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Let Qn denote a random symmetric n by n matrix, whose upper diagonal entries are i.i.d. Bernoulli random variables (which take values 0 and 1 with probability 1/2). We prove that Qn is non-singular with probability 1 − O(n −1/8+δ) for any fixed δ > 0. The proof uses a quadratic version of Littlewood-Offord type results concerning the concentration functions… (More)
This is the first of two papers which construct a purely algebraic counterpart to the theory of Gromov-Witten invariants (at all genera). These Gromov-Witten type invariants depend on a Calabi-Yau A∞ category, which plays the role of the target in ordinary Gromov-Witten theory. When we use an appropriate A∞ version of the derived category of coherent… (More)
If f (x 1 ,. .. , xn) is a polynomial dependent on a large number of independent Bernoulli random variables, what can be said about the maximum concentration of f on any single value? For linear polynomials, this reduces to one version of the classical Littlewood-Offord problem: Given nonzero constants a 1 ,. .. an, what is the maximum number of sums of the… (More)
This note gives a construction of a dual version of the ribbon graph decomposition of the moduli spaces of Riemann surfaces.
BACKGROUND The objective of this study was to determine the acute and chronic fixation strengths achieved by fibrin or polyethylene glycol (PEG) sealants to secure biologic mesh at the esophageal hiatus in a porcine model. METHODS For this study, 32 female domestic pigs were divided into four groups of 8 each. The four groups respectively received acute… (More)
This paper gives a way to renormalise certain quantum field theories on compact manifolds. Examples include Yang-Mills theory (in dimension 4 only), Chern-Simons theory and holomorphic Chern-Simons theory. The method is within the framework of the Batalin-Vilkovisky formalism. Chern-Simons theory is renor-malised in a way respecting all symmetries (up to… (More)
This paper gives a construction, using heat kernels, of differential forms on the moduli space of metrised ribbon graphs, or equivalently on the moduli space of Riemann surfaces with boundary. The construction depends on a manifold with a bundle of Frobenius algebras, satisfying various conditions. These forms satisfy gluing conditions which mean they form… (More)