Related papers: Why the Kirnberger Kernel Is So Small
Let $q>2$ be an odd integer. For each integer $x$ with $0<x<q$ and $(q,x)= 1$, we know that there exists one and only one $\bar{x}$ with $0<\bar{x}<q$ such that $x\bar{x}\equiv1(\bmod q)$. A Lehmer number is defined to be any integer $a$…
Let $H=\langle n_1, \ldots ,n_4\rangle$ be a numerical semigroup generated by $4$ elements, which is symmetric and let $k[H]$ be the semigroup ring of $H$ over a field $k$. H. Bresinski proved that the defining ideal of $k[H]$ is minimally…
How much one has learned from an experiment is quantifiable by the information gain, also known as the Kullback-Leibler divergence. The narrowing of the posterior parameter distribution $P(\theta|D)$ compared with the prior parameter…
The nature of the super-massive black hole candidates in galactic nuclei can be tested by analyzing the profile of the K$\alpha$ iron line observed in their X-ray spectrum. In this paper, we consider the possibility that the spacetime in…
Perhaps the most significant drawback, which the Copenhagen interpretation (still the most popular interpretation of quantum theory) suffers from, is the classical-quantum divide between the large classical systems that carry out…
One of us (L.S.) and H. Verlinde independently conjectured a holographic duality between the double-scaled SYK model at infinite temperature and dimensionally reduced $(2+1)$-dimensional de Sitter space [1]-[8]. Beyond the statement that…
Classic calculations of the magnetic moments mu_p and mu_n of the nucleons using the traditional exponential kernel show instability with respect to variations of the Borel mass as well as arbitrariness with respect to the choice of the…
A GR-segment for an artin algebra is a sequence of Gabriel-Roiter measures, which is closed under direct predecessors and successors. The number of the GR-segments indexed by natural numbers $\mathbb{N}$ and integers $\mathbb{Z}$ probably…
The rate of normal approximation for the integral norm of kernel density estimators is investigated in the case of densities with power-type singularities. The quantities from the formulations of published results by the author are…
An important feature of kernel mean embeddings (KME) is that the rate of convergence of the empirical KME to the true distribution KME can be bounded independently of the dimension of the space, properties of the distribution and smoothness…
We compare the statistics of tin whisker diameters to that of the underlying film grains. Both are well approximated by the lognormal distributions. However, the parameters of those distributions can be rather different, not confirming the…
The perception of consonance/dissonance of musical harmonies is strongly correlated with their periodicity. This is shown in this article by consistently applying recent results from psychophysics and neuroacoustics, namely that the just…
We present a procedure for computing the log-canonical threshold of an arbitrary ideal generated by binomials and monomials. The computation of the log canonical threshold is reduced to the problem of computing the minimum of a function,…
Central, standard, and Christoffel words are three strongly interrelated classes of binary finite words which represent a finite counterpart of characteristic Sturmian words. A natural arithmetization of the theory is obtained by…
While each atom species in PbSe corresponds to a single crystallographic site and transport measurements reveal a single carrier density, $^{207}$Pb NMR reveals a more complicated picture than previously thought comprising three discrete…
We first revisit the problem of estimating the spot volatility of an It\^o semimartingale using a kernel estimator. We prove a Central Limit Theorem with optimal convergence rate for a general two-sided kernel. Next, we introduce a new…
A partial Steiner triple system whose triples can be partitioned into $s$ partial parallel classes, each of size $m$, is a $signal$ $set$, denoted $\mbox{SS}(v,s,m)$. A $Kirkman$ $signal$ $set$ $\mbox{KSS}(v,m)$ is an $\mbox{SS}(v,s,m)$…
A critical length has recently been identified that appears to provide a fundamental limit distinguishing quantum behavior from classical behavior. Because of the unique association between critical length and mass, it appears that we can…
We consider the problem of discriminating two different quantum states in the setting of asymptotically many copies, and determine the optimal strategy that minimizes the total probability of error. This leads to the identification of the…
Estimating the Kullback-Leibler (KL) divergence between random variables is a fundamental problem in statistical analysis. For continuous random variables, traditional information-theoretic estimators scale poorly with dimension and/or…