相关论文: Cusps of primes in dense subsequences -- Bypassing…

Using a Lubachevsky-Stillinger-like growth algorithm combined with biased SWAP Monte Carlo and transient degrees of freedom, we generate ultradense disordered jammed ellipse packings. For all aspect ratios $\alpha$, these packings exhibit…

For an elliptic curve $E$ defined over a number field $K$, the heuristic density of the set of primes of $K$ for which $E$ has cyclic reduction is given by an inclusion-exclusion sum $\delta_{E/K}$ involving the degrees of the $m$-division…

The spectrum of an admissible subalgebra $\mathscr{A}(G)$ of $\mathscr{LUC}(G)$, the algebra of right uniformly continuous functions on a locally compact group $G$, constitutes a semigroup compactification $G^\mathscr{A}$ of $G$. In this…

In this paper, we study a density version of the Waring-Goldbach problem. Suppose that A is a subset of the primes, and the lower density of A in the primes is larger than 1-1/2k. We prove that every sufficiently large natural number n…

Under the name prime decomposition (pd), a unique decomposition of an arbitrary $N$-dimensional density matrix $\rho$ into a sum of seperable density matrices with dimensions given by the coprime factors of $N$ is introduced. For a class of…

Quartetting ($\alpha$-like clustering) occurs in low density matter ($\le 0.03$ fm$^{-3}$) which exists, e.g., at the surface of nuclei. It is of interest for the $\alpha$ preformation to calculate the $\alpha$ decay of heavy nuclei such as…

Deep representation learning has become one of the most widely adopted approaches for visual search, recommendation, and identification. Retrieval of such representations from a large database is however computationally challenging.…

Dense regions in networks are an indicator of interesting and unusual information. However, most existing methods only consider simple, undirected, unweighted networks. Complex networks in the real-world often have rich information though:…

Let $f(x_1,\ldots,x_s)$ be a translation invariant indefinite quadratic form of integer coefficients with $s\ge 10$. Let $\mathcal{A}\subseteq \mathcal{P}\cap \{1,2,\ldots,X\}$. Let $X$ be sufficiently large. Subject to a rank condition, we…

An efficient integer factorization algorithm would reduce the security of all variants of the RSA cryptographic scheme to zero. Despite the passage of years, no method for efficiently factoring large semiprime numbers in a classical…

Deep Learning (DL) has achieved unprecedented success in various application domains. Meanwhile, model pruning has emerged as a viable solution to reduce the footprint of DL models in mobile applications, without compromising their…

Let $K$ be a compact subset of the complex plane $\mathbb C.$ Let $P(K)$ and $R(K)$ be the closures in $C(K)$ of analytic polynomials and rational functions with poles off $K,$ respectively. Let $A(K) \subset C(K)$ be the algebra of…

Frugal computing is becoming an important topic for environmental reasons. In this context, several techniques have been proposed to reduce the storage of scientific data by dedicated compression methods specially tailored for arrays of…

We prove a conjecture of Medvedev and Scanlon for endomorphisms of connected commutative linear algebraic groups $G$ defined over an algebraically closed field $\mathbb{k}$ of characteristic $0$. That is, if $\Phi\colon G\longrightarrow G$…

We consider the free additive convolution semigroup $\lbrace \mu^{\boxplus t}:\,t\ge 1\rbrace$ and determine the local behavior of the density of $\mu^{\boxplus t}$ at the endpoints and at any singular point of its support. We then study…

Establishing precisely how stars and interstellar medium distribute within the central 100 pc area around an AGN, down to the pc scale, is key for understanding how the very final transfer of matter from kpc scale to the sub-parsec size of…

We show that, for many choices of finite tuples of generators $X = (x_1, \dots , x_d)$ of a tracial von Neumann algebra $(M, \tau)$ satisfying certain decomposition properties (non-primeness, possessing a Cartan subalgebra, or property…

For a polynomial $F(t,A_1,\ldots,A_n)\in\mathbf{F}_p[t,A_1,\ldots,A_n]$ ($p$ being a prime number) we study the factorization statistics of its specializations $$F(t,a_1,\ldots,a_n)\in\mathbf{F}_p[t]$$ with $(a_1,\ldots,a_n)\in S$, where…

Simulations have established that each halo of collisionless dark matter is expected to contain a $\rho = A r^{-1.5}$ density cusp at its center. This prompt cusp is a relic of the halo's earliest moments and has a mass comparable to the…

We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…