arXiv research

Verifies knot conjecture for 24-crossing knots.

Paper compares ML models for a wall-following robot, achieving high accuracy.

The study identifies flat manifolds with unique cusp cross-sections in arithmetic hyperbolic manifolds.

There is an elegant relation found by Fabricius-Bjerre [Math. Scand 40 (1977) 20--24] among the double tangent lines, crossings, inflections points, and cusps of a singular curve in the plane. We give a new generalization to singular curves in RP^2. We note that the quantities in the formula are naturally dual to each …

Purpose: To determine if deep learning networks could be trained to forecast a future 24-2 Humphrey Visual Field (HVF). Participants: All patients who obtained a HVF 24-2 at the University of Washington. Methods: All datapoints from consecutive 24-2 HVFs from 1998 to 2018 were extracted from a University of Washington …

Classifies flat knots up to 8 crossings using Lyndon words.

New method uses quandle rings to distinguish knots and their mirrors.

Paper shows string cobordism at 24 dims can be determined by elliptic genus.

Cross-domain recommendation can alleviate the data sparsity problem in recommender systems. To transfer the knowledge from one domain to another, one can either utilize the neighborhood information or learn a direct mapping function. However, all existing methods ignore the high-order connectivity information in cross-…

Study optimizes trading in multiple assets with cross-effects.

Four hyperbolic 24-cell 4-manifolds with one cusp are identified.

Constructs links that are both quasi-alternating and almost alternating.

Given a knot complement X and its p-fold cyclic cover X_p, we identify twisted polynomials associated to 1-dimensional linear representations of the fundamental group of X_p with twisted polynomials associated to related p-dimensional linear representations of the fundamental group of X. This provides a simpler and fas…

Study of characteristic numbers in 24-dimensional String manifolds.

In this paper, by combining modularity of the Witten genus and the modular forms constructed by Liu and Wang, we establish mod 3 congruence properties of certain twisted signatures of 24 dimensional string manifolds.

We prove that among four-dimensional ideal right-angled hyperbolic polytopes the 24-cell is of minimal volume and of minimal facet number. As a corollary, a dimension bound for ideal right-angled hyperbolic polytopes is obtained.

We describe the construction of a Lie superalgebra associated to an arbitrary supersymmetric M-theory background, and discuss some examples. We prove that for backgrounds with more than 24 supercharges, the bosonic subalgebra acts locally transitively. In particular, we prove that backgrounds with more than 24 supersym…

We describe a family of 4-dimensional hyperbolic orbifolds, constructed by deforming an infinite volume orbifold obtained from the ideal, hyperbolic 24-cell by removing two walls. This family provides an infinite number of infinitesimally rigid, infinite covolume, geometrically finite discrete subgroups of the isometry…

CDA framework infers channel influence from aggregated data without user identifiers.

Machine-learning algorithms have gained popularity in recent years in the field of ecological modeling due to their promising results in predictive performance of classification problems. While the application of such algorithms has been highly simplified in the last years due to their well-documented integration in co…

Given a lattice L of R^n, a polytope D is called a Delaunay polytope in L if the set of its vertices is S\cap L where S is a sphere having no lattice points in its interior. D is called perfect if the only ellipsoid in R^n that contains S\cap L is exactly S. For a vector v of the Leech lattice Λ_{24} we define Λ_{24}(v…

Acute kidney injury (AKI) commonly occurs in hospitalized patients and can lead to serious medical complications. In order to optimally predict AKI before it develops at any time during a hospital stay, we present a novel framework in which AKI is continually predicted automatically from EHR data over the entire hospit…

We implement a Tensor Train layer in the TensorFlow Neural Machine Translation (NMT) model using the t3f library. We perform training runs on the IWSLT English-Vietnamese '15 and WMT German-English '16 datasets with learning rates $\in \{0.0004,0.0008,0.0012\}$, maximum ranks $\in \{2,4,8,16\}$ and a range of core dime…

This note shows every integer can be a signature of a hyperbolic 4-manifold.

The paper studies solutions to the Yamabe equation on asymptotically flat manifolds and their behavior at infinity.

