相关论文: Breaking Symmetry with Different Orderings

An update of the ODEtools Maple package, for the analytical solving of 1st and 2nd order ODEs using Lie group symmetry methods, is presented. The set of routines includes an ODE-solver and user-level commands realizing most of the relevant…

We investigate the possibility that supersymmetry is not a fundamental symmetry of nature, but emerges as an accidental approximate global symmetry at low energies. This can occur if the visible sector is non-supersymmetric at high scales,…

Within a Kuhn-Tucker cavity method introduced in a former paper, we study optimal stability learning for situations, where in the replica formalism the replica symmetry may be broken, namely (i) the case of a simple perceptron above the…

We recall the concept of Baxterisation of an R-matrix, or of a monodromy matrix, which corresponds to build, from one point in the $ R$-matrix parameter space, the algebraic variety where the spectral parameter(s) live. We show that the…

The rate vs. distance problem is a long-standing open problem in coding theory. Recent papers have suggested a new way to tackle this problem by appealing to a new hierarchy of linear programs. If one can find good dual solutions to these…

I briefly review the basic challenges and virtues of models breaking the electroweak symmetry dynamically. I will then introduce the (ultra) minimal walking technicolor models whose construction has been made possible thanks to recent…

We consider the numerical irreducible decomposition of a positive dimensional solution set of a polynomial system into irreducible factors. Path tracking techniques computing loops around singularities connect points on the same irreducible…

We study the properties of secret sharing schemes, where a random secret value is transformed into shares distributed among several participants in such a way that only the qualified groups of participants can recover the secret value. We…

We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…

Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations, we extend to the third order by differentiating the second order equation. This yields criteria for linearizability of a…

While not generally a conservation law, any symmetry of the equations of motion implies a useful reduction of any second-order equationto a first-order equation between invariants, whose solutions (first integrals) can then be integrated by…

There has been recent interest in the use of machine learning (ML) approaches within mathematical software to make choices that impact on the computing performance without affecting the mathematical correctness of the result. We address the…

In this paper we explore a symmetry-based search space reduction technique which can speed up optimal pathfinding on undirected uniform-cost grid maps by up to 38 times. Our technique decomposes grid maps into a set of empty rectangles,…

Lineage tracing, the tracking of living cells as they move and divide, is a central problem in biological image analysis. Solutions, called lineage forests, are key to understanding how the structure of multicellular organisms emerges. We…

This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of…

The high performance of tree ensemble classifiers benefits from a large set of rules, which, in turn, makes the models hard to understand. To improve interpretability, existing methods extract a subset of rules for approximation using model…

Codes over permutations under the infinity norm have been recently suggested as a coding scheme for correcting limited-magnitude errors in the rank modulation scheme. Given such a code, we show that a simple relabeling operation, which…

A well-known result by Palamidessi tells us that \pimix (the \pi-calculus with mixed choice) is more expressive than \pisep (its subset with only separate choice). The proof of this result argues with their different expressive power…

We study vertex-ordering problems in loop-free digraphs subject to constraints on the left-going arcs, focusing on existence conditions and computational complexity. As an intriguing special case, we explore vertex-specific lower and upper…

Linearizing two partial orders to maximize the number of adjacencies and minimize the number of breakpoints is APX-hard. This holds even if one of the two partial orders is already a linear order and the other is an interval order, or if…