A Reliable Residual Based A Posteriori Error Estimator for a Quadratic Finite Element Method for the Elliptic Obstacle Problem

A residual based a posteriori error estimator is derived for a quadratic finite element method (FEM) for the elliptic obstacle problem. The error estimator involves various residuals consisting of the data of the problem, discrete solution and a Lagrange multiplier related to the obstacle constraint. The choice of the discrete Lagrange multiplier yields an error estimator that is comparable with the error estimator in the case of linear FEM. Further, an a priori error estimate is derived to show that the discrete Lagrange multiplier converges at the same rate as that of the discrete solution of the obstacle problem. The numerical experiments of adaptive FEM show optimal order convergence. This demonstrates that the quadratic FEM for obstacle problem exhibits optimal performance.

A Remark on the A Posteriori Error Analysis of Discontinuous Galerkin Methods for the Obstacle Problem

We revisit the a posteriori error analysis of discontinuous Galerkin methods for the obstacle problem derived in 25]. Under a mild assumption on the trace of obstacle, we derive a reliable a posteriori error estimator which does not involve min/max functions. A key in this approach is an auxiliary problem with discrete obstacle. Applications to various discontinuous Galerkin finite element methods are presented. Numerical experiments show that the new estimator obtained in this article performs better.

Deciphering complex patterns of class-I HLA-peptide cross-reactivity via hierarchical grouping

T-cell responses in humans are initiated by the binding of a peptide antigen to a human leukocyte antigen (HLA) molecule. The peptide-HLA complex then recruits an appropriate T cell, leading to cell-mediated immunity. More than 2000 HLA class-I alleles are known in humans, and they vary only in their peptide-binding grooves. The polymorphism they exhibit enables them to bind a wide range of peptide antigens from diverse sources. HLA molecules and peptides present a complex molecular recognition pattern, as many peptides bind to a given allele and a given peptide can be recognized by many alleles. A powerful grouping scheme that not only provides an insightful classification, but is also capable of dissecting the physicochemical basis of recognition specificity is necessary to address this complexity. We present a hierarchical classification of 2010 class-I alleles by using a systematic divisive clustering method. All-pair distances of alleles were obtained by comparing binding pockets in the structural models. By varying the similarity thresholds, a multilevel classification was obtained, with 7 supergroups, each further subclassifying to yield 72 groups. An independent clustering performed based only on similarities in their epitope pools correlated highly with pocket-based clustering. Physicochemical feature combinations that best explain the basis of clustering are identified. Mutual information calculated for the set of peptide ligands enables identification of binding site residues contributing to peptide specificity. The grouping of HLA molecules achieved here will be useful for rational vaccine design, understanding disease susceptibilities and predicting risk of organ transplants.

Algorithm for Autonomous Reorganization of Mobile Wireless Camera Sensor Networks to Improve Coverage

In this paper, sensing coverage by wireless camera-embedded sensor networks (WCSNs), a class of directional sensors is studied. The proposed work facilitates the autonomous tuning of orientation parameters and displacement of camera-sensor nodes in the bounded field of interest (FoI), where the network coverage in terms of every point in the FoI is important. The proposed work is first of its kind to study the problem of maximizing coverage of randomly deployed mobile WCSNs which exploits their mobility. We propose an algorithm uncovered region exploration algorithm (UREA-CS) that can be executed in centralized and distributed modes. Further, the work is extended for two special scenarios: 1) to suit autonomous combing operations after initial random WCSN deployments and 2) to improve the network coverage with occlusions in the FoI. The extensive simulation results show that the performance of UREA-CS is consistent, robust, and versatile to achieve maximum coverage, both in centralized and distributed modes. The centralized and distributed modes are further analyzed with respect to the computational and communicational overheads.

