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.

Fermion Electric Dipole Moments in R-parity violating Supersymmetry

In this talk I discuss some aspects of the study of electric dipole moments (EDMs) of the fermions, in the context of R-parity violating (\rpv) Supersymmetry (SUSY). I will start with a brief general discussion of how dipole moments, in general, serve as a probe of physics beyond the Standard Model (SM) and an even briefer summary of \rpv SUSY. I will follow by discussing a general method of analysis for obtaining the leading fermion mass dependence of the dipole moments and present its application to \rpv SUSY case. Then I will summarise the constraints that the analysis of $e,n$ and $Hg$ EDMs provide for the case of trilinear \rpv SUSY couplings and make a few comments on the case of bilinear \rpv, where the general method of analysis proposed by us does not work.

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.

Temporal Moments for Reactive Transport through Fractured Impermeable/Permeable Formations

The transport of reactive solutes through fractured porous formations has been analyzed. The transport through the porous block is represented by a general multiprocess nonequilibrium equation (MPNE), which, for the fracture, is represented by an advection-dispersion equation with linear equilibrium sorption and first-order transformation. An implicit finite-difference technique has been used to solve the two coupled equations. The transport characteristics have been analyzed in terms of zeroth, first, and second temporal moments of the solute in the fracture. The solute behavior for fractured impermeable and fractured permeable formations are first compared and the effects of various fracture and matrix transport parameters are analyzed. Subsequently, the transport through a fractured permeable formation is analyzed to ascertain the effect of equilibrium sorption, rate-limited sorption, and the multiprocess nonequilibrium transport process. It was found that the temporal moments were nearly identical for the fractured impermeable and permeable formations when both the diffusion coefficient and the first-order transformation coefficient were relatively large. The multiprocess nonequilibrium model resulted in a smaller mass recovery in the fracture and higher dispersion than the equilibrium and rate-limited sorption models. DOI: 10.1061/(ASCE)HE.19435584.0000586. (C) 2012 American Society of Civil Engineers.

An Adaptive Conditional Zero-Forcing Decoder With Full-Diversity, Least Complexity and Essentially-ML Performance for STBCs

A low complexity, essentially-ML decoding technique for the Golden code and the three antenna Perfect code was introduced by Sirianunpiboon, Howard and Calderbank. Though no theoretical analysis of the decoder was given, the simulations showed that this decoding technique has almost maximum-likelihood (ML) performance. Inspired by this technique, in this paper we introduce two new low complexity decoders for Space-Time Block Codes (STBCs)-the Adaptive Conditional Zero-Forcing (ACZF) decoder and the ACZF decoder with successive interference cancellation (ACZF-SIC), which include as a special case the decoding technique of Sirianunpiboon et al. We show that both ACZF and ACZF-SIC decoders are capable of achieving full-diversity, and we give a set of sufficient conditions for an STBC to give full-diversity with these decoders. We then show that the Golden code, the three and four antenna Perfect codes, the three antenna Threaded Algebraic Space-Time code and the four antenna rate 2 code of Srinath and Rajan are all full-diversity ACZF/ACZF-SIC decodable with complexity strictly less than that of their ML decoders. Simulations show that the proposed decoding method performs identical to ML decoding for all these five codes. These STBCs along with the proposed decoding algorithm have the least decoding complexity and best error performance among all known codes for transmit antennas. We further provide a lower bound on the complexity of full-diversity ACZF/ACZF-SIC decoding. All the five codes listed above achieve this lower bound and hence are optimal in terms of minimizing the ACZF/ACZF-SIC decoding complexity. Both ACZF and ACZF-SIC decoders are amenable to sphere decoding implementation.

