Analysis of an Interior Penalty Method for Fourth Order Problems on Polygonal Domains

Error analysis for a stable C (0) interior penalty method is derived for general fourth order problems on polygonal domains under minimal regularity assumptions on the exact solution. We prove that this method exhibits quasi-optimal order of convergence in the discrete H (2), H (1) and L (2) norms. L (a) norm error estimates are also discussed. Theoretical results are demonstrated by numerical experiments.

An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order

This paper presents a singular edge-based smoothed finite element method (sES-FEM) for mechanics problems with singular stress fields of arbitrary order. The sES-FEM uses a basic mesh of three-noded linear triangular (T3) elements and a special layer of five-noded singular triangular elements (sT5) connected to the singular-point of the stress field. The sT5 element has an additional node on each of the two edges connected to the singular-point. It allows us to represent simple and efficient enrichment with desired terms for the displacement field near the singular-point with the satisfaction of partition-of-unity property. The stiffness matrix of the discretized system is then obtained using the assumed displacement values (not the derivatives) over smoothing domains associated with the edges of elements. An adaptive procedure for the sES-FEM is proposed to enhance the quality of the solution with minimized number of nodes. Several numerical examples are provided to validate the reliability of the present sES-FEM method. (C) 2012 Elsevier B.V. All rights reserved.

Active Sequential Hypothesis Testing with Application to a Visual Search Problem

We consider a visual search problem studied by Sripati and Olson where the objective is to identify an oddball image embedded among multiple distractor images as quickly as possible. We model this visual search task as an active sequential hypothesis testing problem (ASHT problem). Chernoff in 1959 proposed a policy in which the expected delay to decision is asymptotically optimal. The asymptotics is under vanishing error probabilities. We first prove a stronger property on the moments of the delay until a decision, under the same asymptotics. Applying the result to the visual search problem, we then propose a ``neuronal metric'' on the measured neuronal responses that captures the discriminability between images. From empirical study we obtain a remarkable correlation (r = 0.90) between the proposed neuronal metric and speed of discrimination between the images. Although this correlation is lower than with the L-1 metric used by Sripati and Olson, this metric has the advantage of being firmly grounded in formal decision theory.

Truthful multi-armed bandit mechanisms for multi-slot sponsored search auctions

In pay-per-click sponsored search auctions which are currently extensively used by search engines, the auction for a keyword involves a certain number of advertisers (say k) competing for available slots (say m) to display their advertisements (ads for short). A sponsored search auction for a keyword is typically conducted for a number of rounds (say T). There are click probabilities mu(ij) associated with each agent slot pair (agent i and slot j). The search engine would like to maximize the social welfare of the advertisers, that is, the sum of values of the advertisers for the keyword. However, the search engine does not know the true values advertisers have for a click to their respective advertisements and also does not know the click probabilities. A key problem for the search engine therefore is to learn these click probabilities during the initial rounds of the auction and also to ensure that the auction mechanism is truthful. Mechanisms for addressing such learning and incentives issues have recently been introduced. These mechanisms, due to their connection to the multi-armed bandit problem, are aptly referred to as multi-armed bandit (MAB) mechanisms. When m = 1, exact characterizations for truthful MAB mechanisms are available in the literature. Recent work has focused on the more realistic but non-trivial general case when m > 1 and a few promising results have started appearing. In this article, we consider this general case when m > 1 and prove several interesting results. Our contributions include: (1) When, mu(ij)s are unconstrained, we prove that any truthful mechanism must satisfy strong pointwise monotonicity and show that the regret will be Theta T7) for such mechanisms. (2) When the clicks on the ads follow a certain click precedence property, we show that weak pointwise monotonicity is necessary for MAB mechanisms to be truthful. (3) If the search engine has a certain coarse pre-estimate of mu(ij) values and wishes to update them during the course of the T rounds, we show that weak pointwise monotonicity and type-I separatedness are necessary while weak pointwise monotonicity and type-II separatedness are sufficient conditions for the MAB mechanisms to be truthful. (4) If the click probabilities are separable into agent-specific and slot-specific terms, we provide a characterization of MAB mechanisms that are truthful in expectation.

Similarity relations in visual search predict rapid visual categorization

How do we perform rapid visual categorization?It is widely thought that categorization involves evaluating the similarity of an object to other category items, but the underlying features and similarity relations remain unknown. Here, we hypothesized that categorization performance is based on perceived similarity relations between items within and outside the category. To this end, we measured the categorization performance of human subjects on three diverse visual categories (animals, vehicles, and tools) and across three hierarchical levels (superordinate, basic, and subordinate levels among animals). For the same subjects, we measured their perceived pair-wise similarities between objects using a visual search task. Regardless of category and hierarchical level, we found that the time taken to categorize an object could be predicted using its similarity to members within and outside its category. We were able to account for several classic categorization phenomena, such as (a) the longer times required to reject category membership; (b) the longer times to categorize atypical objects; and (c) differences in performance across tasks and across hierarchical levels. These categorization times were also accounted for by a model that extracts coarse structure from an image. The striking agreement observed between categorization and visual search suggests that these two disparate tasks depend on a shared coarse object representation.

Performance of a class of multi-robot deploy and search strategies based on centroidal voronoi configurations

This article considers a class of deploy and search strategies for multi-robot systems and evaluates their performance. The application framework used is deployment of a system of autonomous mobile robots equipped with required sensors in a search space to gather information. The lack of information about the search space is modelled as an uncertainty density distribution. The agents are deployed to maximise single-step search effectiveness. The centroidal Voronoi configuration, which achieves a locally optimal deployment, forms the basis for sequential deploy and search (SDS) and combined deploy and search (CDS) strategies. Completeness results are provided for both search strategies. The deployment strategy is analysed in the presence of constraints on robot speed and limit on sensor range for the convergence of trajectories with corresponding control laws responsible for the motion of robots. SDS and CDS strategies are compared with standard greedy and random search strategies on the basis of time taken to achieve reduction in the uncertainty density below a desired level. The simulation experiments reveal several important issues related to the dependence of the relative performances of the search strategies on parameters such as the number of robots, speed of robots and their sensor range limits.

