Related papers: Root system chip-firing I: Interval-firing
The RFMP is an iterative regularization method for a class of linear inverse problems. It has proved to be applicable to problems which occur, for example, in the geosciences. In the early publications [Fischer2011] and [FischerMichel2012],…
Root separation bounds play an important role as a complexity measure in understanding the behaviour of various algorithms in computational algebra, e.g., root isolation algorithms. A classic result in the univariate setting is the…
Inspired by the infinite families of finite and affine root systems, we consider a "stretching" operation on general crystallographic root systems which, on the level of Coxeter diagrams, replaces a vertex with a path of unlabeled edges. We…
The interval graph for a set of intervals on a line consists of one vertex for each interval, and an edge for each intersecting pair of intervals. A probe interval graph is a variant that is motivated by an application to genomics, where…
We study integrals of completely integrable quantum systems associated with classical root systems. We review integrals of the systems invariant under the corresponding Weyl group and as their limits we construct enough integrals of the…
Most proof systems for concurrent programs assume the underlying memory model to be sequentially consistent (SC), an assumption which does not hold for modern multicore processors. These processors, for performance reasons, implement…
We present a logically principled foundation for systematizing, in a way that works with any computational effect and evaluation order, SMT constraint generation seen in refinement type systems for functional programming languages. By…
The purpose of this article is to show how the root number of a modular form changes by twisting in terms of the local Weil-Deligne representation at each prime ideal. As an application, we show how one can for each odd prime $p$, determine…
A type assignment system for lambda-calculus enjoys the principal typing property if every typable term M has a special typing, called principal, from which all typings for M can be obtained via suitable operations. The existence of…
Mixed integer linear programming (MILP) is a powerful representation often used to formulate decision-making problems under uncertainty. However, it lacks a natural mechanism to reason about objects, classes of objects, and relations.…
In various areas of applied numerics, the problem of calculating the logarithm of a matrix A emerges. Since series expansions of the logarithm usually do not converge well for matrices far away from the identity, the standard numerical…
The availability of machine learning systems that can effectively perform arbitrary tasks has led to synthetic labels from these systems being used in applications of statistical inference, such as data analysis or model evaluation. The…
A dynamical system is said to undergo rate-induced tipping when it fails to track its quasi-equilibrium state due to an above-critical-rate change of system parameters. We study a prototypical model for rate-induced tipping, the saddle-node…
This paper is devoted to the study of infinitesimal limit cycles that can bifurcate from zero-Hopf equilibria of differential systems based on the averaging method. We develop an efficient symbolic program using Maple for computing the…
Developing particle-in-cell (PIC) methods using finite element basis sets, and without auxiliary divergence cleaning methods, was a long standing problem until recently. It was shown that if consistent spatial basis functions are used, one…
We consider the following problem of labeling points in a dynamic map that allows rotation. We are given a set of points in the plane labeled by a set of mutually disjoint labels, where each label is an axis-aligned rectangle attached with…
The aim of this chapter is to provide an adequate graph theoretic framework for the description of periodic bifurcations which have recently been discovered in descendant trees of finite p-groups. The graph theoretic concepts of rooted…
Integer factorization is a fundamental problem in algorithmic number theory and computer science. It is considered as a one way or trapdoor function in the (RSA) cryptosystem. To date, from elementary trial division to sophisticated methods…
Large language models have shown their ability to become effective few-shot learners with prompting, revolutionizing the paradigm of learning with data scarcity. However, this approach largely depends on the quality of prompt…
The implicit graph conjecture states that every sufficiently small, hereditary graph class has a labeling scheme with a polynomial-time computable label decoder. We approach this conjecture by investigating classes of label decoders defined…