Comparison of a priori and a posteriori meshes for singularly perturbed nonlinear parameterized problems

This paper deals with the adaptive mesh generation for singularly perturbed nonlinear parameterized problems with a comparative research study on them. We propose an a posteriori error estimate for singularly perturbed parameterized problems by moving mesh methods with fixed number of mesh points. The well known a priori meshes are compared with the proposed one. The comparison results show that the proposed numerical method is highly effective for the generation of layer adapted a posteriori meshes. A numerical experiment of the error behavior on different meshes is carried out to highlight the comparison of the approximated solutions. (C) 2015 Elsevier B.V. All rights reserved.

Minimization Problems Based on Relative alpha-Entropy I: Forward Projection

Minimization problems with respect to a one-parameter family of generalized relative entropies are studied. These relative entropies, which we term relative alpha-entropies (denoted I-alpha), arise as redundancies under mismatched compression when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the usual relative entropy (Kullback-Leibler divergence). Just like relative entropy, these relative alpha-entropies behave like squared Euclidean distance and satisfy the Pythagorean property. Minimizers of these relative alpha-entropies on closed and convex sets are shown to exist. Such minimizations generalize the maximum Renyi or Tsallis entropy principle. The minimizing probability distribution (termed forward I-alpha-projection) for a linear family is shown to obey a power-law. Other results in connection with statistical inference, namely subspace transitivity and iterated projections, are also established. In a companion paper, a related minimization problem of interest in robust statistics that leads to a reverse I-alpha-projection is studied.

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.

Part II: A Fully Integrated RF PA in 28-nm CMOS With Device Design for Optimized Performance and ESD Robustness

In this paper, we report drain-extended MOS device design guidelines for the RF power amplifier (RF PA) applications. A complete RF PA circuit in a 28-nm CMOS technology node with the matching and biasing network is used as a test vehicle to validate the RF performance improvement by a systematic device design. A complete RF PA with 0.16-W/mm power density is reported experimentally. By simultaneous improvement of device-circuit performance, 45% improvement in the circuit RF power gain, 25% improvement in the power-added efficiency at 1-GHz frequency, and 5x improvement in the electrostatic discharge robustness are reported experimentally.

Lower-Bound Axisymmetric Formulation for Geomechanics Problems Using Nonlinear Optimization

A lower-bound limit analysis formulation, by using two-dimensional finite elements, the three-dimensional Mohr-Coulomb yield criterion, and nonlinear optimization, has been given to deal with an axisymmetric geomechanics stability problem. The optimization was performed using an interior point method based on the logarithmic barrier function. The yield surface was smoothened (1) by removing the tip singularity at the apex of the pyramid in the meridian plane and (2) by eliminating the stress discontinuities at the corners of the yield hexagon in the pi-plane. The circumferential stress (sigma(theta)) need not be assumed. With the proposed methodology, for a circular footing, the bearing-capacity factors N-c, N-q, and N-gamma for different values of phi have been computed. For phi = 0, the variation of N-c with changes in the factor m, which accounts for a linear increase of cohesion with depth, has been evaluated. Failure patterns for a few cases have also been drawn. The results from the formulation provide a good match with the solutions available from the literature. (C) 2014 American Society of Civil Engineers.

Unique Covering Problems with Geometric Sets

The Exact Cover problem takes a universe U of n elements, a family F of m subsets of U and a positive integer k, and decides whether there exists a subfamily(set cover) F' of size at most k such that each element is covered by exactly one set. The Unique Cover problem also takes the same input and decides whether there is a subfamily F' subset of F such that at least k of the elements F' covers are covered uniquely(by exactly one set). Both these problems are known to be NP-complete. In the parameterized setting, when parameterized by k, Exact Cover is W1]-hard. While Unique Cover is FPT under the same parameter, it is known to not admit a polynomial kernel under standard complexity-theoretic assumptions. In this paper, we investigate these two problems under the assumption that every set satisfies a given geometric property Pi. Specifically, we consider the universe to be a set of n points in a real space R-d, d being a positive integer. When d = 2 we consider the problem when. requires all sets to be unit squares or lines. When d > 2, we consider the problem where. requires all sets to be hyperplanes in R-d. These special versions of the problems are also known to be NP-complete. When parameterizing by k, the Unique Cover problem has a polynomial size kernel for all the above geometric versions. The Exact Cover problem turns out to be W1]-hard for squares, but FPT for lines and hyperplanes. Further, we also consider the Unique Set Cover problem, which takes the same input and decides whether there is a set cover which covers at least k elements uniquely. To the best of our knowledge, this is a new problem, and we show that it is NP-complete (even for the case of lines). In fact, the problem turns out to be W1]-hard in the abstract setting, when parameterized by k. However, when we restrict ourselves to the lines and hyperplanes versions, we obtain FPT algorithms.

