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It is possible to represent each of a number of Markov chains as an evolving sequence of connected subsets of a directed acyclic graph that grow in the following way: initially, all vertices of the graph are unoccupied, particles are fed in…
Convolution trees, loopy belief propagation, and fast numerical p-convolution are combined for the first time to efficiently solve networks with several additive constraints between random variables. An implementation of this "convolution…
There is a rich literature for modeling binary and polychotomous responses. However, existing methods are inadequate for handling combinatorial responses, where each response is an integer array under additional constraints. Such data are…
In a previous paper, we showed that a compartmental stochastic process model of SARS-CoV-2 transmission could be fit to time series data and then reinterpreted as a collection of interacting branching processes drawn from a dynamic degree…
We review several competing chaining methods to estimate the supremum, the diameter of the range or the modulus of continuity of a stochastic process in terms of tail bounds of their two-dimensional distributions. Then we show how they can…
The relative importance of the intrinsic and extrinsic factors determining the variety of geometric shapes exhibited by dendritic trees remains unclear. This question was addressed by developing a model of the growth of dendritic trees…
We study the enumeration of spinal tree-child phylogenetic networks, a rigid family of tree-child networks in which all internal vertices lie on a single root--to--leaf path. We provide two complementary combinatorial frameworks. First, we…
The aim of this paper is the analysis and selection of stock trading systems that combine different models with data of different nature, such as financial and microeconomic information. Specifically, based on previous work by the authors…
While there has been much interest in adapting conventional clustering procedures---and in higher dimensions, persistent homology methods---to directed networks, little is known about the convergence of such methods. In order to even…
In this paper, we study a parallel version of Galton-Watson processes for the random generation of tree-shaped structures. Random trees are useful in many situations (testing, binary search, simulation of physics phenomena,...) as attests…
Consider the tesselation of the hyperbolic plane by m-gons, l per vertex. In its 1-skeleton, we compute the growth series of vertices, geodesics, tuples of geodesics with common extremities. We also introduce and enumerate "holly trees", a…
Mechanistic network models specify the mechanisms by which networks grow and change, allowing researchers to investigate complex systems using both simulation and analytical techniques. Unfortunately, it is difficult to write likelihoods…
This paper demonstrates the advantages of sharing information about unknown features of covariates across multiple model components in various nonparametric regression problems including multivariate, heteroscedastic, and semi-continuous…
The goal of these lectures is to review some mathematical aspects of random tree models used in evolutionary biology to model gene trees or species trees. We start with stochastic models of tree shapes (finite trees without edge lengths),…
Complex distribution networks are pervasive in biology. Examples include nutrient transport in the slime mold \emph{Physarum polycephalum} as well as mammalian and plant venation. Adaptive rules are believed to guide development of these…
We present a link-by-link rule-based method for constructing all members of the ensemble of spanning trees for any recursively generated, finitely articulated graph, such as the DGM net. The recursions allow for many large-scale properties…
Our work introduces an approach for estimating the contribution of attachment mechanisms to the formation of growing networks. We present a generic model in which growth is driven by the continuous attachment of new nodes according to…
Inspired by numerical homotopy methods we propose a combinatorial homotopy algorithm for finding all isolated solutions to a tropical polynomial systems of n tropical polynomials in n variables. In particular, a tropicalisation of the…
Neural Combinatorial Optimization aims to learn to solve a class of combinatorial problems through data-driven methods and notably through employing neural networks by learning the underlying distribution of problem instances. While, so far…
Our ability to uncover complex network structure and dynamics from data is fundamental to understanding and controlling collective dynamics in complex systems. Despite recent progress in this area, reconstructing networks with stochastic…