Study knots with large SL2(C) character varieties.
problem Knots with high-dimensional character varieties.
method Two diagrammatic constructions: split link diagrams and rational tangle replacements; braids and orientation-reversing involutions.
result Conjecture that all Turk's head knots Th(p,q) with p and q odd are X-large. The paper finds new graph covers with exceptionally low degree.
problem Graph covers with primitive homology not spanned by lifts.
method Focused on finite p-group deck groups, developed a character table-based algorithm. result Found the smallest known nontrivial examples with covering degree 128.
This paper describes a conditional neural network architecture for Mandarin Chinese polyphone disambiguation. The system is composed of a bidirectional recurrent neural network component acting as a sentence encoder to accumulate the context correlations, followed by a prediction network that maps the polyphonic charac…
For statistical learning, categorical variables in a table are usually considered as discrete entities and encoded separately to feature vectors, e.g., with one-hot encoding. "Dirty" non-curated data gives rise to categorical variables with a very high cardinality but redundancy: several categories reflect the same ent…
Revisit Fenn's table theorem from a differential-topological perspective.
problem Prove zero-existence theorem on a cylinder and horizontal square-table theorem under Fenn's boundary conditions.
method Differential-topological approach.
result Prove horizontal square-table theorem under more general boundary conditions.
Study detects synthetic tabular data across different tables.
problem Detecting synthetic tabular data in varied tables.
method Four table-agnostic detectors combined with preprocessing schemes.
result Cross-table learning possible with naive preprocessing, but cross-table transfer challenging.
Proves a generalized table theorem for odd Euler characteristic surfaces.
problem Proving a generalized table theorem for surfaces with odd Euler characteristic.
method Using the square peg problem for smooth curves, the result is generalized to real valued functions on Riemannian surfaces with odd Euler characteristic.
result Proves the table conjecture for even functions on the two sphere.
CTSyn generates high-quality synthetic tabular data.
problem Challenges in generating high-quality synthetic tabular data.
method Diffusion-based generative foundation model with autoencoder and conditional latent diffusion.
result CTSyn outperforms existing table synthesizers on standard benchmarks.
Upper bounds for surface-links in the Yoshikawa table are estimated.
problem Estimating Kirby-Thompson invariants of surface-links.
method Using tri-plane diagrams and L-, L*-invariants.
result Upper bounds for surface-links in the Yoshikawa table are obtained.
This paper compiles and calculates triple point numbers for surface-links in Yoshikawa's table.
problem Determining the triple point number of surface-links in Yoshikawa's table.
method Using broken sheet diagrams, the paper compiles known triple point numbers and calculates or bounds the remaining ones.
result Compilation and calculation of triple point numbers for surface-links in Yoshikawa's table.
The paper proves geometric properties of square tables and saddle surfaces.
problem The mathematical table problem from a geometric-topological perspective.
method Geometric-topological proofs on cylinder, saddle surfaces, and level sets of Fenn graphs.
result Zero-existence theorem on a cylinder, proving Fenn's square-table theorem under different boundary conditions.
Machine learning speeds up search procedures for sorted tables.
problem Improving the speed of sorted table search procedures.
method Systematic experimental comparison of efficient implementations with learned counterparts.
result Learned data structures can significantly speed up search procedures.
Machine learning recreates the periodic table from element properties.
problem Recreating the periodic table using machine learning.
method Unsupervised machine learning with GTM for feature embedding.
result PTG autonomously generates various periodic table layouts.
Method finds differential equations for integrable billiard tables.
problem Finding differential equations for integrable billiard tables.
method Introducing a method to find differential equations for functions defining tables.
result Illustrated method in three billiard systems.
Billiard trajectories and geodesics are closely related geometrically.
problem Understanding the relationship between billiard trajectories and geodesics on surfaces.
method Establishing mutual approximation results for billiard trajectories and geodesic segments on surfaces.
result For Riemannian billiard tables, there are families of fold-type surfaces such that every sequence of geodesic segments on these surfaces has a subsequence that converges to a billiard trajectory.
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.
problem Non-stationarity and multimodality in financial time-series data.
method Bilinear Normalization (BiN) incorporated into TABL networks.
result BiN-TABL outperforms other normalization methods in financial 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.
problem Proving compactness of isospectral Birkhoff billiard tables.
method Derived a hierarchical structure for integral invariants and used interpolating Hamiltonian.
result Compactness of equivalence classes of marked length isospectral Birkhoff billiard tables.
Method combines clustering and matrix completion for missing data in I/O tables.
problem Reconstructing missing entries in World Input-Output (I/O) matrices due to data collection issues.
method Hierarchical clustering and Matrix Completion with LASSO-like nuclear norm penalty.
result The method effectively predicts missing values from previous and similar countries' data.
