相关论文: Pseudo Unique Sink Orientations
We study the singular locus on the algebraic surface $\S_n$ of genus 2 curves with a $(n, n)$-split Jacobian. Such surface was computed by Shaska in \cite{deg3} for $n=3$, and Shaska at al. in \cite{deg5} for $n=5$. We show that the…
We show that any unimodular real 3-qubit gate can be expressed as the product of at most 14 CNOT gates plus single-qubit gates, improving on the bound of 16 CNOTs due to Wei and Di. Our method uses the exotic triality symmetry of…
A wide range of equations related to free surface motion in two dimensions exhibit the formation of cusp singularities either in time, or as function of a parameter. We review a number of specific examples, relating in particular to fluid…
In many problems in Computational Physics and Chemistry, one finds a special kind of sparse matrices, termed "banded matrices". These matrices, which are defined as having non-zero entries only within a given distance from the main…
It is shown that embedding of flipped SU(5) in a five-dimensional SO(10) enables exact unification of the gauge coupling constants. The demand for the unification uniquely determines both the compactification scale and the cutoff scale.…
We construct a family of $4d$ $\mathcal{N}=1$ theories that we call $E^\sigma_\rho[USp(2N)]$ which exhibit a novel type of $4d$ IR duality very reminiscent of the mirror duality enjoyed by the $3d$ $\mathcal{N}=4$ $T^\sigma_\rho[SU(N)]$…
We provide a necessary and sufficient condition for the uniqueness of penalized least-squares estimators whose penalty term is given by a norm with a polytope unit ball, covering a wide range of methods including SLOPE, PACS, fused,…
The behavior of the simplex algorithm is a widely studied subject. Specifically, the question of the existence of a polynomial pivot rule for the simplex algorithm is of major importance. Here, we give exponential lower bounds for three…
We characterize some variations of pseudoskeleton (also called CUR) decompositions for matrices and tensors over arbitrary fields. These characterizations extend previous results to arbitrary fields and to decompositions which use…
In this survey, we review part of the theory of superisolated surface singularities (SIS) and its applications including some new and recent developments. The class of SIS singularities is, in some sense, the simplest class of germs of…
All quantum gates with one and two qubits may be described by elements of $Spin$ groups due to isomorphisms $Spin(3) \simeq SU(2)$ and $Spin(6) \simeq SU(4)$. However, the group of $n$-qubit gates $SU(2^n)$ for $n > 2$ has bigger dimension…
In this paper, we study biconservative hypersurfaces of index 2 in $\mathbb E^{5}_{2}$. We give the complete classification of biconservative hypersurfaces with diagonalizable shape operator at exactly three distinct principal curvatures.…
We calculate the single-valued and spinor representations of $SO_4$, the orientation-preserved subgroup of $O_4$, on the base of our previous work on four-dimensional cubic group $O_4$.
Our method studies the complex task of object-centric 3D understanding from a single RGB-D observation. As it is an ill-posed problem, existing methods suffer from low performance for both 3D shape and 6D pose and size estimation in complex…
A rigid set in a curve complex of a surface is a subcomplex such that every locally injective simplicial map from the set into the curve complex is induced by a homeomorphism of the surface. In this paper, we find finite rigid sets in the…
We determine the number of cusps of minimal Picard modular surfaces. The proof also counts cusps of other Picard modular surfaces of arithmetic interest. Consequently, for each N > 0 there are finitely many commensurability classes of…
We consider smooth 1-parameter families of plane curves tangent to a semicubic parabola, when the curvature radius of their curves at the tangency point vanishes at the cusp point. We find the $\A$-normal form of these families, their…
Self-shrinkers are hypersurfaces that shrink homothetically under mean curvature flow; these solitons model the singularities of the flow. It it presently known that an entire self-shrinking graph must be a hyperplane. In this paper we show…
In this paper, we study structured symmetric tensors. We introduce several new classes of structured symmetric tensors: completely decomposable (CD) tensors, strictly sum of squares (SSOS) tensors and SOS$^*$ tensors. CD tensors have…
In the hyperspace of subcontinua of a compact surface we consider a second order Hausdorff distance. This metric space is compactified in such a way that the stable foliation of a pseudo-Anosov map is naturally identified with a…