Action of N-bromosuccinimide on sperm whale myoglobin

Previously, it was reported from this laboratory that the heme groups of hemoglobin are “buried” within globin at pH 4.0 and not dissociated, on the basis of the obiligatory requirement of urea for the reaction of N-bromosuccinimide with the heme groups of hemoglobin at pH4.0, and also on the basis of the “normalization” of the spectrum of hemoglobin at this pH in the presence of urea or sucrose. In the present study, it has been shown that the behaviour of sperm whale myoglobin with respect to its reaction with N-bromosuccinimide and with respect to spectral “normalization” in urea or sucrose are essentially similar to that of hemoglobin. It has also been demonstrated that the spectral “normalization” obtained with crystalline hemin is not identical with that obtained with either hemoglobin or myoglobin. The bearing of the results of the present study on the earlier work on hemoglobin is indicated.

Reciprocity relation in scattering by media subjected to an external magnetic field

Krishnan's reciprocity theorem in colloid optics, ρ{variant}u=1+l/ρ{variant}h/1+1/ρ{variant}v is generalised for the case when the scattering medium is subjected to an external orienting field. It is shown theoretically that a general relation of the type IBA=I′AB results in this case, where IBA is the intensity of the component of the scattered light having its electric vector inclined at an angle B to the vertical with the incident light polarised at an angle A to the vertical, the external field direction being parallel to the incident beam. I′AB is the corresponding intensity with the magnetic field parallel of the scattered ray. Experimental verification of the above generalisation is also given.

Polarisation studies on the Raman spectra of cubic crystals - Part I. Sodium chlorate

neral expressions have been derived for the intensities of the three classes of Raman lines namely totally symmetric A, doubly degenerate E and triply degenerate F, in the case of cubic crystals under the following conditions. The direction of the incident beam which is polarised with its electric vector inclined at an angle α to the normal to the scattering plane makes an angle Θ with one of the cubic axes of the crystal. The transversely scattered light is analysed by a double image prism with its principal axes inclined at angle β to the normal to the scattering plane, which is horizontal. For incident unpolarised light and Θ=22 1/2°, and the scattered light being analysed by a double image prism rotated through 45° from the position when its principal axes are vertical and horizontal ρ{variant} for A lines is equal to one, for E lines >1 and for F lines <1. This gives a method of classifying the Raman lines of a cubic crystal in a single setting. The results have been experimentally verified in sodium chlorate.

Voting Paths

We consider a variant of the popular matching problem here. The input instance is a bipartite graph $G=(\mathcal{A}\cup\mathcal{P},E)$, where vertices in $\mathcal{A}$ are called applicants and vertices in $\mathcal{P}$ are called posts. Each applicant ranks a subset of posts in an order of preference, possibly involving ties. A matching $M$ is popular if there is no other matching $M'$ such that the number of applicants who prefer their partners in $M'$ to $M$ exceeds the number of applicants who prefer their partners in $M$ to $M'$. However, the “more popular than” relation is not transitive; hence this relation is not a partial order, and thus there need not be a maximal element here. Indeed, there are simple instances that do not admit popular matchings. The questions of whether an input instance $G$ admits a popular matching and how to compute one if it exists were studied earlier by Abraham et al. Here we study reachability questions among matchings in $G$, assuming that $G=(\mathcal{A}\cup\mathcal{P},E)$ admits a popular matching. A matching $M_k$ is reachable from $M_0$ if there is a sequence of matchings $\langle M_0,M_1,\dots,M_k\rangle$ such that each matching is more popular than its predecessor. Such a sequence is called a length-$k$ voting path from $M_0$ to $M_k$. We show an interesting property of reachability among matchings in $G$: there is always a voting path of length at most 2 from any matching to some popular matching. Given a bipartite graph $G=(\mathcal{A}\cup\mathcal{P},E)$ with $n$ vertices and $m$ edges and any matching $M_0$ in $G$, we give an $O(m\sqrt{n})$ algorithm to compute a shortest-length voting path from $M_0$ to a popular matching; when preference lists are strictly ordered, we have an $O(m+n)$ algorithm. This problem has applications in dynamic matching markets, where applicants and posts can enter and leave the market, and applicants can also change their preferences arbitrarily. After any change, the current matching may no longer be popular, in which case we are required to update it. However, our model demands that we switch from one matching to another only if there is consensus among the applicants to agree to the switch. Hence we need to update via a voting path that ends in a popular matching. Thus our algorithm has applications here.

