Related papers: Bounds on tree distribution in number theory
Geometry of networks endowed with a causal structure is discussed using the conventional framework of equilibrium statistical mechanics. The popular growing network models appear as particular causal models. We focus on a class of tree…
We study probability distributions over free algebras of trees. Probability distributions can be seen as particular (formal power) tree series [Berstel et al 82, Esik et al 03], i.e. mappings from trees to a semiring K . A widely studied…
To any rooted tree, we associate a sequence of numbers that we call the logarithmic factorials of the tree. This provides a generalization of Bhargava's factorials to a natural combinatorial setting suitable for studying questions around…
Motivated by the work of Lov\'asz and Szegedy on the convergence and limits of dense graph sequences, we investigate the convergence and limits of finite trees with respect to sampling in normalized distance. Based on separable real trees,…
Given a solution to a recursive distributional equation, a natural (and non-trivial) question is whether the corresponding recursive tree process is endogenous. That is, whether the random environment almost surely defines the tree process.…
We identify the mean growth of the independence number of random binary search trees and random recursive trees and show normal fluctuations around their means. Similarly we also show normal limit laws for the domination number and…
In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.
Reconstructing a parsimonious phylogenetic network that displays multiple phylogenetic trees is an important problem in theory of phylogenetics, where the complexity of the inferred networks is measured by reticulation numbers. The…
A degree sequence is a sequence ${\bf s}=(N_i,i\geq 0)$ of non-negative integers satisfying $1+\sum_i iN_i=\sum_i N_i<\infty$. We are interested in the uniform distribution $\mathbb{P}_{{\bf s}}$ on rooted plane trees whose degree sequence…
The extremal characteristics of random structures, including trees, graphs, and networks, are discussed. A statistical physics approach is employed in which extremal properties are obtained through suitably defined rate equations. A variety…
In this paper we elaborate on the structure of the semigroup tree and the regularities on the number of descendants of each node observed earlier. These regularites admit two different types of behavior and in this work we investigate which…
We present a simple yet rigorous approach to the determination of the spectral dimension of random trees, based on the study of the massless limit of the Gaussian model on such trees. As a byproduct, we obtain evidence in favor of a new…
A closed-form formula is derived for the number of occurrences of matches of a multiset of patterns among all ordered (plane-planted) trees with a given number of edges. A pattern looks like a tree, with internal nodes and leaves, but also…
We show that the transience or recurrence of a random walk in certain random environments on an arbitrary infinite locally finite tree is determined by the branching number of the tree, which is a measure of the average number of branches…
This paper introduces a declarative framework to specify and reason about distributions of data over computing nodes in a distributed setting. More specifically, it proposes distribution constraints which are tuple and equality generating…
In the first part we associate a periodic sequence to a partition and study the connection the distribution of elements of uniform limit of the sequences. Then some facts of statistical independence of these limits are proved
Inferring the processes underlying the emergence of observed patterns is a key challenge in theoretical ecology. Much effort has been made in the past decades to collect extensive and detailed information about the spatial distribution of…
Despite widespread interest and practical use, the theoretical properties of random forests are still not well understood. In this paper we contribute to this understanding in two ways. We present a new theoretically tractable variant of…
We determine the limit of the expected value and the variance of the protection number of the root in simply generated trees, in P\'olya trees, and in unlabelled non-plane binary trees, when the number of vertices tends to infinity.…
The ideas of the constraint-based statistics are introduced. The axiom and six theorems of the constraint-based statistics are established.