We consider finite group-actions on closed, orientable and nonorientable 3-manifolds; such a finite group-action leaves invariant the two handlebodies of a Heegaard splitting of M of some genus g. The maximal possible order of a finite group-action of an orientable or nonorientable handlebody of genus g > 1 is 24(g-1),…

We identify 998 closed hyperbolic 3-manifolds whose volumes are rationally related to Dedekind zeta values, with coprime integers $a$ and $b$ giving $a/b vol(M)=(-D)^{3/2}/(2π)^{2n-4} (ζ_K(2))/(2ζ(2))$ for a manifold M whose invariant trace field $K$ has a single complex place, discriminant $D$, degree $n$, and Dedekin…

The spectral asymptotics for linear elasticity with mixed boundary conditions are shown to be old results.

CoIFNet unifies imputation and forecasting for robust multivariate time series prediction with missing values.

Survey of recent austere submanifold results.

Identifying patients who will be discharged within 24 hours can improve hospital resource management and quality of care. We studied this problem using eight years of Electronic Health Records (EHR) data from Stanford Hospital. We fit models to predict 24 hour discharge across the entire inpatient population. The best …

We construct new families of quasimorphisms on many groups acting on CAT(0) cube complexes. These quasimorphisms have a uniformly bounded defect of 12, and they "see" all elements that act hyperbolically on the cube complex. We deduce that all such elements have stable commutator length at least 1/24. The group actions…

This is the Proceedings of the ICML Workshop on #Data4Good: Machine Learning in Social Good Applications, which was held on June 24, 2016 in New York.

Inspired by the paper on quantum knots and knot mosaics [23] and grid diagrams (or arc presentations), used extensively in the computations of Heegaard-Floer knot homology [2,3,7,24], we construct the more concise representation of knot mosaics and grid diagrams via mirror-curves. Tame knot theory is equivalent to knot…

New formulas link string bordism to integers.

Paper distills ensemble ENSO forecasts into simpler models for better diagnostics.

We explore some generalizations of fullerenes F_v (simple polyhedra with v vertices and only 5- and 6-gonal faces) seen as (d-1)-dimensional simple manifolds (preferably, spherical or polytopal) with only 5- and 6-gonal 2-faces. First, finite and planar (infinite) 3-fullerenes are described. Three infinite families of …

Knots have been considered to be useful models for simulating molecular chains such as DNA and proteins. One quantity that we are interested on molecular knots is the minimum number of monomers necessary to realize a knot. In this paper we consider every knot in the cubic lattice. Especially the minimal length of a kno…

Estimates inverse temperature of Ising models with a single sample.

FastForest boosts Random Forest speed by 24%.

We classify four-dimensional shrinking Ricci solitons satisfying $Sec \geq \frac{1}{24} R$, where $Sec$ and $R$ denote the sectional and the scalar curvature, respectively. They are isometric to either $\mathbb{R}^{4}$ (and quotients), $\mathbb{S}^{4}$, $\mathbb{RP}^{4}$ or $\mathbb{CP}^{2}$ with their standard metrics…

Two geometric realizations of $F(4)$ Lie superalgebra found.

We show that the set of even positive definite lattices that arise from smooth, simply-connected 4-manifolds bounded by a fixed homology 3-sphere can depend on more than the ranks of the lattices. We provide two homology 3-spheres with distinct sets of such lattices, each containing a distinct nonempty subset of the ra…

Built the smallest non-commensurable hyperbolic 4-manifold.

This is a survey talk on one of the best known quantum knot invariants, the colored Jones polynomial of a knot, and its relation to the algebraic/geometric topology and hyperbolic geometry of the knot complement. We review several aspects of the colored Jones polynomial, emphasizing modularity, stability and effective …

We classify non-dilatonic NS-NS type II supergravity backgrounds admitting a consistent absolute parallelism. They are all given by parallelised Lie groups admitting scalar flat bi-invariant lorentzian metrics. There are seven different classes, some of them containing moduli. For each class we determine the amount of …

Let $ξ$ and $η$ be two non--commuting isometries of the hyperbolic $3$--space $\mathbb{H}^3$ so that $Γ=\langleξ,η\rangle$ is a purely loxodromic free Kleinian group. For $γ\inΓ$ and $z\in\mathbb{H}^3$, let $d_γz$ denote the distance between $z$ and $γ\cdot z$. Let $z_1$ and $z_2$ be the mid-points of the shortest geod…

Stablecoins offer efficient settlement but externalize costs and risks.