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.
An explicit solution found for maximizing/minimizing agreement in a 2x2 table.
We present a 2x2 Lax representation for discrete circular nets of constant negative Gauß curvature. It is tightly linked to the 4D consistency of the Lax representation of discrete K-nets (in asymptotic line parametrization). The description gives rise to Bäcklund transformations and an associated family. All the membe…
We interpret an open orbit in a 32-dimensional representation space of Spin(9,1) x SL(2,R) as a substitute for the non-existent group of invertible 2x2 matrices over the octonions and study various natural homogeneous subspaces. The approach is via twistor geometry in eight dimensions.
In this paper we show how generalized quaternions, including 2X2 matrices, can be used to find solutions of a non-commuting equation intimately connected with braid groups. These solutions can then be used to find polynomial invariants of virtual knots and links.
We introduce a new integrable system hierarchy which is a restriction of the AKNS nxn hierarchy coming from an unusual splitting of the loop algebra. This splitting comes from an automorphism of the loop algebra instead of an automorphism of SL(n,C). It is known that the 2x2 KdV is the standard KdV hierarchy.
Revisit Fenn's table theorem from a differential-topological perspective.
Using geometrical approach exposed in arXiv:math/0304245 and arXiv:nlin/0511012, we explore the Camassa-Holm equation (both in its initial scalar form, and in the form of 2x2-system). We describe Hamiltonian and symplectic structures, recursion operators and infinite series of symmetries and conservation laws (local an…
Using the representation of the isometries as 2x2 invertible matrices over the division algebra $\H$ of quaternions, we give an algebraic characterization of the dynamical types of the orientation-preserving isometries of the hyperbolic 5-space. We also determine the conjugacy classes and the conjugacy classes of centr…
The Kinetic Gas Theory like two-agent money exchange models, recently introduced in the Econophysics of Wealth distributions, are revisited. The emergence of Boltzmann-Gibbs like distribution of individual money to Pareto's law in the tail of the distribution is examined in terms of 2x2 Transition matrix with a general…
Study detects synthetic tabular data across different tables.
Proves a generalized table theorem for odd Euler characteristic surfaces.
CTSyn generates high-quality synthetic tabular data.
Upper bounds for surface-links in the Yoshikawa table are estimated.
This paper compiles and calculates triple point numbers for surface-links in Yoshikawa's table.
The paper proves geometric properties of square tables and saddle surfaces.
Machine learning speeds up search procedures for sorted tables.
Identifying dependency in multivariate data is a common inference task that arises in numerous applications. However, existing nonparametric independence tests typically require computation that scales at least quadratically with the sample size, making it difficult to apply them to massive data. Moreover, resampling i…
Machine learning recreates the periodic table from element properties.
Method finds differential equations for integrable billiard tables.
Billiard trajectories and geodesics are closely related geometrically.
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 matrices. In this work, we propose to generalize this result by considering the representations…
This document contains tables with the classification of prehomogeneous modules for reductive algebraic groups with up to two simple factors due to Sato, Kimura and many others, as well as corresponding tables of the étale modules appearing in this list, determined by the author. It is intended as a convenient referenc…
BiN normalizes financial time-series for better forecasting.
Descriptive titles provide crucial context for interpreting tables that are extracted from web pages and are a key component of table-based web applications. Prior approaches have attempted to produce titles by selecting existing text snippets associated with the table. These approaches, however, are limited by their d…
This note corrects errors in Hatcher and Oertel's table of boundary slopes of Montesinos knots which have projections with 10 or fewer crossings.
Compactness proven for isospectral Birkhoff billiard tables.
Method combines clustering and matrix completion for missing data in I/O tables.
TableQnA answers web queries about lists and superlatives from HTML tables.
Proposes -table for statistical SHAP explanations in regression models.
The paper presents a new algebraic structure for planar surfaces.
We give a complete characterization of the relationship between the shape of a Euclidean polygon and the symbolic dynamics of its billiard flow. We prove that the only pairs of tables that can have the same bounce spectrum are right-angled tables that differ by an affine map. The main tool is a new theorem that establi…
To study embeddings of tangles in knots, we use quandle cocycle invariants. Computations are carried out for the tables of knots and tangles, to investigate which tangles may or may not embed in knots in the tables.
Robotic table tennis learns efficient policies to return balls at 100Hz.
Open problem: Establishing bounds for Cayley-table completion to discover discrete algorithmic axioms.
Improved method for encoding contingency tables reduces mutual information bias.
We present in this paper experiments on Table Recognition in hand-written registry books. We first explain how the problem of row and column detection is modeled, and then compare two Machine Learning approaches (Conditional Random Field and Graph Convolutional Network) for detecting these table elements. Evaluation wa…
We present a novel approach for estimating conditional probability tables, based on a joint, rather than independent, estimate of the conditional distributions belonging to the same table. We derive exact analytical expressions for the estimators and we analyse their properties both analytically and via simulation. We …
Enumerated all genus two handlebody-knots with seven crossings.
Paper develops a model for verifying facts in tables without pre-retrieved evidence.
We develop a theory of bid and ask price dynamics where the two prices form due to interaction of buy and sell orders. In this model the two prices are represented by eigenvalues of a 2x2 price operator corresponding to "bid" and "ask" eigenstates. Matrix elements of price operator fluctuate in time which results in ph…
Taxicab correspondence analysis visualizes sparse text data sets.
E. Gutkin found a remarkable class of convex billiard tables in the plane which have a constant angle invariant curve. In this paper we prove that in dimension 3 only round sphere has such a property. For dimension greater than 3 it must be either a sphere or to have a very special geometric properties. In 2-dimensiona…
Minimum braids are a complete invariant of knots and links. This paper defines minimum braids, describes how they can be generated, presents tables for knots up to ten crossings and oriented links up to nine crossings, and uses minimum braids to study graph trees, amphicheirality, unknotting numbers, and periodic table…
The paper studies billiards in symmetric tables and finds a measure bound for maximizing orbits.
We introduce a notion of natural orderings of elements of finite connected quandles of order . When the elements of such a quandle are already ordered naturally, any automophism on is a natural ordering. Although there are many natural orderings, the operation tables for such orderings coincide when the perm…
Table of symmetric diagrams for knots up to 10 crossings.
This paper, to be regularly updated, lists those prime knots with the fewest possible number of crossings for which values of basic knot invariants, such as the unknotting number or the smooth 4-genus, are unknown. This list is being developed in conjunction with "KnotInfo" (www.indiana.edu/~knotinfo), a web-based tabl…
If a curve in R^3 is closed, then the curvature and the torsion are periodic functions satisfying some additional constraints. We show that these constraints can be naturally formulated in terms of the spectral problem for a 2x2 matrix differential operator. This operator arose in the theory of the self-focusing Nonlin…