A FRAMEWORK FOR THE ERROR ANALYSIS OF DISCONTINUOUS FINITE ELEMENT METHODS FOR ELLIPTIC OPTIMAL CONTROL PROBLEMS AND APPLICATIONS TO C-0 IP METHODS

In this article, an abstract framework for the error analysis of discontinuous Galerkin methods for control constrained optimal control problems is developed. The analysis establishes the best approximation result from a priori analysis point of view and delivers a reliable and efficient a posteriori error estimator. The results are applicable to a variety of problems just under the minimal regularity possessed by the well-posedness of the problem. Subsequently, the applications of C-0 interior penalty methods for a boundary control problem as well as a distributed control problem governed by the biharmonic equation subject to simply supported boundary conditions are discussed through the abstract analysis. Numerical experiments illustrate the theoretical findings.

Graph Modification Problems: A Modern Perspective

We give an overview of recent results and techniques in parameterized algorithms for graph modification problems.

Protein Structure and Function: Looking through the Network of Side-Chain Interactions

Network theory has become an excellent method of choice through which biological data are smoothly integrated to gain insights into complex biological problems. Understanding protein structure, folding, and function has been an important problem, which is being extensively investigated by the network approach. Since the sequence uniquely determines the structure, this review focuses on the networks of non-covalently connected amino acid side chains in proteins. Questions in structural biology are addressed within the framework of such a formalism. While general applications are mentioned in this review, challenging problems which have demanded the attention of scientific community for a long time, such as allostery and protein folding, are considered in greater detail. Our aim has been to explore these important problems through the eyes of networks. Various methods of constructing protein structure networks (PSN) are consolidated. They include the methods based on geometry, edges weighted by different schemes, and also bipartite network of protein-nucleic acid complexes. A number of network metrics that elegantly capture the general features as well as specific features related to phenomena, such as allostery and protein model validation, are described. Additionally, an integration of network theory with ensembles of equilibrium structures of a single protein or that of a large number of structures from the data bank has been presented to perceive complex phenomena from network perspective. Finally, we discuss briefly the capabilities, limitations, and the scope for further explorations of protein structure networks.

DETERMINISTIC ALGORITHMS FOR MATCHING AND PACKING PROBLEMS BASED ON REPRESENTATIVE SETS

In this work, we study the well-known r-DIMENSIONAL k-MATCHING ((r, k)-DM), and r-SET k-PACKING ((r, k)-SP) problems. Given a universe U := U-1 ... U-r and an r-uniform family F subset of U-1 x ... x U-r, the (r, k)-DM problem asks if F admits a collection of k mutually disjoint sets. Given a universe U and an r-uniform family F subset of 2(U), the (r, k)-SP problem asks if F admits a collection of k mutually disjoint sets. We employ techniques based on dynamic programming and representative families. This leads to a deterministic algorithm with running time O(2.851((r-1)k) .vertical bar F vertical bar. n log(2)n . logW) for the weighted version of (r, k)-DM, where W is the maximum weight in the input, and a deterministic algorithm with running time O(2.851((r-0.5501)k).vertical bar F vertical bar.n log(2) n . logW) for the weighted version of (r, k)-SP. Thus, we significantly improve the previous best known deterministic running times for (r, k)-DM and (r, k)-SP and the previous best known running times for their weighted versions. We rely on structural properties of (r, k)-DM and (r, k)-SP to develop algorithms that are faster than those that can be obtained by a standard use of representative sets. Incorporating the principles of iterative expansion, we obtain a better algorithm for (3, k)-DM, running in time O(2.004(3k).vertical bar F vertical bar . n log(2)n). We believe that this algorithm demonstrates an interesting application of representative families in conjunction with more traditional techniques. Furthermore, we present kernels of size O(e(r)r(k-1)(r) logW) for the weighted versions of (r, k)-DM and (r, k)-SP, improving the previous best known kernels of size O(r!r(k-1)(r) logW) for these problems.

