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Consider an algorithm performing a computation on a huge random object. Is it necessary to generate the entire object up front, or is it possible to provide query access to the object and sample it incrementally "on-the-fly"? Such an…
Starting from the Random Phase Approximation (RPA), we generalize the schematic model of separable interaction defning subspaces of ph excitations with different coupling constants between them. This ansatz simplifies the RPA eigenvalue…
We consider the problem of studying the simulation capabilities of the dynamics of arbitrary networks of finite states machines. In these models, each node of the network takes two states 0 (passive) and 1 (active). The states of the nodes…
The premise of automated alert correlation is to accept that false alerts from a low level intrusion detection system are inevitable and use attack models to explain the output in an understandable way. Several algorithms exist for this…
Models of reaction diffusion processes usually employ discrete lattice models with particles interacting at the same site, resulting in localized reactions in the continuum limit. Here, various non-local interactions are considered, and two…
For reaction-diffusion processes without exclusion, in which the particles can exist in the same site of a one-dimensional lattice, we study all the integrable models which can be obtained by imposing a boundary condition on the master…
Two-point density-density correlation functions for the diffusive binary reaction system $A+A\to\emptyset$ are obtained in one dimension via Monte Carlo simulation. The long-time behavior of these correlation functions clearly deviates from…
In random cellular systems, both observation and maximum entropy inference give a specific form to the topological pair correlation: it is bi-affine in the cells number of edges with coefficients depending on the distance between the two…
A two species reaction-diffusion model, in which particles diffuse on a one-dimensional lattice and annihilate when meeting each other, has been investigated. Mean field equations for general choice of reaction rates have been solved…
We calculate correlation functions of exactly-solvable one-dimensional flat-band models by utilizing the "molecular-orbital" representation. The models considered in this paper have a gapped ground state with flat-band being fully occupied,…
We study the zero sets of the independence polynomial on recursive sequences of graphs. We prove that for a maximally independent starting graph and a stable and expanding recursion algorithm, the zeros of the independence polynomial are…
Independent sample generation is the prevailing paradigm in modern diffusion-based generative models of AI. We ask a different question: can samples \emph{coordinate} through shared population statistics to transport probability mass more…
This paper develops computationally feasible methods for estimating random effects models in the context of regression modelling of multiple independent time series of discrete valued counts in which there is serial dependence. Given…
Deciding which predictors to use plays an integral role in deriving statistical models in a wide range of applications. Motivated by the challenges of predicting events across a telecommunications network, we propose a semi-automated, joint…
We propose a model for deterministic distributed function computation by a network of identical and anonymous nodes, with bounded computation and storage capabilities that do not scale with the network size. Our goal is to characterize the…
We introduce the coverage correlation coefficient, a novel nonparametric measure of statistical association designed to quantifies the extent to which two random variables have a joint distribution concentrated on a singular subset with…
The full hierarchy of multiple-point correlation functions for diffusion-limited annihilation, A + A -> 0, is obtained analytically and explicitly, following the method of intervals. In the long time asymptotic limit, the correlation…
Interaction models describe distributed systems as algebraic terms, with gates marking interaction points between local views. Composing local models into a coherent global one requires aligning these gates while respecting the algebraic…
The quality of generalized linear models (GLMs), frequently used by insurance companies, depends on the choice of interacting variables. The search for interactions is time-consuming, especially for data sets with a large number of…
For a variety of pattern-avoiding classes, we describe the limiting distribution for the number of fixed points for involutions chosen uniformly at random from that class. In particular we consider monotone patterns of arbitrary length as…