An Optimizing Code Generator for a Class of Lattice-Boltzmann Computations

The Lattice-Boltzmann method (LBM), a promising new particle-based simulation technique for complex and multiscale fluid flows, has seen tremendous adoption in recent years in computational fluid dynamics. Even with a state-of-the-art LBM solver such as Palabos, a user has to still manually write the program using library-supplied primitives. We propose an automated code generator for a class of LBM computations with the objective to achieve high performance on modern architectures. Few studies have looked at time tiling for LBM codes. We exploit a key similarity between stencils and LBM to enable polyhedral optimizations and in turn time tiling for LBM. We also characterize the performance of LBM with the Roofline performance model. Experimental results for standard LBM simulations like Lid Driven Cavity, Flow Past Cylinder, and Poiseuille Flow show that our scheme consistently outperforms Palabos-on average by up to 3x while running on 16 cores of an Intel Xeon (Sandybridge). We also obtain an improvement of 2.47x on the SPEC LBM benchmark.

Two player game variant of the Erdos-Szekeres problem

The classical Erdos-Szekeres theorem states that a convex k-gon exists in every sufficiently large point set. This problem has been well studied and finding tight asymptotic bounds is considered a challenging open problem. Several variants of the Erdos-Szekeres problem have been posed and studied in the last two decades. The well studied variants include the empty convex k-gon problem, convex k-gon with specified number of interior points and the chromatic variant. In this paper, we introduce the following two player game variant of the Erdos-Szekeres problem: Consider a two player game where each player playing in alternate turns, place points in the plane. The objective of the game is to avoid the formation of the convex k-gon among the placed points. The game ends when a convex k-gon is formed and the player who placed the last point loses the game. In our paper we show a winning strategy for the player who plays second in the convex 5-gon game and the empty convex 5-gon game by considering convex layer configurations at each step. We prove that the game always ends in the 9th step by showing that the game reaches a specific set of configurations.

A new class of high strength high temperature Cobalt based gamma-gamma ` Co-Mo-Al alloys stabilized with Ta addition

The present paper reports a new class of Co based superalloys that has gamma-gamma' microstructure and exhibits much lower density compared to other commercially available Co superalloys including Co-Al-W based alloys. The basic composition is Co-10Al-5Mo (at%) with addition of 2 at% Ta for stabilization of gamma' phase. The gamma-gamma' microstructure evolves through solutionising and aging treatment. Using first principles calculations, we observe that Ta plays a crucial role in stabilizing gamma' phase. By addition of Ta in the basic stoichiometric composition Co-3(Al, Mo), the enthalpy of formation (Delta H-f) of L1(2) structure (gamma' phase) becomes more negative in comparison to DO19 structure. The All of the L12 structure becomes further more negative by the occupancy of Ni and Ti atoms in the lattice suggesting an increase in the stability of the gamma' precipitates. Among large number of alloys studied experimentally, the paper presents results of detailed investigations on Co-10Al-5Mo-2Ta, Co-30Ni-10Al-5Mo-2Ta and Co-30Ni-10Al-5Mo-2Ta-2Ti. To evaluate the role alloying elements, atom probe tomography investigations were carried out to obtain partition coefficients for the constituent elements. The results show strong partitioning of Ni, Al, Ta and Ti in ordered gamma' precipitates. 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Minimization Problems Based on Relative alpha-Entropy II: Reverse Projection

In part I of this two-part work, certain minimization problems based on a parametric family of relative entropies (denoted I-alpha) were studied. Such minimizers were called forward I-alpha-projections. Here, a complementary class of minimization problems leading to the so-called reverse I-alpha-projections are studied. Reverse I-alpha-projections, particularly on log-convex or power-law families, are of interest in robust estimation problems (alpha > 1) and in constrained compression settings (alpha < 1). Orthogonality of the power-law family with an associated linear family is first established and is then exploited to turn a reverse I-alpha-projection into a forward I-alpha-projection. The transformed problem is a simpler quasi-convex minimization subject to linear constraints.

A Variant of the Hadwiger-Debrunner (p, q)-Problem in the Plane

Let X be a convex curve in the plane (say, the unit circle), and let be a family of planar convex bodies such that every two of them meet at a point of X. Then has a transversal of size at most . Suppose instead that only satisfies the following ``(p, 2)-condition'': Among every p elements of , there are two that meet at a common point of X. Then has a transversal of size . For comparison, the best known bound for the Hadwiger-Debrunner (p, q)-problem in the plane, with , is . Our result generalizes appropriately for if is, for example, the moment curve.

