Related papers: A Breakthrough in Sphere Packing: The Search for M…
A sphere packing bound (SPB) with a prefactor that is polynomial in the block length $n$ is established for codes on a length $n$ product channel $W_{[1,n]}$ assuming that the maximum order $1/2$ Renyi capacity among the component channels,…
The partition function and the one- and two-body distribution functions are evaluated for two hard spheres with different sizes constrained into a spherical pore. The equivalent problem for hard disks is addressed too. We establish a…
We derive basic differential geometric formulae for surfaces in hyperbolic space represented as envelopes of horospheres. The dual notion of parallel hypersurfaces is also studied. The representation is applied to prove existence and…
Our present knowledge of neutrinos can be summarized in terms of the "standard neutrino scenario". Phenomenology of this scenario as well as attempts to uncover physics behind neutrino mass and mixing are described. Goals of future studies…
In this note, we construct non-lattice sphere packings in dimensions $19$, $20$, $21$, $23$, $44$, $45$, and $47$, demonstrating record densities that surpass all previously documented results in these dimensions. The construction involves…
This paper provides the currently best known upper bound on the density of a packing in three-dimensional Euclidean space of two types of spheres whose size ratio is the largest one that allows the insertion of a small sphere in each…
This article reviews some recent developments in Astroparticle Physics. Due to the extension of the field only part of the results and developments can be covered. The status of the search for Dark Matter, some recent results on Cosmic Rays…
A few aspects of the mechanism of confinement of color by monopole condensation are reviewed.
New results from Super-Kamiokande, K2K and SNO not only have spurred on the interest in neutrino oscillation physics, but also have started to shift the interest from discovery to precision measurements. Future projects focusing on…
A close look of Google's GNoME inorganic materials dataset [Nature 624, 80 (2023)], and 11 things you would like to know.
A famous result of Hausdorff states that a sphere with countably many points removed can be partitioned into three pieces A,B,C such that A is congruent to B (i.e., there is an isometry of the sphere which sends A to B), B is congruent to…
The current status of searches for ultra-high energy neutrinos and photons using air showers is reviewed. Regarding both physics and observational aspects, possible future research directions are indicated.
The purpose of the New York Workshop on Computer, Earth and Space Sciences is to bring together the New York area's finest Astronomers, Statisticians, Computer Scientists, Space and Earth Scientists to explore potential synergies between…
In every dimension $d \geq 2$, we give an explicit formula that expresses the values of any Schwartz function on $\mathbb{R}^d$ only in terms of its restrictions, and the restrictions of its Fourier transform, to all origin-centered spheres…
The method, proposed in \cite{Za22} to derive the densest packing fraction of random disc and sphere packings, is shown to yield in two dimensions too high a value that (i) violates the very assumption underlying the method and (ii)…
The recent results from the Soudan 2, MACRO and SuperKamiokande experiments on atmospheric neutrino oscillations are summarized and discussed. Some features of possible future atmospheric neutrino experiments are presented.
Despite its amazing quantitative successes and contributions to revolutionary technologies, physics currently faces many unsolved mysteries ranging from the meaning of quantum mechanics to the nature of the dark energy that will determine…
The black hole paradigm, while remarkably successful, raises fundamental questions-both classical and quantum-about the nature of spacetime, horizons, and singularities. Black hole mimickers, horizonless ultra-compact objects, have emerged…
The working group on Spin Physics at the XXIV International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS2016) witnessed a significant progress in the theoretical and experimental investigations aiming at unveiling the…
This is a review article about the most recent developments on the field of neutrino mass. The first part of the review introduces the idea of neutrino masses and mixing angles, summarizes the most recent experimental data then discusses…