Related papers: A class of multifractal processes constructed usin…
(Multi-type) branching processes are a natural and well-studied model for generating random infinite trees. Branching processes feature both nondeterministic and probabilistic branching, generalizing both transition systems and Markov…
Scaling properties of time series are usually studied in terms of the scaling laws of empirical moments, which are the time average estimates of moments of the dynamic variable. Nonlinearities in the scaling function of empirical moments…
In this paper the multi-dimensional random walk models governed by distributed fractional order differential equations and multi-term fractional order differential equations are constructed. The scaling limits of these random walks to a…
In this paper we consider the problem of graph-based transductive classification, and we are particularly interested in the directed graph scenario which is a natural form for many real world applications. Different from existing research…
We revisit a simple model class for machine learning on graphs, where a random walk on a graph produces a machine-readable record, and this record is processed by a deep neural network to directly make vertex-level or graph-level…
Many tasks in graph machine learning, such as link prediction and node classification, are typically solved by using representation learning, in which each node or edge in the network is encoded via an embedding. Though there exists a lot…
We investigate the genealogical structure of general critical or subcritical continuous-state branching processes. Analogously to the coding of a discrete tree by its contour function, this genealogical structure is coded by a real-valued…
We study random trees which are invariant in law under the operation of contracting each edge independently with probability $p\in(0,1)$. We show that all such trees can be constructed through Poissonian sampling from a certain class of…
Markov jump processes are continuous-time stochastic processes with a wide range of applications in both natural and social sciences. Despite their widespread use, inference in these models is highly non-trivial and typically proceeds via…
Graph embedding based on random-walks supports effective solutions for many graph-related downstream tasks. However, the abundance of embedding literature has made it increasingly difficult to compare existing methods and to identify…
Branching processes are widely used to model the viral epidemic evolution. For more adequate investigation of viral epidemic modelling, we suggest to apply branching processes with transport of particles usually called branching random…
This paper contributes to the study of a new and remarkable family of stochastic processes that we will term class $\Sigma^{r}(H)$. This class is potentially interesting because it unifies the study of two known classes: the class…
A multiplicative cascade can be thought of as a randomization of a measure on the boundary of a tree, constructed from an iid collection of random variables attached to the tree vertices. Given an initial measure with certain regularity…
Diffusion processes with branching play an important role in statistical dynamics. They are a common approach to the computing of quantum mechanical groundstates, and serve as models for population dynamics and as physical pictures for…
We revise the Levy's construction of Brownian motion as a simple though still rigorous approach to operate with various Gaussian processes. A Brownian path is explicitly constructed as a linear combination of wavelet-based "geometrical…
Graph representation learning (also known as network embedding) has been extensively researched with varying levels of granularity, ranging from nodes to graphs. While most prior work in this area focuses on node-level representation,…
An important part of many machine learning workflows on graphs is vertex representation learning, i.e., learning a low-dimensional vector representation for each vertex in the graph. Recently, several powerful techniques for unsupervised…
The discrete class algorithm presented in this paper is an efficient simulation tool for stochastic processes governed by a reasonably small set of transition rates. The algorithm is presented, its performance compared to prevailing methods…
It is well known that the behaviour of a branching process is completely described by the generating function of the offspring law and its fixed points. Branching random walks are a natural generalization of branching processes: a branching…
In [Aldous,Pitman,1998] a tree-valued Markov chain is derived by pruning off more and more subtrees along the edges of a Galton-Watson tree. More recently, in [Abraham,Delmas,2012], a continuous analogue of the tree-valued pruning dynamics…