Inversion of moments to retrieve joint probabilities in quantum sequential measurements

A sequence of moments obtained from statistical trials encodes a classical probability distribution. However, it is well known that an incompatible set of moments arises in the quantum scenario, when correlation outcomes associated with measurements on spatially separated entangled states are considered. This feature, viz., the incompatibility of moments with a joint probability distribution, is reflected in the violation of Bell inequalities. Here, we focus on sequential measurements on a single quantum system and investigate if moments and joint probabilities are compatible with each other. By considering sequential measurement of a dichotomic dynamical observable at three different time intervals, we explicitly demonstrate that the moments and the probabilities are inconsistent with each other. Experimental results using a nuclear magnetic resonance system are reported here to corroborate these theoretical observations, viz., the incompatibility of the three-time joint probabilities with those extracted from the moment sequence when sequential measurements on a single-qubit system are considered.

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.

Expansions of tau hadronic spectral function moments in a nonpower QCD perturbation theory with tamed large order behavior

The moments of the hadronic spectral functions are of interest for the extraction of the strong coupling alpha(s) and other QCD parameters from the hadronic decays of the tau lepton. Motivated by the recent analyses of a large class of moments in the standard fixed-order and contour-improved perturbation theories, we consider the perturbative behavior of these moments in the framework of a QCD nonpower perturbation theory, defined by the technique of series acceleration by conformal mappings, which simultaneously implements renormalization-group summation and has a tame large-order behavior. Two recently proposed models of the Adler function are employed to generate the higher-order coefficients of the perturbation series and to predict the exact values of the moments, required for testing the properties of the perturbative expansions. We show that the contour-improved nonpower perturbation theories and the renormalization-group-summed nonpower perturbation theories have very good convergence properties for a large class of moments of the so-called ``reference model,'' including moments that are poorly described by the standard expansions. The results provide additional support for the plausibility of the description of the Adler function in terms of a small number of dominant renormalons.

Vorticity moments in four numerical simulations of the 3D Navier-Stokes equations

The issue of intermittency in numerical solutions of the 3D Navier-Stokes equations on a periodic box 0, L](3) is addressed through four sets of numerical simulations that calculate a new set of variables defined by D-m(t) = (pi(-1)(0) Omega(m))(alpha m) for 1 <= m <= infinity where alpha(m) = 2m/(4m - 3) and Omega(m)(t)](2m) = L-3 integral(v) vertical bar omega vertical bar(2m) dV with pi(0) = vL(-2). All four simulations unexpectedly show that the D-m are ordered for m = 1,..., 9 such that Dm+1 < D-m. Moreover, the D-m squeeze together such that Dm+1/D-m NE arrow 1 as m increases. The values of D-1 lie far above the values of the rest of the D-m, giving rise to a suggestion that a depletion of nonlinearity is occurring which could be the cause of Navier-Stokes regularity. The first simulation is of very anisotropic decaying turbulence; the second and third are of decaying isotropic turbulence from random initial conditions and forced isotropic turbulence at fixed Grashof number respectively; the fourth is of very-high-Reynolds-number forced, stationary, isotropic turbulence at up to resolutions of 4096(3).

Conditional silencing of topoisomerase I gene of Mycobacterium tuberculosis validates its essentiality for cell survival

Topoisomerases are an important class of enzymes for regulating the DNA transaction processes. Mycobacterium tuberculosis (Mtb) is one of the most formidable pathogens also posing serious challenges for therapeutic interventions. The organism contains only one type IA topoisomerase (Rv3646c), offering an opportunity to test its potential as a candidate drug target. To validate the essentiality of M.tuberculosis topoisomerase I (TopoI(Mt)) for bacterial growth and survival, we have generated a conditionally regulated strain of topoI in Mtb. The conditional knockdown mutant exhibited delayed growth on agar plate. In liquid culture, the growth was drastically impaired when TopoI expression was suppressed. Additionally, novobiocin and isoniazid showed enhanced inhibitory potential against the conditional mutant. Analysis of the nucleoid revealed its altered architecture upon TopoI depletion. These studies establish the essentiality of TopoI for the M.tuberculosis growth and open up new avenues for targeting the enzyme.

