286,311 research outputs found
Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order epsilon-expansion of generalized hypergeometric functions with one half-integer value of parameter
We continue the study of the construction of analytical coefficients of the
epsilon-expansion of hypergeometric functions and their connection with Feynman
diagrams. In this paper, we show the following results:
Theorem A: The multiple (inverse) binomial sums of arbitrary weight and depth
(see Eq. (1.1)) are expressible in terms of Remiddi-Vermaseren functions.
Theorem B: The epsilon expansion of a hypergeometric function with one
half-integer value of parameter (see Eq. (1.2)) is expressible in terms of the
harmonic polylogarithms of Remiddi and Vermaseren with coefficients that are
ratios of polynomials. Some extra materials are available via the www at this
http://theor.jinr.ru/~kalmykov/hypergeom/hyper.htmlComment: 24 pages, latex with amsmath and JHEP3.cls; v2: some typos corrected
and a few references added; v3: few references added
The massless higher-loop two-point function
We introduce a new method for computing massless Feynman integrals
analytically in parametric form. An analysis of the method yields a criterion
for a primitive Feynman graph to evaluate to multiple zeta values. The
criterion depends only on the topology of , and can be checked
algorithmically. As a corollary, we reprove the result, due to Bierenbaum and
Weinzierl, that the massless 2-loop 2-point function is expressible in terms of
multiple zeta values, and generalize this to the 3, 4, and 5-loop cases. We
find that the coefficients in the Taylor expansion of planar graphs in this
range evaluate to multiple zeta values, but the non-planar graphs with crossing
number 1 may evaluate to multiple sums with roots of unity. Our
method fails for the five loop graphs with crossing number 2 obtained by
breaking open the bipartite graph at one edge
Neural networks art: solving problems with multiple solutions and new teaching algorithm
A new discrete neural networks adaptive resonance theory (ART), which allows solving problems with multiple solutions, is developed. New algorithms neural networks teaching ART to prevent degradation and reproduction classes at training noisy input data is developed. Proposed learning algorithms discrete ART networks, allowing obtaining different classification methods of input
Multi-path Summation for Decoding 2D Topological Codes
Fault tolerance is a prerequisite for scalable quantum computing.
Architectures based on 2D topological codes are effective for near-term
implementations of fault tolerance. To obtain high performance with these
architectures, we require a decoder which can adapt to the wide variety of
error models present in experiments. The typical approach to the problem of
decoding the surface code is to reduce it to minimum-weight perfect matching in
a way that provides a suboptimal threshold error rate, and is specialized to
correct a specific error model. Recently, optimal threshold error rates for a
variety of error models have been obtained by methods which do not use
minimum-weight perfect matching, showing that such thresholds can be achieved
in polynomial time. It is an open question whether these results can also be
achieved by minimum-weight perfect matching. In this work, we use belief
propagation and a novel algorithm for producing edge weights to increase the
utility of minimum-weight perfect matching for decoding surface codes. This
allows us to correct depolarizing errors using the rotated surface code,
obtaining a threshold of . This is larger than the threshold
achieved by previous matching-based decoders (), though
still below the known upper bound of .Comment: 19 pages, 13 figures, published in Quantum, available at
https://quantum-journal.org/papers/q-2018-10-19-102
Universal Interface of TAUOLA Technical and Physics Documentation
Because of their narrow width, tau decays can be well separated from their
production process. Only spin degrees of freedom connect these two parts of the
physics process of interest for high energy collision experiments. In the
following, we present a Monte Carlo algorithm which is based on that property.
The interface supplements events generated by other programs, with tau decays.
Effects of spin, genuine weak corrections or of new physics may be taken into
account at the time when a tau decay is generated and written into an event
record.Comment: 1+44 pages, 17 eps figure
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