Profiling k-Iteration Paths : A Generalization of the Ball-Larus Profiling Algorithm

The Ball-Larus path-profiling algorithm is an efficient technique to collect acyclic path frequencies of a program. However, longer paths -those extending across loop iterations - describe the runtime behaviour of programs better. We generalize the Ball-Larus profiling algorithm for profiling k-iteration paths - paths that can span up to to k iterations of a loop. We show that it is possible to number suchk-iteration paths perfectly, thus allowing for an efficient profiling algorithm for such longer paths. We also describe a scheme for mixed-mode profiling: profiling different parts of a procedure with different path lengths. Experimental results show that k-iteration profiling is realistic.

Generalization of Dynkin's Identity and Some Applications

Let X(t) be a right continuous temporally homogeneous Markov pro- cess, Tt the corresponding semigroup and A the weak infinitesimal genera- tor. Let g(t) be absolutely continuous and r a stopping time satisfying E.( S f I g(t) I dt) < oo and E.( f " I g'(t) I dt) < oo Then for f e 9iJ(A) with f(X(t)) right continuous the identity Exg(r)f(X(z)) - g(O)f(x) = E( 5 " g'(s)f(X(s)) ds) + E.( 5 " g(s)Af(X(s)) ds) is a simple generalization of Dynkin's identity (g(t) 1). With further restrictions on f and r the following identity is obtained as a corollary: Ex(f(X(z))) = f(x) + k! Ex~rkAkf(X(z))) + n-1E + (n ) )!.E,(so un-1Anf(X(u)) du). These identities are applied to processes with stationary independent increments to obtain a number of new and known results relating the moments of stopping times to the moments of the stopped processes.

Analysis,Insights and Generalization of a Fast Decentralized Relay Selection Mechanism

Relay selection for cooperative communications has attracted considerable research interest recently. While several criteria have been proposed for selecting one or more relays and analyzed, mechanisms that perform the selection in a distributed manner have received relatively less attention. In this paper, we analyze a splitting algorithm for selecting the single best relay amongst a known number of active nodes in a cooperative network. We develop new and exact asymptotic analysis for computing the average number of slots required to resolve the best relay. We then propose and analyze a new algorithm that addresses the general problem of selecting the best Q >= 1 relays. Regardless of the number of relays, the algorithm selects the best two relays within 4.406 slots and the best three within 6.491 slots, on average. Our analysis also brings out an intimate relationship between multiple access selection and multiple access control algorithms.

Thermomechanical generalization of pin joints in finite plates

The understanding of thermoelastic behaviour of joints is significant in order to ensure the integrity of large and complex structures exposed to a thermal environment, particularly in fields such as aerospace and nuclear engineering. Thermomechanical generalization of partial contact behaviour of a pin joint under combined in-plane mechanical loading and on-axis unidirectional heat flow has already been established by the authors for the analytically simpler domains of large plates. This paper successfully extends the on-going investigation to a single pin in a finite rectangular isotropic plate as a two-dimensional abstraction from a practical situation of a multipin fastener joint. The finite element method is used to analyse the joint problem under on-axis thermomechanical loading and unified load-contact relationships are established for a class of loading conditions.

Generalization of Abrams' law

Considering cement based composites as chemically bonded ceramics (CBC) the consequent strength development with age is essentially a constant volume solidification process, such that the hydrated gel particles fill the space resulting in the compatible gel space ratios. Analysis has been done of the extensively used graphical method of mix design (British method of mix design) i.e., the relation between the compressive strength and the free water - cement ratio. By considering the strength (S) at w/c 0.5 (S-0.5) as the reference state to reflect the synergetic effects between constituents of concrete a generalized relationship obtained is of the form {S/S-0.5} = a + b {1/(w/c)}.

Thermomechanical generalization of partial contact in pin joints

Mechanical fasteners introduce structural weakness, still they are an essential constituent of most structures as they permit interchangeability of parts and flexible construction programs; Variable temperature operations of Aerospace and Nuclear structures make it imperative to investigate the thermoelastic behaviour of joints. This paper explores analytically similar mechanical and thermal parameters to generalise the thermomechanical behaviour of a pin joint in an isotropic Sheet for a class of configurations. This generalization enables virtually direct application of existing information regarding joints under pure mechanical loading to joints subjected to combined thermomechanical loading, thus reducing the efforts of both the analyst and the designer by an order of magnitude. Copyright (C) 1996 Published by Elsevier Science Ltd.