A four-timescale algorithm for constrained stochastic optimization of RED

The overall performance of random early detection (RED) routers in the Internet is determined by the settings of their associated parameters. The non-availability of a functional relationship between the RED performance and its parameters makes it difficult to implement optimization techniques directly in order to optimize the RED parameters. In this paper, we formulate a generic optimization framework using a stochastically bounded delay metric to dynamically adapt the RED parameters. The constrained optimization problem thus formulated is solved using traditional nonlinear programming techniques. Here, we implement the barrier and penalty function approaches, respectively. We adopt a second-order nonlinear optimization framework and propose a novel four-timescale stochastic approximation algorithm to estimate the gradient and Hessian of the barrier and penalty objectives and update the RED parameters. A convergence analysis of the proposed algorithm is briefly sketched. We perform simulations to evaluate the performance of our algorithm with both barrier and penalty objectives and compare these with RED and a variant of it in the literature. We observe an improvement in performance using our proposed algorithm over RED, and the above variant of it.

Parallel circuit partitioning on a reduced array architecture

The physical design of a VLSI circuit involves circuit partitioning as a subtask. Typically, it is necessary to partition a large electrical circuit into several smaller circuits such that the total cross-wiring is minimized. This problem is a variant of the more general graph partitioning problem, and it is known that there does not exist a polynomial time algorithm to obtain an optimal partition. The heuristic procedure proposed by Kernighan and Lin1,2 requires O(n2 log2n) time to obtain a near-optimal two-way partition of a circuit with n modules. In the VLSI context, due to the large problem size involved, this computational requirement is unacceptably high. This paper is concerned with the hardware acceleration of the Kernighan-Lin procedure on an SIMD architecture. The proposed parallel partitioning algorithm requires O(n) processors, and has a time complexity of O(n log2n). In the proposed scheme, the reduced array architecture is employed with due considerations towards cost effectiveness and VLSI realizability of the architecture.The authors are not aware of any earlier attempts to parallelize a circuit partitioning algorithm in general or the Kernighan-Lin algorithm in particular. The use of the reduced array architecture is novel and opens up the possibilities of using this computing structure for several other applications in electronic design automation.

Reliability models for existing structures based on dynamic state estimation and data based asymptotic extreme value analysis

The problem of time variant reliability analysis of existing structures subjected to stationary random dynamic excitations is considered. The study assumes that samples of dynamic response of the structure, under the action of external excitations, have been measured at a set of sparse points on the structure. The utilization of these measurements m in updating reliability models, postulated prior to making any measurements, is considered. This is achieved by using dynamic state estimation methods which combine results from Markov process theory and Bayes' theorem. The uncertainties present in measurements as well as in the postulated model for the structural behaviour are accounted for. The samples of external excitations are taken to emanate from known stochastic models and allowance is made for ability (or lack of it) to measure the applied excitations. The future reliability of the structure is modeled using expected structural response conditioned on all the measurements made. This expected response is shown to have a time varying mean and a random component that can be treated as being weakly stationary. For linear systems, an approximate analytical solution for the problem of reliability model updating is obtained by combining theories of discrete Kalman filter and level crossing statistics. For the case of nonlinear systems, the problem is tackled by combining particle filtering strategies with data based extreme value analysis. In all these studies, the governing stochastic differential equations are discretized using the strong forms of Ito-Taylor's discretization schemes. The possibility of using conditional simulation strategies, when applied external actions are measured, is also considered. The proposed procedures are exemplifiedmby considering the reliability analysis of a few low-dimensional dynamical systems based on synthetically generated measurement data. The performance of the procedures developed is also assessed based on a limited amount of pertinent Monte Carlo simulations. (C) 2010 Elsevier Ltd. All rights reserved.