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We present a graph model for a background independent, relational approach to spacetime emergence. The general idea and the graph main features, detailed in [1], are discussed. This is a combinatorial (dynamical) metric graph, colored on…
The outcome of elections is strongly dependent on the districting choices, making thus possible (and frequent) the gerrymandering phenomenon, i.e.\ politicians suitably changing the shape of electoral districts in order to win the…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…
Isoradial graphs are a natural generalization of regular graphs which give, for many models of statistical mechanics, the right framework for studying models at criticality. In this survey paper, we first explain how isoradial graphs…
An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…
Graphs are ubiquitous data structures for representing interactions between entities. With an emphasis on the use of graphs to represent chemical molecules, we explore the task of learning to generate graphs that conform to a distribution…
The well-defined but intricate course of time evolution exhibited by many naturally occurring phenomena suggests some source of dynamic order sustaining it. In spite of its obviousness as a problem, it has remained absent from the…
We introduce a two-dimensional discrete-time dynamical system which represents the evolution of an angle and angular velocity. While the angle evolves by a fixed amount in every step, the evolution of the angular velocity is governed by a…
We consider the problem of learning causal directed acyclic graphs from an observational joint distribution. One can use these graphs to predict the outcome of interventional experiments, from which data are often not available. We show…
Predicting future trajectories of surrounding obstacles is a crucial task for autonomous driving cars to achieve a high degree of road safety. There are several challenges in trajectory prediction in real-world traffic scenarios, including…
The spacetime discreteness of causal set theory has enabled the formulation of novel spacetime dynamics. In these so-called "growth" dynamics, a causal set spacetime is generated probabilistically by means of a random walk on certain tree…
In this paper, we propose a path following replicator dynamic, and investigate its potentials in uncovering the underlying cluster structure of a graph. The proposed dynamic is a generalization of the discrete replicator dynamic. The…
We propose a covariate-dependent discrete graphical model for capturing dynamic networks among discrete random variables, allowing the dependence structure among vertices to vary with covariates. This discrete dynamic network encompasses…
We prove a version of Bass' finitistic dimension conjecture for path algebras over arbitrary directed graphs. It is known that the path algebra of a finite directed graph is hereditary, hence it has finite finitistic dimension, when the…
Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…
Directed acyclic graph (DAG) learning is a central task in structure discovery and causal inference. Although the field has witnessed remarkable advances over the past few years, it remains statistically and computationally challenging to…
A dynamical network, a graph whose nodes are dynamical systems, is usually characterized by a large dimensional space which is not always accesible due to the impossibility of measuring all the variables spanning the state space. Therefore,…
The series of equilibrium states reached by disordered packings of rigid, frictionless discs in two dimensions, under gradually varying stress, are studied by numerical simulations. Statistical properties of trajectories in configuration…
Research on the similarity of a graph to being a tree - called the treewidth of the graph - has seen an enormous rise within the last decade, but a practically fast algorithm for this task has been discovered only recently by Tamaki (ESA…
Iterations of odd piecewise continuous maps with two discontinuities, i.e., symmetric discontinuous bimodal maps, are studied. Symbolic dynamics is introduced. The tools of kneading theory are used to study the homology of the discrete…