Related papers: Monotone Property Thresholds
Paper [1] derived the probability density function (PDF) of a sum of products of two correlated complex Gaussian zero-mean random variables (RVs) that has been applied to calculate the error probabilities of a \emph{M}-ary phase shift…
The general possible form of meanfield parameterization in a running frame in terms of current, energy and density functionals are examined under the restrictions of Galilean invariance. It is found that only two density-dependent…
The present paper considers a problem of estimating a linear functional $\Phi=\int_{-\infty}^\infty \varphi(x) f(x)dx$ of an unknown deconvolution density $f$ on the basis of i.i.d. observations $Y_i = \theta_i + \xi_i$ where $\xi_i$ has a…
The probability distribution function (PDF) of the mass surface density is an essential characteristic of the structure of molecular clouds or the interstellar medium in general. Observations of the PDF of molecular clouds indicate a…
This paper examines Poisson stable (including stationary, periodic, almost periodic, Levitan almost periodic, Bohr almost automorphic, pseudo-periodic, Birkhoff recurrent, pseudo-recurrent, etc.) measures and limit theorems for stochastic…
We prove some new results and unify the proofs of old ones involving complete monotonicity of expressions involving gamma and $q$-gamma functions, $0 < q < 1$. Each of these results implies the infinite divisibility of a related probability…
This paper is focused on the Monotonicity Principle (MP) for nonlinear materials with piecewise growth exponent. This results are relevant because enables the use of a fast imaging method based on MP, to the wide class of problems with two…
Error entropy is a important nonlinear similarity measure, and it has received increasing attention in many practical applications. The default kernel function of error entropy criterion is Gaussian kernel function, however, which is not…
We simplify the proof of some widely used theoretical theorems, extending their applicability, while correcting some erroneous results. We also generalize key results and present new results that contribute to the development of the theory.…
This paper has been withdrawn by the author(s), due to the existence of a much better paper in http://arxiv.org/abs/cs.CR/0207027
Gaussian mixture models (GMMs) are ubiquitous in statistical learning, particularly for unsupervised problems. While full GMMs suffer from the overparameterization of their covariance matrices in high-dimensional spaces, spherical GMMs…
We consider possibly degenerate and singular elliptic equations in a possibly anisotropic medium. We obtain monotonicity results for the energy density, rigidity results for the solutions and classification results for the…
In this manuscript, we present the complete monotonicity of functions defined in terms of the poly-double gamma function \begin{align*} \psi_2^{(n)}(x) = (-1)^{n+1} n! \sum_{k=0}^{\infty} \dfrac{(1+k)}{(x+k)^{n+1}}, \quad x > 0, \ n\geq 2.…
In this paper, we prove the restricted isometry property of block diagonal random matrices with elements from $\varphi$-sub-Gaussian variables, which extends the previously known results for the sub-Gaussian case. A crucial ingredient of…
Poisson boundary is a measurable $\Gamma$-space canonically associated with a group $\Gamma$ and a probability measure $\mu$ on it. The collection of all measurable $\Gamma$-equivariant quotients, known as $\mu$-boundaries, of the Poisson…
We study the strong unique continuation property backwards in time for the nonlocal equation in $\mathbb{R}^{n} \times \mathbb{R}$ \begin{equation}\label{one} (\partial_t - \Delta)^{s} u = V(x,t)u \end{equation} for $s \in (0,1)$. Our main…
The least trimmed squares (LTS) estimator is popular in location, regression, machine learning, and AI literature. Despite the empirical version of least trimmed squares (LTS) being repeatedly studied in the literature, the population…
The study of random Fourier series, linear combinations of trigonometric functions whose coefficients are independent (in our case Gaussian) random variables with polynomially bounded means and standard deviations, dates back to Norbert…
In a recent paper, Mazucheli et al. (2019) introduced the unit-Gompertz (UG) distribution and studied some of its properties. In a complementary work, Anis and De (2020) corrected some of the subtle errors in the original paper and studied…
In this paper, we introduce a new energy density function $\mathscr Y$ on the projective bundle $\mathbb{P}(T_M)\>M$ for a smooth map $f:(M,h)\>(N,g)$ between Riemannian manifolds $$\mathscr Y=g_{ij}f^i_\alpha f^j_\beta \frac{W^\alpha…