Bending Of Circular Plate On Elastic-Foundation

The governing differential equation of linear, elastic, thin, circular plate of uniform thickness, subjected to uniformly distributed load and resting on Winkler-Pasternak type foundation is solved using ``Chebyshev Polynomials''. Analysis is carried out using Lenczos' technique, both for simply supported and clamped plates. Numerical results thus obtained by perturbing the differential equation for plates without foundation are compared and are found to be in good agreement with the available results. The effect of foundation on central deflection of the plate is shown in the form of graphs.

Improvement in Intrusion Detection With Advances in Sensor Fusion

Various intrusion detection systems (IDSs) reported in the literature have shown distinct preferences for detecting a certain class of attack with improved accuracy, while performing moderately on the other classes. In view of the enormous computing power available in the present-day processors, deploying multiple IDSs in the same network to obtain best-of-breed solutions has been attempted earlier. The paper presented here addresses the problem of optimizing the performance of IDSs using sensor fusion with multiple sensors. The trade-off between the detection rate and false alarms with multiple sensors is highlighted. It is illustrated that the performance of the detector is better when the fusion threshold is determined according to the Chebyshev inequality. In the proposed data-dependent decision ( DD) fusion method, the performance optimization of ndividual IDSs is first addressed. A neural network supervised learner has been designed to determine the weights of individual IDSs depending on their reliability in detecting a certain attack. The final stage of this DD fusion architecture is a sensor fusion unit which does the weighted aggregation in order to make an appropriate decision. This paper theoretically models the fusion of IDSs for the purpose of demonstrating the improvement in performance, supplemented with the empirical evaluation.

Proximinality in Banach spaces

In this paper, we study approximatively τ-compact and τ-strongly Chebyshev sets, where τ is the norm or the weak topology. We show that the metric projection onto τ-strongly Chebyshev sets are norm-τ continuous. We characterize approximatively τ-compact and τ-strongly Chebyshev hyperplanes and use them to characterize factor reflexive proximinal subspaces in τ-almost locally uniformly rotund spaces. We also prove some stability results on approximatively τ-compact and τ-strongly Chebyshev subspaces.

Selection of intrusion detection system threshold bounds for effective sensor fusion

The motivation behind the fusion of Intrusion Detection Systems was the realization that with the increasing traffic and increasing complexity of attacks, none of the present day stand-alone Intrusion Detection Systems can meet the high demand for a very high detection rate and an extremely low false positive rate. Multi-sensor fusion can be used to meet these requirements by a refinement of the combined response of different Intrusion Detection Systems. In this paper, we show the design technique of sensor fusion to best utilize the useful response from multiple sensors by an appropriate adjustment of the fusion threshold. The threshold is generally chosen according to the past experiences or by an expert system. In this paper, we show that the choice of the threshold bounds according to the Chebyshev inequality principle performs better. This approach also helps to solve the problem of scalability and has the advantage of failsafe capability. This paper theoretically models the fusion of Intrusion Detection Systems for the purpose of proving the improvement in performance, supplemented with the empirical evaluation. The combination of complementary sensors is shown to detect more attacks than the individual components. Since the individual sensors chosen detect sufficiently different attacks, their result can be merged for improved performance. The combination is done in different ways like (i) taking all the alarms from each system and avoiding duplications, (ii) taking alarms from each system by fixing threshold bounds, and (iii) rule-based fusion with a priori knowledge of the individual sensor performance. A number of evaluation metrics are used, and the results indicate that there is an overall enhancement in the performance of the combined detector using sensor fusion incorporating the threshold bounds and significantly better performance using simple rule-based fusion.

Stability Analysis of Composite Skew Plates Using a Dynamic Method

Stability analysis is carried out considering free lateral vibrations of simply supported composite skew plates that are subjected to both direct and shear in-plane forces. An oblique stress component representation is used, consistent with the skew-geometry of the plate. A double series, expressed in Chebyshev polynomials, is used here as the assumed deflection surface and Ritz method of solution is employed. Numerical results for different combinations of side ratios, skew angle, and in-plane loadings that act individually or in combination are obtained. In this method, the in-plane load parameter is varied until the fundamental frequency goes to zero. The value of the in-plane load then corresponds to a critical buckling load. Plots of frequency parameter versus in-plane loading are given for a few typical cases. Details of crossings and quasi degeneracies of these curves are presented.

Chance constrained uncertain classification via robust optimization

This paper studies the problem of constructing robust classifiers when the training is plagued with uncertainty. The problem is posed as a Chance-Constrained Program (CCP) which ensures that the uncertain data points are classified correctly with high probability. Unfortunately such a CCP turns out to be intractable. The key novelty is in employing Bernstein bounding schemes to relax the CCP as a convex second order cone program whose solution is guaranteed to satisfy the probabilistic constraint. Prior to this work, only the Chebyshev based relaxations were exploited in learning algorithms. Bernstein bounds employ richer partial information and hence can be far less conservative than Chebyshev bounds. Due to this efficient modeling of uncertainty, the resulting classifiers achieve higher classification margins and hence better generalization. Methodologies for classifying uncertain test data points and error measures for evaluating classifiers robust to uncertain data are discussed. Experimental results on synthetic and real-world datasets show that the proposed classifiers are better equipped to handle data uncertainty and outperform state-of-the-art in many cases.

