Related papers: Why the Kirnberger Kernel Is So Small

Most music theory books are like medieval medical textbooks: they contain unjustified superstition, non-reasoning, and funny symbols glorified by Latin phrases. How does music, in particular harmony, actually work, presented as a real,…

A random geometric graph (RGG) with kernel $K$ is constructed by first sampling latent points $x_1,\ldots,x_n$ independently and uniformly from the $d$-dimensional unit sphere, then connecting each pair $(i,j)$ with probability $K(\langle…

We give a short new proof that for each non-elementary Kleinian group $\Gamma$, the exponent of convergence of an arbitrary non-trivial normal subgroup is bounded below by half of the exponent of convergence of $\Gamma$, and that strict…

The scalar strangeness content of the nucleon, characterized by the so-called strangeness-nucleon sigma term, is of fundamental importance in understanding its sea-quark flavor structure. We report a determination of the octet baryon sigma…

Let m be a probability measure supported on some infinite and compact set K in the complex plane and let p_n(z) be the corresponding degree n orthonormal polynomial with positive leading coefficient. Let v_n be the normalized zero counting…

We prove the conjectures on the ($L^{\infty}$)-sizes of the spaces of Siegel cusp forms of degree $n$, weight $k$, for any congruence subgroup in the weight aspect as well as for all principal congruence subgroups in the level aspect, in…

Various convergence results for the Bergman kernel of the Hilbert space of all polynomials in \C^{n} of total degree at most k, equipped with a weighted norm, are obtained. The weight function is assumed to be C^{1,1}, i.e. it is…

The problem of estimating the kernel mean in a reproducing kernel Hilbert space (RKHS) is central to kernel methods in that it is used by classical approaches (e.g., when centering a kernel PCA matrix), and it also forms the core inference…

Let $k[X]{:=} k[x_0,x_1,..., x_n]$ be a polynomial algebra over a field $k$ of characteristic zero. We offer an algorithm for calculation of kernel of Weitzenb\"ok derivation ${d(x_i)=x_{i-1}}, ...,$ ${d(x_0)=0}$, ${i=1... n}$ that is based…

In this paper we partially answer a question of P. Tukia about the size of the difference between the big horospheric limit set and the horospheric limit set of a Kleinian group. We mainly investigate the case of normal subgroups of…

We obtain point separated Noise Kernel for the Reissner Nordstr\"{o}m metric.The Noise Kernel defines the fluctuations of the quantum stress tensor and is of central importance to Semiclassical Stochastic Gravity.The metric is modeled as…

We consider kernel estimators of the instantaneous frequency of a slowly evolving sinusoid in white noise. The expected estimation error consists of two terms. The systematic bias error grows as the kernel halfwidth increases while the…

We study the convergence of Bernstein type operators leading to two results. The first: The kernel $K_n$ of the Bernstein-Durrmeyer operator at each point $x \in (0, 1)$ $\unicode{x2013}$ that is $K_n(x, t) dt$ $\unicode{x2013}$ once…

We establish existence of Stein kernels for probability measures on $\mathbb{R}^d$ satisfying a Poincar\'e inequality, and obtain bounds on the Stein discrepancy of such measures. Applications to quantitative central limit theorems are…

The odd-even staggering of the yield of final reaction products has been studied as a function of proton (Z) and neutron (N) numbers for the collisions 84 Kr+112 Sn and 84 Kr+124 Sn at 35 MeV/nucleon, in a wide range of elements (up to Z ~…

When a spinning-down neutron star undergoes a phase transition that produces quark matter in its core, a Super-Giant Glitch of the order ${\Delta} \Omega/\Omega\sim 0.3$ occurs on time scales from 0.05 seconds to a few minutes. The energy…

Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately,…

A new definition of musical pitch is proposed. A Finite-Difference Time Domain (FDTM) model of the cochlea is used to calculate spike trains caused by tone complexes and by a recorded classical guitar tone. All harmonic tone complexes,…

We study singular integral operators with kernels that are more singular than standard Calder\'on-Zygmund kernels, but less singular than bi-parameter product Calder\'on-Zygmund kernels. These kernels arise as restrictions to two dimensions…

The paper proves that the number of k-skip-n-grams for a corpus of size $L$ is $$\frac{Ln + n + k' - n^2 - nk'}{n} \cdot \binom{n-1+k'}{n-1}$$ where $k' = \min(L - n + 1, k)$.