相关论文: Regenerative Composition Structures
The classical Gaussian ensembles of random matrices can be constructed by maximizing Boltzmann-Gibbs-Shannon's entropy, S_{BGS} = - \int d{\bf H} [P({\bf H})] \ln [P({\bf H})], with suitable constraints. Here we construct and analyze…
In this paper we introduce a framework for option model composition. Option models are temporal abstractions that, like macro-operators in classical planning, jump directly from a start state to an end state. Prior work has focused on…
Consider a class of decomposable combinatorial structures, using different types of atoms $\Atoms = \{\At_1,\ldots ,\At_{|{\Atoms}|}\}$. We address the random generation of such structures with respect to a size $n$ and a targeted…
Renewal processes are zero-dimensional processes defined by independent intervals of time between zero crossings of a random walker. We subject renewal processes them to stochastic resetting by setting the position of the random walker to…
It is well known that there exist non-isomorphic compact groups with isomorphic representation rings (fusion rules). Nevertheless, considerable structural information about the group can be reconstructed from its representation ring. We…
We study a random code ensemble with a hierarchical structure, which is closely related to the generalized random energy model with discrete energy values. Based on this correspondence, we analyze the hierarchical random code ensemble by…
We provide a new geometric representation of a family of fragmentation processes by nested laminations, which are compact subsets of the unit disk made of noncrossing chords. We specifically consider a fragmentation obtained by cutting a…
Conditional distributions, as defined by the Markov category framework, are studied in the setting of matrix algebras (quantum systems). Their construction as linear unital maps are obtained via a categorical Bayesian inversion procedure.…
The Ewens sampling formula with parameter $\alpha$ is the distribution on $S_n$ which gives each $\pi\in S_n$ weight proportional to $\alpha^{C(\pi)}$, where $C(\pi)$ is the number of cycles of $\pi$. We show that, for any fixed $\alpha$,…
The random connection model is a random graph whose vertices are given by the points of a Poisson process and whose edges are obtained by randomly connecting pairs of Poisson points in a position dependent but independent way. We study…
Bose-condensed systems with broken global gauge symmetry are considered. The description of these systems, as has been shown by Hohenberg and Martin, possesses an internal inconsistency, resulting in either nonconserving theories or…
We introduce $Recursive~Jigsaw~Reconstruction$, a technique for analyzing reconstructed particle interactions in the presence of kinematic and combinatoric unknowns associated with unmeasured and indistinguishable particles, respectively.…
In probabilistic modelling, joint distributions are often of more interest than their marginals, but the standard composition of stochastic channels is defined by marginalization. Last year at ACT, the notion of 'copy-composition' was…
A relationally exchangeable structure is a random combinatorial structure whose law is invariant with respect to relabeling its relations, as opposed to its elements. Aside from exchangeable random partitions, examples include edge…
When identical particles on a line collide, they merge and continue as one. Exact determinantal formulas have long been available for particles conditioned never to collide, but collisions change the number of particles, and exact…
This paper develops an analogy between the cycle structure of, on the one hand, random permutations with cycle lengths restricted to lie in an infinite set $S$ with asymptotic density $\sigma$ and, on the other hand, permutations selected…
We consider fixed-point equations for probability distributions on isometry classes of measured metric spaces. The construction is required to be recursive and tree-like, but we allow loops for the geodesics between points in the support of…
In the past several years a wide range of methods for the construction of regression trees and other estimators based on the recursive partitioning of samples have appeared in the statistics literature. Many applications involve data…
A new definition of random sets is proposed. It is based on the distance in measurable space and uses negative definite kernels for continuation from initial space to that of random sets. This approach has no connection to Hausdorff…
Using statistical physics methods, we study generative diffusion models in the regime where the dimension of space and the number of data are large, and the score function has been trained optimally. Our analysis reveals three distinct…