Generalization of the collision cone approach for motion safety in 3-D environments

Avoidance of collision between moving objects in a 3-D environment is fundamental to the problem of planning safe trajectories in dynamic environments. This problem appears in several diverse fields including robotics, air vehicles, underwater vehicles and computer animation. Most of the existing literature on collision prediction assumes objects to be modelled as spheres. While the conservative spherical bounding box is valid in many cases, in many other cases, where objects operate in close proximity, a less conservative approach, that allows objects to be modelled using analytic surfaces that closely mimic the shape of the object, is more desirable. In this paper, a collision cone approach (previously developed only for objects moving on a plane) is used to determine collision between objects, moving in 3-D space, whose shapes can be modelled by general quadric surfaces. Exact collision conditions for such quadric surfaces are obtained and used to derive dynamic inversion based avoidance strategies.

On improving the generalization of SVM classifier

The generalization performance of the SVM classifier depends mainly on the VC dimension and the dimensionality of the data. By reducing the VC dimension of the SVM classifier, its generalization performance is expected to increase. In the present paper, we argue that the VC dimension of SVM classifier can be reduced by applying bootstrapping and dimensionality reduction techniques. Experimental results showed that bootstrapping the original data and bootstrapping the projected (dimensionally reduced) data improved the performance of the SVM classifier.

Generalization of deviated linear cyclic pursuit

Earlier work on cyclic pursuit systems has shown that using heterogeneous gains for agents in linear cyclic pursuit, the point of convergence (rendezvous point) can be chosen arbitrarily. But there are some restrictions on this set of reachable points. The use of deviated cyclic pursuit, as discussed in this paper, expands this set of reachable points to include points which are not reachable by any known linear cyclic pursuit scheme. The limits on the deviations are determined by stability considerations. Such limits have been analytically obtained in this paper along with results on the expansion in reachable set and the latter has also been verified through simulations.

Global response sensitivity analysis using probability distance measures and generalization of Sobol's analysis

The study introduces two new alternatives for global response sensitivity analysis based on the application of the L-2-norm and Hellinger's metric for measuring distance between two probabilistic models. Both the procedures are shown to be capable of treating dependent non-Gaussian random variable models for the input variables. The sensitivity indices obtained based on the L2-norm involve second order moments of the response, and, when applied for the case of independent and identically distributed sequence of input random variables, it is shown to be related to the classical Sobol's response sensitivity indices. The analysis based on Hellinger's metric addresses variability across entire range or segments of the response probability density function. The measure is shown to be conceptually a more satisfying alternative to the Kullback-Leibler divergence based analysis which has been reported in the existing literature. Other issues addressed in the study cover Monte Carlo simulation based methods for computing the sensitivity indices and sensitivity analysis with respect to grouped variables. Illustrative examples consist of studies on global sensitivity analysis of natural frequencies of a random multi-degree of freedom system, response of a nonlinear frame, and safety margin associated with a nonlinear performance function. (C) 2015 Elsevier Ltd. All rights reserved.

A Generalization of Gravity

I consider theories of gravity built not just from the metric and affine connection, but also other (possibly higher rank) symmetric tensor(s). The Lagrangian densities are scalars built from them, and the volume forms are related to Cayley's hyperdeterminants. The resulting diff-invariant actions give rise to geometric theories that go beyond the metric paradigm (even metric-less theories are possible), and contain Einstein gravity as a special case. Examples contain theories with generalizeations of Riemannian geometry. The 0-tensor case is related to dilaton gravity. These theories can give rise to new types of spontaneous Lorentz breaking and might be relevant for ``dark'' sector cosmology.

No-reference image quality assessment using modified extreme learning machine classifier

In this paper, we present a machine learning approach to measure the visual quality of JPEG-coded images. The features for predicting the perceived image quality are extracted by considering key human visual sensitivity (HVS) factors such as edge amplitude, edge length, background activity and background luminance. Image quality assessment involves estimating the functional relationship between HVS features and subjective test scores. The quality of the compressed images are obtained without referring to their original images ('No Reference' metric). Here, the problem of quality estimation is transformed to a classification problem and solved using extreme learning machine (ELM) algorithm. In ELM, the input weights and the bias values are randomly chosen and the output weights are analytically calculated. The generalization performance of the ELM algorithm for classification problems with imbalance in the number of samples per quality class depends critically on the input weights and the bias values. Hence, we propose two schemes, namely the k-fold selection scheme (KS-ELM) and the real-coded genetic algorithm (RCGA-ELM) to select the input weights and the bias values such that the generalization performance of the classifier is a maximum. Results indicate that the proposed schemes significantly improve the performance of ELM classifier under imbalance condition for image quality assessment. The experimental results prove that the estimated visual quality of the proposed RCGA-ELM emulates the mean opinion score very well. The experimental results are compared with the existing JPEG no-reference image quality metric and full-reference structural similarity image quality metric.

