Related papers: On some threshold-one attractive interacting parti…
We investigate the tractability of a simple fusion of two fundamental structures on graphs, a spanning tree and a perfect matching. Specifically, we consider the following problem: given an edge-weighted graph, find a minimum-weight…
Decision tree learning is increasingly being used for pointwise inference. Important applications include causal heterogenous treatment effects and dynamic policy decisions, as well as conditional quantile regression and design of…
The threshold model has been widely adopted as a prototype for studying contagion processes on social networks. In this paper, we consider individual interactions in groups of three or more vertices and study the threshold model on…
We establish a functional weak law of large numbers for observable macroscopic state variables of interacting particle systems (e.g., voter and contact processes) over fast time-varying sparse random networks of interactions. We show that,…
We consider continuous-time consensus systems whose interactions satisfy a form or reciprocity that is not instantaneous, but happens over time. We show that these systems have certain desirable properties: They always converge…
A voter sits on each vertex of an infinite tree of degree $k$, and has to decide between two alternative opinions. At each time step, each voter switches to the opinion of the majority of her neighbors. We analyze this majority process when…
We study a class of swarming problems wherein particles evolve dynamically via pairwise interaction potentials and a velocity selection mechanism. We find that the swarming system undergoes various changes of state as a function of the…
This paper proposes a new lens for studying threshold games played on networks when the thresholds are heterogeneous. These are games where agents have two possible actions, and prefer action 1 if and only if enough of their neighbours…
We present an explicit connected spanning structure that appears in a random graph just above the connectivity threshold with high probability.
A non-autonomous system is proposed to model the seasonal pattern of dengue fever. We found that an approximate threshold condition for infection persistence describes all possible behavior of the system. As far as we know, the kind of…
We study simple interacting particle systems on heterogeneous networks, including the voter model and the invasion process. These are both two-state models in which in an update event an individual changes state to agree with a neighbor.…
It is known that the limiting behavior of the contact process strongly depends upon the geometry of the graph on which particles evolve: while the contact process on the regular lattice exhibits only two phases, the process on homogeneous…
An non-autonomous system is proposed to model the seasonal pattern of dengue fever. We found that an approximate threshold condition for infection persistence describes all possible behavior of the system. As far as we know, the kind of…
We study the dynamics of the voter and Moran processes running on top of complex network substrates where each edge has a weight depending on the degree of the nodes it connects. For each elementary dynamical step the first node is chosen…
The time process of transport on randomly evolving trees is investigated. By introducing the notions of living and dead nodes a model of random tree evolution is constructed which describes the spreading in time of objects corresponding to…
This article introduces a model for interacting vertex-reinforced random walks, each taking values on a complete sub-graph of a locally finite undirected graph. The transition probability for a walk to a given vertex depends on the…
We consider survival probabilities for the discrete time process in one dimension, which is known as the Domany-Kinzel model. A convergence theorem for infinite systems can be obtained in the nonattractive case.
Recent generalization of the coevolving voter model (J. Toruniewska et al, PRE 96 (2017) 042306) is further generalized here, including spin-dependent probability of rewiring. Mean field results indicate that either the system splits into…
A little over 25 years ago Pemantle pioneered the study of the contact process on trees, and showed that on homogeneous trees the critical values $\lambda_1$ and $\lambda_2$ for global and local survival were different. He also considered…
Uniqueness of effective interaction defined in an extension of the Kohn-Sham theory is proved, if the model with a non-degenerate ground state exists and to reproduce a correlation function as well as the single-particle density of an…