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We characterize the outcomes of a canonical deterministic model for the intergenerational transmission of capital that features differential fertility. A fertility function determines the relationship between parental capital and the number…

Generative adversarial nets (GANs) have become a preferred tool for tasks involving complicated distributions. To stabilise the training and reduce the mode collapse of GANs, one of their main variants employs the integral probability…

We explore conditions for a class of functions defined via an integral representation to be a probability generating function of some positive integer valued random variable. Interest in and research on this question is motivated by an…

Working in the framework of the Color Glass Condensate effective theory of high energy QCD, we revisit the momentum space entanglement entropy of the soft gluons produced in high energy dilute-dense collisions. We extend the work…

We present a general framework for deriving entropy production rates (EPRs) in active matter systems driven by non-Gaussian active fluctuations. Employing the probability-flow equivalence technique, we rigorously obtain an entropy…

Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide…

Causal representation learning seeks to uncover causal relationships among high-level latent variables from low-level, entangled, and noisy observations. Existing approaches often either rely on deep neural networks, which lack…

Continual learning aims to acquire new tasks while preserving performance on previously learned ones, but most methods struggle with catastrophic forgetting. Existing approaches typically treat all layers uniformly, often trading stability…

Dynamic recommendation is essential for modern recommender systems to provide real-time predictions based on sequential data. In real-world scenarios, the popularity of items and interests of users change over time. Based on this…

Multivariate functional data that are cross-sectionally compositional data are attracting increasing interest in the statistical modeling literature, a major example being trajectories over time of compositions derived from cause-specific…

Cumulants of a fluctuating current can be obtained from a free energy-like generating function which for Markov processes equals the largest eigenvalue of a generalized generator. We determine this eigenvalue with the DMRG for stochastic…

In this paper, we study distributions that describe markets with linear stochastic demand. We express the price elasticity of expected demand in terms of the mean residual demand (MRD) function of the demand distribution and characterize…

Feature generation can significantly enhance learning outcomes, particularly for tasks with limited data. An effective way to improve feature generation is to expand the current feature space using existing features and enriching the…

This article presents a new class of generalized transmuted lifetime distributions which includes a large number of lifetime distributions as sub-family. Several important mathematical quantities such as density function, distribution…

In the recent information-theoretic literature, the concept of extropy has been studied for order statistics. In the present communication we consider a cumulative analogue of extropy in the same vein of cumulative residual (past) entropy…

We derive recursions for the probability distribution of random sums by computer algebra. Unlike the well-known Panjer-type recursions, they are of finite order and thus allow for computation in linear time. This efficiency is bought by the…

Dynamic contingency screening is a challenging task in dynamic security assessment, when traditional numerical approaches are computationally intensive and often not able to repeatedly solve full AC power flow for all possible contingencies…

We introduce a new type of graphical model called a "cumulative distribution network" (CDN), which expresses a joint cumulative distribution as a product of local functions. Each local function can be viewed as providing evidence about…

Nowadays, the transition from a conventional generation system to a renewable generation system is one of the most difficult challenges for system operators and companies. There are several reasons: the long-standing impact of investment…

In this paper, we propose a new and unified approach for nonparametric regression and conditional distribution learning. Our approach simultaneously estimates a regression function and a conditional generator using a generative learning…