Finite volume evolution Galerkin method for hyperbolic conservation laws with spatially varying flux functions

We present a generalization of the finite volume evolution Galerkin scheme [M. Lukacova-Medvid'ova,J. Saibertov'a, G. Warnecke, Finite volume evolution Galerkin methods for nonlinear hyperbolic systems, J. Comp. Phys. (2002) 183 533-562; M. Luacova-Medvid'ova, K.W. Morton, G. Warnecke, Finite volume evolution Galerkin (FVEG) methods for hyperbolic problems, SIAM J. Sci. Comput. (2004) 26 1-30] for hyperbolic systems with spatially varying flux functions. Our goal is to develop a genuinely multi-dimensional numerical scheme for wave propagation problems in a heterogeneous media. We illustrate our methodology for acoustic waves in a heterogeneous medium but the results can be generalized to more complex systems. The finite volume evolution Galerkin (FVEG) method is a predictor-corrector method combining the finite volume corrector step with the evolutionary predictor step. In order to evolve fluxes along the cell interfaces we use multi-dimensional approximate evolution operator. The latter is constructed using the theory of bicharacteristics under the assumption of spatially dependent wave speeds. To approximate heterogeneous medium a staggered grid approach is used. Several numerical experiments for wave propagation with continuous as well as discontinuous wave speeds confirm the robustness and reliability of the new FVEG scheme.

A linear programming approach for estimating the structure of a sparse linear genetic network from transcript profiling data

Background: A genetic network can be represented as a directed graph in which a node corresponds to a gene and a directed edge specifies the direction of influence of one gene on another. The reconstruction of such networks from transcript profiling data remains an important yet challenging endeavor. A transcript profile specifies the abundances of many genes in a biological sample of interest. Prevailing strategies for learning the structure of a genetic network from high-dimensional transcript profiling data assume sparsity and linearity. Many methods consider relatively small directed graphs, inferring graphs with up to a few hundred nodes. This work examines large undirected graphs representations of genetic networks, graphs with many thousands of nodes where an undirected edge between two nodes does not indicate the direction of influence, and the problem of estimating the structure of such a sparse linear genetic network (SLGN) from transcript profiling data. Results: The structure learning task is cast as a sparse linear regression problem which is then posed as a LASSO (l1-constrained fitting) problem and solved finally by formulating a Linear Program (LP). A bound on the Generalization Error of this approach is given in terms of the Leave-One-Out Error. The accuracy and utility of LP-SLGNs is assessed quantitatively and qualitatively using simulated and real data. The Dialogue for Reverse Engineering Assessments and Methods (DREAM) initiative provides gold standard data sets and evaluation metrics that enable and facilitate the comparison of algorithms for deducing the structure of networks. The structures of LP-SLGNs estimated from the INSILICO1, INSILICO2 and INSILICO3 simulated DREAM2 data sets are comparable to those proposed by the first and/or second ranked teams in the DREAM2 competition. The structures of LP-SLGNs estimated from two published Saccharomyces cerevisae cell cycle transcript profiling data sets capture known regulatory associations. In each S. cerevisiae LP-SLGN, the number of nodes with a particular degree follows an approximate power law suggesting that its degree distributions is similar to that observed in real-world networks. Inspection of these LP-SLGNs suggests biological hypotheses amenable to experimental verification. Conclusion: A statistically robust and computationally efficient LP-based method for estimating the topology of a large sparse undirected graph from high-dimensional data yields representations of genetic networks that are biologically plausible and useful abstractions of the structures of real genetic networks. Analysis of the statistical and topological properties of learned LP-SLGNs may have practical value; for example, genes with high random walk betweenness, a measure of the centrality of a node in a graph, are good candidates for intervention studies and hence integrated computational – experimental investigations designed to infer more realistic and sophisticated probabilistic directed graphical model representations of genetic networks. The LP-based solutions of the sparse linear regression problem described here may provide a method for learning the structure of transcription factor networks from transcript profiling and transcription factor binding motif data.

Systematic Construction of Linear Transform Based Full-Diversity, Rate-One Space-Time Frequency Codes

In this paper, we generalize the existing rate-one space frequency (SF) and space-time frequency (STF) code constructions. The objective of this exercise is to provide a systematic design of full-diversity STF codes with high coding gain. Under this generalization, STF codes are formulated as linear transformations of data. Conditions on these linear transforms are then derived so that the resulting STF codes achieve full diversity and high coding gain with a moderate decoding complexity. Many of these conditions involve channel parameters like delay profile (DP) and temporal correlation. When these quantities are not available at the transmitter, design of codes that exploit full diversity on channels with arbitrary DIP and temporal correlation is considered. Complete characterization of a class of such robust codes is provided and their bit error rate (BER) performance is evaluated. On the other hand, when channel DIP and temporal correlation are available at the transmitter, linear transforms are optimized to maximize the coding gain of full-diversity STF codes. BER performance of such optimized codes is shown to be better than those of existing codes.