Related papers: Combinatorial analysis of growth models for series…

We study a random fragmentation process and its associated random tree. The process has earlier been studied by Dean and Majumdar (J. Phys. A: Math. Gen., vol. 35, L501--L507), who found a phase transition: the number of fragmentations is…

This article introduces a flexible and adaptive nonparametric method for estimating the association between multiple covariates and power spectra of multiple time series. The proposed approach uses a Bayesian sum of trees model to capture…

A model for growing information networks is introduced where nodes receive new links through j-redirection, i.e. the probability for a node to receive a link depends on the number of paths of length j arriving at this node. In detail, when…

We present new algorithm for growth of non-clustered planar graphs by aggregation of cells with given distribution of size and constraint of connectivity k=3 per node. The emergent graph structures are controlled by two parameters--chemical…

In this paper we present a generalized model for network growth that links the microscopical agent strategies with the large scale behavior. This model is intended to reproduce the largest number of features of the Internet network at the…

Structure and dynamics of complex networks usually deal with degree distributions, clustering, shortest path lengths and other graph properties. Although these concepts have been analysed for graphs on abstract spaces, many networks happen…

Series-parallel networks are a class of graphs on which many NP-hard problems have tractable solutions. In this paper, we examine performance measures on leader-follower consensus on series-parallel networks. We show that a distributed…

We study the averaging-based distributed optimization solvers over random networks. We show a general result on the convergence of such schemes using weight-matrices that are row-stochastic almost surely and column-stochastic in expectation…

The metric space of phylogenetic trees defined by Billera, Holmes, and Vogtmann, which we refer to as BHV space, provides a natural geometric setting for describing collections of trees on the same set of taxa. However, it is sometimes…

In the 1970's, Balas introduced the concept of disjunctive programming, which is optimization over unions of polyhedra. One main result of his theory is that, given linear descriptions for each of the polyhedra to be taken in the union, one…

We introduce two lattice growth models: aggregation of $l$-dimensional boxes and aggregation of partitions with $l$ parts. We describe properties of the models: the parameter set of aggregations, the moments of the random variable of the…

We present asymptotic and finite-sample results on the use of stochastic blockmodels for the analysis of network data. We show that the fraction of misclassified network nodes converges in probability to zero under maximum likelihood…

We destroy a finite tree of size $n$ by cutting its edges one after the other and in uniform random order. Informally, the associated cut-tree describes the genealogy of the connected components created by this destruction process. We…

We propose a new method for quantitative characterization of spatial network-like patterns with loops, such as surface fracture patterns, leaf vein networks and patterns of urban streets. Such patterns are not well characterized by purely…

We study the structure of the asymptotic expansion of the probability that a combinatorial object is connected. We show that the coefficients appearing in those asymptotics are integers and can be interpreted as the counting sequences of…

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,…

Random forests are a statistical learning technique that use bootstrap aggregation to average high-variance and low-bias trees. Improvements to random forests, such as applying Lasso regression to the tree predictions, have been proposed in…

We introduce the Graph Mixture Density Networks, a new family of machine learning models that can fit multimodal output distributions conditioned on graphs of arbitrary topology. By combining ideas from mixture models and graph…

Motivated by distributed machine learning settings such as Federated Learning, we consider the problem of fitting a statistical model across a distributed collection of heterogeneous data sets whose similarity structure is encoded by a…

We propose a model of a growing network, in which preferential linking is combined with partial inheritance of connectivity (number of incoming links) of individual nodes by new ones. The nontrivial version of this model is solved exactly…