arXiv research

Minimal covolume group found in hyperbolic 3-space.

The paper confirms a conjecture linking link bipyramid volume and Mahler measure.

We utilize ideal bipyramids to obtain new upper bounds on volume for hyperbolic link complements in terms of the combinatorics of their projections.

Generalizing previous constructions, we present a dual pair of decompositions of the complement of a link L into bipyramids, given any multi-crossing projection of L. When L is hyperbolic, this gives new upper bounds on the volume of L given its multi-crossing projection. These bounds are realized by three closely rela…

We present explicit geometric decompositions of the complement of tiling links, which are alternating links whose projection graphs are uniform tilings of the 2-sphere, the Euclidean plane or the hyperbolic plane. This requires generalizing the angle structures program of Casson and Rivin for triangulations with a mixt…

We present explicit geometric decompositions of the hyperbolic complements of alternating $k$-uniform tiling links, which are alternating links whose projection graphs are $k$-uniform tilings of $S^2$, $\mathbb{E}^2$, or $\mathbb{H}^2$. A consequence of this decomposition is that the volumes of spherical alternating $k…

Paper presents a new triangular form for flat systems.

Paper presents a new flat triangular form for systems.

We consider the problem of approximate joint triangularization of a set of noisy jointly diagonalizable real matrices. Approximate joint triangularizers are commonly used in the estimation of the joint eigenstructure of a set of matrices, with applications in signal processing, linear algebra, and tensor decomposition.…

Sharp bounds for spanning tree entropy in planar lattices.

Introduces triangular transport for uncertain data.

Solves problem of describing transformations for upper triangular Toeplitz operators.

Triangular flows ensure statistical consistency and fast rates in generative modeling.

Paper uses GNNs to efficiently detect profitable triangular arbitrage opportunities.

We create a smooth manifold of triangular meshes with a geodesically complete metric.

Discretizes Helfrich-type energies on surfaces using triangular complexes.

We study the problem to provide a triangular form based on implicit differential equations for non-linear multi-input systems with respect to the flatness property. Furthermore, we suggest a constructive method for the transformation of a given system into that special triangular shape, if possible. The well known Brun…

We first show that there are in fact triangular arbitrage opportunities in the spot foreign exchange markets, analyzing the time dependence of the yen-dollar rate, the dollar-euro rate and the yen-euro rate. Next, we propose a model of foreign exchange rates with an interaction. The model includes effects of triangular…

We investigate triangular arbitrage within the spot foreign exchange market using high-frequency executable prices. We show that triangular arbitrage opportunities do exist, but that most have short durations and small magnitudes. We find intra-day variations in the number and length of arbitrage opportunities, with la…

The study investigates linearizability of Poisson structures on groupoids.

New method for conditional sampling using M-GANs, likely-free inference.

New method uses neural maps to efficiently sample lattice QCD distributions.

Multifractal detrended cross-correlation methodology is described and applied to Foreign exchange (Forex) market time series. Fluctuations of high frequency exchange rates of eight major world currencies over 2010-2018 period are used to study cross-correlations. The study is motivated by fundamental questions in compl…

Study finds conditions for operator fields to be in strictly upper triangular form in small dimensions.

In this paper we look for closed expressions to calculate the number of colourings of prime knots for given linear Alexander quandles. For this purpose the colouring matrices are simplified to a triangular form, when possible. The operations used to perform this triangularization preserve the property that the entries …

Model shows triangular arbitrage key to cross-currency correlations in forex markets.

This paper explores the relationship between Leibniz algebras and Nijenhuis operators.

New basis confirms Thurston's conjecture and reveals knot configurations.

We study the problem of computing the matrix exponential of a block triangular matrix in a peculiar way: Block column by block column, from left to right. The need for such an evaluation scheme arises naturally in the context of option pricing in polynomial diffusion models. In this setting a discretization process pro…

We introduce a microscopic model which describes the dynamics of each dealer in multiple foreign exchange markets, taking account of the triangular arbitrage transaction. The model reproduces the interaction among the markets well. We explore the relation between the parameters of the present microscopic model and the …

The Vol-Det Conjecture relates the volume and the determinant of a hyperbolic alternating link in $S^3$. We use exact computations of Mahler measures of two-variable polynomials to prove the Vol-Det Conjecture for many infinite families of alternating links. We conjecture a new lower bound for the Mahler measure of cer…

Let X be a simply connected compact Riemannian symmetric space, let U be the universal covering group of the identity component of the isometry group of X, and let \g denote the complexification of the Lie algebra of U, \g=\u^\C. Each \u-compatible triangular decomposition \g=\n_- + \h + \n_+ determines a Poisson Lie g…

We study controlled systems which are uniformly observable and differentially observable with an order larger than the system state dimension. We establish that they may be transformed into a (partial) triangular canonical form but with possibly non locally Lipschitz functions. We characterize the points where this Lip…

We examine doing probabilistic descent over manifolds implicitly defined by a set of polynomials with rational coefficients. The system of polynomials is assumed to be triangularized. An application of Whitney's embedding theorem allows us to work in a reduced dimensional embedding space. A numerical continuation metho…

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{…

Examines discrete curvature's relation to smooth curvature in 3 spaces.

Two algorithms create high-quality triangular meshes for surfaces with guaranteed angles.

Develops theory for conditional optimal transport in infinite-dimensional spaces.

New model for simulating and inferring from inverse problems.

Algorithm learns non-Gaussian graphical models via Hessian scores and triangular transport.

New combinatorial type helps distinguish plane curve topologies.

Somewhat unexpectedly, the study of the family of twisted knots revealed a hidden structure behind exclusive Racah matrices $\bar S$, which control non-associativity of the representation product in a peculiar channel $R\otimes \bar R \otimes R \longrightarrow R$. These $\bar S$ are simultaneously symmetric and orthogo…

New framework for learning KR maps from data, ensuring stable generalization.

A new neural network for efficient density estimation.

It is known, since works of Burde and de Rham, that one can detect the roots of the Alexander polynomial of a knot by the study of the representations of the knot group into the group of the invertible upper triangular $2x2$ matrices. In this work, we propose to generalize this result by considering the representations…

Researchers compute the cohomology ring of a foliation defined by a group action.

Study limits of convex domains in projective plane, proving specific results.

We find a normal form for two-input flat discrete-time systems.