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.

Near-optimal large-MIMO detection using randomized MCMC and randomized search algorithms

Low-complexity near-optimal detection of signals in MIMO systems with large number (tens) of antennas is getting increased attention. In this paper, first, we propose a variant of Markov chain Monte Carlo (MCMC) algorithm which i) alleviates the stalling problem encountered in conventional MCMC algorithm at high SNRs, and ii) achieves near-optimal performance for large number of antennas (e.g., 16×16, 32×32, 64×64 MIMO) with 4-QAM. We call this proposed algorithm as randomized MCMC (R-MCMC) algorithm. Second, we propose an other algorithm based on a random selection approach to choose candidate vectors to be tested in a local neighborhood search. This algorithm, which we call as randomized search (RS) algorithm, also achieves near-optimal performance for large number of antennas with 4-QAM. The complexities of the proposed R-MCMC and RS algorithms are quadratic/sub-quadratic in number of transmit antennas, which are attractive for detection in large-MIMO systems. We also propose message passing aided R-MCMC and RS algorithms, which are shown to perform well for higher-order QAM.

Clustering using Levy Flight Cuckoo Search

In this paper, a comparative study is carried using three nature-inspired algorithms namely Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and Cuckoo Search (CS) on clustering problem. Cuckoo search is used with levy flight. The heavy-tail property of levy flight is exploited here. These algorithms are used on three standard benchmark datasets and one real-time multi-spectral satellite dataset. The results are tabulated and analysed using various techniques. Finally we conclude that under the given set of parameters, cuckoo search works efficiently for majority of the dataset and levy flight plays an important role.

On Selection of Search Space Dimension in Compressive Sampling Matching Pursuit

Compressive Sampling Matching Pursuit (CoSaMP) is one of the popular greedy methods in the emerging field of Compressed Sensing (CS). In addition to the appealing empirical performance, CoSaMP has also splendid theoretical guarantees for convergence. In this paper, we propose a modification in CoSaMP to adaptively choose the dimension of search space in each iteration, using a threshold based approach. Using Monte Carlo simulations, we show that this modification improves the reconstruction capability of the CoSaMP algorithm in clean as well as noisy measurement cases. From empirical observations, we also propose an optimum value for the threshold to use in applications.

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.

Variance-Reduced Particle Filters for Structural System Identification Problems

A few variance reduction schemes are proposed within the broad framework of a particle filter as applied to the problem of structural system identification. Whereas the first scheme uses a directional descent step, possibly of the Newton or quasi-Newton type, within the prediction stage of the filter, the second relies on replacing the more conventional Monte Carlo simulation involving pseudorandom sequence with one using quasi-random sequences along with a Brownian bridge discretization while representing the process noise terms. As evidenced through the derivations and subsequent numerical work on the identification of a shear frame, the combined effect of the proposed approaches in yielding variance-reduced estimates of the model parameters appears to be quite noticeable. DOI: 10.1061/(ASCE)EM.1943-7889.0000480. (C) 2013 American Society of Civil Engineers.

Multiple parents crossover operators: A new approach removes the overlapping solutions for sequencing problems

Maintaining population diversity throughout generations of Genetic Algorithms (GAs) is key to avoid premature convergence. Redundant solutions is one cause for the decreasing population diversity. To prevent the negative effect of redundant solutions, we propose a framework that is based on the multi-parents crossover (MPX) operator embedded in GAs. Because MPX generates diversified chromosomes with good solution quality, when a pair of redundant solutions is found, we would generate a new offspring by using the MPX to replace the redundant chromosome. Three schemes of MPX will be examined and will be compared against some algorithms in literature when we solve the permutation flowshop scheduling problems, which is a strong NP-Hard sequencing problem. The results indicate that our approach significantly improves the solution quality. This study is useful for researchers who are trying to avoid premature convergence of evolutionary algorithms by solving the sequencing problems.

Linearization of Drucker-Prager yield criterion for axisymmetric problems: implementation in lower-bound limit analysis

The linearization of the Drucker-Prager yield criterion associated with an axisymmetric problem has been achieved by simulating a sphere with the truncated icosahedron with 32 faces and 60 vertices. On this basis, a numerical formulation has been proposed for solving an axisymmetric stability problem with the usage of the lower-bound limit analysis, finite elements, and linear optimization. To compare the results, the linearization of the Mohr-Coulomb yield criterion, by replacing the three cones with interior polyhedron, as proposed earlier by Pastor and Turgeman for an axisymmetric problem, has also been implemented. The two formulations have been applied for determining the collapse loads for a circular footing resting on a cohesive-friction material with nonzero unit weight. The computational results are found to be quite convincing. (C) 2013 American Society of Civil Engineers.

A peer-peer particle swarm optimizer

Particle Swarm Optimization is a parallel algorithm that spawns particles across a search space searching for an optimized solution. Though inherently parallel, they have distinct synchronizations points which stumbles attempts to create completely distributed versions of it. In this paper, we attempt to create a completely distributed peer-peer particle swarm optimization in a cluster of heterogeneous nodes. Since, the original algorithm requires explicit synchronization points we modified the algorithm in multiple ways to support a peer-peer system of nodes. We also modify certain aspect of the basic PSO algorithm and show how certain numerical problems can take advantage of the same thereby yielding fast convergence.