arXiv research

Prism complexes help classify 3-manifolds, especially Seifert fiber spaces.

Researchers find braid words for knots yielding prism manifolds.

New classification of hyperbolic Coxeter prisms.

Hyperbolic knots decompose into prism orbifolds.

Every prism manifold can be parametrized by a pair of relatively prime integers $p>1$ and $q$. In our earlier papers, we determined a complete list of prism manifolds $P(p, q)$ that can be realized by positive integral surgeries on knots in $S^3$ when $q<0$ or $q>p$; in the present work, we solve the case when $0<q<p$.…

We continue our study of the realization problem for prism manifolds. Every prism manifold can be parametrized by a pair of relatively prime integers $p>1$ and $q$. We determine a complete list of prism manifolds $P(p, q)$ that can be realized by positive integral surgeries on knots in $S^3$ when $q>p$. The methodology…

Proves a conjecture about prism shapes with nonnegative curvature.

Study flat metrics from right prisms, finding non-lattice surfaces with translation coverings.

In this paper we calculate the number of equivariant diffeomorphism classes of small covers over a prism.

PRISM integrates diverse rewards in MORL, improving sample efficiency and Pareto coverage.

We derive an analytic formula for the dual Jacobian matrix of a generalised hyperbolic tetrahedron. Two cases are considered: a mildly truncated and a prism truncated tetrahedron. The Jacobian for the latter arises as an analytic continuation of the former, that falls in line with a similar behaviour of the correspondi…

PRISM identifies simplex vertices from noisy data.

The spherical manifold realization problem asks which spherical three-manifolds arise from surgeries on knots in $S^3$. In recent years, the realization problem for C, T, O, and I-type spherical manifolds has been solved, leaving the D-type manifolds (also known as the prism manifolds) as the only remaining case. Every…

In this paper, based upon the basic theory for glued manifolds in M.W. Hirsch (1976) \cite[Chapter 8, §2 Gluing Manifolds Together]{h}, we give a method of constructing homeomorphisms between two small covers over simple convex polytopes. As a result we classify, up to homeomorphism, all small covers over a 3-dimension…

Explicitly constructed 5-manifolds tessellated by prisms.

Asymmetry PRISM outperforms CPU and GPU solvers for institutional rebalancing.

PRISM-FCP improves federated prediction robustness against Byzantine attacks.

Person re-identification (re-id), an emerging problem in visual surveillance, deals with maintaining entities of individuals whilst they traverse various locations surveilled by a camera network. From a visual perspective re-id is challenging due to significant changes in visual appearance of individuals in cameras wit…

The study examines the systole of 3-manifolds with positive scalar curvature.

Study shows space of persistence diagrams doesn't have Yu's property A.

In this paper, we classify all of the five-sided three-dimensional hyperbolic polyhedra with one ideal vertex, which have the shape of a triangular prism. We show how to find each such polyhedron in the upper half-space model by considering lines and circles in the plane. Finally, we give matrix generators in $\mathrm{…

In arxiv:1205.1274 Rieck and Yamashita defined the link volume of 3-manifolds and studied some of its basic properties. Many of these properties are similar to the corresponding properties of the hyperbolic volume. In this paper we calculate the link volume of an infinite family of prism manifolds. As a corollary, we s…

PRISM infers model structures and parameters from simulations, controlling complexity at test time.

We classify $n$-dimensional geometric graph manifolds with nonnegative scalar curvature, and first show that if $n>3$, the universal cover splits off a codimension 3 Euclidean factor. We then proceed with the classification of the 3-dimensional case by showing that such a manifold is either a lens space or a prism mani…

PRISM-VQ combines financial priors with vector quantization for better stock prediction.

PRISM provides real-time SLAM with uncertainty estimates for agent and map states.

Study develops curvature for contact-sequence networks, revealing temporal dynamics.

We show that every knot can be realized as a billiard trajectory in a convex prism. This solves a conjecture of Jones and Przytycki.

This paper explores how deep learning models can fit data exactly and why this is important.

The paper identifies five extreme learning regimes for large linear autoencoders.

Study of alternating links on nonorientable surfaces, extending results to nonorientable projections.

Cosmologists are taking a renewed interest in multiconnected spherical 3-manifolds (spherical spaceforms) as possible models for the physical universe. To understand the formation of large scale structures in such a universe, cosmologists express physical quantities, such as density fluctuations in the primordial plasm…

After having investigated the regular prisms and prism tilings in the $\SLR$ space in the previous work \cite{Sz13-1} of the second author, we consider the problem of geodesic ball packings related to those tilings and their symmetry groups $\mathbf{pq2_1}$. $\SLR$ is one of the eight Thurston geometries that can be de…

We extend Choe's idea in \cite{choe} to nonpolyhedral calibrated surfaces and give some examples of polyhedral sets over right prisms and nonpolyhedral calibrated surfaces.

The paper finds hyperbolic small knots in many 3-manifolds.

The paper constructs free boundary minimal surfaces in product spaces using eigenvalue methods.

The article studies crystallizations of small covers over simple polytopes and finds unique crystallizations for the $n$-simplex.

Smooth knots with odd Conway polynomial terms have inscribed trefoils.

New formula calculates volumes of ideal hyperbolic drums.

Ray marching method visualizes flat surfaces efficiently.

Observational data hints at a finite universe, with spherical manifolds such as the Poincare dodecahedral space tentatively providing the best fit. Simulating the physics of a model universe requires knowing the eigenmodes of the Laplace operator on the space. The present article provides explicit polynomial eigenmodes…

Many in-hospital mortality risk prediction scores dichotomize predictive variables to simplify the score calculation. However, hard thresholding in these additive stepwise scores of the form "add x points if variable v is above/below threshold t" may lead to critical failures. In this paper, we seek to develop risk pre…

We find all Heegaard diagrams with the property "alternating" or "weakly alternating" on a genus two orientable closed surface. Using these diagrams we give infinitely many genus two 3--manifolds, each admits an automorphism whose non-wondering set consists of two Williams solenoids, one attractor and one repeller. The…

We propose to study the problem of few-shot learning with the prism of inference on a partially observed graphical model, constructed from a collection of input images whose label can be either observed or not. By assimilating generic message-passing inference algorithms with their neural-network counterparts, we defin…

A vertex-transitive map $X$ is a map on a surface on which the automorphism group of $X$ acts transitively on the set of vertices of $X$. If the face-cycles at all the vertices in a map are of same type then the map is called a semi-equivelar map. Clearly, a vertex-transitive map is semi-equivelar. Converse of this is …

Complexity results for recognizing elliptic 3-manifolds.

We study prismatics sets analogously to simplical sets except that realization involves prisms, i.e., products of simplices rather than just simplices. Particular examples are the prismatic subdivision of a simplicial set S and the prismatic star of S. Both have the same homotopy type as S and in particular the latter …

Let $X$ be a real-analytic manifold and $g\colon X\to{\mathbf R}^n$ a proper triangulable subanalytic map. Given a subanalytic $r$-form $ω$ on $X$ whose pull-back to every non singular fiber of $g$ is exact, we show tha $ω$ has a relative primitive: there is a subanalytic $(r-1)$-form $Ω$ such that $dgΛ(ω-dΩ)=0$. The p…