Interference Alignment for the Multi-Antenna Compound Wiretap Channel

We study a wiretap channel model where the sender has $M$ transmit antennas and there are two groups consisting of $J_1$ and $J_2$ receivers respectively. Each receiver has a single antenna. We consider two scenarios. First we consider the compound wiretap model -- group 1 constitutes the set of legitimate receivers, all interested in a common message, whereas group 2 is the set of eavesdroppers. We establish new lower and upper bounds on the secure degrees of freedom. Our lower bound is based on the recently proposed \emph{real interference alignment} scheme. The upper bound provides the first known example which illustrates that the \emph{pairwise upper bound} used in earlier works is not tight. The second scenario we study is the compound private broadcast channel. Each group is interested in a message that must be protected from the other group. Upper and lower bounds on the degrees of freedom are developed by extending the results on the compound wiretap channel.Comment: Minor edits. Submitted to IEEE Trans. Inf. Theor

Data-Driven Chance Constrained Optimization under Wasserstein Ambiguity Sets

We present a data-driven approach for distributionally robust chance constrained optimization problems (DRCCPs). We consider the case where the decision maker has access to a finite number of samples or realizations of the uncertainty. The chance constraint is then required to hold for all distributions that are close to the empirical distribution constructed from the samples (where the distance between two distributions is defined via the Wasserstein metric). We first reformulate DRCCPs under data-driven Wasserstein ambiguity sets and a general class of constraint functions. When the feasibility set of the chance constraint program is replaced by its convex inner approximation, we present a convex reformulation of the program and show its tractability when the constraint function is affine in both the decision variable and the uncertainty. For constraint functions concave in the uncertainty, we show that a cutting-surface algorithm converges to an approximate solution of the convex inner approximation of DRCCPs. Finally, for constraint functions convex in the uncertainty, we compare the feasibility set with other sample-based approaches for chance constrained programs.Comment: A shorter version is submitted to the American Control Conference, 201

Continuous wavelet transform on local fields

The main objective of this paper is to define the mother wavelet on local fields and study the continuous wavelet transform (CWT) and some of their basic properties. its inversion formula, the Parseval relation and associated convolution are also studied

A Search for the Higgs Boson in H->ZZ->2leptons 2jets Mode

A search for the Standard Model Higgs boson decaying to two Z bosons with subsequent decay to a final state with two leptons and two quark-jets, H->ZZ->2l 2jets, where \ell = e, {\mu}, is discussed. It is based on an integrated luminosity of 1 fb-1 of proton-proton collision data at center of mass energy sqrt(s) = 7 TeV collected by the CMS experiment at the LHC. The data are compared to the expected Standard Model backgrounds. No evidence for the Higgs boson is found and upper limits are placed on its production cross section over the range of masses between 200 GeV and 600 GeV.Comment: To appear in the Proceedings of the DPF 2011 Conferenc