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Is it possible to detect if the sample paths of a stochastic process almost surely admit a finite expansion with respect to some/any basis? The determination is to be made on the basis of a finite collection of discretely/noisily observed sample paths. We ...
Let P be a finite point set in the plane. A \emph{c-ordinary triangle} in P is a subset of P consisting of three non-collinear points such that each of the three lines determined by the three points contains at most c points of P. Motivated by a question o ...
The present thesis deals with problems arising from discrete mathematics, whose proofs make use of tools from algebraic geometry and topology. The thesis is based on four papers that I have co-authored, three of which have been published in journals, and o ...
In this paper, a polar code for the m-user multiple access channel (MAC) with binary inputs is constructed. In particular, Arıkan’s polarization technique applied individually to each user will polarize any m-user binary input MAC into a finite collection ...
Sampling schemes on the sphere require O(L^2) samples to perfectly sample and reconstruct a signal with bandwidth L. If the signal in question is a low-pass observation of a finite collection of spikes or rotations of a known function, we can use less samp ...
We describe a decision procedure for a logic that supports 1) finite collections of elements (sets or multisets), 2) the cardinality operator, 3) a total order relation on elements, and 4) min and max operators on entire collections. Among the applications ...
Here we present a method of constructing steerable wavelet frames in L2(Rd ) that generalizes and unifies previous approaches, including Simoncelli's pyramid and Riesz wavelets. The motivation for steerable wavelets is the nee ...
Here we present a method of constructing steerable wavelet frames in L-2(R-d) that generalizes and unifies previous approaches, including Simoncelli's pyramid and Riesz wavelets. The motivation for steerable wavelets is the need to more accurately account ...
Given a set P of n points in ℝd, let d1 > d2 >...denote all distinct inter-point distances generated by point pairs in P. It was shown by Schur, Martini, Perles, and Kupitz that there is at most oned-dimensional regular simplex of edge length d1 whos ...
