Nonparametric Simultaneous Sparse Recovery: an Application to Source Localization

We consider multichannel sparse recovery problem where the objective is to find good recovery of jointly sparse unknown signal vectors from the given multiple measurement vectors which are different linear combinations of the same known elementary vectors. Many popular greedy or convex algorithms perform poorly under non-Gaussian heavy-tailed noise conditions or in the face of outliers. In this paper, we propose the usage of mixed $\ell_{p,q}$ norms on data fidelity (residual matrix) term and the conventional $\ell_{0,2}$-norm constraint on the signal matrix to promote row-sparsity. We devise a greedy pursuit algorithm based on simultaneous normalized iterative hard thresholding (SNIHT) algorithm. Simulation studies highlight the effectiveness of the proposed approaches to cope with different noise environments (i.i.d., row i.i.d, etc) and outliers. Usefulness of the methods are illustrated in source localization application with sensor arrays.Comment: Paper appears in Proc. European Signal Processing Conference (EUSIPCO'15), Nice, France, Aug 31 -- Sep 4, 201

Transmission Eigenvalues for a Class of Non-Compactly Supported Potentials

Let $\Omega\subseteq\mathbb R^n$ be a non-empty open set for which the Sobolev embedding $H_0^2(\Omega)\longrightarrow L^2(\Omega)$ is compact, and let $V\in L^\infty(\Omega)$ be a potential taking only positive real values and satisfying the asymptotics $V(\cdot)\asymp\left\langle\cdot\right\rangle^{-\alpha}$ for some $\alpha\in\left]3,\infty\right[$. We establish the discreteness of the set of real transmission eigenvalues for both Schr\"odinger and Helmholtz scattering with these potentials

Preaching to the choir? Economic analysis of Church Growth

Economic theory, applied economic modeling and econometric methods offer advantageous tools for analyzing numerous organizations, institutions and social contexts which are not inherently downright economical by nature, as religious markets. In contemporary rational choice religious market models, church growth is assumed to depend on surplus resources available for church development. These extra resources can exist as volunteer work and extra monetary contributions, delivered by enthusiasts and active members, signaling devotion and personal sacrifice. These inputs produce more members and attendants into churches. These hypotheses are tested by applying religious market data from Finland. Models are estimated by comparing data from the dominant state church and the competitive free-church. Both models seem to give support for previous argumentation, emphasizing the importance of volunteer activism and surplus efforts for the church growth.church growth, rational choice, religion, cost-benefit analysis, voluntary work

Regularized MM-estimators of scatter matrix

In this paper, a general class of regularized $M$-estimators of scatter matrix are proposed which are suitable also for low or insufficient sample support (small $n$ and large $p$) problems. The considered class constitutes a natural generalization of $M$-estimators of scatter matrix (Maronna, 1976) and are defined as a solution to a penalized $M$-estimation cost function that depend on a pair $(\alpha,\beta)$ of regularization parameters. We derive general conditions for uniqueness of the solution using concept of geodesic convexity. Since these conditions do not include Tyler's $M$-estimator, necessary and sufficient conditions for uniqueness of the penalized Tyler's cost function are established separately. For the regularized Tyler's $M$-estimator, we also derive a simple, closed form and data dependent solution for choosing the regularization parameter based on shape matrix matching in the mean squared sense. An iterative algorithm that converges to the solution of the regularized $M$-estimating equation is also provided. Finally, some simulations studies illustrate the improved accuracy of the proposed regularized $M$-estimators of scatter compared to their non-regularized counterparts in low sample support problems. An example of radar detection using normalized matched filter (NMF) illustrate that an adaptive NMF detector based on regularized $M$-estimators are able to maintain accurately the preset CFAR level and at at the same time provide similar probability of detection as the (theoretical) NMF detector.Comment: Submitted to IEEE Transactions on Signal Processing (contains a corrected proof of convergence of the proposed iterative algorithm

Exponential Sums Related to Maass Forms

We estimate short exponential sums weighted by the Fourier coefficients of a Maass form. This requires working out a certain transformation formula for non-linear exponential sums, which is of independent interest. We also discuss how the results depend on the growth of the Fourier coefficients in question. As a byproduct of these considerations, we can slightly extend the range of validity of a short exponential sum estimate for holomorphic cusp forms. The short estimates allow us to reduce smoothing errors. In particular, we prove an analogue of an approximate functional equation previously proven for holomorphic cusp form coefficients. As an application of these, we remove the logarithm from the classical upper bound for long linear sums weighted by Fourier coefficients of Maass forms, the resulting estimate being the best possible. This also involves improving the upper bounds for long linear sums with rational additive twists, the gains again allowed by the estimates for the short sums. Finally, we shall use the approximate functional equation to bound somewhat longer short exponential sums.Comment: 58 p

The European Union and the United Nations Convention on the Law of the Sea

This Essay comments on EU participation in UNCLOS and its implementation. It addresses first the nature of the EU as a contracting party and outlines the modalities for its participation. It then reviews the international implementation of the UNCLOS obligations and the implementation/status of the Convention under EU law

Trading Nokia: The roles of the Helsinki vs the New York stock exchanges

We use the Autoregressive Conditional Duration (ACD) framework of Engle and Russell (1998) to study the effect of trading volume on price duration (ie the time lapse between consecutive price changes) of a stock listed both in the domestic and the foreign market. As a case study we use the example of Nokia’s share, which is actively traded both in the Helsinki Stock Exchange and the New York Stock Exchange (NYSE). We find asymmetry in the volume-price duration relationship between the two markets. In the NYSE the negative relationship is much stronger and exists both during and outside common trading hours. Outside common trading hours no such relationship is significant in Helsinki. Based on the theory of Easley and O’Hara (1992), these results could be interpreted in that informed investors in Nokia mainly trade in the US market whereas Helsinki is the more liquidity-oriented trading place.cross-listing; Autoregressive Conditional Duration; market microstructure