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Many of the stochastic models used in inference of phylogenetic trees from biological sequence data have polynomial parameterization maps. The image of such a map --- the collection of joint distributions for a model --- forms the model…
We study the non-equilibrium dynamics of a one-dimensional complex Sachdev-Ye-Kitaev chain by directly solving for the steady state Green's functions in terms of small perturbations around their equilibrium values. The model exhibits…
We propose generalized random forests, a method for non-parametric statistical estimation based on random forests (Breiman, 2001) that can be used to fit any quantity of interest identified as the solution to a set of local moment…
We introduce a graph partitioning problem motivated by computational topology and propose two algorithms that produce approximate solutions. Specifically, given a weighted, undirected graph $G$ and a positive integer $k$, we desire to find…
Nonequilibrium Green's functions provide a powerful tool for computing the dynamical response and particle exchange statistics of coupled quantum systems. We formulate the theory in terms of the density matrix in Liouville space and…
Some general aspects of nonlinear transport phenomena are discussed on the basis of two kinds of formulations obtained by extending Kubo's perturbational scheme of the density matrix and Zubarev's non-equilibrium statistical operator…
Nonequilibrium quantum dynamics can give rise to the emergence of novel steady states. We propose a scheme for driving an initially uncorrelated thermal state to generate customized correlation functions by determining and reverse…
We study infinite tree and ultrametric matrices, and their action on the boundary of the tree. For each tree matrix we show the existence of a symmetric random walk associated to it and we study its Green potential. We provide a…
We study graph estimation and density estimation in high dimensions, using a family of density estimators based on forest structured undirected graphical models. For density estimation, we do not assume the true distribution corresponds to…
Predictions of fatalities from violent conflict on the PRIO-GRID-month (pgm) level are characterized by high levels of uncertainty, limiting their usefulness in practical applications. We discuss the two main sources of uncertainty for this…
The many-body theory of photoemission in solids is reviewed with emphasis on methods based on response theory. The classification of diagrams into loss and no-loss diagrams is discussed and related to Keldysh path-ordering book-keeping.…
We study random two-dimensional spanning forests in the plane that can be viewed both in the discrete case and in their appropriately taken scaling limits as a uniformly chosen spanning tree with some Poissonian deletion of edges or points.…
Transport equations for autonomous driven Fermionic quantum systems are derived with the help of statistical assumptions and of the Markov approximation. The statistical assumptions hold if the system consists of subsystems within which…
We have developed a steady state theory of complex transport networks used to model the flow of commodity, information, viruses, opinions, or traffic. Our approach is based on the use of the Markov chains defined on the graph…
We consider Markov jump processes on a graph described by a rate matrix that depends on various control parameters. We derive explicit expressions for the static responses of edge currents and steady-state probabilities. We show that they…
We give factorizations for weighted spanning tree enumerators of Cartesian products of complete graphs, keeping track of fine weights related to degree sequences and edge directions. Our methods combine Kirchhoff's Matrix-Tree Theorem with…
Space plasmas are generally characterized by non-Maxwellian distributions with suprathermal populations, as routinely revealed by in situ observations. Such departures from standard Maxwellian distributions can be understood as signatures…
This study investigates how visibility graphs constructed from Monte Carlo Markov Chain time series of spin models capture the critical behavior of the system. More precisely, we show that this approach identifies continuous phase…
Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…
We explore two- and three-state Markov models driven out of thermal equilibrium by non-potential forces to demonstrate basic properties of the steady heat capacity based on the concept of quasistatic excess heat. It is shown that large…