As-You-Go Deployment of a 2-Connected Wireless Relay Network for Sensor-Sink Interconnection

A person walks along a line (which could be an idealisation of a forest trail, for example), placing relays as he walks, in order to create a multihop network for connecting a sensor at a point along the line to a sink at the start of the line. The potential placement points are equally spaced along the line, and at each such location the decision to place or not to place a relay is based on link quality measurements to the previously placed relays. The location of the sensor is unknown apriori, and is discovered as the deployment agent walks. In this paper, we extend our earlier work on this class of problems to include the objective of achieving a 2-connected multihop network. We propose a network cost objective that is additive over the deployed relays, and accounts for possible alternate routing over the multiple available paths. As in our earlier work, the problem is formulated as a Markov decision process. Placement algorithms are obtained for two source location models, which yield a discounted cost MDP and an average cost MDP. In each case we obtain structural results for an optimal policy, and perform a numerical study that provides insights into the advantages and disadvantages of multi-connectivity. We validate the results obtained from numerical study experimentally in a forest-like environment.

Event-triggered Sampling and Reconstruction of Sparse Real-valued Trigonometric Polynomials

We propose data acquisition from continuous-time signals belonging to the class of real-valued trigonometric polynomials using an event-triggered sampling paradigm. The sampling schemes proposed are: level crossing (LC), close to extrema LC, and extrema sampling. Analysis of robustness of these schemes to jitter, and bandpass additive gaussian noise is presented. In general these sampling schemes will result in non-uniformly spaced sample instants. We address the issue of signal reconstruction from the acquired data-set by imposing structure of sparsity on the signal model to circumvent the problem of gap and density constraints. The recovery performance is contrasted amongst the various schemes and with random sampling scheme. In the proposed approach, both sampling and reconstruction are non-linear operations, and in contrast to random sampling methodologies proposed in compressive sensing these techniques may be implemented in practice with low-power circuitry.

Damage Detection Sensitivity, Specificity and Classification Data Analysis for SHM Systems Design, Verification and Validation

In this paper, we consider applying derived knowledge base regarding the sensitivity and specificity of damage(s) to be detected by an SHM system being designed and qualified. These efforts are necessary toward developing capabilities in SHM system to classify reliably various probable damages through sequence of monitoring, i.e., damage precursor identification, detection of damage and monitoring its progression. We consider the particular problem of visual and ultrasonic NDE based SHM system design requirements, where the damage detection sensitivity and specificity data definitions for a class of structural components are established. Methodologies for SHM system specification creation are discussed in details. Examples are shown to illustrate how the physics of damage detection scheme limits particular damage detection sensitivity and specificity and further how these information can be used in algorithms to combine various different NDE schemes in an SHM system to enhance efficiency and effectiveness. Statistical and data driven models to determine the sensitivity and probability of damage detection (POD) has been demonstrated for plate with varying one-sided line crack using optical and ultrasonic based inspection techniques.

Exact Phase Retrieval in Principal Shift-Invariant Spaces

We address the problem of phase retrieval from Fourier transform magnitude spectrum for continuous-time signals that lie in a shift-invariant space spanned by integer shifts of a generator kernel. The phase retrieval problem for such signals is formulated as one of reconstructing the combining coefficients in the shift-invariant basis expansion. We develop sufficient conditions on the coefficients and the bases to guarantee exact phase retrieval, by which we mean reconstruction up to a global phase factor. We present a new class of discrete-domain signals that are not necessarily minimum-phase, but allow for exact phase retrieval from their Fourier magnitude spectra. We also establish Hilbert transform relations between log-magnitude and phase spectra for this class of discrete signals. It turns out that the corresponding continuous-domain counterparts need not satisfy a Hilbert transform relation; notwithstanding, the continuous-domain signals can be reconstructed from their Fourier magnitude spectra. We validate the reconstruction guarantees through simulations for some important classes of signals such as bandlimited signals and piecewise-smooth signals. We also present an application of the proposed phase retrieval technique for artifact-free signal reconstruction in frequency-domain optical-coherence tomography (FDOCT).