arXiv research

This paper finds upper bounds for lattice stick numbers of rational links with specific stick configurations.

Computes presentations for specific arithmetic hyperbolic lattices.

Upper bound for lattice stick number of spatial graphs.

The cubic lattice stick index of a knot type is the least number of sticks necessary to construct the knot type in the 3-dimensional cubic lattice. We present the cubic lattice stick index of various knots and links, including all (p,p+1)-torus knots, and show how composing and taking satellites can be used to obtain t…

Transformations studied in graphs with edges and vertices of degree zero or one.

A celebrated theorem of Hadwiger states that the Euler-Poincaré characteristic is the the unique invariant and continuous valuation on the distributive lattice of compact polyhedra in R^n that assigns value one to each convex non-empty such polyhedron. This paper provides an analogue of Hadwiger's result for finitely p…

The paper finds incommensurable lattices in complex models of Baumslag-Solitar groups.

Spin Lefschetz fibrations can represent any group and lattice point.

The B-quadrilateral lattice (BQL) provides geometric interpretation of Miwa's discrete BKP equation within the quadrialteral lattice (QL) theory. After discussing the projective-geometric properties of the lattice we give the algebro-geometric construction of the BQL ephasizing the role of Prym varieties and the corres…

New lattice path method for statistical inference of persistent diagrams.

The lattice stick number of a knot type is defined to be the minimal number of straight line segments required to construct a polygon presentation of the knot type in the cubic lattice. In this paper, we mathematically prove that the trefoil knot $3_1$ and the figure-8 knot $4_1$ are the only knot types of lattice stic…

This work compares lattice-free and lattice-based training criteria for LVCSR.

Finite presentations for skein algebras linked to gauge field theory.

The paper refines transformations of lattice diagrams and introduces dotted diagrams.

L-CNNs preserve gauge symmetry in lattice simulations.

Study complex hyperbolic lattices and their subgroups, proving new finiteness properties.

A lattice based method will be presented for numerical investigations of Ricci flow. The method will be applied to the particular case of 2-dimensional axially symmetric initial data on manifolds with S^2 topology. Results will be presented that show that the method works well and agrees with results obtained using con…

New methods classify convex lattice polygons for affine dimers.

The lattice stick number $s_L(K)$ of a knot $K$ is defined to be the minimal number of straight line segments required to construct a stick presentation of $K$ in the cubic lattice. In this paper, we find an upper bound on the lattice stick number of a nontrivial knot $K$, except trefoil knot, in terms of the minimal c…

Algorithm constructs surfaces with specific Veech groups in lattice strata.

Knot lattice homology invariant of smooth knot type in rational homology spheres.

In the present article, we provide examples of fake quadrics, that is, minimal complex surfaces of general type with the same numerical invariants as the smooth quadric in $\PP ^3$ which are quotients of the bidisc by an irreducible lattice of automorphisms. Moreover, we list classes of arithmetic lattices over a real …

Unified framework for complex financial networks using lattice theory.

Study series invariants of plumbed 3-manifolds using root lattices.

LatticeNet segments 3D point clouds faster and more efficiently.

Paper presents an efficient approach for integrating LSTM language models in LVCSR systems.

The objective of this paper is to present some geometric aspects of surfaces associated with theta function solutions of the periodic 2D-Toda lattice. For this purpose we identify the $(N^2-1)$-dimensional Euclidean space with the ${\frak su}(N)$ algebra which allows us to construct the generalized Weierstrass formula …

Miura-type transformations (MTs) are an essential tool in the theory of integrable nonlinear partial differential and difference equations. We present a geometric method to construct MTs for differential-difference (lattice) equations from Darboux-Lax representations (DLRs) of such equations. The method is applicable t…

Stochastic normalizing flows improve lattice field theory simulations.

We present an intriguing question about lattice points in triangles where Pick's formula is "almost correct". The question has its origin in knot theory, but its statement is purely combinatorial. After more than 30 years the topological question was recently solved, but the lattice point problem is still open.

New MCMC method samples from lattice distributions efficiently.

The paper presents presentations for Euclidean Picard modular groups.

Lat-Net compresses Lattice Boltzmann simulations using neural networks.

The paper introduces lattice homology for integrally closed submodules and applies it to geometric invariants.

P. Buser and P. Sarnak showed in 1994 that the maximum, over the moduli space of Riemann surfaces of genus s, of the least conformal length of a nonseparating loop, is logarithmic in s. We present an application of (polynomially) dense Euclidean packings, to estimates for an analogous 2-dimensional conformal systolic i…

Study quasi-isometric embeddings in symmetric spaces and Lie groups.

New method reconstructs strain and lattice spacing from neutron data.

Novel trading strategy for generalized lattice markets ensures positive profits.

In this article we perform a computational study of Polyrakis algorithms presented in [12,13]. These algorithms are used for the determination of the vector sublattice and the minimal lattice-subspace generated by a finite set of positive vectors of R^k. The study demonstrates that our findings can be very useful in th…

The lattice cohomology of a plumbed 3--manifold $M$ associated with a connected negative definite plumbing graph is an important tool in the study of topological properties of $M$, and in the comparison of the topological properties with analytic ones when $M$ is realized as complex analytic singularity link. By defini…

The paper develops a theory of surplus invariance in vector lattices.

New framework for detecting complex interactions in multivariate data.

Hybrid subgroups found in non-arithmetic PU(2,1) lattices.

New non-arithmetic lattice found in PU(3,1)

Study on manifolds with higher-rank lattice actions in projective and conformal classes.

Proof shows volumes of certain geometric representations are always integers.

Data compression speeds up machine learning loss calculations.

New property identifies arithmetic lattices from nonuniform lattices.