13,784 research outputs found
GLC actors, artificial chemical connectomes, topological issues and knots
Based on graphic lambda calculus, we propose a program for a new model of
asynchronous distributed computing, inspired from Hewitt Actor Model, as well
as several investigation paths, concerning how one may graft lambda calculus
and knot diagrammatics
ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra
Background: Many biological systems are modeled qualitatively with discrete
models, such as probabilistic Boolean networks, logical models, Petri nets, and
agent-based models, with the goal to gain a better understanding of the system.
The computational complexity to analyze the complete dynamics of these models
grows exponentially in the number of variables, which impedes working with
complex models. Although there exist sophisticated algorithms to determine the
dynamics of discrete models, their implementations usually require
labor-intensive formatting of the model formulation, and they are oftentimes
not accessible to users without programming skills. Efficient analysis methods
are needed that are accessible to modelers and easy to use. Method: By
converting discrete models into algebraic models, tools from computational
algebra can be used to analyze their dynamics. Specifically, we propose a
method to identify attractors of a discrete model that is equivalent to solving
a system of polynomial equations, a long-studied problem in computer algebra.
Results: A method for efficiently identifying attractors, and the web-based
tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other
analysis methods for discrete models. ADAM converts several discrete model
types automatically into polynomial dynamical systems and analyzes their
dynamics using tools from computer algebra. Based on extensive experimentation
with both discrete models arising in systems biology and randomly generated
networks, we found that the algebraic algorithms presented in this manuscript
are fast for systems with the structure maintained by most biological systems,
namely sparseness, i.e., while the number of nodes in a biological network may
be quite large, each node is affected only by a small number of other nodes,
and robustness, i.e., small number of attractors
Two-loop Integral Reduction from Elliptic and Hyperelliptic Curves
We show that for a class of two-loop diagrams, the on-shell part of the
integration-by-parts (IBP) relations correspond to exact meromorphic one-forms
on algebraic curves. Since it is easy to find such exact meromorphic one-forms
from algebraic geometry, this idea provides a new highly efficient algorithm
for integral reduction. We demonstrate the power of this method via several
complicated two-loop diagrams with internal massive legs. No explicit elliptic
or hyperelliptic integral computation is needed for our method.Comment: minor changes: more references adde
Azurite: An algebraic geometry based package for finding bases of loop integrals
For any given Feynman graph, the set of integrals with all possible powers of
the propagators spans a vector space of finite dimension. We introduce the
package {\sc Azurite} ({\bf A ZUR}ich-bred method for finding master {\bf
I}n{\bf TE}grals), which efficiently finds a basis of this vector space. It
constructs the needed integration-by-parts (IBP) identities on a set of
generalized-unitarity cuts. It is based on syzygy computations and analyses of
the symmetries of the involved Feynman diagrams and is powered by the computer
algebra systems {\sc Singular} and {\sc Mathematica}. It can moreover
analytically calculate the part of the IBP identities that is supported on the
cuts.Comment: Version 1.1.0 of the package Azurite, with parallel computations. It
can be downloaded from
https://bitbucket.org/yzhphy/azurite/raw/master/release/Azurite_1.1.0.tar.g
Comments on worldsheet theories dual to free large N gauge theories
We continue to investigate properties of the worldsheet conformal field
theories (CFTs) which are conjectured to be dual to free large N gauge
theories, using the mapping of Feynman diagrams to the worldsheet suggested in
hep-th/0504229. The modular invariance of these CFTs is shown to be built into
the formalism. We show that correlation functions in these CFTs which are
localized on subspaces of the moduli space may be interpreted as delta-function
distributions, and that this can be consistent with a local worldsheet
description given some constraints on the operator product expansion
coefficients. We illustrate these features by a detailed analysis of a specific
four-point function diagram. To reliably compute this correlator we use a novel
perturbation scheme which involves an expansion in the large dimension of some
operators.Comment: 43 pages, 16 figures, JHEP format. v2: added reference
Implicitization of surfaces via geometric tropicalization
In this paper we further develop the theory of geometric tropicalization due
to Hacking, Keel and Tevelev and we describe tropical methods for
implicitization of surfaces. More precisely, we enrich this theory with a
combinatorial formula for tropical multiplicities of regular points in
arbitrary dimension and we prove a conjecture of Sturmfels and Tevelev
regarding sufficient combinatorial conditions to compute tropical varieties via
geometric tropicalization. Using these two results, we extend previous work of
Sturmfels, Tevelev and Yu for tropical implicitization of generic surfaces, and
we provide methods for approaching the non-generic cases.Comment: 20 pages, 6 figures. Mayor reorganization and exposition improved.
The results on geometric tropicalization have been extended to any dimension.
In particular, Conjecture 2.8 is now Theorem 2.
-persistent homology of finite topological spaces
Let be a finite poset. We will show that for any reasonable
-persistent object in the category of finite topological spaces, there
is a weighted graph, whose clique complex has the same -persistent
homology as
QCD Amplitudes: new perspectives on Feynman integral calculus
I analyze the algebraic patterns underlying the structure of scattering
amplitudes in quantum field theory. I focus on the decomposition of amplitudes
in terms of independent functions and the systems of differential equations the
latter obey. In particular, I discuss the key role played by unitarity for the
decomposition in terms of master integrals, by means of generalized cuts and
integrand reduction, as well as for solving the corresponding differential
equations, by means of Magnus exponential series.Comment: Presented at Rencontres de Moriond 201
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