Generally speaking optical character recognition algorithms tend to perfonn better when presented with homogeneous data. This paper studies a method that is designed to increase the homogeneity of training data, based on an understanding of the types of degradations that occur during the printing and scanning process, and how these degradations affect the homogeneity of the data. While it has b...

We investigate the problem of detecting periodic trends within a string S of length n, arriving in the streaming model, containing at most k wildcard characters, where k = o(n). A wildcard character is a special character that can be assigned any other character. We say S has wildcard-period p if there exists an assignment to each of the wildcard characters so that in the resulting stream the l...

For a function φ in L(0, 1), extended to the whole real line as an odd periodic function of period 2, we ask when the collection of dilates φ(nx), n = 1, 2, 3, . . . , constitutes a Riesz basis or a complete sequence in L(0, 1). The problem translates into a question concerning multipliers and cyclic vectors in the Hilbert space H of Dirichlet series f(s) = ∑ n ann, where the coefficients an ar...

Much of this is joint work with Amy Ksir, the rest is " in progress ". 1 Motivation Let F = C temporarily and let X be a non-singular projective curve of genus > 1 with automorphism group G. This group acts on the vector space of differentials on X and, more generally, on the Riemann-Roch space of a G-equivariant divisor D. Question: What are these representations? Can we compute their char-act...

In recent work by Etingof, Henriques, Kamnitzer, and the author, a presentation and explicit basis was given for the rational co-homology of the real locus M0,n(R) of the moduli space of stable genus 0 curves with n marked points. We determine the graded character of the action of Sn on this space (induced by permutations of the marked points), both in the form of a plethystic formula for the c...

In physics, the number of observed spatial dimensions (three) is usually taken as an empirical fact, without a deep theoretical explanation. In this paper, we provide a possible simple geometric explanation for the 3-D character of the proper space. We also provide a simple geometric explanation for the number of additional spatial dimensions that some physical theories use. Specifically, it is...