Related papers: Volume computation for sparse boolean quadric rela…
For a graph $G=(V,E)$ with $v(G)$ vertices the partition function of the random cluster model is defined by $$Z_G(q,w)=\sum_{A\subseteq E(G)}q^{k(A)}w^{|A|},$$ where $k(A)$ denotes the number of connected components of the graph $(V,A)$.…
AC optimal power flow (AC~OPF) is a challenging non-convex optimization problem that plays a crucial role in power system operation and control. Recently developed convex relaxation techniques provide new insights regarding the global…
We propose a DC proximal Newton algorithm for solving nonconvex regularized sparse learning problems in high dimensions. Our proposed algorithm integrates the proximal Newton algorithm with multi-stage convex relaxation based on the…
Many modern data analysis algorithms either assume or are considerably more efficient if the distances between the data points satisfy a metric. These algorithms include metric learning, clustering, and dimension reduction. As real data…
This is a continuation of our previous work (Advances in Mathematics 450 (2024), Paper No. 109768). In this paper, we characterize complete metrics with finite total Q-curvature as normal metrics for all dimensional cases. Secondly, we…
We introduce a cyclotomic representation for finite $q$-hypergeometric series and $q$-deformed amplitudes that separates algebraic structure from evaluation. By expressing each summand in a sparse exponent basis over irreducible cyclotomic…
We describe preliminary results of a detailed numerical analysis of the volume operator as formulated by Ashtekar and Lewandowski. Due to a simplified explicit expression for its matrix elements, it is possible for the first time to treat…
One of the most widely studied convex relaxations in combinatorial optimization is the relaxation of the cut polytope $\mathscr C^N$ to the elliptope $\mathscr E^N$, which corresponds to the degree 2 sum-of-squares (SOS) relaxation of…
We consider the problem of computing the Lebesgue volume of compact basic semi-algebraic sets. In full generality, it can be approximated as closely as desired by a converging hierarchy of upper bounds obtained by applying the Moment-SOS…
In this article, we are interested in the asymptotic analysis of a finite volume scheme for one dimensional linear kinetic equations, with either Fokker-Planck or linearized BGK collision operator. Thanks to appropriate uniform estimates,…
It is demonstrated that the susceptibility spectra of supercooled propylene carbonate as measured by depolarized-light-scattering, dielectric-loss, and incoherent quasi-elastic neutron-scattering spectroscopy within the GHz window are…
The signed volume function for polyhedra can be generalized to a mean volume function for volume elements by averaging over the triangulations of the underlying polyhedron. If we consider these up to translation and scaling, the resulting…
This paper studies the algebraic boundary of the elliptope $\mathcal{E}(G)$ of a graph $G$. In particular, we completely characterize the algebraic boundary of $\mathcal{E}(G)$ when $G$ is cycle completable. In this case, the boundary is a…
The class of generalized gamma convolutions (GGC) is closed with respect to (wrt) change of scales, weak limits and addition and multiplication of independent random variables. Our main result adds the new property that GGC is also closed…
Twin-width is a structural width parameter introduced by Bonnet, Kim, Thomass\'e and Watrigant [FOCS 2020]. Very briefly, its essence is a gradual reduction (a contraction sequence) of the given graph down to a single vertex while…
The free sum is a basic geometric operation among convex polytopes. This note focuses on the relationship between the normalized volume of the free sum and that of the summands. In particular, we show that the normalized volume of the free…
Estimating unknown rotations from noisy measurements is an important step in SfM and other 3D vision tasks. Typically, local optimization methods susceptible to returning suboptimal local minima are used to solve the rotation averaging…
We report extensive simulations of the relaxation dynamics of a self-avoiding polymer confined inside a cylindrical pore. In particular, we concentrate on examining how confinement influences the scaling behavior of the global relaxation…
We consider the Gross-Pitaevskii equation with a confining ring potential with a Gaussian profile. By introducing a rotating sinusoidal perturbation, we numerically highlight the nucleation of quantum vortices in a particular regime…
A new efficient algorithm is presented for finding all simple cycles that satisfy a length constraint in a directed graph. When the number of vertices is non-trivial, most cycle-finding problems are of practical interest for sparse graphs…