Related papers: Order-2 Delaunay Triangulations Optimize Angles
We study algebraic and topological properties of subsets of preorders on a group. In particular we study properties of the composition of two preorders, generalize a topological theorem of \cite{S} in the case of standard orders and show…
Let $S$ be a finite set of points in the Euclidean plane. Let $D$ be a Delaunay triangulation of $S$. The {\em stretch factor} (also known as {\em dilation} or {\em spanning ratio}) of $D$ is the maximum ratio, among all points $p$ and $q$…
We design an algorithm which finds an $\epsilon$-approximate stationary point (with $\|\nabla F(x)\|\le \epsilon$) using $O(\epsilon^{-3})$ stochastic gradient and Hessian-vector products, matching guarantees that were previously available…
In projection-based model order reduction, a reduced-order approximation of the original full-order system is obtained by projecting it onto a reduced subspace that contains its dominant characteristics. The problem of frequency-weighted…
In a previous work of the first authors, a non-holonomic model, generalising the micromorphic models and allowing for curvature (disclinations) to arise from the kinematic values, was presented. In the present paper, a generalisation of the…
For strongly convex objectives that are smooth, the classical theory of gradient descent ensures linear convergence relative to the number of gradient evaluations. An analogous nonsmooth theory is challenging. Even when the objective is…
Second-order polynomials generalize classical first-order ones in allowing for additional variables that range over functions rather than values. We are motivated by their applications in higher-order computational complexity theory,…
Mechanical systems are usually modeled by second-order Ordinary Differential Equations (ODE) which take the form $\ddot{q} = f(t, q, \dot{q})$. While simulation methods tailored to these equations have been studied, using them in direct…
We investigate two classes of multivariate polynomials with variables indexed by the edges of a uniform hypergraph and coefficients depending on certain patterns of union of edges. These polynomials arise naturally to model job-occupancy in…
This paper establishes the equivalence of the Aubin property and the strong regularity for generalized equations over $C^2$-cone reducible sets. This result resolves a long-standing question in variational analysis and extends the…
An algorithm is proposed for solving optimization problems arising in neural network training for supervised learning. The unique feature of the algorithm is the use of an auxiliary loss, in addition to the original loss employed for model…
Selection lemmas are classical results in discrete geometry that have been well studied and have applications in many geometric problems like weak epsilon nets and slimming Delaunay triangulations. Selection lemma type results typically…
The classical rearrangement inequality provides bounds for the sum of products of two sequences under permutations of terms and show that similarly ordered sequences provide the largest value whereas opposite ordered sequences provide the…
We give a complete characterization of degree two rational maps with potential good reduction over local fields. We show this happens exactly when the map corresponds to an integral point in the moduli space. We detail an algorithm by which…
It is shown that the structure of the generalized quadrangle of order two is fully encoded in the properties of the Desargues configuration. A point of the quadrangle is represented by a geometric hyperplane of the Desargues configuration…
Given a set $P$ of $n$ points in the plane, we show how to compute in $O(n \log n)$ time a subgraph of their Delaunay triangulation that has maximum degree 7 and is a strong planar $t$-spanner of $P$ with $t =(1+ \sqrt{2})^2 *\delta$, where…
Considering a differential operator of third order that does not increase the degree of polynomials, we analyse some properties of elements of the dual space of 2-orthogonal polynomial eigenfunctions. In two classes of such generic…
Kupavskii, Volostnov, and Yarovikov have recently shown that any set of $n$ points in general position in the plane has at least as many (partial) triangulations as the convex $n$-gon. We generalize this in two directions: we show that…
Recently a majorization method for optimizing partition functions of log-linear models was proposed alongside a novel quadratic variational upper-bound. In the batch setting, it outperformed state-of-the-art first- and second-order…
This paper considers convex optimization problems where nodes of a network have access to summands of a global objective. Each of these local objectives is further assumed to be an average of a finite set of functions. The motivation for…