arXiv research

Study shows non-existence of certain contact structures on odd-dimensional manifolds.

Improved analysis for nonconvex SGD methods with flexible sampling.

We explain a connection between the algebraic and geometric properties of groups of contact transformations, open book decompositions, and flexible Legendrian embeddings. The main result is that, if a closed contact manifold $(V, ξ)$ has a supporting open book whose pages are flexible Weinstein manifolds, then the conn…

Alternative proof of Dynnikov's three-page index for torus links.

PAGE optimizes nonconvex problems with optimal convergence rates.

The paper refines the three-page index for links, proving a new bound and characterizing specific links.

Study the spectrum of Page's metric on complex projective spaces.

Optimizes web page freshness with limited crawling frequencies.

We construct a series of finitely presented semigroups. The centers of these semigroups encode uniquely up to rigid ambient isotopy in 3-space all non-oriented spatial graphs. This encoding is obtained by using three-page embeddings of graphs into the product of the line with the cone on three points. By exploiting thr…

Extracts main content from web pages using neural sequence labeling.

Extends deformation theory to higher-page analogues of manifolds.

Improved linear upper bound for ribbonlength of knots.

PAGE is a simple gradient estimator for nonconvex optimization problems.

New invariant distinguishes Legendrian surfaces in 5-manifolds.

The spectral sequence's $E_k$-page is a link invariant for $k\ge 3$.

We construct a contact 5-manifold supported by infinitely many distinct open books with the identity monodromy and pairwise exotic Stein pages (i.e. pages are pairwise homeomorphic but non-diffeomorphic Stein fillings of a fixed contact 3-manifold), moreover we describe a process of generating infinitely many such exam…

Optimization is commonly employed to determine the content of web pages, such as to maximize conversions on landing pages or click-through rates on search engine result pages. Often the layout of these pages can be decoupled into several separate decisions. For example, the composition of a landing page may involve dec…

In this paper, we study some classes of submanifolds of codimension one and two in the Page space. These submanifolds are totally geodesic. We also compute their curvature and show that some of them are constant curvature spaces. Finally we give information on how the Page space is related to some other metrics on the …

Generative models predict page quality without training, useful for low-resource settings.

CUQ-GNN adapts uncertainty quantification for graph data, improving on GPN.

The paper extends Hawking--Page solutions to various spacetimes with singularities.

Scalable web crawling using noisy change-indicating signals.

Freya PAGE optimizes nonconvex optimization with heterogeneous, asynchronous workers.

TailedTS dataset benchmarks heavy-tailed time series forecasting and periodicity quantification.

Unified framework for discrete diffusion modeling with flexible noising processes.

We construct, somewhat non-standard, Legendrian surgery diagrams for some Stein fillable contact structures on some plumbing trees of circle bundles over spheres. We then show how to put such a surgery diagram on the pages of an open book for $S^3,$ with relatively low genus. Thus we produce open books with low genus p…

A new bandit algorithm for web page item display.

Algorithm constructs Kirby diagrams for 4D open books.

In this note, we define a new invariant of a Legendrian knot in a contact manifold using an open book decomposition supporting the contact structure. We define the support genus sg(L) of a Legendrian knot L in a contact 3-manifold (M, ξ) as the minimal genus of a page of an open book of M supporting the contact structu…

In this note we define three invariants of contact structures in terms of open books supporting the contact structures. These invariants are the support genus (which is the minimal genus of a page of a supporting open book for the contact structure), the binding number (which is the minimal number of binding components…

New non-Kähler manifolds constructed with specific properties.

Study homotopy groups of open books and their pages, pages, and bindings.

Given any closed, connected, orientable $3$--manifold and integers $g\geq g(M), D > 0$, we show the existence of knots in $M$ whose genus $g$ bridge number is greater than $D$. These knots lie in a page of an open book decomposition of $M$, and the proof proceeds by examining the action of the map induced by the monodr…

The project aims to research on combining deep learning specifically Long-Short Memory (LSTM) and basic statistics in multiple multistep time series prediction. LSTM can dive into all the pages and learn the general trends of variation in a large scope, while the well selected medians for each page can keep the special…

Study on embeddings of surfaces in 4-manifolds and their mapping classes.

The contents of this 98-page paper have been subsumed into the 191-page paper "A colored sl(N)-homology for links in S^3" (arXiv:0907.0695v1 [math.GT]), in which we further develop the theory and use it to construct a colored link homology.

Mozilla Research is developing Servo, a parallel web browser engine, to exploit the benefits of parallelism and concurrency in the web rendering pipeline. Parallelization results in improved performance for pinterest.com but not for google.com. This is because the workload of a browser is dependent on the web page it i…

Recently, the development and implementation of phishing attacks require little technical skills and costs. This uprising has led to an ever-growing number of phishing attacks on the World Wide Web. Consequently, proactive techniques to fight phishing attacks have become extremely necessary. In this paper, we propose H…

Study on stability of minimal submanifolds in specific Einstein manifolds.

A spectral sequence is established, whose $E_{2}$ page is Bar-Natan's variant of Khovanov homology and which abuts to a deformation of instanton homology for knots and links. This spectral sequence arises as a specialization of a spectral sequence whose $E_{2}$ page is a characteristic-2 version of $F_{5}$ homology, in…

On a compact $\partial\bar\partial$-manifold $X$, one has the Hodge decomposition: the de Rham cohomology groups split into subspaces of pure-type classes as $H_{dR}^k (X)=\oplus_{p+q=k}H^{p,\,q}(X)$, where the $H^{p,\,q}(X)$ are canonically isomorphic to the Dolbeault cohomology groups $H_{\bar\partial}^{p,\,q}(X)$. F…

A search engine recommends to the user a list of web pages. The user examines this list, from the first page to the last, and clicks on all attractive pages until the user is satisfied. This behavior of the user can be described by the dependent click model (DCM). We propose DCM bandits, an online learning variant of t…

Introduces new cohomologies on complex manifolds, extending classical Bott-Chern and Aeppli.

We show that the page at which the Lee spectral sequence collapses gives a bound on the unknotting number, u(K). In particular, for knots with u(K)<3, we show that the Lee spectral sequence must collapse at the E_2 page. An immediate corollary is that the Knight Move Conjecture is true when u(K)<3.

This paper presents a Convolutional Neural Network (CNN) based page segmentation method for handwritten historical document images. We consider page segmentation as a pixel labeling problem, i.e., each pixel is classified as one of the predefined classes. Traditional methods in this area rely on carefully hand-crafted …

Classifies Einstein metrics on 4-manifolds with specific symmetry groups.

Paper tackles score following in full-page sheet music images.

We prove that the quasi-Einstein metrics found by Lü, Page and Pope on $\mathbb{C}P^{1}$-bundles over Fano Kähler-Einstein bases are conformally Kähler and that the Kähler class of the conformal metric is a multiple of the first Chern class. A detailed study of the lowest-dimensional example of such metrics on $\mathbb…