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In this paper, we continue our study of blade arrangements and the positroidal subdivisions which are induced by them on $\Delta_{k,n}$. A blade is a tropical hypersurface which is generated by a system of $n$ affine simple roots of type…

Combinatorics · Mathematics 2022-10-14 Nick Early

We consider static solutions of the sine-Gordon theory defined on a cylinder, which can be either periodic or quasi-periodic in space. They are described by the different modes of a simple pendulum moving in an inverted effective potential…

High Energy Physics - Theory · Physics 2015-06-26 I. Bakas , C. Sourdis

A textile structure is a periodic arrangement of threads in the thickened plane. A topological classification of textile structures is harder than for classical knots and links that are non-periodic and restricted to a bounded region. The…

Geometric Topology · Mathematics 2020-07-30 Matt Bright , Vitaliy Kurlin

We introduce a new approach to an enumerative problem closely linked with the geometry of branched coverings; that is, we study the number of ways a permutation can be decomposed into a product of a given number of 2-cycles, 3-cycles, etc.…

Combinatorics · Mathematics 2007-05-23 John Irving

A dressing technique is used to improve zero range potential (ZRP) model. We consider a Darboux transformation starting with a ZRP, the result of the "dressing" gives a potential with non-zero range that depends on a seed solution…

Quantum Physics · Physics 2009-11-10 S. Leble , S. Yalunin

We perform the dimensional reduction of the spacetime of a stack of N D3-branes by the ``twist'' identification of a circle to obtain a new Melvin background. In the near-horizon limit the background becomes the magnetic-flux deformed…

High Energy Physics - Theory · Physics 2009-11-11 Wung-Hong Huang

Segmented strings in flat space are piecewise linear classical string solutions. Kinks between the segments move with the speed of light and their worldlines form a lattice on the worldsheet. This idea can be generalized to AdS$_3$ where…

High Energy Physics - Theory · Physics 2016-03-16 David Vegh

The abelian pattern matching problem consists in finding all substrings of a text which are permutations of a given pattern. This problem finds application in many areas and can be solved in linear time by a naive sliding window approach.…

Data Structures and Algorithms · Computer Science 2018-03-08 Simone Faro , Arianna Pavone

In this paper we address two different problems related with the factorization of an RSA module N. First we can show that factoring is equivalent in deterministic polynomial time to counting points on a pair of twisted Elliptic curves…

Number Theory · Mathematics 2019-11-26 Luis Dieulefait , Jorge Urroz

Mixed-integer mathematical programs are among the most commonly used models for a wide set of problems in Operations Research and related fields. However, there is still very little known about what can be expressed by small mixed-integer…

Discrete Mathematics · Computer Science 2017-12-07 Alfonso Cevallos , Stefan Weltge , Rico Zenklusen

We determine the all-loop dressing phases of the AdS3/CFT2 integrable system related to type IIB string theory on AdS3 x S3 x T4 by solving the recently found crossing relations and studying their singularity structure. The two resulting…

High Energy Physics - Theory · Physics 2013-09-18 Riccardo Borsato , Olof Ohlsson Sax , Alessandro Sfondrini , Bogdan Stefanski , Alessandro Torrielli

We propose a new numerical algorithm to construct a structured numerical elliptic grid of a doubly connected domain. Our method is applicable to domains with boundaries defined by two contour lines of a two-dimensional function. The…

Numerical Analysis · Mathematics 2018-08-14 Matthias Wiesenberger , Markus Held , Lukas Einkemmer

A step 2 branching decomposition of spaces of homogeneous Hermitian monogenic polynomials in C^n is established with explicit embedding factors in terms of the generalized Jacobi polynomials, which allows for an inductive construction of an…

Complex Variables · Mathematics 2013-05-17 F. Brackx , H. De Schepper , R. Lavicka , V. Soucek

We present a simple algorithm to obtain solutions that generalize the Israel--Wilson--Perj\'es class for the low-energy limit of heterotic string theory toroidally compactified from D=d+3 to three dimensions. A remarkable map existing…

High Energy Physics - Theory · Physics 2010-11-19 Alfredo Herrera-Aguilar , Oleg Kechkin

In the minimum common string partition (MCSP) problem two related input strings are given. "Related" refers to the property that both strings consist of the same set of letters appearing the same number of times in each of the two strings.…

Data Structures and Algorithms · Computer Science 2017-02-02 Christian Blum , Günther R. Raidl

We introduce polytopal cell complexes associated with partial acyclic orientations of a simple graph, which generalize acyclic orientations. Using the theory of cellular resolutions, two of these polytopal cell complexes are observed to…

Combinatorics · Mathematics 2015-02-10 Benjamin Iriarte Giraldo

We present a loop group description for curves in $\mathbb{R}^3$, and apply it to classify the circletons: Circles dressed by simple factors.

Differential Geometry · Mathematics 2015-08-04 Martin Kilian

We classify the simplest rational elements in a twisted loop group, and prove that dressing actions of them on proper indefinite affine spheres give the classical Tzitz\'eica transformation and its dual. We also give the group point of view…

Differential Geometry · Mathematics 2007-05-23 Erxiao Wang

Two string-like solutions to the equations of motion of the low-energy effective action for the heterotic string are found, each a source of electric and magnetic fields. The first carries an electric current equal to the electric charge…

High Energy Physics - Theory · Physics 2009-10-22 Daniel Waldram

The problem of identifying splice sites consists of two sub-problems: finding their boundaries, and characterizing their sequence markers. Other splicing elements---including, enhancers and silencers---that occur in the intronic and exonic…

Quantitative Methods · Quantitative Biology 2012-06-27 Christine Lo , Boyko Kakaradov , Daniel Lokshtanov , Christina Boucher