Related papers: Le logo du CNRS est-il convexe ?
We state that any constant curvature Riemannian metric with conical singularities of constant sign curvature on a compact (orientable) surface $S$ can be realized as a convex polyhedron in a Riemannian or Lorentzian) space-form. Moreover…
We present a full general relativistic analytic solution for a radiation-pressure supported equilibrium fluid torus orbiting a rotating neutron star (NS). Previously developed analytical methods are thoroughly applied in the Hartle-Thorne…
There is a common need to search of molecular databases for compounds resembling some shape, what suggests having similar biological activity while searching for new drugs. The large size of the databases requires fast methods for such…
Very recently Richter and Rogers proved that any convex geometry can be represented by a family of convex polygons in the plane. We shall generalize their construction and obtain a wide variety of convex shapes for representing convex…
In the previous manuscript, new tilings (tessellations) were presented using convex pentagonal tiles belonging to Type 1 and Type 5. The convex pentagon tilings are related to heptiamond tilings. Later, the authors found Johannes Hindriks'…
The first three sections of this survey represent an updated and much expanded version of the abstract of my talk at FPSAC'2010: new results are incorporated and several concrete conjectures on the interactions between the three…
The radial mean bodies of parameter $p>-1$ of a convex body $K \subseteq \mathbb R^n$ are radial sets introduced in [4] by Gardner and Zhang. They are known to be convex for $p\geq 0$. We prove that if $K \subseteq \mathbb R^2$ is a convex…
Having in mind the well known model of Euclidean convex hypersurfaces [4], [5], and the ideas in [1] many authors defined and investigate convex hypersurfaces of a Riemannian manifold. As it was proved by the first author in [7], there…
Computational Social Science (CSS), aiming at utilizing computational methods to address social science problems, is a recent emerging and fast-developing field. The study of CSS is data-driven and significantly benefits from the…
We introduce polyhedral cones associated with $m$-hemimetrics on $n$ points, and, in particular, with $m$-hemimetrics coming from partitions of an $n$-set into $m+1$ blocks. We compute generators and facets of the cones for small values of…
A convex envelope for the problem of finding the best approximation to a given matrix with a prescribed rank is constructed. This convex envelope allows the usage of traditional optimization techniques when additional constraints are added…
The modified SNIP indicator of Elsevier, as recently explained by Waltman et al. (2013) in this journal, solves some of the problems which Leydesdorff & Opthof (2010 and 2011) indicated in relation to the original SNIP indicator (Moed, 2010…
Group equivariant neural networks have been explored in the past few years and are interesting from theoretical and practical standpoints. They leverage concepts from group representation theory, non-commutative harmonic analysis and…
Implicit Neural Representations (INRs) have emerged as a promising method for representing diverse data modalities, including 3D shapes, images, and audio. While recent research has demonstrated successful applications of INRs in image and…
The mathematical treatment and graphical representation of Special Relativity (SR) are well established, yet carry deep implications that remain hard to visualize. This paper presents a new graphical interpretation of the geometry of SR…
In this paper, we survey recent progress on the Null Penrose Conjecture, including a proof of the conjecture for smooth null cones that are foliated by doubly convex spheres.
We provide a specific representation of convex polynomials nonnegative on a convex (not necessarily compact) basic closed semi-algebraic subset K of Rn. Namely, they belong to a specific subset of the quadratic module generated by the…
We introduce a geometric realization of noncommutative singularity resolutions. To do this, we first present a new conjectural method of obtaining conventional resolutions using coordinate rings of matrix-valued functions. We verify this…
Selfridge, along with Sutherland and Marr provided some of the earliest proposals for how to program computers to recognize shapes. Their emphasis on filtering for contour features, especially the orientation of boundary segments, was…
As a natural application of the {\it theory of geometric averaging} in Finsler geometry and generalized Finsler geometry, a new approach to investigate {\it generalized Finsler geometry}, based on a convex invariance of the average…