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Best subset selection is an important problem in regression analysis,which has many applications in computer science and medicine. However, the existing best subset selection methods have some limitat...
How to select the active variables which have significant impact on the event of interest is a very important and meaningful problem in the statistical analysis of ultrahigh-dimensional data. In many ...
A finite collection of unit vectors S ⊂ Rn is called a spherical two-distance set if there are two numbers a and b such that the inner products of distinct vectors from S are either a or b. We p...
We consider the problem of positioning a cloud of points in the Euclidean space R d, using noisy measurements of a subset of pairwise distances. This task has applications in various areas, such as se...
The Kolmogorov]Smirnov distance is an important tool for constructing confidence sets and tests in univariate problems. In multivariate settings, an analogous role is played by the halfspace di...
This paper describes a method for estimating the distance between a robot and its surrounding environment using best ellipsoid fit. The method consists of the following two stages. First we approximat...
Let $G=(V_G, E_G)$ be a simple connected graph. The eccentric distance sum of $G$ is defined as $\xi^{d}(G) = \sum_{v\in V_G}\varepsilon_{G}(v)D_{G}(v)$, where $\varepsilon_G(v)$ is the eccentricity o...
We prove a normalized version of the restricted invertibility principle obtained by Spielman-Srivastava. Applying this result, we get a new proof of the proportional Dvoretzky-Rogers factorization the...
A \emph{group distance magic labeling} or a $\gr$-distance magic labeling of a graph $G(V,E)$ with $|V | = n$ is an injection $f$ from $V$ to an Abelian group $\gr$ of order $n$ such that the weight $...
A slice distance for the class of weak abelian Lp-bundles in 3 dimensions was introduced in a previous article in collaboration with Tristan Rivi\`ere, where it was used to prove the closure of such c...
Abstract: A metric space $\mathrm{M}=(M;\de)$ is {\em homogeneous} if for every isometry $f$ of a finite subspace of $\mathrm{M}$ to a subspace of $\mathrm{M}$ there exists an isometry of $\mathrm{M}$...
Abstract: For a finite set of points $P$ in $R^d$, the function $d_P:R^d \to R_+$ measures Euclidean distance to the set $P$. We study the number of critical points of $d_P$ when $P$ is random. In par...
Abstract: Probabilistic submeasures generalizing the classical (numerical) submeasures are introduced and discussed in connection with some classes of aggregation functions. A special attention is pai...
Abstract: The reverse degree distance is a connected graph invariant closely related to the degree distance proposed in mathematical chemistry. We determine the unicyclic graphs of given girth, number...
Abstract: It is shown that under some conditions the distance between densities of free convolutions of two pairs of probability measures is smaller than the maximum of the Levy distance between the c...

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