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作者：Cook, Nicholas A.; Dembo, Amir
作者单位：Duke University; Stanford University
摘要：We consider general exponential random graph models (ERGMs) where the sufficient statistics are functions of homomorphism counts for a fixed collection of simple graphs F-k. Whereas previous work has shown a degeneracy phenomenon in dense ERGMs, we show this can be cured by raising the sufficient statistics to a fractional power. We rigorously establish the naive mean-field approximation for the partition function of the corresponding Gibbs measures, and in case of ferromagnetic models with va...
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作者：Lavenant, Hugo; Zhang, Stephen; Kim, Young-Heon; Schiebinger, Geoffrey
作者单位：Bocconi University; Bocconi University; University of British Columbia
摘要：We devise a theoretical framework and a numerical method to infer trajectories of a stochastic process from samples of its temporal marginals. This problem arises in the analysis of single -cell RNA-sequencing data, which provide high-dimensional measurements of cell states but cannot track the trajectories of the cells over time. We prove that for a class of stochastic processes it is possible to recover the ground truth trajectories from limited samples of the temporal marginals at each time...
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作者：Djete, Mao fabrice; Touzi, Nizar
作者单位：Universite Paris Cite; Institut Polytechnique de Paris; ENSTA Paris
摘要：We introduce a mean field model for optimal holding of a representative agent of her peers as a natural expected scaling limit from the corresponding N-agent model. The induced mean field dynamics appear naturally in a form which is not covered by standard McKean-Vlasov stochastic differential equations. We study the corresponding mean field game of mutual holding in the absence of common noise. Our first main result provides an explicit equilibrium of this mean field game, defined by a bang-b...
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作者：Ball, Frank; Sirl, David; Trapman, Pieter
作者单位：University of Nottingham; Stockholm University
摘要：We investigate final outcome properties of an SIR (susceptible -k infective -k recovered) epidemic model defined on a population of large subcommunities in which there is stronger disease transmission within the communities than between them. Our analysis involves approximation of the epidemic process by a chain of within-community large outbreaks spreading between the communities. We derive law of large numbers and central limit type results for the number of individuals and the number of com...
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作者：Last, Guenter; Penrose, Mathew d.; Zuyev, Sergei
作者单位：Helmholtz Association; Karlsruhe Institute of Technology; University of Bath; Chalmers University of Technology
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作者：Donoho, David l.; Kipnis, A. lon
作者单位：Stanford University; Reichman University
摘要：Consider a multiple hypothesis testing setting involving rare/weak effects: relatively few tests, out of possibly many, deviate from their null hypothesis behavior. Summarizing the significance of each test by a p-value, we construct a global test against the joint null using the higher criticism (HC) statistics of these p-values. We calibrate the rare/weak model using parameters controlling the asymptotic distribution of nonnull p-values near zero. We derive a region in the parameter space wh...
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作者：Kim, Seonwoo; Sau, Federico
作者单位：Korea Institute for Advanced Study (KIAS); University of Trieste
摘要：We consider the symmetric inclusion process on a general finite graph. Our main result establishes universal upper and lower bounds for the spectral gap of this interacting particle system in terms of the spectral gap of the random walk on the same graph. In the regime in which the gamma-like reversible measures of the particle systems are log-concave, our bounds match, yielding a version for the symmetric inclusion process of the celebrated Aldous' spectral gap conjecture originally formulate...
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作者：Durmus, Alain; Eberle, Andreas
作者单位：Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique; University of Bonn
摘要：Inexact Markov chain Monte Carlo methods rely on Markov chains that do not exactly preserve the target distribution. Examples include the unadjusted Langevin algorithm (ULA) and unadjusted Hamiltonian Monte Carlo (uHMC). This paper establishes bounds on Wasserstein distances between the invariant probability measures of inexact MCMC methods and their target distributions with a focus on understanding the precise dependence of this asymptotic bias on both dimension and discretization step size....
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作者：Bjornberg, Jakob E.; Mailler, Cecile; Moerters, Peter; Ueltschi, Daniel
作者单位：Chalmers University of Technology; University of Gothenburg; University of Bath; University of Cologne; University of Warwick
摘要：We investigate a disordered variant of Pitman's Chinese restaurant process where tables carry i.i.d. weights. Incoming customers choose to sit at an occupied table with a probability proportional to the product of its occupancy and its weight, or they sit at an unoccupied table with a probability proportional to a parameter 6 > 0. This is a system out of equilibrium where the proportion of customers at any given table converges to zero almost surely. We show that for weight distributions in an...
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作者：Harris, Simon c.; Palau, Sandra; Pardo, Juan carlos
作者单位：University of Auckland; Universidad Nacional Autonoma de Mexico
摘要：We investigate the genealogy of a sample of k >= 2 particles chosen uniformly without replacement from a population alive at large times in a critical discrete-time Galton-Watson process in a varying environment (GWVE). We will show that subject to an explicit deterministic time-change involving only the mean and variances of the varying offspring distributions, the sample genealogy always converges to the same universal genealogical structure; it has the same tree topology as Kingman's coales...
