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We introduce higher order mean curvatures of screen almost conformal (SAC) half-lightlike submanifolds of indefinite contact manifolds, admitting a semi-symmetric non-metric connection, and use them to generalize some known results of [6].…
There are typically several nonisomorphic graphs having a given degree sequence, and for any two degree sequence terms it is often possible to find a realization in which the corresponding vertices are adjacent and one in which they are…
We propose a method for obtaining parsimonious decompositions of networks into higher order interactions which can take the form of arbitrary motifs.The method is based on a class of analytically solvable generative models, where vertices…
We discuss the problem of optimizing the distance function from a given point, subject to polynomial constraints. A key algebraic invariant that governs its complexity is the Euclidean distance degree, which pertains to first-order…
Conditions, related to the so-called bending problem are considered for hypersurfaces of a pseudo-Euclidean space. Corresponding theorems are proved.
Closed form expressions are given for computing the parameters and vectors that identify and define the $n-1$ dimensional conic section that results from the intersection of a hyperplane with an $n$-dimensional conic section: cone,…
The class of the hypercomplex pseudo-Hermitian manifolds is considered. The flatness of the considered manifolds with the 3 parallel complex structures is proved. Conformal transformations of the metrics are introduced. The conformal…
We consider hyperplane arrangements generated by generic points and study their intersection lattices. These arrangements are known to be equivalent to discriminantal arrangements. We show a fundamental structure of the intersection…
A method is presented for forming polynomial interpolants on squares and cubes, which are more efficient in the so-called Euclidean degree than other commonly used methods with the same number of collocation points. These methods have…
The quotient of a finite-dimensional vector space by the action of a finite subgroup of automorphisms is usually a singular variety. Under appropriate assumptions, the McKay correspondence relates the geometry of nice resolutions of…
Bisectors are equidistant hypersurfaces between two points and are basic objects in a metric geometry. They play an important part in understanding the action of subgroups of isometries on a metric space. In many metric geometries…
We introduce an innovative method for incremental nonparametric probabilistic inference in high-dimensional state spaces. Our approach leverages \slices from high-dimensional surfaces to efficiently approximate posterior distributions of…
We formulate and prove a Riemann-Hilbert correspondence between $\hbar$-differential equations and sheaf quantizations, which can be considered as a correspondence between two kinds of quantizations (deformation and sheaf quantization) of…
Recently, many methods to interpret and visualize deep neural network predictions have been proposed and significant progress has been made. However, a more class-discriminative and visually pleasing explanation is required. Thus, this…
Establishing correspondences between two images requires both local and global spatial context. Given putative correspondences of feature points in two views, in this paper, we propose Order-Aware Network, which infers the probabilities of…
We analyze single particle coherence and interference in the presence of particle loss and derive an inequality that relates the preservation of coherence, the creation of superposition with the vacuum, and the degree of particle loss. We…
We propose a fast, accurate matching method for estimating dense pixel correspondences across scenes. It is a challenging problem to estimate dense pixel correspondences between images depicting different scenes or instances of the same…
Recovering the spatial layout of the cameras and the geometry of the scene from extreme-view images is a longstanding challenge in computer vision. Prevailing 3D reconstruction algorithms often adopt the image matching paradigm and presume…
Saliency prediction is a well studied problem in computer vision. Early saliency models were based on low-level hand-crafted feature derived from insights gained in neuroscience and psychophysics. In the wake of deep learning breakthrough,…
We study correspondences of zero-dimensional subschemes of a smooth variety X "aligned" in the same way in inside the appropriate product of Hilbert schemes. We show that such correspondences have etale covering by other such…