A recurrence relation between equal mass two-loop sunrise diagrams differing in dimensionality by 2 is derived and it's solution in terms of Gauss' 2 F 1 and Appell's F 2 hypergeometric functions is presented. For arbitrary space-time dimension d the imaginary part of the diagram on the cut is found to be the 2 F 1 hypergeometric function with argument proportional to the maximum of the Kibble ...

Abstract It is tempting to evaluate F2(x, 1) and similar univariate specializations of Appell’s functions by evaluating the apparent power series at x = 0 straight away using the Gauss formula for 2F1(1). But this kind of naive evaluation can lead to errors as the 2F1(1) coefficients might eventually diverge; then the actual power series at x = 0 might involve branching terms. This paper demons...

We introduce Mean-for-Mode estimation, a variant of an uncollapsed Gibbs sampler that we use to train LDA on a GPU. The algorithm combines benefits of both uncollapsed and collapsed Gibbs samplers. Like a collapsed Gibbs sampler — and unlike an uncollapsed Gibbs sampler — it has good statistical performance, and can use sampling complexity reduction techniques such as sparsity. Meanwhile, like ...

let h be a finite dimensional complex hilbert space, b(h)+ be the set of all positive semi-definite operators on h and phi is a (not necessarily linear) unital map of b(h) + preserving the entropy-gibbs transformation. then there exists either a unitary or an anti-unitary operator u on h such that phi(a) = uau* for any b(h) +. thermodynamics, a branch of physics that is concerned with the study...