Related papers: Planar additive bases for rectangles
We present a novel approach for nonparametric regression using wavelet basis functions. Our proposal, $\texttt{waveMesh}$, can be applied to non-equispaced data with sample size not necessarily a power of 2. We develop an efficient proximal…
Orthogonal Fractional Factorial Designs and in particular Orthogonal Arrays are frequently used in many fields of application, including medicine, engineering and agriculture. In this paper we present a methodology and an algorithm to find…
The least square solution of minimum norm of a rectangular linear system of equations can be found out iteratively by using matrix splittings. However, the convergence of such an iteration scheme arising out of a matrix splitting is…
Matrices are typically considered over fields or rings. Motivated by applications in parametric differential equations and data-driven modeling, we suggest to study matrices with entries from a Hilbert space and present an elementary theory…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
A canonical minimal free resolution of an arbitrary co-artinian lattice ideal over the polynomial ring is constructed over any field whose characteristic is 0 or any but finitely many positive primes. The differential has a closed-form…
We design and mathematically analyze sampling-based algorithms for regularized loss minimization problems that are implementable in popular computational models for large data, in which the access to the data is restricted in some way. Our…
An oriented graph is said positively multiplicative when its adjacency matrix $A$ embeds in a matrix algebra admitting a basis $\mathsf{B}$ with nonnegative structure constants in which the matrix of the multiplication by $A$ coincides with…
An ordered set $S$ of vertices of a graph $G$ is a resolving set for $G$ if every vertex is uniquely determined by its vector of distances to the vertices in $S$. The metric dimension of G is the minimum cardinality of a resolving set. In…
A flat torus is the quotient of the Euclidean plane over a lattice generated by a basis, and an axis-aligned rectangular tiling of a flat torus is a partition into finitely many rectangles whose sides are axis-aligned. We provide the…
Let $A$ be a finite commutative ring with unity $1 \neq 0.$ An ideal of $A$ is said to be essential if it has a non-zero intersection with every non-zero ideal of $A.$ The essential graph of $A$ is a simple undirected graph whose vertex set…
The Harborth graph is the smallest known example of a 4-regular planar unit-distance graph. In this paper we give an analytical description of the coordinates of its vertices for a particular embedding in the Euclidean plane. More…
We study the problem of minimum enclosing rectangle with outliers, which asks to find, for a given set of $n$ planar points, a rectangle with minimum area that encloses at least $(n-t)$ points. The uncovered points are regarded as outliers.…
We use computational experiments to find the rectangles of minimum perimeter into which a given number n of non-overlapping congruent circles can be packed. No assumption is made on the shape of the rectangles. In many of the packings…
Least square estimators for graphical models for cardinal paired comparison data with and without covariates are rigorously analyzed. Novel, graph--based, necessary and sufficient conditions that guarantee strong consistency, asymptotic…
Parallel addition in integer base is used for speeding up multiplication and division algorithms. $k$-block parallel addition has been introduced by Kornerup in 1999: instead of manipulating single digits, one works with blocks of fixed…
This work introduces the causal bootstrap, a framework for bounding smeared spectral observables from finite non-perturbative Euclidean data. The method optimizes over the convex set of positive spectral densities compatible with the data…
Planar ornaments, a.k.a. wallpapers, are regular repetitive patterns which exhibit translational symmetry in two independent directions. There are exactly $17$ distinct planar symmetry groups. We present a fully automatic method for…
We present new tests to identify stationary position-dependent additive shear biases in weak gravitational lensing data sets. These tests are important diagnostics for currently ongoing and planned cosmic shear surveys, as such biases…
When searching for new gravitational-wave or electromagnetic sources, the $n$ signal parameters (masses, sky location, frequencies,...) are unknown. In practice, one hunts for signals at a discrete set of points in parameter space, with a…