TableQnA answers web queries about lists and superlatives from HTML tables.
problem Answer web queries about lists and superlatives from HTML tables.
method Extract intent from queries, use structure-aware matching, and train models with automatic data generation.
result Significantly higher precision and coverage for list and superlative queries.
Proposes φ-table for statistical SHAP explanations in regression models.
problem Lack of clear directional summaries, uncertainty, and fidelity in SHAP feature importance.
method SHAP importance selection, fitting a standardized linear surrogate, reporting coefficients, uncertainty, fidelity, and stability.
result Extends SHAP into a statistical global explanation with direction, uncertainty, fidelity, and stability.
An explicit solution found for maximizing/minimizing agreement in a 2x2 table.
problem Maximizing or minimizing agreement between clusterings with given marginals.
method Formal framework for several agreement measures, explicit solution for 2x2 table.
result An explicit solution for the 2x2 case.
New neural network layer handles OOV words in NLP tasks without pre-training.
problem Handling out-of-vocabulary words in natural language processing.
method Contextual-compositional neural network layer that attends to character sequence and context.
result Improves performance on 23 languages in joint tagging tasks.
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.
problem Developing efficient robotic table tennis strategies.
method Model-free reinforcement learning using evolutionary search on CNN-based policies.
result Robots can develop multi-modal styles (forehand and backhand) with 80% return rate.
Open problem: Establishing bounds for Cayley-table completion to discover discrete algorithmic axioms.
problem Discovering discrete algorithmic axioms missing in deep learning.
method Cayley-table completion as a testbed for algorithmic complexity minimization.
result Formal exact recovery bounds for Cayley-table completion.
Improved method for encoding contingency tables reduces mutual information bias.
problem Mutual information bias in measuring label similarity.
method Improved method for encoding contingency tables to reduce information cost.
result Better bound on reduced mutual information in typical use cases.
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.
problem Counting genus two handlebody-knots with specific crossings.
method Extending an existing table of genus two handlebody-knots.
result Enumerated all genus two handlebody-knots with seven crossings.
Paper develops a model for verifying facts in tables without pre-retrieved evidence.
problem Verification of factual claims in structured data, especially in open-domain settings.
method Joint reranking-and-verification model that fuses evidence documents.
result Model achieves comparable performance to closed-domain state-of-the-art on TabFact dataset.
Taxicab correspondence analysis visualizes sparse text data sets.
problem Visualization of extremely sparse contingency tables.
method Robust variant of correspondence analysis for sparse data.
result Visualized an 8265-dimensional textual data set.
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…
The theory of differential characters is developed completely from a de Rham - Federer viewpoint. Characters are defined as equivalence classes of special currents, called sparks, which appear naturally in the theory of singular connections. There are many different spaces of currents which yield the character groups. …
The paper studies billiards in symmetric tables and finds a measure bound for maximizing orbits.
problem Understanding the measure of maximizing orbits in symmetric billiard tables.
method Introduced a closed invariant set of locally maximizing orbits and gave an effective bound on its measure.
result An effective bound on the measure of the invariant set in terms of the isoperimetric defect of the curve.
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…
Character scheme of small Seifert 3-manifolds is reduced if and only if no exceptional abelian character exists.
problem Character scheme of small Seifert 3-manifolds and its reduction condition.
method Complete description of the SL2(C)-character scheme of small Seifert 3-manifolds.
result Character scheme is reduced if and only if no exceptional abelian character exists, and exceptional abelian character has multiplicity 2.
We introduce a notion of natural orderings of elements of finite connected quandles of order n. When the elements of such a quandle Q are already ordered naturally, any automophism on Q 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.
problem Finding symmetric diagrams for strongly invertible knots.
method Compilation of symmetric diagrams for knots up to 10 crossings.
result Similarity of transversal diagrams to symmetric union diagrams for strongly invertible knots.
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…
Quantum character varieties unify four construction methods.
problem No specific problem stated; unification of approaches.
method Four different approaches to construction.
result Unified understanding of quantum character varieties.
We show that for any knot there exist only finitely many irreducible metabelian characters in the SL(2,C)-character variety of the knot group, and the number is given explicitly by using the determinant of the knot. Then it turns out that for any 2-bridge knot a section of the SL(2,C)-character va…
Study of orbifold Chern character using superconnections.
problem Chern character for orbifold settings.
method Use of flat antiholomorphic superconnections and Riemann-Roch-Grothendieck theorem.
result Uniqueness of orbifold Chern character proven.
Character varieties get a natural Poisson structure.
problem Character varieties of surfaces.
method Natural Poisson structure.
result Character varieties have a Poisson structure.
SAVeD detects dataset versions without metadata, improving accuracy and separation.
problem Difficulty in identifying similar versions of structured datasets.
method Contrastive learning with modified SimCLR pipeline, generating and contrasting augmented table views.
result SAVeD achieves higher accuracy and separation scores on unseen tables.