Related papers: A Few Surprising Integrals
We present a model for spectral theory of families of selfadjoint operators, and their corresponding unitary one-parameter groups (acting in Hilbert space.) The models allow for a scale of complexity, indexed by the natural numbers…
The survey provides classification results for integrable one-field evolution equations of orders 2, 3 and 5 with the constant separant. The classification is based on necessary integrability conditions following from the existence of the…
There are many variations on partition functions for graph homomorphisms or colorings. The case considered here is a counting or hard constraint problem in which the range or color graph carries a free and vertex transitive Abelian group…
The algorithmic independence of conditionals, which postulates that the causal mechanism is algorithmically independent of the cause, has recently inspired many highly successful approaches to distinguish cause from effect given only…
The sensitive dependence of chaos on parameters is a topic of great interest in the study of integrability and stability of dynamical systems. Previous work has proposed ways to identify the sensitive dependence on parameters by topological…
We describe proofs of the standard generating formulas for unsigned and signed Stirling numbers of the first kind that follow from a natural combinatorial interpretation based on cycle-colored permutations.
We observe that a simple condition suffices to describes non-forking independence over models in a stable theory. Under mild assumptions, this description can be extended to non-forking independence over algebraically closed subsets,…
The final step of most large-scale structure analyses involves the comparison of power spectra or correlation functions to theoretical models. It is clear that the theoretical models have parameter dependence, but frequently the…
This paper introduces and investigates some properties of algebras constructed from the algebra of polynomials via derivation and integration operators using a process presented by Dzhumadildaev in a previous work. In particular, we…
Motivated by the observation that the counting function of a certain base-3 colored partition contains the even perfect numbers as a subsequence, we begin by defining a sequence of polynomials in four variables and discuss their properties…
Let $X$ be a smooth polarized algebraic surface over the compex number field. We discuss the invariants obtained from the moduli stacks of semistable sheaves of arbitrary ranks on $X$. For that purpose, we construct the virtual fundamental…
Graphical models are a key class of probabilistic models for studying the conditional independence structure of a set of random variables. Circular variables are special variables, characterized by periodicity, arising in several contexts…
We prove that in the Ryabov paper an application of the geometric Kharlamov method to the Goryachev system yields noncommutative "new variables of separation" instead of the standard canonical variables of separation.
The spectral independence approach of Anari et al. (2020) utilized recent results on high-dimensional expanders of Alev and Lau (2020) and established rapid mixing of the Glauber dynamics for the hard-core model defined on weighted…
Colouring the vertices of a graph $G$ according to certain conditions can be considered as a random experiment and a discrete random variable $X$ can be defined as the number of vertices having a particular colour in the proper colouring of…
We prove that proper coloring distinguishes between block-factors and finitely dependent stationary processes. A stochastic process is finitely dependent if variables at sufficiently well-separated locations are independent; it is a…
We consider the question of determining whether or not a given system of fractional-order differential equations is (asymptotically) stable. In particular, we admit systems where each constituent equation may have its own order, independent…
A seminal result in the ICA literature states that for $AY = \varepsilon$, if the components of $\varepsilon$ are independent and at most one is Gaussian, then $A$ is identified up to sign and permutation of its rows (Comon, 1994). In this…
We present a wide class of differential systems in any dimension that are either integrable or complete integrable. In particular, our result enlarges a known family of planar integrable systems. We give an extensive list of examples that…
We study the behavior of multidegrees in families and the existence of numerical criteria to detect integral dependence. We show that mixed multiplicities of modules are upper semicontinuous functions when taking fibers and that projective…