arXiv research

Modern e-commerce catalogs contain millions of references, associated with textual and visual information that is of paramount importance for the products to be found via search or browsing. Of particular significance is the book category, where the author name(s) field poses a significant challenge. Indeed, books writ…

A new method for name disambiguation in academic networks using multi-view attention and recurrent neural networks.

In supervised machine learning for author name disambiguation, negative training data are often dominantly larger than positive training data. This paper examines how the ratios of negative to positive training data can affect the performance of machine learning algorithms to disambiguate author names in bibliographic …

This work addresses the problem of author name homonymy in the Web of Science. Aiming for an efficient, simple and straightforward solution, we introduce a novel probabilistic similarity measure for author name disambiguation based on feature overlap. Using the researcher-ID available for a subset of the Web of Science…

The authors derive a McShane identity for once-punctured super tori. Relying upon earlier work on super Teichmüller theory by the last two-named authors, they further develop the supergeometry of these surfaces and establish asymptotic growth rate of their length spectra.

We conjecture a Verlinde type formula for the moduli space of Higgs sheaves on a surface with a holomorphic 2-form. The conjecture specializes to a Verlinde formula for the moduli space of sheaves. Our formula interpolates between $K$-theoretic Donaldson invariants studied by the first named author and Nakajima-Yoshiok…

Author name disambiguation in bibliographic databases is the problem of grouping together scientific publications written by the same person, accounting for potential homonyms and/or synonyms. Among solutions to this problem, digital libraries are increasingly offering tools for authors to manually curate their publica…

We review the state of the art of our understanding of the conformal geometry of the irrational rotation algebra. This was sparked by a paper by Cohen and Connes. We review the more recent progress made by Connes and the second named author and the work of the authors of this review.

Survey on complex Monge-Ampère equations in Hermitian contexts.

We complete the classification, initiated by the second named author, of homogeneous singular Riemannian foliations of spheres that are lifts of foliations produced from Clifford systems.

The author proposes a finance trading strategy named Entropy Oriented Trading and apply thermodynamics on the strategy. The state variables are chosen so that the strategy satisfies the second law of thermodynamics. Using the law, the author proves that the rate of investment (ROI) of the strategy is equal to or more t…

In this paper we investigate the differential geometric and algebro-geometric properties of the noncollapsing limit in the continuity method that was introduced by the first two named authors in \cite{LaTi14}.

Researchers prove rigidity of first conformal Steklov eigenvalue on specific shapes.

We present a procedure for asymptotic gluing of hyperboloidal initial data sets that preserves the shear-free condition. Our construction is modeled on a previous gluing construction by the last three named authors, but with significant modifications that incorporate the shear-free condition. We rely on the special Höl…

The paper proves a unique orbit for a specific genus 3 curve.

Constructs minimal surfaces in balls, maximizing eigenvalues.

Extends complex manifold structures to line bundles, revealing new projective manifolds.

We construct prime amphicheiral knots that have free period 2. This settles an open question raised by the second named author, who proved that amphicheiral hyperbolic knots cannot admit free periods and that prime amphicheiral knots cannot admit free periods of order >2.

Study convolution of invariant valuations on Lie groups.

2-dimensional knots and links are studied in the article. The notion of parity is introduced via techniques similar to the ones used by the second named author in 1-dimensional case. By using parity new invariants are constructed and known invariants are refined.

Completes classification of G2-structures on specific nilpotent Lie groups.

Motivated by a previous work of Zheng and the second named author, we study pinching constants of compact Kähler manifolds with positive holomorphic sectional curvature. In particular we prove a gap theorem following the work of Petersen and Tao on Riemannian manifolds with almost quarter-pinched sectional curvature.

This paper completes the classification of certain nilpotent Lie groups with specific geometric structures.

We construct a weak 2-functor from the bicategory of oriented tangles to a bicategory of Lagrangian cospans. This functor simultaneously extends the Burau representation of the braid groups, its generalization to tangles due to Turaev and the first-named author, and the Alexander module of 1 and 2-dimensional links.

In this paper we survey some recent contributions by the authors to the theory of null holomorphic curves in the complex Euclidean space $\mathbb C^3$, as well as their applications to null holomorphic curves in the special linear group $SL_2(\mathbb C)$, minimal surfaces in the Euclidean space $\mathbb R^3$, and const…

In this paper we show that the Chern numbers of a smooth Mori fibre space in dimension three are bounded in terms of the underlying topological manifold. We also generalise a theorem of Cascini and the second named author on the boundedness of Chern numbers of certain threefolds to the case of negative Kodaira dimensio…

Linking authors of short-text contents has important usages in many applications, including Named Entity Recognition (NER) and human community detection. However, certain challenges lie ahead. Firstly, the input short-text contents are noisy, ambiguous, and do not follow the grammatical rules. Secondly, traditional tex…

We prove the spacetime positive mass theorem in dimensions less than eight. This theorem states that for any asymptotically flat initial data set satisfying the dominant energy condition, the ADM energy-momentum vector $(E,P)$ of the initial data satisfies the inequality $E \ge |P|$. Previously, this theorem was proven…

Authors prove quantum invariant conjecture for figure-eight knot complement.