Maximum Margin Classifiers with Specified False Positive and False Negative Error Rates

This paper addresses the problem of maximum margin classification given the moments of class conditional densities and the false positive and false negative error rates. Using Chebyshev inequalities, the problem can be posed as a second order cone programming problem. The dual of the formulation leads to a geometric optimization problem, that of computing the distance between two ellipsoids, which is solved by an iterative algorithm. The formulation is extended to non-linear classifiers using kernel methods. The resultant classifiers are applied to the case of classification of unbalanced datasets with asymmetric costs for misclassification. Experimental results on benchmark datasets show the efficacy of the proposed method.

Clustering Based Large Margin Classification: A Scalable Approach using SOCP Formulation

This paper presents a novel Second Order Cone Programming (SOCP) formulation for large scale binary classification tasks. Assuming that the class conditional densities are mixture distributions, where each component of the mixture has a spherical covariance, the second order statistics of the components can be estimated efficiently using clustering algorithms like BIRCH. For each cluster, the second order moments are used to derive a second order cone constraint via a Chebyshev-Cantelli inequality. This constraint ensures that any data point in the cluster is classified correctly with a high probability. This leads to a large margin SOCP formulation whose size depends on the number of clusters rather than the number of training data points. Hence, the proposed formulation scales well for large datasets when compared to the state-of-the-art classifiers, Support Vector Machines (SVMs). Experiments on real world and synthetic datasets show that the proposed algorithm outperforms SVM solvers in terms of training time and achieves similar accuracies.

Static balancing of a four-bar linkage and its cognates

Motivated by the need to statically balance the inherent elastic forces in linkages, this paper presents three techniques to statically balance a four-bar linkage loaded by a zero-free-length spring attached between its coupler point and an anchor point on the ground. The number of auxiliary links and balancing springs required for the three techniques is less than or equal to that of the only technique currently in the literature. One of the three techniques does not require auxiliary links. In these techniques, the set of values for the spring constants and the ground-anchor point of the balancing springs can vary over a one-parameter family. Thrice as many balancing choices are available when the cognates are considered. The ensuing numerous options enable a user to choose the most practical solution. To facilitate the evaluation of the balancing choices for all the cognates, Roberts-Chebyshev cognate theorem is extended to statically balanced four-bar linkages. (C) 2011 Elsevier Ltd. All rights reserved.

Robust formulations for clustering-based large-scale classification

Chebyshev-inequality-based convex relaxations of Chance-Constrained Programs (CCPs) are shown to be useful for learning classifiers on massive datasets. In particular, an algorithm that integrates efficient clustering procedures and CCP approaches for computing classifiers on large datasets is proposed. The key idea is to identify high density regions or clusters from individual class conditional densities and then use a CCP formulation to learn a classifier on the clusters. The CCP formulation ensures that most of the data points in a cluster are correctly classified by employing a Chebyshev-inequality-based convex relaxation. This relaxation is heavily dependent on the second-order statistics. However, this formulation and in general such relaxations that depend on the second-order moments are susceptible to moment estimation errors. One of the contributions of the paper is to propose several formulations that are robust to such errors. In particular a generic way of making such formulations robust to moment estimation errors is illustrated using two novel confidence sets. An important contribution is to show that when either of the confidence sets is employed, for the special case of a spherical normal distribution of clusters, the robust variant of the formulation can be posed as a second-order cone program. Empirical results show that the robust formulations achieve accuracies comparable to that with true moments, even when moment estimates are erroneous. Results also illustrate the benefits of employing the proposed methodology for robust classification of large-scale datasets.

Estimation of Probabilistic Bounds on Phase CPI and Relevance in WCET Analysis

Estimating program worst case execution time(WCET) accurately and efficiently is a challenging task. Several programs exhibit phase behavior wherein cycles per instruction (CPI) varies in phases during execution. Recent work has suggested the use of phases in such programs to estimate WCET with minimal instrumentation. However the suggested model uses a function of mean CPI that has no probabilistic guarantees. We propose to use Chebyshev's inequality that can be applied to any arbitrary distribution of CPI samples, to probabilistically bound CPI of a phase. Applying Chebyshev's inequality to phases that exhibit high CPI variation leads to pessimistic upper bounds. We propose a mechanism that refines such phases into sub-phases based on program counter(PC) signatures collected using profiling and also allows the user to control variance of CPI within a sub-phase. We describe a WCET analyzer built on these lines and evaluate it with standard WCET and embedded benchmark suites on two different architectures for three chosen probabilities, p={0.9, 0.95 and 0.99}. For p= 0.99, refinement based on PC signatures alone, reduces average pessimism of WCET estimate by 36%(77%) on Arch1 (Arch2). Compared to Chronos, an open source static WCET analyzer, the average improvement in estimates obtained by refinement is 5%(125%) on Arch1 (Arch2). On limiting variance of CPI within a sub-phase to {50%, 10%, 5% and 1%} of its original value, average accuracy of WCET estimate improves further to {9%, 11%, 12% and 13%} respectively, on Arch1. On Arch2, average accuracy of WCET improves to 159% when CPI variance is limited to 50% of its original value and improvement is marginal beyond that point.

