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We describe Galois connections which arise between two kinds of combinatorial structures, both of which generalize trees with labelled leaves, and then apply those connections to a family of polytopes. The graphs we study can be imbued with…
We provide precise asymptotic estimates for the number of general phylogenetic networks by using analytic combinatorial methods. Recently, this approach is studied by Fuchs, Gittenberger, and the author himself (Australasian Journal of…
We introduce a novel stochastic growth process, the record-driven growth process, which originates from the analysis of a class of growing networks in a universal limiting regime. Nodes are added one by one to a network, each node…
Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…
In this paper algebraic and combinatorial properties and a computation of the number of the spanning trees are developed for certain graphs. To this purpose, an original method, independent of the spectrum of the Laplacian matrix associated…
The article addresses combinatorial evolution and forecasting of communication protocol for wireless sensor networks (ZigBee). Morphological tree structure (a version of and-or tree) is used as a hierarchical model for the protocol. Three…
Understanding the dynamics of road networks has theoretical implications for urban science and practical applications for sustainable long-term planning. Various generative models to explain road network growth have been introduced in the…
A growing set of applications consider the process of network formation by using subgraphs as a tool for generating the network topology. One of the pressing research challenges is thus to be able to use these subgraphs to understand the…
Mechanistic models can provide an intuitive and interpretable explanation of network growth by specifying a set of generative rules. These rules can be defined by domain knowledge about real-world mechanisms governing network growth or may…
We consider the tributary structure of Howard's drainage model studied by Gangopadhyay et. al. Conditional on the event that the tributary survives up to time $n$, we show that, as a sequence of random metric spaces, scaled tributary…
Random forests are decision tree ensembles that can be used to solve a variety of machine learning problems. However, as the number of trees and their individual size can be large, their decision making process is often incomprehensible. In…
System performance for networks composed of interconnected subsystems can be increased if the traditionally separated subsystems are jointly optimized. Recently, parallel and distributed optimization methods have emerged as a powerful tool…
We propose and analyze a stochastic model which explains, analytically, the cutoff behavior of real scale-free networks previously modeled computationally by Amaral et al. [Proc. Natl. Acad. Sci. U.S.A. 97, 11149 (2000)] and others. We…
Given an $\mathbb{N}$-weighted tree automaton, we give a decision procedure for exponential vs polynomial growth (with respect to the input size) in quadratic time, and an algorithm that computes the exact polynomial degree of growth in…
In this paper, we consider the problem of exploring structural regularities of networks by dividing the nodes of a network into groups such that the members of each group have similar patterns of connections to other groups. Specifically,…
In this paper we present a combinatorial optimisation view on the routing problem for connectionless packet networks by using the metaphor of a landscape. We examine the main properties of the routing landscapes as we define them and how…
We discuss a notion of convergence for binary trees that is based on subtree sizes. In analogy to recent developments in the theory of graphs, posets and permutations we investigate some general aspects of the topology, such as a…
The junction-tree representation provides an attractive structural property for organizing a decomposable graph. In this study, we present two novel stochastic algorithms, which we call the junction-tree expander and junction-tree collapser…
This document presents a combinatorial framework for analyzing assembly systems using generating functions. We explore the theory through concrete examples, such as linear polymers, and develop recursive equations to characterize valid…
Widely used closed product-form networks have emerged recently as a primary model of stochastic growth of sub-cellular structures, e.g., cellular filaments. In the baseline model, homogeneous monomers attach and detach stochastically to…