arXiv research

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

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

New classification of hyperbolic Coxeter prisms.

Hyperbolic knots decompose into prism orbifolds.

Ballinger et al. have determined the list of all prism manifolds that are possibly realizable by Dehn surgeries on knots in $S^3$. In this paper, we explicitly find braid words of primitive/Seifert-fibered knots on which surface slope surgeries yield all the prism manifolds listed above. This completes the solution to …

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…

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…

Rectangular diagrams help analyze foliations in 3-sphere.

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.

We prove the following comparison theorem for metrics with nonnegative scalar curvature, also known as the dihedral rigidity conjecture by Gromov: for $n\le 7$, if an $n$-dimensional prism has nonnegative scalar curvature and weakly mean convex faces, then its dihedral angle cannot be everywhere not larger than its Euc…

Improved bounds for knot crossings in different mosaic patterns.

PRISM-FCP improves federated prediction robustness against Byzantine attacks.

New proof for symmetric spaces with rectangular lattices.

Rectangular peg problem solved for many curves.

Proves a theorem for comparing surfaces in 3D space.

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…

If a rectangular diagram represents the trivial knot, then it can be deformed into the rectangular diagram with only two vertical edges by a finite sequence of merge operations and exchange operations, without increasing the number of vertical edges, which was shown by I. A. Dynnikov. We show in this paper that we need…

In this paper Legendrian graphs in $(\mathbb{R}^3,ξ_{\mathrm{st}})$ are considered modulo Legendrian isotopy and edge contraction. To a Legendrian graph we associate a (generalized) rectangular diagram --- a purely combinatorial object. Moves of rectangular diagrams are introduced so that equivalence classes of Legendr…

Paper studies S-rectangular DR-RL models for robust reinforcement learning with near-optimal sample complexity.

The study improves inequalities for link diagrams and introduces weak rectangular diagrams.

We introduce a simple combinatorial way, which we call a rectangular diagram of a surface, to represent a surface in the three-sphere. It has a particularly nice relation to the standard contact structure on $\mathbb S^3$ and to rectangular diagrams of links. By using rectangular diagrams of surfaces we are going, in p…

Rectangular mosaics extend virtual knot studies to larger polygons.

Study reveals $1/f$ noise in signals made from nonoverlapping rectangular pulses.

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

We claim that the recently discovered universal-matrix precursor for the $F$ functions, which define the differential expansion of colored polynomials for twist and double braid knots, can be extended from rectangular to non-rectangular representations. This case is far more interesting, because it involves multiplicit…

We conjecture a closed-form expression of HOMFLY-PT invariants of double twist knots colored by rectangular Young diagrams where the twist is encoded in interpolation Macdonald polynomials. We also put forth a conjecture of cyclotomic expansions of HOMFLY-PT polynomials colored by rectangular Young diagrams for any kno…

If a rectangular diagram represents the trivial knot, then it can be deformed into the trivial rectangular diagram with only four edges by a finite sequence of merge operations and exchange operations, without increasing the number of edges, which was shown by I. A. Dynnikov. Using this, Henrich and Kauffman gave an up…

A correspondence is studied by H. Matsuda between front projections of Legendrian links in the standard contact structure for 3-space and rectangular diagrams. In this paper, we introduce braided rectangular diagrams, and study a relationship with Legendrian links in the standard contact structure for 3-space. We show …

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.

New framework for higher-order singular-value derivatives of rectangular matrices.

New transformations preserve link isotopy, showing complexity differences.

Paper studies robust MDPs, improving sample complexity and asymptotic performance.

Study inequalities for singular values of rectangular matrices.

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…

Deep learning classifies knots using rectangular diagrams.

Factorization of the differential expansion coefficients for HOMFLY-PT polynomials of double braids, discovered in arXiv:1606.06015 in the case of rectangular representations $R$, is extended to the first non-rectangular representations $R=[2,1]$ and $R=[3,1]$. This increases chances that such factorization will take p…

In the present paper a criteria for a rectangular diagram to admit a simplification is given in terms of Legendrian knots. It is shown that there are two types of simplifications which are mutually independent in a sense. A new proof of the monotonic simplification theorem for the unknot is given. It is shown that a mi…

We elaborate on the recent observation that evolution for twist knots simplifies when described in terms of triangular evolution matrix ${\cal B}$, not just its eigenvalues $Λ$, and provide a universal formula for ${\cal B}$, applicable to arbitrary rectangular representation $R=[r^s]$. This expression is in terms of s…