Kernelization complexity of possible winner and coalitional manipulation problems in voting

In the POSSIBLE WINNER problem in computational social choice theory, we are given a set of partial preferences and the question is whether a distinguished candidate could be made winner by extending the partial preferences to linear preferences. Previous work has provided, for many common voting rules, fixed parameter tractable algorithms for the POSSIBLE WINNER problem, with number of candidates as the parameter. However, the corresponding kernelization question is still open and in fact, has been mentioned as a key research challenge 10]. In this paper, we settle this open question for many common voting rules. We show that the POSSIBLE WINNER problem for maximin, Copeland, Bucklin, ranked pairs, and a class of scoring rules that includes the Borda voting rule does not admit a polynomial kernel with the number of candidates as the parameter. We show however that the COALITIONAL MANIPULATION problem which is an important special case of the POSSIBLE WINNER problem does admit a polynomial kernel for maximin, Copeland, ranked pairs, and a class of scoring rules that includes the Borda voting rule, when the number of manipulators is polynomial in the number of candidates. A significant conclusion of our work is that the POSSIBLE WINNER problem is harder than the COALITIONAL MANIPULATION problem since the COALITIONAL MANIPULATION problem admits a polynomial kernel whereas the POSSIBLE WINNER problem does not admit a polynomial kernel. (C) 2015 Elsevier B.V. All rights reserved.

Effect of Magnetic Field on Photoresponse of Cobalt Integrated Zinc Oxide Nanorods

Cobalt integrated zinc oxide nanorod (Co-ZnO NR) array is presented as a novel heterostructure for ultraviolet (UV) photodetector (PD). Defect states in Co-ZnO NRs surface induces an enhancement in photocurrent as compared to pristine ZnO NRs PD. Presented Co-ZnO NRs PD is highly sensitive to external magnetic field that demonstrated 185.7% enhancement in response current. It is concluded that the opposite polarizations of electron and holes in the presence of external magnetic field contribute to effective separation of electron hole pairs that have drifted upon UV illumination. Moreover, Co-ZnO NRs PD shows a faster photodetection speed (1.2 s response time and 7.4 s recovery time) as compared to the pristine ZnO NRs where the response and recovery times are observed as 38 and 195 s, respectively.

Fabrication of Microfluidic-Nanofluidic Channels with Integrated Electrodes

We report on the fabrication of microfluidc-nanofluidic channels on Si incorporated with embedded metallic interconnects. The device aids the study of motion of dispersed particles relative to the fluid under the influence of spatially uniform electric field. Optical lithography in combination with focused ion beam technique was used to fabricate the microfluidic-nanofluidic channels, respectively. Focused ion beam technique was also used for embedding the electrodes in the nanochannel. Gold contact pads were deposited using sputtering. The substrate was finally anodically bonded to a glass substrate.

SMO: An Integrated Approach to Intra-array and Inter-array Storage Optimization

The polyhedral model provides an expressive intermediate representation that is convenient for the analysis and subsequent transformation of affine loop nests. Several heuristics exist for achieving complex program transformations in this model. However, there is also considerable scope to utilize this model to tackle the problem of automatic memory footprint optimization. In this paper, we present a new automatic storage optimization technique which can be used to achieve both intra-array as well as inter-array storage reuse with a pre-determined schedule for the computation. Our approach works by finding statement-wise storage partitioning hyper planes that partition a unified global array space so that values with overlapping live ranges are not mapped to the same partition. Our heuristic is driven by a fourfold objective function which not only minimizes the dimensionality and storage requirements of arrays required for each high-level statement, but also maximizes inter statement storage reuse. The storage mappings obtained using our heuristic can be asymptotically better than those obtained by any existing technique. We implement our technique and demonstrate its practical impact by evaluating its effectiveness on several benchmarks chosen from the domains of image processing, stencil computations, and high-performance computing.