Related papers: Monotone Property Thresholds
This paper introduces a novel framework to construct the probability density function (PDF) of non-negative continuous random variables. The proposed framework uses two functions: one is the survival function (SF) of a non-negative…
We investigate the hypothesized existence of an S-matrix for gravity, and some of its expected general properties. We first discuss basic questions regarding existence of such a matrix, including those of infrared divergences and…
Given a positive function $f$ on $(0,\infty)$ and a non-zero real parameter $\theta$, we consider a function $I_f^\theta(A,B,X)=Tr X^*(f(L_AR_B^{-1})R_B)^\theta(X)$ in three matrices $A,B>0$ and $X$. In the literature $\theta=\pm1$ has been…
In this paper the conditions are investigated for the occurrence of the so-called macroscopic irreversibility property and the related phenomenon of decay to kinetic equilibrium which may characterize the $1-$body probability density…
We review some of the basic mathematical results about density functional theory.
A scale invariant model containing dilaton $\phi$ and dust (as a model of matter) is studied where the shift symmetry $\phi\to\phi +const.$ is spontaneously broken at the classical level due to intrinsic features of the model. The dilaton…
We present a physical model for polarized and unpolarized structure functions and parton density functions (PDFs) of the proton and the neutron. It reproduces the data on F_2^p(x,Q^2) for 0.00001<x<1 and 2.5<Q^2<5000 GeV^2,…
This paper was withdrawn by the authors due to significant new findings. A new paper on the same topic has been submitted as physics/0310159.
We propose a modified gravity theory that propagates only two local gravitational degrees of freedom and that does not have an Einstein frame. According to the classification in JCAP 01 (2019) 017 [arXiv:1810.01047 [gr-qc]], this is a…
In "VC density in some theories without the independence property" the authors asked whether any partial order of finite width has the VC1 property (i.e. every formula in one variable has UDTFS in one parameter). We give a negative answer…
Consider the Mills ratio $f(x)=\big(1-\Phi(x)\big)/\phi(x), \, x\ge 0$, where $\phi$ is the density function of the standard Gaussian law and $\Phi$ its cumulative distribution.We introduce a general procedure to approximate $f$ on the…
This paper defines Lebesgue measure preserving Thompson's monoid, denoted by $\mathbb{G}$, which is modeled on Thompson's group $\mathbb{F}$ except that the elements of $\mathbb{G}$ are non-invertible. Moreover, it is required that the…
Individual phases are commonly considered as the building blocks of materials. However, the accurate theoretical prediction of properties of individual phases remains elusive. The top-down approach by decoding genomic building blocks of…
This paper has been withdrawn by the authors due to a gap in the proof of the main result (in 5.3).
This article is a rough, quirky overview of both the history and present state of the art of density functional theory. The field is so huge that no attempt to be comprehensive is made. We focus on the underlying exact theory, the origin of…
The classification of topological materials is revisited using advanced computational workflows that integrate hybrid density functional theory calculations with exact Hartree-Fock exchange. Unlike previous studies, our workflow optimizes…
In this paper, we propose a new approach for deriving probabilistic inequalities. Our main idea is to exploit the information of underlying distributions by virtue of the monotone likelihood ratio property and Berry-Essen inequality.…
We introduce a certain variant (or regularization) $\tilde{\Lambda}^\mu_n$ of the standard Christoffel function $\Lambda^\mu_n$ associated with a measure $\mu$ on a compact set $\Omega\subset \mathbb{R}^d$. Its reciprocal is now a…
The field of property testing of probability distributions, or distribution testing, aims to provide fast and (most likely) correct answers to questions pertaining to specific aspects of very large datasets. In this work, we consider a…
This paper has been withdrawn. A significantly revised version will be posted in the near future.