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The family of Groves mechanisms, which includes the well-known VCG mechanism (also known as the Clarke mechanism), is a family of efficient and strategy-proof mechanisms. Unfortunately, the Groves mechanisms are generally not budget…
In this work, we study the contraction conditions of iterative algorithms for stationary and finite-horizon discrete-time regularized mean-field games (MFGs) with multiple populations, where each population only interacts with the state…
Optimization is important in machine learning problems, and quasi-Newton methods have a reputation as the most efficient numerical schemes for smooth unconstrained optimization. In this paper, we consider the explicit superlinear…
In a fully 3-D system such as a stellarator, the toroidal mode number $n$ ceases to be a good quantum number--all $n$s within a given mode family being coupled. It is found that the discrete spectrum of unstable ideal MHD…
The improving multi-armed bandits problem is a formal model for allocating effort under uncertainty, motivated by scenarios such as investing research effort into new technologies, performing clinical trials, and hyperparameter selection…
We introduce a new five-parameter family of size distributions on the semi-finite interval $[x_0, \infty), x_0 \geqslant 0$, with two attractive features. First, it interpolates between power laws, such as the Pareto distribution, and power…
Hidden regular variation defines a subfamily of distributions satisfying multivariate regular variation on $\mathbb{E} = [0, \infty]^d \backslash \{(0,0, ..., 0) \} $ and models another regular variation on the sub-cone $\mathbb{E}^{(2)} =…
A new family of continuous distribution is proposed by using Kumaraswamy-G (Cordeiro and de Castro, 2011) distribution as the base line distribution in the Marshal-Olkin (Marshall and Olkin, 1997) construction. A number of known…
Motivated by some cutting edge circular data such as from Smart Home technologies and roulette spins from online and casino, we construct some new rich classes of discrete distributions on the circle. We give four new general methods of…
The aim of this article is to introduce a new family of distributions, which generalizes the skew normal distribution (SN). This new family, called Beta skew-normal (BSN), arises naturally when we consider the distributions of order…
We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable models for the phenomenon of mode-locking…
In random parameter estimation, Bayesian lower bounds (BLBs) for the mean-square error have been noticed to not be tight in a number of cases, even when the sample size, or the signal-to-noise ratio, grow to infinity. In this paper, we…
Introduced by M\"uller et al. in their seminal paper \cite{muller}, fractional stochastic dominance (SD) offers a nuanced approach to ordering distributions. In this paper, we propose a fundamentally new framework by replacing the fixed…
The paper proposes a novel regularization procedure for machine learning. The proposed high-order regularization (HR) provides new insight into regularization, which is widely used to train a neural network that can be utilized to…
Through viewing out the literature, many generated distributions took a new special form of probability density function (PDF) in which it is written as a linear combination of n other distributions. Therefore, we define in this paper a new…
The mathematical properties of a family of generalized beta distribution, including beta-normal, skewed-t, log-F, beta-exponential, beta-Weibull distributions have recently been studied in several publications. This paper applies these…
In the following, we introduce new proportional hazard (PH) processes, which are derived by a marginal transformation applied to complementary power function distribution (CPFD) processes. Also, we introduce two new Pareto processes, which…
Random matrix theory (RMT) universality is the defining property of quantum mechanical chaotic systems, and can be probed by observables like the spectral form factor (SFF). In this paper, we describe systematic deviations from RMT…
In this note, we extend the regularity theory for monotone measure-preserving maps, also known as optimal transports for the quadratic cost optimal transport problem, to the case when the support of the target measure is an arbitrary convex…
This is a survey of a new type of relativistic space-time framework; the so-called quasi-metric framework. The basic geometric structure underlying quasi-metric relativity is quasi-metric space-time; this is defined as a 4-dimensional…