Steady mixed convection flow of Maxwell fluid over an exponentially stretching vertical surface with magnetic field and viscous dissipation

The steady mixed convection flow and heat transfer from an exponentially stretching vertical surface in a quiescent Maxwell fluid in the presence of magnetic field, viscous dissipation and Joule heating have been studied. The stretching velocity, surface temperature and magnetic field are assumed to have specific exponential function forms for the existence of the local similarity solution. The coupled nonlinear ordinary differential equations governing the local similarity flow and heat transfer have been solved numerically by Chebyshev finite difference method. The influence of the buoyancy parameter, viscous dissipation, relaxation parameter of Maxwell fluid, magnetic field and Prandtl number on the flow and heat transfer has been considered in detail. The Nusselt number increases significantly with the Prandtl number, but the skin friction coefficient decreases. The Nusselt number slightly decreases with increasing viscous dissipation parameter, but the skin friction coefficient slightly increases. Maxwell fluid reduces both skin friction coefficient and Nusselt number, whereas buoyancy force enhances them.

Frequency Domain Based Solution for Certain Class of Wave Equations: An exhaustive study of Numerical Solutions

The paper discusses the frequency domain based solution for a certain class of wave equations such as: a second order partial differential equation in one variable with constant and varying coefficients (Cantilever beam) and a coupled second order partial differential equation in two variables with constant and varying coefficients (Timoshenko beam). The exact solution of the Cantilever beam with uniform and varying cross-section and the Timoshenko beam with uniform cross-section is available. However, the exact solution for Timoshenko beam with varying cross-section is not available. Laplace spectral methods are used to solve these problems exactly in frequency domain. The numerical solution in frequency domain is done by discretisation in space by approximating the unknown function using spectral functions like Chebyshev polynomials, Legendre polynomials and also Normal polynomials. Different numerical methods such as Galerkin Method, Petrov- Galerkin method, Method of moments and Collocation method or the Pseudo-spectral method in frequency domain are studied and compared with the available exact solution. An approximate solution is also obtained for the Timoshenko beam with varying cross-section using Laplace Spectral Element Method (LSEM). The group speeds are computed exactly for the Cantilever beam and Timoshenko beam with uniform cross-section and is compared with the group speeds obtained numerically. The shear mode and the bending modes of the Timoshenko beam with uniform cross-section are separated numerically by applying a modulated pulse as the shear force and the corresponding group speeds for varying taper parameter in are obtained numerically by varying the frequency of the input pulse. An approximate expression for calculating group speeds corresponding to the shear mode and the bending mode, and also the cut-off frequency is obtained. Finally, we show that the cut-off frequency disappears for large in, for epsilon > 0 and increases for large in, for epsilon < 0.

Instabilities in a fluid overlying an inclined anisotropic and inhomogeneous porous layer

In this paper, linear stability analysis on a Newtonian fluid film flowing under the effect of gravity over an inclined porous medium saturated with the same fluid in isothermal condition is carried out. The focus is placed on the effect of the anisotropic and inhomogeneous variations in the permeability of the porous medium on the shear mode and surface mode instabilities. The fluid-porous system is modelled by a coupled two-dimensional Navier-Stokes/Darcy problem. The perturbation equations are solved numerically using the Chebyshev collocation method. Detailed stability characteristics as a function of the depth ratio (the ratio of the depth of the fluid layer to that of the porous layer), the anisotropic parameter (the ratio of the permeability in the direction of the basic flow to that in the direction transverse to the basic flow) and the inhomogeneity functions are presented.

Spectral solutions to the Korteweg-de-Vries and nonlinear Schrodinger equations

In this paper, we present the solutions of 1-D and 2-D non-linear partial differential equations with initial conditions. We approach the solutions in time domain using two methods. We first solve the equations using Fourier spectral approximation in the spatial domain and secondly we compare the results with the approximation in the spatial domain using orthogonal functions such as Legendre or Chebyshev polynomials as their basis functions. The advantages and the applicability of the two different methods for different types of problems are brought out by considering 1-D and 2-D nonlinear partial differential equations namely the Korteweg-de-Vries and nonlinear Schrodinger equation with different potential function. (C) 2015 Elsevier Ltd. All rights reserved.