arXiv research

We give various results and applications using the connection $(E,\nabla)$ associated with a $d$-web. Precisely, we exhibit fundamental invariants of the web related to the differential equation of first order which presents the web. They cast some new lights on the connection and its construction, both conceptually an…

Locality-sensitive hashing speeds up web app security testing.

We investigate the space of abelian relations of planar webs admitting infinitesimal automorphisms. As an application, we construct 4k-14 new algebraic families of global exceptionnal k-webs on the projective plane, for each k >4.

Study local invariants of divergence-free webs in geometry.

The curvature of web curves is studied in 3D manifolds.

Efficiently projects points onto polytopes, especially useful in web-scale applications.

The study establishes a criterion for the holomorphy of curvature in smooth webs and applies it to dual webs of homogeneous foliations.

Extracts main content from web pages using neural sequence labeling.

Generative model improves web table titles.

New invariants detect a specific graph in spatial webs.

Developed R package for creating nomograms for any ML algorithms.

Transfer learning improves understanding of users on new Web platforms.

Donut detects anomalies in web KPIs without labels.

A family of algebraic curves covering a projective variety $X$ is called a web of curves on $X$ if it has only finitely many members through a general point of $X$. A web of curves on $X$ induces a web-structure, in the sense of local differential geometry, in a neighborhood of a general point of $X$. We study how the …

We propose the Legendrian web in a contact three manifold as a second order generalization of the planar web. An Abelian relation for a Legendrian web is analogously defined as an additive equation among the first integrals of its foliations. For a class of Legendrian $\, d$-webs defined by simple second order ODE's, w…

Machine learning detects survey validity from user behavior.

In this paper we define an explicit basis for the $\mathfrak{gl}_n$-web algebra $H_n(\vec{k})$ (the $\mathfrak{gl}_n$ generalization of Khovanov's arc algebra) using categorified $q$-skew Howe duality. Our construction is a $\mathfrak{gl}_n$-web version of Hu--Mathas' graded cellular basis and has two major application…

Formula calculates MOY webs and link polynomials.

We find an invariant characterization of planar webs of maximum rank. For 4-webs, we prove that a planar 4-web is of maximum rank three if and only if it is linearizable and its curvature vanishes. This result leads to the direct web-theoretical proof of the Poincaré's theorem: a planar 4-web of maximum rank is lineari…

Paper introduces a new web robot traffic generator.

Classifies hexagonal circular 3-webs with cubic polar curves.

We construct flat 3-webs via semi-simple geometric Frobenius manifolds of dimension three and give geometric interpretation of the Chern connection of the web. These webs turned out to be biholomorphic to the characteristic webs on the solutions of the corresponding associativity equation. We show that such webs are he…

We investigate the linearizability problem for different classes of 4-webs in the plane. In particular, we apply a recently found in [AGL] the linearizability conditions for 4-webs in the plane to confirm that a 4-web MW (Mayrhofer's web) with equal curvature forms of its 3-subwebs and a nonconstant basic invariant is …

In the present paper we study geometric structures associated with webs of hypersurfaces. We prove that with any geodesic (n+2)-web on an n-dimensional manifold there is naturally associated a unique projective structure and, provided that one of web foliations is pointed, there is also associated a unique affine struc…

Projective invariants described for 3-web geometry, resolving Gronwall's conjecture.

New instanton homology for webs counts Tait colorings.

We define parameter dependent $\mathfrak{gl}_2$-foams and their associated web and arc algebras, and verify that they specialize to several known $\mathfrak{sl}_2$ or $\mathfrak{gl}_2$ constructions related to higher link and tangle invariants. Moreover, we show that all these specializations are equivalent, and we ded…

This paper has been withdrawn by the authors due to the fact that the webs considered in the paper are ``Veronese-like webs'' which are different from Veronese webs.

Investigates webs related to cluster algebras and polylogarithms.

Investigates stochastic networks on disordered lattices, converging to Brownian web in 2D.

Much information available on the web is copied, reused or rephrased. The phenomenon that multiple web sources pick up certain information is often called trend. A central problem in the context of web data mining is to detect those web sources that are first to publish information which will give rise to a trend. We p…

For a four-dimensional (nonisoclinicly geodesic) three-web W (3, 2, 2), a transversal distribution $Δ$ is defined by the torsion tensor of the web. In general, this distribution is not integrable. The authors find necessary and sufficient conditions of its integrability and prove the existence theorem for webs W (3, 2,…

In this paper we study the linearizability problem for 3-webs on a 2-dimensional manifold. With an explicit computation based on the theory developed in the paper "On the linearizability of 3-webs" (Nonlinear analysis 47, (2001) pp. 2643-2654), we examine a 3-web whose linearizability was claimed in the same paper. We …

Veronese webs appear as the natural way of passing to the quotient of curves in the projective space. In thi paper, we give the link between classical multidimensionnal webs and veronse webs by mean of interpolation.

New hexagonal circular 3-webs with reducible curves classified.

In this paper, we reconstruct Kuperberg's $G_2$ web space. We introduce a new web (a trivalent diagram) and new relations between Kuperberg's web diagrams and the new diagram. Using the $G_2$ webs, we define crossing formulas corresponding to R-matrices associated to some $G_2$ irreducible representations and calculate…

In probabilistic approaches to classification and information extraction, one typically builds a statistical model of words under the assumption that future data will exhibit the same regularities as the training data. In many data sets, however, there are scope-limited features whose predictive power is only applicabl…

A 3-web is linearizable, resolving a controversy.

New method infers missing categorical data from Web markup.

Gronwall conjecture states that a planar 3-web which admits more than one distinct linearization is locally equivalent to an algebraic web. We give a partial answer to the conjecture in the affirmative for the class of planar 3-webs with the web curvature that vanishes to order three at a point. The differential relati…

We find relative differential invariants of orders eight and nine for a planar nonparallelizable 3-web such that their vanishing is necessary and sufficient for a 3-web to be linearizable. This solves the Blaschke conjecture for 3-webs. As a side result, we show that the number of linearizations in the Gronwall conject…

GANs generate realistic cosmic web models in seconds, overcoming computational limits.

Geodesic flows with specific integrals are linked to special 4-webs.

Geometrically interprets integrability of geodesic flow using web theory.

The Gronwall conjecture states that a planar 3-web of foliations which admits more than one distinct linearizations is locally equivalent to an algebraic web. We propose an analogue of the Gronwall conjecture for the 3-web of foliations by Legendrian curves in a contact three manifold. The Legendrian Gronwall conjectur…

Voice-controlled e-commerce app enhances user experience for visually impaired.

We study non-flat planar 3-webs with infinitesimal symmetries. Using multi-dimensional Schwarzian derivative we give a criterion for linearization of such webs and present a projective classification thereof. Using this classification we show that the Gronwall conjecture is true for 3-webs admitting infinitesimal symme…

Proves Nakai webs have rank 0 or 1, provides examples.