Building Support Vector Machines in the Context of Regularised Least Squares

This paper formulates a linear kernel support vector machine (SVM) as a regularized least-squares (RLS) problem. By defining a set of indicator variables of the errors, the solution to the RLS problem is represented as an equation that relates the error vector to the indicator variables. Through partitioning the training set, the SVM weights and bias are expressed analytically using the support vectors. It is also shown how this approach naturally extends to Sums with nonlinear kernels whilst avoiding the need to make use of Lagrange multipliers and duality theory. A fast iterative solution algorithm based on Cholesky decomposition with permutation of the support vectors is suggested as a solution method. The properties of our SVM formulation are analyzed and compared with standard SVMs using a simple example that can be illustrated graphically. The correctness and behavior of our solution (merely derived in the primal context of RLS) is demonstrated using a set of public benchmarking problems for both linear and nonlinear SVMs.

Positive almost Dunford-Pettis operators and their duality

We study some properties of almost Dunford-Pettis operators and we characterize pairs of Banach lattices for which the adjoint of an almost Dunford-Pettis operator inherits the same property and look at conditions under which an operator is almost Dunford-Pettis whenever its adjoint is.

The Hindered Self-Help: Housing Policies, Politics And Poverty In Kolkata, India

The housing dimension in Kolkata has been changing in recent years. Since 1991, the city has initiated housing reform that has taken many forms and manifestations characterized by the reduction in social allocation, cutbacks in public funding and promotion of a real estate culture in close partnership between the state and private actors. There has been increasing concern about the housing condition of the poor in the deserted slums and bustee settlements amidst the evident ‘poor blindness’ in housing and investment policies. Against this background the paper discusses self-help housing in Kolkata. It seeks to answer a simple question – why the concept of self-help has not been recognised as a viable policy option for a city with widespread slums and bustee settlements by visiting the complex urban context of Kolkata set within the city's politics, poverty and policies. The paper concludes that there is a need to recognise the existing structural duality in the city and support self-help housing as a parallel housing approach.

Genotypic and phenotypic diversity of the noncapsulated Haemophilus influenzae:Adaptation and pathogenesis in the human airways

The human respiratory tract contains a highly adapted microbiota including commensal and opportunistic pathogens. Noncapsulated or nontypable Haemophilus influenzae (NTHi) is a human-restricted member of the normal airway microbiota in healthy carriers and an opportunistic pathogen in immunocompromised individuals. The duality of NTHi as a colonizer and as a symptomatic infectious agent is closely related to its adaptation to the host, which in turn greatly relies on the genetic plasticity of the bacterium and is facilitated by its condition as a natural competent. The variable genotype of NTHi accounts for its heterogeneous gene expression and variable phenotype, leading to differential host-pathogen interplay among isolates. Here we review our current knowledge of NTHi diversity in terms of genotype, gene expression, antigenic variation, and the phenotypes associated with colonization and pathogenesis. The potential benefits of NTHi diversity studies discussed herein include the unraveling of pathogenicity clues, the generation of tools to predict virulence from genomic data, and the exploitation of a unique natural system for the continuous monitoring of long-term bacterial evolution in human airways exposed to noxious agents. Finally, we highlight the challenge of monitoring both the pathogen and the host in longitudinal studies, and of applying comparative genomics to clarify the meaning of the vast NTHi genetic diversity and its translation to virulence phenotypes.

Secrecy Capacity Analysis Over κ–μ Fading Channels: Theory and Applications

In this paper, we consider the transmission of confidential information over a κ-μ fading channel in the presence of an eavesdropper who also experiences κ-μ fading. In particular, we obtain novel analytical solutions for the probability of strictly positive secrecy capacity (SPSC) and a lower bound of secure outage probability (SOPL) for independent and non-identically distributed channel coefficients without parameter constraints. We also provide a closed-form expression for the probability of SPSC when the μ parameter is assumed to take positive integer values. Monte-Carlo simulations are performed to verify the derived results. The versatility of the κ-μ fading model means that the results presented in this paper can be used to determine the probability of SPSC and SOPL for a large number of other fading scenarios, such as Rayleigh, Rice (Nakagamin), Nakagami-m, One-Sided Gaussian, and mixtures of these common fading models. In addition, due to the duality of the analysis of secrecy capacity and co-channel interference (CCI), the results presented here will have immediate applicability in the analysis of outage probability in wireless systems affected by CCI and background noise (BN). To demonstrate the efficacy of the novel formulations proposed here, we use the derived equations to provide a useful insight into the probability of SPSC and SOPL for a range of emerging wireless applications, such as cellular device-to-device, peer-to-peer, vehicle-to-vehicle, and body centric communications using data obtained from real channel measurements.

Joint Information and Jamming Beamforming for Secrecy Rate Maximization in Cognitive Radio Networks

In this paper, we consider the secure beamforming design for an underlay cognitive radio multiple-input singleoutput broadcast channel in the presence of multiple passive eavesdroppers. Our goal is to design a jamming noise (JN) transmit strategy to maximize the secrecy rate of the secondary system. By utilizing the zero-forcing method to eliminate the interference caused by JN to the secondary user, we study the joint optimization of the information and JN beamforming for secrecy rate maximization of the secondary system while satisfying all the interference power constraints at the primary users, as well as the per-antenna power constraint at the secondary transmitter. For an optimal beamforming design, the original problem is a nonconvex program, which can be reformulated as a convex program by applying the rank relaxation method. To this end, we prove that the rank relaxation is tight and propose a barrier interior-point method to solve the resulting saddle point problem based on a duality result. To find the global optimal solution, we transform the considered problem into an unconstrained optimization problem. We then employ Broyden-Fletcher-Goldfarb-Shanno (BFGS) method to solve the resulting unconstrained problem which helps reduce the complexity significantly, compared to conventional methods. Simulation results show the fast convergence of the proposed algorithm and substantial performance improvements over existing approaches.