Related papers: Randomness and semigenericity
We develop and explore the idea of recognition of languages (in the general sense of subsets of topological algebras) as preimages of clopen sets under continuous homomorphisms into Stone topological algebras. We obtain an Eilenberg…
We give a model-theoretic account for several results regarding sequences of random variables appearing in Berkes & Rosenthal \cite{Berkes-Rosenthal:AlmostExchangeableSequences}. In order to do this, {itemize} We study and compare three…
A finite W-algebra is an associative algebra constructed from a semisimple Lie algebra and its nilpotent element. In this survey we review recent developments in the representation theory of W-algebras. We emphasize various interactions…
We introduce a hierarchical classification of theories that describe systems with fundamentally limited information content. This property is introduced in an operational way and gives rise to the existence of mutually complementary…
Quantum $L_\infty$ algebras are higher loop generalizations of cyclic $L_\infty$ algebras. Motivated by the problem of defining morphisms between such algebras, we construct a linear category of $(-1)$-shifted symplectic vector spaces and…
A free semigroupoid algebra is the closure of the algebra generated by a TCK family of a graph in the weak operator topology. We obtain a structure theory for these algebras analogous to that of free semigroup algebra. We clarify the role…
We present and investigate an extension of the classical random graph to a general class of inhomogeneous random graph models, where vertices come in different types, and the probability of realizing an edge depends on the types of its…
If w is a word in d>1 letters and G is a finite group, evaluation of w on a uniformly randomly chosen d-tuple in G gives a random variable with values in G, which may or may not be uniform. It is known that if G ranges over finite simple…
We call an $\alpha \in \mathbb{R}$ regainingly approximable if there exists a computable nondecreasing sequence $(a_n)_n$ of rational numbers converging to $\alpha$ with $\alpha - a_n < 2^{-n}$ for infinitely many $n \in \mathbb{N}$. We…
Relational models for contingency tables are generalizations of log-linear models, allowing effects associated with arbitrary subsets of cells in a possibly incomplete table, and not necessarily containing the overall effect. In this…
We examine properties of generic automorphisms of the random poset, with the goal of explicitly characterizing them. We associate to each automorphism an auxiliary first-order structure, consisting of the random poset equipped with an…
Words are sequences of letters over a finite alphabet. We study two intimately related topics for this object: quasi-randomness and limit theory. With respect to the first topic we investigate the notion of uniform distribution of letters…
Consider a finite-dimensional, complex Lie algebra G and a semi-simple automorphism {\alpha}. This note aims to give a short and simple proof for explicit upper bounds for the derived length of the radical R and the rank of a Levi…
For a given graph $G$ of minimum degree at least $k$, let $G_p$ denote the random spanning subgraph of $G$ obtained by retaining each edge independently with probability $p=p(k)$. We prove that if $p \ge \frac{\log k + \log \log k +…
An a priori semimeasure (also known as "algorithmic probability" or "the Solomonoff prior" in the context of inductive inference) is defined as the transformation, by a given universal monotone Turing machine, of the uniform measure on the…
For every fixed graph $H$ and every fixed $0 < \alpha < 1$, we show that if a graph $G$ has the property that all subsets of size $\alpha n$ contain the ``correct'' number of copies of $H$ one would expect to find in the random graph…
The most developed aspect of the theory of finite semigroups is their classification in pseudovarieties. The main motivation for investigating such entities comes from their connection with the classification of regular languages via…
We propose a new notion of positivity for topological field theories (TFTs), based on S. Eilenberg's concept of completeness for semirings. We show that a complete ground semiring, a system of fields on manifolds and a system of action…
Terwilliger algebras are a subalgebra of a matrix algebra that are constructed from association schemes over finite sets. In 2010, Rie Tanaka defined what it means for a Terwilliger algebra to be almost commutative. In that paper she gave…
A conformal change of $TM\oplus T^*M$ is a morphism of the form $(X,\alpha)\mapsto(X,e^\tau\alpha)$ $(X\in TM,\alpha\in T^*M,\tau\in C^\infty(M))$. We characterize the generalized almost complex and almost Hermitian structures that are…