Related papers: A Constructive Heuristic Sieve for the Twin Prime …
The wrapped normal distribution arises when a the density of a one-dimensional normal distribution is wrapped around the circle infinitely many times. At first look, evaluation of its probability density function appears tedious as an…
This paper considers a probabilistic-analytical approach to determining asymptotics of prime objects on the initial interval of the natural series. The author proposes a new method based on the construction of a probability space. An…
Let a and b be non-zero rational numbers that are multiplicatively independent. We study the natural density of the set of primes p for which the subgroup of the multiplicative group of the finite field with p elements generated by (a\mod…
We report a rigorous theory to show the origin of the unexpected periodic behavior seen in the consecutive differences between prime numbers. We also check numerically our findings to ensure that they hold for finite sequences of primes,…
The linear complexity and the $k$-error linear complexity of a binary sequence are important security measures for key stream strength. By studying binary sequences with the minimum Hamming weight, a new tool named as hypercube theory is…
Assigning weights to a large pool of objects is a fundamental task in a wide variety of applications. In this article, we introduce the concept of structured high-dimensional probability simplexes, in which most components are zero or near…
We introduce a wide class of deterministic subsets of primes of zero relative density and we prove Roth's Theorem in these sets, namely, we show that any subset of them with positive relative upper density contains infinitely many…
For integers x and k, let T(x;2k) denote the number of twin prime pairs (p,p+2k) with a distance 2k<=2x**0.5 and p<=x (not p+2k<=x). Let Tg(x;2x**0.5) denote the average of T(x;2k) for all 2k<=2x**0.5. Logically, T(x;2k) should be a…
Dickson conjectured that a set of polynomials will take on infinitely many simultaneous prime values. Later others, such as Hardy and Littlewood, gave estimates for the number of these primes. In this article we look at this conjecture,…
We investigate the convergence properties of a stochastic primal-dual splitting algorithm for solving structured monotone inclusions involving the sum of a cocoercive operator and a composite monotone operator. The proposed method is the…
In this paper we propose a stochastic primal dual fixed point method (SPDFP) for solving the sum of two proper lower semi-continuous convex function and one of which is composite. The method is based on the primal dual fixed point method…
Diffusion generative models unlock new possibilities for inverse problems as they allow for the incorporation of strong empirical priors in scientific inference. Recently, diffusion models are repurposed for solving inverse problems using…
Two-sample hypothesis testing for network comparison presents many significant challenges, including: leveraging repeated network observations and known node registration, but without requiring them to operate; relaxing strong structural…
This work proposes elementary proofs of several related primes counting problems, based on an elementary weighted sieve. The subsets of primes considered here are the followings: the subset of twin primes PT = {p and p + 2 are primes}, the…
Efficient sampling for the conditional time integrated variance process in the Heston stochastic volatility model is key to the simulation of the stock price based on its exact distribution. We construct a new series expansion for this…
We establish, utilizing the Hardy-Littlewood Circle Method, an asymptotic formula for the number of pairs of primes whose differences lie in the image of a fixed polynomial. We also include a generalization of this result where differences…
We propose a hierarchical tensor-network approach for approximating high-dimensional probability density via empirical distribution. This leverages randomized singular value decomposition (SVD) techniques and involves solving linear…
A modified totient function ($\phi_2$) is seen to play a significant role in the study of the twin prime distribution. The function is defined as $\phi_2(n):=\#\{a\le n ~\vert ~\textrm{$a(a+2)$ is coprime to $n$}\}$ and is shown here to…
This paper investigates the robust optimal control of sampled-data stochastic systems with multiplicative noise and distributional ambiguity. We consider a class of discrete-time optimal control problems where the controller \emph{jointly}…
An important and yet difficult problem in fitting multivariate mixture models is determining the mixture complexity. We develop theory and a unified framework for finding the nonparametric maximum likelihood estimator of a multivariate…