Related papers: Consistency of Relations over Monoids
We consider a family of 3D models for the axi-symmetric incompressible Navier-Stokes equations. The models are derived by changing the strength of the convection terms in the axisymmetric Navier-Stokes equations written using a set of…
For group presentations with cyclic symmetry, there is a connection between asphericity and the dynamics of the shift automorphism. For the class of groups $G_n(k,l)$ described by the cyclic presentations $\mathcal{P}_n(k,l) =…
It is shown how different globally coupled map systems can be analyzed under a common framework by focusing on the dynamics of their respective global coupling functions. We investigate how the functional form of the coupling determines the…
We prove that a pointed one dimensional family of varieties $\mathcal{X}\to {b\in B}$ in positive characteristics is locally stable iff the log pair $(\mathcal{X'}, \mathcal{X}'_{b'})$ arising from its base change to the perfectoid base…
We introduce MTT, a dependent type theory which supports multiple modalities. MTT is parametrized by a mode theory which specifies a collection of modes, modalities, and transformations between them. We show that different choices of mode…
Suppose that $M$ is a topological monoid satisfying $\pi_0M=\mathbb{N}$ to which the McDuff-Segal group-completion theorem applies. This implies that a certain map $f: \mathbb{M}_{\infty}\rightarrow \Omega BM$ defined on an infinite mapping…
This article is devoted to the study of monoids which can be endowed with a shuffle product with coefficients in a semiring. We show that, when the multiplicities do not belong to a ring with prime characteristic, such a monoid is a monoid…
We introduce "synchronous algebras", an algebraic structure tailored to recognize automatic relations (aka. synchronous relations, or regular relations). They are the equivalent of monoids for regular languages, however they conceptually…
In this note we clarify the relationship between the local and global definitions of dual pairs in Poisson geometry. It turns out that these are not equivalent. For the passage from local to global one needs a connected fiber hypothesis…
How does connectivity impact network dynamics? We address this question by linking network characteristics on two scales. On the global scale we consider the coherence of overall network dynamics. We show that such \emph{global coherence}…
In previous work we proved that, for categories of free finite-dimensional modules over a commutative semiring, linear compact-closed symmetric monoidal structure is a property, rather than a structure. That is, if there is such a…
A sufficient condition for the stability of a system resulting from the interconnection of dynamical systems is given by the small gain theorem. Roughly speaking, to apply this theorem, it is required that the gains composition is…
We consider the three-dimensional stable matching problem with cyclic preferences, a problem originally proposed by Knuth. Despite extensive study of the problem by experts from different areas, the question of whether every instance of…
Classical sufficient conditions for ensuring the robust stability of a dynamical system in feedback with a nonlinearity include passivity, small gain, circle, and conicity theorems. We present a generalized version of these results for…
In this work, we characterize a class of nonlinear monotone dynamical systems that have a certain translation invariance property which goes by the name of plus-homogeneity; usually called "topical" systems. Such systems need not be…
Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional condition on its rate of increase compared to the sample size. On the…
In this paper, we introduce quantile coherency to measure general dependence structures emerging in the joint distribution in the frequency domain and argue that this type of dependence is natural for economic time series but remains…
Two-dimensional coupled map lattices have global stability properties that depend on the coupling between individual maps and their neighborhood. The action of the neighborhood on individual maps can be implemented in terms of "causal"…
This paper proves that robustness implies generalization via data-dependent generalization bounds. As a result, robustness and generalization are shown to be connected closely in a data-dependent manner. Our bounds improve previous bounds…
We formalize a minimal setting in which a chronology (a strict partial order on events) is forced by consistency of distributed information under local composability. The system maintains distributed records interpreted as constraints over…