相关论文: Uniform Growth, Actions on Trees and $GL_2$

Global internal symmetries act unitarily on local observables or states of a quantum system. In this note, we aim to generalise this statement to extended observables by considering unitary actions of finite global 2-group symmetries…

Many real-world problems require making sequences of decisions where the outcomes of each decision are probabilistic and uncertain, and the availability of different actions is constrained by the outcomes of previous actions. There is a…

We propose Causal Interaction Trees for identifying subgroups of participants that have enhanced treatment effects using observational data. We extend the Classification and Regression Tree algorithm by using splitting criteria that focus…

The minimum linear arrangement problem on a network consists of finding the minimum sum of edge lengths that can be achieved when the vertices are arranged linearly. Although there are algorithms to solve this problem on trees in polynomial…

We demonstrate a method for proving precise concentration inequalities in uniformly random trees on $n$ vertices, where $n\geq1$ is a fixed positive integer. The method uses a bijection between mappings…

We study the growth of typical groups from the family of $p$-groups of intermediate growth constructed by the second author. We find that, in the sense of category, a generic group exhibits oscillating growth with no universal upper bound.…

Let Mod(S) denote the mapping class group of a compact, orientable surface S. We prove that finitely generated subgroups of Mod(S) which are not virtually abelian have uniform exponential growth with minimal growth rate bounded below by a…

We classify unital associative conformal algebras of linear growth and provide new examples of such.

In the past many papers have appeared which simulated surface growth with different growth models. The results showed that, if models differed only slightly in their `growth' rules, the resulting surfaces may belong to different…

Let $k$ be an algebraically closed field of characteristic $p>0$ and $C$ a connected nonsingular projective curve over $k$ with genus $g \geq 2$. Let $(C,G)$ be a "big action", i.e. a pair $(C,G)$ where $G$ is a $p$-subgroup of the…

Motivated from the study of eccentricity, center, and sum of eccentricities in graphs and trees, we introduce several new distance-based global and local functions based on the smallest distance from a vertex to some leaf (called the…

The group $GL(2,Z)$ acts in a natural way on the set of pairs of $n\times n$-matrices determined up to a simultaneous conjugation. For $n=3$ we write explicit formulas for action of generators of $GL(2,Z)$ in the terms of spectral data of…

Tree-based ensemble methods such as random forests, gradient-boosted trees, and Bayesianadditive regression trees have been successfully used for regression problems in many applicationsand research studies. In this paper, we study ensemble…

We present an algorithm for classification tasks on big data. Experiments conducted as part of this study indicate that the algorithm can be as accurate as ensemble methods such as random forests or gradient boosted trees. Unlike ensemble…

We study linear actions of finite groups in small dimensions, up to equivariant birationality.

We prove that if the group generated by a Mealy automaton acts level-transitively on a regular rooted tree, then the semigroup generated by the dual automaton has exponential growth, hence giving a decision procedure of exponential growth…

In this communication, the approach of phenomenological universalities of growth are considered to describe the behaviour of a system showing oscillatory growth. Two phenomenological classes are proposed to consider the behaviour of a…

In this paper we construct uniformly expanding random walks on smooth manifolds. In higher dimensions, our definition of uniform expansion measures the growth of subspaces rather than single vectors. Potrie showed that given any open set…

Let $G$ be a group acting properly by isometries and with a strongly contracting element on a geodesic metric space. Let $N$ be an infinite normal subgroup of $G$, and let $\delta_N$ and $\delta_G$ be the growth rates of $N$ and $G$ with…

In this article, we establish maximal inequalities and deduce ergodic theorems for state-preserving actions of amenable, locally compact, second-countable groups on tracial non-commutative $L^1$-spaces. As a further consequence, in…