Hardware Accelerator for 3D Method of Moments based Parasitic Extraction

A Field Programmable Gate Array (FPGA) based hardware accelerator for multi-conductor parasitic capacitance extraction, using Method of Moments (MoM), is presented in this paper. Due to the prohibitive cost of solving a dense algebraic system formed by MoM, linear complexity fast solver algorithms have been developed in the past to expedite the matrix-vector product computation in a Krylov sub-space based iterative solver framework. However, as the number of conductors in a system increases leading to a corresponding increase in the number of right-hand-side (RHS) vectors, the computational cost for multiple matrix-vector products present a time bottleneck, especially for ill-conditioned system matrices. In this work, an FPGA based hardware implementation is proposed to parallelize the iterative matrix solution for multiple RHS vectors in a low-rank compression based fast solver scheme. The method is applied to accelerate electrostatic parasitic capacitance extraction of multiple conductors in a Ball Grid Array (BGA) package. Speed-ups up to 13x over equivalent software implementation on an Intel Core i5 processor for dense matrix-vector products and 12x for QR compressed matrix-vector products is achieved using a Virtex-6 XC6VLX240T FPGA on Xilinx's ML605 board.

Accelerating method of moments based package-board 3D parasitic extraction using FPGA

In this article, a Field Programmable Gate Array (FPGA)-based hardware accelerator for 3D electromagnetic extraction, using Method of Moments (MoM) is presented. As the number of nets or ports in a system increases, leading to a corresponding increase in the number of right-hand-side (RHS) vectors, the computational cost for multiple matrix-vector products presents a time bottleneck in a linear-complexity fast solver framework. In this work, an FPGA-based hardware implementation is proposed toward a two-level parallelization scheme: (i) matrix level parallelization for single RHS and (ii) pipelining for multiple-RHS. The method is applied to accelerate electrostatic parasitic capacitance extraction of multiple nets in a Ball Grid Array (BGA) package. The acceleration is shown to be linearly scalable with FPGA resources and speed-ups over 10x against equivalent software implementation on a 2.4GHz Intel Core i5 processor is achieved using a Virtex-6 XC6VLX240T FPGA on Xilinx's ML605 board with the implemented design operating at 200MHz clock frequency. (c) 2016 Wiley Periodicals, Inc. Microwave Opt Technol Lett 58:776-783, 2016

Sidewall inclined slot in a rectangular waveguide: Theory and experiment

A novel analysis to compute the admittance characteristics of the slots cut in the narrow wall of a rectangular waveguide, which includes the corner diffraction effects and the finite waveguide wall thickness, is presented. A coupled magnetic field integral equation is formulated at the slot aperture which is solved by the Galerkin approach of the method of moments using entire domain sinusoidal basis functions. The externally scattered fields are computed using the finite difference method (FDM) coupled with the measured equation of invariance (MEI). The guide wall thickness forms a closed cavity and the fields inside it are evaluated using the standard FDM. The fields scattered inside the waveguide are formulated in the spectral domain for faster convergence compared to the traditional spatial domain expansions. The computed results have been compared with the experimental results and also with the measured data published in previous literature. Good agreement between the theoretical and experimental results is obtained to demonstrate the validity of the present analysis.

Some limit theorems for regenerative queues

We consider a single server queue with the interarrival times and the service times forming a regenerative sequence. This traffic class includes the standard models: lid, periodic, Markov modulated (e.g., BMAP model of Lucantoni [18]) and their superpositions. This class also includes the recently proposed traffic models in high speed networks, exhibiting long range dependence. Under minimal conditions we obtain the rates of convergence to stationary distributions, finiteness of stationary moments, various functional limit theorems and the continuity of stationary distributions and moments. We use the continuity results to obtain approximations for stationary distributions and moments of an MMPP/GI/1 queue where the modulating chain has a countable state space. We extend all our results to feedforward networks where the external arrivals to each queue can be regenerative. In the end we show that the output process of a leaky bucket is regenerative if the input process is and hence our results extend to a queue with arrivals controlled by a leaky bucket.