A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Maximal rank Coxeter quotients found for 1.7M knots up to 16 crossings.
Listed 19,513 prime knots with arc index 12-16.
For any given number of crossings , there exists a formula to determine the number of 2-bridge knots of crossings, and indeed it is a simple matter to actually construct presentations of these knots. However, the determination of whether a given (prime) knot is a 2-bridge knot remains a nontrivial exercise, and …
Paper shows a lower bound for composite knots crossing number.
Computes knot types using HOMFLY-PT polynomial.
We introduced concept of meander knots, 2-component meander links and multi-component meander links and derived different families of meander knots and links from open meanders with at most 16 crossings. We also defined semi-meander knots (or knots with ordered Gauss code) and their product.
For a torus knot K, we bound the crosscap number c(K) in terms of the genus g(K) and crossing number n(K): c(K) \leq [(g(K)+9)/6] and c(K) \leq [(n(K) + 16)/12]. The (6n-2,3) torus knots show that these bounds are sharp.
Minimal grid diagrams for 15,735 knots with 14 crossings and arc index 14.
This paper disproves a conjecture about knot projections under specific homotopy conditions.
Study identifies prime strongly positive amphicheiral knots with double symmetry.
The study examines biorderability of prime knots up to eight crossings.
K-fold Cross Validation is commonly used to evaluate classifiers and tune their hyperparameters. However, it assumes that data points are Independent and Identically Distributed (i.i.d.) so that samples used in the training and test sets can be selected randomly and uniformly. In Human Activity Recognition datasets, we…
Improved bounds on volume-det inequality for links with many twists.
New methods compute Alexander polynomials for complex knots.
LPL optimizes embeddings to align local neighborhoods, improving cross-lingual word alignment.
This paper analyzes the distribution of genera in 2-bridge knots and proves their asymptotic normality.
New superbridge index calculations for knots with odd edges.
We present a phenomenological study of stock price fluctuations of individual companies. We systematically analyze two different databases covering securities from the three major US stock markets: (a) the New York Stock Exchange, (b) the American Stock Exchange, and (c) the National Association of Securities Dealers A…
Investigates ropelength of complex knots and links.
Computing unlinking number is usually very difficult and complex problem, therefore we define BJ-unlinking number and recall Bernhard-Jablan conjecture stating that the classical unknotting/unlinking number is equal to the BJ-unlinking number. We compute BJ-unlinking number for various families of knots and links for w…
New techniques improve 16-bit training accuracy without 32-bit units.
The splitting number of a link is the minimal number of crossing changes between different components required to convert it into a split link. We obtain a lower bound on the splitting number in terms of the (multivariable) signature and nullity. Although very elementary and easy to compute, this bound turns out to be …
Study proves obstructions to equivariantly slice strongly negative amphichiral knots.
The study restricts circle actions on certain manifolds to dimensions 4, 8, and 16.
FinBERT model identifies key speakers in earnings calls, boosting stock returns.
Statistical machine learning models should be evaluated and validated before putting to work. Conventional k-fold Monte Carlo Cross-Validation (MCCV) procedure uses a pseudo-random sequence to partition instances into k subsets, which usually causes subsampling bias, inflates generalization errors and jeopardizes the r…
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…
A link diagram is said to be lune-free if, when viewed as a 4-regular plane graph it does not have multiple edges between any pair of nodes. We prove that any colored link diagram is equivalent to a colored lune-free diagram with the same number of colors. Thus any colored link diagram with a minimum number of colors (…
Isomorphism classes of Alexander quandles of order 16 are determined, and classes of connected quandles are identified. This paper extends the list of known distinct connected finite Alexander quandles.
The aim of the present paper is the investigation of -structures on 16-dimensional manifolds from the point of view of topology as well as holonomy theory. First we construct several examples. Then we study the necessary topological conditions resulting from the existence of a -reduction of the frame …
Let M be a Riemannian manifold and R its curvature tensor. For a unit vector X tangent to M at a point p, the Jacobi operator is defined by R_X = R(X, .) X$. The manifold M is called pointwise Osserman if, for every point p, the spectrum of the Jacobi operator does not depend of the choice of X, and is called globally …
We investigate polyhedral -manifolds as subcomplexes of the boundary complex of a regular polytope. We call such a subcomplex {\it -Hamiltonian} if it contains the full -skeleton of the polytope. Since the case of the cube is well known and since the case of a simplex was also previously studied (these are so…
New upper bounds on superbridge index for 49 knots, increasing known results to 49.
Study improves machine learning models for GI tract disease detection using comprehensive evaluations and cross-dataset testing.
This is the first part of a series of papers where we compute Euler characteristics, signatures, elliptic genera, and a number of other invariants of smooth manifolds that admit Riemannian metrics with positive sectional curvature and large torus symmetry. In the first part, the focus is on even-dimensional manifolds i…
We show that there are no smooth warped AdS solutions in 10- and 11-dimensional supergravities which preserve strictly more than 16 supersymmetries and have internal space a compact without boundary manifold.
We classify the simply-connected supersymmetric parallelisable backgrounds of heterotic supergravity. They are all given by parallelised Lie groups admitting a bi-invariant lorentzian metric. We find examples preserving 4, 8, 10, 12, 14 and 16 of the 16 supersymmetries.
The 4-dimensional abstract Kummer variety K^4 with 16 nodes leads to the K3 surface by resolving the 16 singularities. Here we present a simplicial realization of this minimal resolution. Starting with a minimal 16-vertex triangulation of K^4 we resolve its 16 isolated singularities - step by step - by simplicial blowu…
Moebius-Kantor graph connects multiple groups and topological properties.
In M-theory vacua with vanishing 4-form F, one can invoke the ordinary Riemannian holonomy H \subset SO(1,10) to account for unbroken supersymmetries n=1, 2, 3, 4, 6, 8, 16, 32. However, the generalized holonomy conjecture, valid for non-zero F, can account for more exotic fractions of supersymmetry, in particular 16<n…
In this paper, we address an issue that the visually impaired commonly face while crossing intersections and propose a solution that takes form as a mobile application. The application utilizes a deep learning convolutional neural network model, LytNetV2, to output necessary information that the visually impaired may l…
The paper explores connections between quaternionic and Cayley calibrations in dimensions 8 and 16.
Formula for colored Links-Gould polynomial with genus bounds.
Calibration in 16D disproves Federer's product question.
Recently, the posit numerical format has shown promise for DNN data representation and compute with ultra-low precision ([5..8]-bit). However, majority of studies focus only on DNN inference. In this work, we propose DNN training using posits and compare with the floating point training. We evaluate on both MNIST and F…
A new approach to protein language models combines latent space prediction with masked language modeling.
Let $\mbox{Len}(K)$ be the minimum length of a knot on the cubic lattice (namely the minimum length necessary to construct the knot in the cubic lattice). This paper provides upper bounds for $\mbox{Len}(K)$ of a nontrivial knot in terms of its crossing number as follows: $\mbox{Len}(K) \leq \min \left\{ \fr…
We give an interpretation of the maximal number of linearly independent vector fields on spheres in terms of the Spin(9) representation on R^16. This casts an insight on the role of Spin(9) as a subgroup of SO(16) on the existence of vector fields on spheres, parallel to the one played by complex, quaternionic and octo…