Related papers: The Harmonic GBC Function Map is a Bijection if th…
We study biharmonic maps between Riemannian manifolds with finite energy and finite bi-energy. We show that if the domain is complete and the target of non-positive curvature, then such a map is harmonic. We then give applications to…
We consider several basic questions pertaining to the geometry of image of a general quadratic map. In general the image of a quadratic map is non-convex, although there are several known classes of quadratic maps when the image is convex.…
This paper studies the geometry of binary hyperdimensional computing (HDC), a computational scheme in which data are encoded using high-dimensional binary vectors. We establish a result about the similarity structure induced by the HDC…
The structural properties of graphs are usually characterized in terms of invariants, which are functions of graphs that do not depend on the labeling of the nodes. In this paper we study convex graph invariants, which are graph invariants…
In this paper, we investigate the geometric properties of complex-valued pluriharmonic mappings defined over convex Reinhardt domains in $\mathbb{C}^n$. We first establish a multidimensional analogue of the Noshiro-Warschawski Theorem,…
We show that the symmetrized bidisc is a $\Bbb C$-convex domain. This provides an example of a bounded $\Bbb C$-convex domain which cannot be exhausted by domains biholomorphic to convex domains.
In this paper, we show that the resonance graph of a plane elementary bipartite graph $G$ can be obtained from an edge by a sequence of peripheral convex expansions with respect to a reducible face decomposition of $G$ if and only if the…
We present effective methods to compute equivariant harmonic maps from the universal cover of a surface into a nonpositively curved space. By discretizing the theory appropriately, we show that the energy functional is strongly convex and…
The use of high-dimensional features has become a normal practice in many computer vision applications. The large dimension of these features is a limiting factor upon the number of data points which may be effectively stored and processed,…
Graph hyperdimensional computing (HDC) has emerged as a promising paradigm for cognitive tasks, emulating brain-like computation with high-dimensional vectors known as hypervectors. While HDC offers robustness and efficiency on…
The purpose of this paper is to generalize the convexity of Mabuchi's functional to the conic setting. We first established a frame to study conic cscK metrics, and then the conic Mabuchi functional was introduced in such a way that conic…
The decoupled Graph Convolutional Network (GCN), a recent development of GCN that decouples the neighborhood aggregation and feature transformation in each convolutional layer, has shown promising performance for graph representation…
The generator coordinate method (GCM) casts the wavefunction as an integral over a weighted set of non-orthogonal single determinantal states. In principle this representation can be used like the configuration interaction (CI) or shell…
We consider the question of whether a given graph drawing $\Gamma$ of a triconnected planar graph $G$ is a weighted barycenter drawing. We answer the question with an elegant arithmetic characterisation using the faces of $\Gamma$. This…
We introduce a new formulation of the Conviqt convolution algorithm in terms of spin harmonics, and apply this to the problem of sidelobe correction for BeyondPlanck, the first end-to-end Bayesian Gibbs sampling framework for CMB analysis.…
We construct an explicit bijection between bipartite pointed maps of an arbitrary surface $\mathbb{S}$, and specific unicellular blossoming maps of the same surface. Our bijection gives access to the degrees of all the faces, and distances…
In the paper we investigate the continuity properties of the mapping $\Phi$ which sends any non-empty compact connected hv-convex planar set $K$ to the associated generalized conic function $f_K$. The function $f_K$ measures the average…
We propose a novel theoretical framework for barycentric interpolation, using concepts recently developed in mathematical physics. Generalized barycentric coordinates are defined similarly to Shepard's method, using positive geometries -…
Spectral graph signal processing is traditionally built on self-adjoint Laplacians, where orthogonal eigenbases yield an energy-preserving Fourier transform and a variational frequency ordering via a real Dirichlet form. Directed networks…
It is proved some results about existence and non existence of unit normal sections of submanifolds of the Euclidean space and sphere which associated Gauss maps are harmonic. Some applications to CMC hypersurfaces of the sphere and…