Let n be an integer ≥ 2. We consider the wave operator = −∂ t + Pn i=1 ∂ xi , where (t, x) = (t, x1, . . . , xn) are the canonical coordinates on Minkowski space R 1,n = R× R . Lie’s prolongation algorithm calculates the Lie algebra of infinitesimal symmetries of to be isomorphic to the conformal Lie algebra g = so(2, n+1) plus an infinite dimensional piece reflecting the fact that is linear. I...

1. Introduction Wavelets are acquiring a visibility and popularity that may soon be on the scale rst enjoyed by fractals a few years back. Like fractals, wavelets have attractive and novel features, both as mathematical entities and in numerous applications. They are often touted as worthwhile alternatives to classical Fourier analysis, which works best when applied to periodic data: wavelet me...

We give an overview of phylogenetic invariants: a technique for reconstructing evolutionary family trees from DNA sequence data. This method is useful in practice and is based on a number of simple ideas from elementary group theory, probability, linear algebra, and commutative algebra.

The second author constructed a topological ribbon Hopf algebra from the unrolled quantum group associated with super Lie sl(2|1). We generalize this fact to context of groups and construct algebras. Then we use such an algebra, discrete Fourier transforms, symmetrized graded integral modified trace define Hennings invariant 3-manifolds endowed cohomology class which contains graph. Finally, no...

One can learn any hypothesis class H with O(log |H|) labeled examples. Alas, learning with so few examples requires saving the examples in memory, and this requires |X | memory states, where X is the set of all labeled examples. This motivates the question of how many labeled examples are needed in case the memory is bounded. Previous work showed, using techniques such as linear algebra and Fou...

Let G be a connected reductive p-adic group and let g be its Lie algebra. LetO be a G-orbit in g. Then the orbital integral μO corresponding to O is an invariant distribution on g, and Harish-Chandra proved that its Fourier transform μ̂O is a locally constant function on the set g′ of regular semisimple elements of g. Furthermore, he showed that a normalized version of the Fourier transform is l...

ious data permutations occurring e.g. in parallel FFT ..and basic linear algebra algorithms can be viewed as Total exchange is an important collectIve communzinstances of the total exchange problem [2]. cation pro~lem in multip.roces~or i.ntercon~~tion netIn this work we present general theory for solving works. It znvolves the dzssemznatlon of dzstlnct mesthe total exchange problem in multidim...

We answer a question raised by Lovász and B. Szegedy [Contractors and connectors in graph algebras, J. Graph Theory 60:1 (2009)] asking for a contractor for the graph parameter counting the number of B-flows of a graph, where B is a subset of a finite Abelian group closed under inverses. We prove our main result using the duality between flows and tensions and finite Fourier analysis.

The Fourier coefficients of modular forms encode very interesting arithmetic data. For example, divisor sums, partition numbers, trace of Frobenius of the reduction modulo primes of an elliptic curve over Q, and more generally, trace of Frobenius of many Galois representations of dimension 2 over finite fields (this being a conjecture of Serre) are all known to be, or conjectured to be, Fourier...

Toroidal Lie algebras are very natural multi-variable generalizations of affine Kac-Moody algebras. The theory of affine Lie algebras is rich and beautiful, having connections with diverse areas of mathematics and physics. Toroidal Lie algebras are also proving themselves to be useful for the applications. Frenkel, Jing and Wang [FJW] used representations of toroidal Lie algebras to construct a...