LiteRed 1.4: a powerful tool for the reduction of the multiloop integrals

We review the Mathematica package LiteRed, version 1.4.Comment: 8 pages, contribution to proceedings of ACAT2013 conferenc

An efficient dual sampling algorithm with Hamming distance filtration

Recently, a framework considering RNA sequences and their RNA secondary structures as pairs, led to some information-theoretic perspectives on how the semantics encoded in RNA sequences can be inferred. In this context, the pairing arises naturally from the energy model of RNA secondary structures. Fixing the sequence in the pairing produces the RNA energy landscape, whose partition function was discovered by McCaskill. Dually, fixing the structure induces the energy landscape of sequences. The latter has been considered for designing more efficient inverse folding algorithms. We present here the Hamming distance filtered, dual partition function, together with a Boltzmann sampler using novel dynamic programming routines for the loop-based energy model. The time complexity of the algorithm is $O(h^2n)$, where $h,n$ are Hamming distance and sequence length, respectively, reducing the time complexity of samplers, reported in the literature by $O(n^2)$. We then present two applications, the first being in the context of the evolution of natural sequence-structure pairs of microRNAs and the second constructing neutral paths. The former studies the inverse fold rate (IFR) of sequence-structure pairs, filtered by Hamming distance, observing that such pairs evolve towards higher levels of robustness, i.e.,~increasing IFR. The latter is an algorithm that constructs neutral paths: given two sequences in a neutral network, we employ the sampler in order to construct short paths connecting them, consisting of sequences all contained in the neutral network.Comment: 8 pages 6 figure

Presenting LiteRed: a tool for the Loop InTEgrals REDuction

Mathematica package LiteRed is described. It performs the heuristic search of the symbolic IBP reduction rules for loop integrals. It implements also several convenient tools for the search of the symmetry relations, construction of the differential equations and dimensional recurrence relations.Comment: 15 pages, 3 figure

On dimensional regularization and mathematical rigour

The controversy concerning the phenomenon of breakdown of dimensional regularization in the problems involving asymptotic expansions of Feynman diagrams in non-Euclidean regimes is discussed with some pertinent bibliographic comments.Comment: 3p, PS. 23-nov-98: maintenanc

DREAM, a program for arbitrary-precision computation of dimensional recurrence relations solutions, and its applications

We present the Mathematica package DREAM for arbitrarily high precision computation of multiloop integrals within the DRA (Dimensional Recurrence & Analyticity) method as solutions of dimensional recurrence relations. Starting from these relations, the package automatically constructs the inhomogeneous solutions and reduces the manual efforts to setting proper homogeneous solutions. DREAM also provides means to define the homogeneous solutions of the higher-order recurrence relations (and can construct those of the first-order recurrence relations automatically). Therefore, this package can be used to apply the DRA method to the topologies with sectors having more than one master integral. Two nontrivial examples are presented: four-loop fully massive tadpole diagrams of cat-eye topology and three-loop cut diagrams which are necessary for computation of the width of the para-positronium decay into four photons. The analytical form of this width is obtained here for the first time to the best of our knowledge.Comment: 17 pages, minor change

A domain-level DNA strand displacement reaction enumerator allowing arbitrary non-pseudoknotted secondary structures

DNA strand displacement systems have proven themselves to be fertile substrates for the design of programmable molecular machinery and circuitry. Domain-level reaction enumerators provide the foundations for molecular programming languages by formalizing DNA strand displacement mechanisms and modeling interactions at the "domain" level - one level of abstraction above models that explicitly describe DNA strand sequences. Unfortunately, the most-developed models currently only treat pseudo-linear DNA structures, while many systems being experimentally and theoretically pursued exploit a much broader range of secondary structure configurations. Here, we describe a new domain-level reaction enumerator that can handle arbitrary non-pseudoknotted secondary structures and reaction mechanisms including association and dissociation, 3-way and 4-way branch migration, and direct as well as remote toehold activation. To avoid polymerization that is inherent when considering general structures, we employ a time-scale separation technique that holds in the limit of low concentrations. This also allows us to "condense" the detailed reactions by eliminating fast transients, with provable guarantees of correctness for the set of reactions and their kinetics. We hope that the new reaction enumerator will be used in new molecular programming languages, compilers, and tools for analysis and verification that treat a wider variety of mechanisms of interest to experimental and theoretical work. We have implemented this enumerator in Python, and it is included in the DyNAMiC Workbench Integrated Development Environment.Comment: Accepted for oral presentation at Verification of Engineered Molecular Devices and Programs (VEMDP), July 17, 2014, Vienna, Austria. 29 pages, conference version. (Revised and expanded journal version is in preparation.

Alternative method of Reduction of the Feynman Diagrams to a set of Master Integrals

We propose a new set of Master Integrals which can be used as a basis for certain multiloop calculations in massless gauge field theories. In these theories we consider three-point Feynman diagrams with arbitrary number of loops. The corresponding multiloop integrals may be decomposed in terms of this set of the Master Integrals. We construct a new reduction procedure which we apply to perform this decomposition.Comment: 6 pages, 3 figures, Talk at ACAT 2016, Valparaiso, Chile, to appear in Proceedings of ACAT 201

FIRE5: a C++ implementation of Feynman Integral REduction

In this paper the C++ version of FIRE is presented - a powerful program performing Feynman integral reduction to master integrals. All previous versions used only Wolfram Mathematica, the current version mostly uses Wolfram Mathematica as a front-end. However, the most complicated part, the reduction itself can now be done by C++, which significantly improves the performance and allows one to reduce Feynman integrals in previously impossible situations.Comment: SFB/CPP-14-6

Topological language for RNA

In this paper we introduce a novel, context-free grammar, {\it RNAFeatures$^*$}, capable of generating any RNA structure including pseudoknot structures (pk-structure). We represent pk-structures as orientable fatgraphs, which naturally leads to a filtration by their topological genus. Within this framework, RNA secondary structures correspond to pk-structures of genus zero. {\it RNAFeatures$^*$} acts on formal, arc-labeled RNA secondary structures, called $\lambda$-structures. $\lambda$-structures correspond one-to-one to pk-structures together with some additional information. This information consists of the specific rearrangement of the backbone, by which a pk-structure can be made cross-free. {\it RNAFeatures$^*$} is an extension of the grammar for secondary structures and employs an enhancement by labelings of the symbols as well as the production rules. We discuss how to use {\it RNAFeatures$^*$} to obtain a stochastic context-free grammar for pk-structures, using data of RNA sequences and structures. The induced grammar facilitates fast Boltzmann sampling and statistical analysis. As a first application, we present an $O(n log(n))$ runtime algorithm which samples pk-structures based on ninety tRNA sequences and structures from the Nucleic Acid Database (NDB).Comment: 29 pages, 13 figures, 1 tabl

Techniques of Distributions in Perturbative Quantum Field Theory (I) Euclidean asymptotic operation for products of singular functions

We present a systematic description of the mathematical techniques for studying multiloop Feynman diagrams which constitutes a full-fledged and inherently more powerful alternative to the BPHZ theory. The new techniques emerged as a formalization of the reasoning behind a recent series of record multiloop calculations in perturbative quantum field theory. It is based on a systematic use of the ideas and notions of the distribution theory. We identify the problem of asymptotic expansion of products of singular functions in the sense of distributions as a key problem of the theory of asymptotic expansions of multiloop Feynman diagrams. Its complete solution for the case of Euclidean Feynman diagrams (the so-called Euclidean asymptotic operation for products of singular functions) is explicitly constructed and studied.Comment: 87 pages, Latex-2.0