Related papers: Effective bi-immunity and randomness

We propose some new results on the comparison of the minimum or maximum order statistic from a random number of non-identical random variables. Under the non-identical set-up, with certain conditions, we prove that random minimum (maximum)…

In this set of three companion manuscripts/articles, we unveil our new results on primality testing and reveal new primality testing algorithms enabled by those results. The results have been classified (and referred to) as…

Time varying susceptibility of host at individual level due to waning and boosting immunity is known to induce rich long-term behavior of disease transmission dynamics. Meanwhile, the impact of the time varying heterogeneity of host…

When in a full exponential family the maximum likelihood estimate (MLE) does not exist, the MLE may exist in the Barndorff-Nielsen completion of the family. We propose a practical algorithm for finding the MLE in the completion based on…

Deep neural networks have amply demonstrated their prowess but estimating the reliability of their predictions remains challenging. Deep Ensembles are widely considered as being one of the best methods for generating uncertainty estimates…

Benchmarking is a fundamental practice in machine learning (ML) for comparing the performance of classification algorithms. However, traditional evaluation methods often overlook a critical aspect: the joint consideration of dataset…

We characterize some major algorithmic randomness notions via differentiability of effective functions. (1) As the main result we show that a real number z in [0,1] is computably random if and only if each nondecreasing computable function…

In assignment problems, the rank distribution of assigned objects is often used to evaluate match quality. Rank-minimizing (RM) mechanisms directly optimize for average rank. While appealing, a drawback is RM mechanisms are not…

Chronic infections of the human immunodeficiency virus (HIV) create a very complex co-evolutionary process, where the virus tries to escape the continuously adapting host immune system. Quantitative details of this process are largely…

By planning through a learned dynamics model, model-based reinforcement learning (MBRL) offers the prospect of good performance with little environment interaction. However, it is common in practice for the learned model to be inaccurate,…

We examine high energy eigenfunctions for the Dirichlet Laplacian on domains where the billiard flow exhibits mixed dynamical behavior. (More generally, we consider semiclassical Schrodinger operators with mixed assumptions on the…

When our immune system encounters foreign antigens (i.e., from pathogens), the B cells that produce our antibodies undergo a cyclic process of proliferation, mutation, and selection, improving their ability to bind to the specific antigen.…

This paper deals with order identification for nested models in the i.i.d. framework. We study the asymptotic efficiency of two generalized likelihood ratio tests of the order. They are based on two estimators which are proved to be…

Missing data arise in most applied settings and are ubiquitous in electronic health records (EHR). When data are missing not at random (MNAR) with respect to measured covariates, sensitivity analyses are often considered. These post-hoc…

Ensemble randomized maximum likelihood (EnRML) is an iterative (stochastic) ensemble smoother, used for large and nonlinear inverse problems, such as history matching and data assimilation. Its current formulation is overly complicated and…

We study higher jumping numbers and generalized test ideals associated to determinantal ideals over a field of positive characteristic. We work in positive characteristic and give a complete characterization of both families for ideals…

In this article, we study several aspects of the intersections of algorithmically random closed sets. First, we answer a question of Cenzer and Weber, showing that the operation of intersecting relatively random closed sets (with respect to…

Much recent work has shown how cross-linguistic variation is constrained by competing pressures from efficient communication. However, little attention has been paid to the role of the systematicity of forms (regularity), a key property of…

To address the needs of modeling uncertainty in sensitive machine learning applications, the setup of distributionally robust optimization (DRO) seeks good performance uniformly across a variety of tasks. The recent multi-distribution…

Existing multi-label ranking (MLR) frameworks only exploit information deduced from the bipartition of labels into positive and negative sets. Therefore, they do not benefit from ranking among positive labels, which is the novel MLR…