Users can explore the world by viewing place related photos on Google Maps. One possible way is to take the nearby photos for viewing. However, for a given geo-location, many photos with view directions not pointing to the desired regions are returned by that world map. To address this problem, prior know the poses in terms of position and view direction of photos is a feasible solution. We can...

Many proofs of the fundamental theorem of algebra rely on the fact that the minimum of the modulus of a complex polynomial over the complex plane is attained at some complex number. The proof then follows by arguing the minimum value is zero. This can be done by proving that at any complex number that is not a zero of the polynomial we can exhibit a direction of descent for the modulus. In this...

Diierential cryptanalysis is a powerful attack developed by Eli Biham and Adi Shamir. It has been successfully applied to many DES-like cryptosystems. We provide a brief introduction to their paper BS91] and show how to apply diierential cryptanalysis to attack the Data Encryption Standard (DES) reduced to 5 rounds.

The Direction of Arrival (DOA) estimation under impulsive noise environments remains open in the field of array signal processing. Inspired by the advantage of correntropy which exhibits a ‘robust statistics’ property, this paper proposes a new operator, namely, the correntropy based correlation (CRCO), for independent and identically distributed (i.i.d) symmetric alpha-stable ðSαSÞ random vari...

We consider a nonlinear fourth-order diffusion equation that arises in denoising of image densities. We propose an alternative direction implicit (ADI) splitting method for its numerical solution. To treat the high-order and mixed derivative terms in the equation we adopt an ADI method by Hundsdorfer and Verwer to the present setting. The paper is furnished with numerical results for the evolut...

We present an extrapolative model of bubbles. In the model, many investors form their demand for a risky asset by weighing two signals—an average of the asset’s past price changes and the asset’s degree of overvaluation. The two signals are in conflict, and investors “waver” over time in the relative weight they put on them. The model predicts that good news about fundamentals can trigger large...

The ADI iteration is closely related to the rational Krylov projection methods for constructing low rank approximations to the solution of Sylvester equation. In this paper we show that the ADI and rational Krylov approximations are in fact equivalent when a special choice of shifts are employed in both methods. We will call these shifts pseudo H2-optimal shifts. These shifts are also optimal i...

I present a potential design of a heterogeneous acoustic sensing network comprised of the Acoustic Embedded Networked Sensing Box (ENSBox) and the Berkeley Mica2 platforms. I also present one potential method of leveraging the presence of Mica2 motes to improve acoustic source localization. More specifically, I present a method of rejecting grating lobes, which may be present in direction-ofarr...

We present a multilevel high order ADI method for separable generalized Helmholtz equations. The discretization method we use is a 1-D fourth order compact nite di erence applied to each directional component of the Laplace operator, resulting a discrete system e ciently solvable by ADI methods. We apply this high order di erence scheme to all levels of grids, and then starting from the coarses...

This paper presents a logarithmic barrier method for solving a semi-definite linear program. The descent direction is the classical Newton direction. We propose alternative ways to determine the step-size along the direction which are more efficient than classical linesearches.