Targeting a better understanding of credit market dynamics, the authors have studied a stochastic model named the Hawkes process. Describing trades arrival times, this kind of model allows for the capture of self-excitement and mutual interactions phenomena. The authors propose here a simple yet conclusive method for f…

It is shown that the mass of an asymptotically flat manifold with a noncompact boundary can be computed in terms of limiting surface integrals involving the Einstein tensor of the interior metric and the Newton tensor attached to the second fundamental form of the boundary. This extends to this setting previous results…

This paper develops Yang-Mills flow on Riemannian manifolds with special holonomy. By analogy with the second-named author's thesis, we find that a supremum bound on a certain curvature component is sufficient to rule out finite-time singularities. Assuming such a bound, we prove that the infinite-time bubbling set is …

We survey the 19th century development of the signature of a quadratic form, and the applications in the 20th and 21st century to the topology of manifolds and dynamical systems. Version 2 is an expanded and corrected version of Version 1, including an Appendix by the second named author "Algebraic L-theory of rings wi…

The authors study the geometry of lightlike hypersurfaces on pseudo-Riemannian manifolds $(M, g)$ of Lorentzian signature. Such hypersurfaces are of interest in general relativity since they can be models of different types of physical horizons. For a lightlike hypersurface $V \subset (M, g)$ of general type and for so…

We extend the Lyapunov-Schmidt analysis of outlying stable CMC spheres in the work of S. Brendle and the second-named author to the "far-off-center" regime and to include general Schwarzschild asymptotics. We obtain sharp existence and non-existence results for large stable CMC spheres that depend very delicately on th…

This is an expository article which describes one approach to the construction and classification of harmonic tori "of finite type", namely, via their ring of polynomial Killing fields. To keep the discussion focussed, the first section is devoted entirely to non-conformal harmonic tori in the 2-sphere. The second sect…

Reduces conjecture for Artin groups to simpler cases.

Fix a K3 lattice $Λ$ of rank two and $L\inΛ$ a big and nef divisor that is positive enough. We prove that the generic $Λ$-polarised K3 surface has an integral nodal rational curve in the linear system $|L|$, in particular strengthening previous work of the first named author. The technique is by degeneration, and also …

Extends deformation theory to higher-page analogues of manifolds.

We give a complete solution of a problem in submanifold theory posed and partially solved by the eminent algebraic geometer Pierre Samuel in 1947. Namely, to determine all pairs of immersions of a given manifold into Euclidean space that have the same Gauss map and induce conformal metrics on the manifold. The case of …

Researchers solved the multiple fibration problem for Seifert 3-orbifolds.

The number of colorings of a knot diagram by a quandle has been shown to be a knot invariant by CJKLS using quandle cohomology methods. In a previous paper by the second named author, the CJKLS invariant was refined and, in particular, it was shown that the number of colorings is an invariant directly without resorting…

This is a substantially revised version. The Kontsevich integral of a knot is a graph-valued invariant which (when graded by the Vassiliev degree of graphs) is characterized by a universal property; namely it is a universal Vassiliev invariant of knots. We introduce a second grading of the Kontsevich integral, the Eule…

Proves finitely generated graded rings for klt singularities.

A natural question in mathematical general relativity is how the ADM mass behaves as a functional on the space of asymptotically flat 3-manifolds of nonnegative scalar curvature. In previous results, lower semicontinuity has been established by the first-named author for pointed $C^2$ convergence, and more generally by…

This exposition gives an introduction to the theory of surfaces in Laguerre geometry and surveys some results, mostly obtained by the authors, about three important classes of surfaces in Laguerre geometry, namely L-isothermic, L-minimal, and generalized L-minimal surfaces. The quadric model of Lie sphere geometry is a…

This paper is a continuation of our work on theta and zeta functions In the previous papers we considered the case of even dimensional rank one symmetric spaces of non-compact type. The present is concerned with the odd-dimensional case, i.e. with odd-dimensional real hyperbolic manifolds. It is the natural appearence …

P. Baird and the second author studied harmonic morphisms from a three-dimensional simply-connected space form to a surface and obtained a complete local and global classification of them. In this paper, we obtain a description of all harmonic morphisms from any three-dimensional Euclidean and spherical space form to a…