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This work presents generalized forgetting recursive least squares (GF-RLS), a generalization of recursive least squares (RLS) that encompasses many extensions of RLS as special cases. First, sufficient conditions are presented for the 1)…
This paper is going to introduce a new method for ranked set sampling with multiple criteria. The method is based on a version of ranked set sampling, introduced by Panahbehagh et al. (2017), which relaxes the restriction of selecting just…
A common problem in health research is that we have a large database with many variables measured on a large number of individuals. We are interested in measuring additional variables on a subsample; these measurements may be newly…
Confronted with the challenge of identifying the most suitable metric to validate the merits of newly proposed models, the decision-making process is anything but straightforward. Given that comparing rankings introduces its own set of…
We examine the limiting behavior of multiple ergodic averages associated with arithmetic progressions whose differences are elements of a fixed integer sequence. For each $\ell$, we give necessary and sufficient conditions under which…
In subgroup analysis, testing the existence of a subgroup with a differential treatment effect serves as protection against spurious subgroup discovery. Despite its importance, this hypothesis testing possesses a complicated nature:…
The study of first-order optimization is sensitive to the assumptions made on the objective functions. These assumptions induce complexity classes which play a key role in worst-case analysis, including the fundamental concept of algorithm…
Group testing is the process of pooling arbitrary subsets from a set of $n$ items so as to identify, with a minimal number of tests, a "small" subset of $d$ defective items. In "classical" non-adaptive group testing, it is known that when…
We show that groups with a mild form of non-positive curvature (a navigable path system) satisfy the weak rank rigidity conjecture: they either have linear divergence or a Morse element. This class includes discrete groups of projective…
Landscape paradigm is ubiquitous in physics and other natural sciences, but it has to be supplemented with both quantitative and qualitatively meaningful tools for analyzing the topography of a given landscape. We here consider dynamic…
We discuss a finite rectangular well as a perturbation for the infinite one with a depth $\lambda^2$ of the former as a perturbation parameter. In particular we consider a behaviour of energy levels in the well as functions of complex…
In this paper we study a new, generalized version of the well-known group testing problem. In the classical model of group testing we are given n objects, some of which are considered to be defective. We can test certain subsets of the…
Roughly speaking, a system is said to be robust if it can resist disturbances and still function correctly. For instance, if the requirement is that the temperature remains in an allowed range $[l,h]$, then a system that remains in a range…
Probabilistic dynamics model ensemble is widely used in existing model-based reinforcement learning methods as it outperforms a single dynamics model in both asymptotic performance and sample efficiency. In this paper, we provide both…
While Szemer\'edi's graph regularity lemma is an indispensable tool for studying extremal problems in graph theory, using it comes with a hefty price, since a worst-case graph may only have regular partitions of tower-type size. It is thus…
Energy functionals describing phase transitions in crystalline solids are often non-quasiconvex and minimizers might therefore not exist. On the other hand, there might be infinitely many gradient Young measures, modelling microstructures,…
Previous work has shown that if an attractive 1/r^2 potential is regularized at short distances by a spherical square-well potential, renormalization allows multiple solutions for the depth of the square well. The depth can be chosen to be…
We give a sharpened form of Siegel Lemma's w. r. t. the maximum norm. This implies a new lower bound on the greatest element of a sum-distinct set of positive integers (Erd\"os-Moser problem). The main tools are Minkowski's theorem on…
A child is considered to have faltered growth when increases in their height or weight starts to decline relative to a suitable comparison population. However, there is currently a lack of consensus on both the choice of anthropometric…
A four-pronged approach to dealing with Social Science Phenomenon is outlined. This methodology is applied to Financial Services, Economic Growth and Well-Being. The four prongs are like the four directions for an army general looking for…