arXiv research

Personalized models explain TB treatment outcomes considering patient context.

Proposes TPIS for early and low-cost TB vs. pneumonia diagnosis.

We investigate Legendrian graphs in $(\R^3, ξ_{std})$. We extend the classical invariants, Thurston-Bennequin number and rotation number to Legendrian graphs. We prove that a graph can be Legendrian realized with all its cycles Legendrian unknots with $tb=-1$ and $rot=0$ if and only if it does not contain $K_4$ as a mi…

Let $ν$ be either the Ozsváth-Szabó $τ$-invariant or the Rasmussen $s$-invariant, suitably normalized. For a knot $K$, Livingston and Naik defined the invariant $t_ν(K)$ to be the minimum of $k$ for which $ν$ of the $k$-twisted positive Whitehead double of $K$ vanishes. They proved that $t_ν(K)$ is bounded above by $-T…

EGDL predicts TB outbreaks with deep learning, integrating epidemiological models.

Let νbe any integer-valued additive knot invariant that bounds the smooth 4-genus of a knot K, |ν(K)| <= g_4(K), and determines the 4-ball genus of positive torus knots, ν(T_{p,q}) = (p-1)(q-1)/2. Either of the knot concordance invariants of Ozsvath-Szabo or Rasmussen, suitably normalized, have these properties. Let D_…

For an integer $n$, write $X_n(K)$ for the 4-manifold obtained by attaching a 2-handle to the 4-ball along the knot $K\subset S^3$ with framing $n$. It is known that if $n< \overline{\text{tb}}(K)$, then $X_n(K)$ admits the structure of a Stein domain, and moreover the adjunction inequality implies there is an upper bo…

Study on hard Legendrian unknots using normal rulings.

The study provides a criterion to compute the total Thurston-Bennequin invariant of Legendrian graphs.

New Legendrian bounds for non-fibered knots in 3-manifolds.

[Original abstract (1992):] The modulus of quasipositivity q(K) of a knot K was introduced as a tool in the knot theory of complex plane curves, and can be applied to Legendrian knot theory in symplectic topology. It has also, however, a straightforward characterization in ordinary knot theory: q(K) is the supremum of …

Machine learning has been an emerging tool for various aspects of infectious diseases including tuberculosis surveillance and detection. However, WHO provided no recommendations on using computer-aided tuberculosis detection software because of the small number of studies, methodological limitations, and limited genera…

Many modern data mining applications are concerned with the analysis of datasets in which the observations are described by paired high-dimensional vectorial representations or "views". Some typical examples can be found in web mining and genomics applications. In this article we present an algorithm for data clusterin…

We study the effect of surgery on transverse knots in contact 3-manifolds. In particular, we investigate the effect of such surgery on open books, the Heegaard Floer contact invariant, and tightness. The overarching theme of this paper is to show that in many contexts, surgery on transverse knots is more natural than s…

DS-FACTO optimizes factorization machines for large-scale datasets.

Constructs Lagrangian skeleta for curve singularities.

Off-policy reinforcement learning with eligibility traces is challenging because of the discrepancy between target policy and behavior policy. One common approach is to measure the difference between two policies in a probabilistic way, such as importance sampling and tree-backup. However, existing off-policy learning …

Legendrian knots can be represented by projections with multi-crossings.

We introduce a new braid-theoretic framework with which to understand the Legendrian and transversal classification of knots, namely a Legendrian Markov Theorem without Stabilization which induces an associated transversal Markov Theorem without Stabilization. We establish the existence of a nontrivial knot-type specif…

New examples of non-simple knots in Lens spaces show rich botany.

We prove that all maximal-tb Legendrian torus links (n,m) in the standard contact 3-sphere, except for (2,m),(3,3),(3,4) and (3,5), admit infinitely many Lagrangian fillings in the standard symplectic 4-ball. This is proven by constructing infinite order Lagrangian concordances which induce faithful actions of the modu…

In this paper we present a new algorithm for computing a low rank approximation of the product $A^TB$ by taking only a single pass of the two matrices $A$ and $B$. The straightforward way to do this is to (a) first sketch $A$ and $B$ individually, and then (b) find the top components using PCA on the sketch. Our algori…

We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning, sparse component analysis, and non-negative matrix factorization. Our algorithm str…

Classifies convex disks with Legendrian boundary in overtwisted contact 3-manifolds.

We classify Legendrian unknots in overtwisted contact structures on $S^3$. In particular, we show that up to contact isotopy for every pair $(n,\pm(n-1))$ with $n>0$ there are exactly two oriented non-loose Legendrian unknots in $S^3$ with Thurston-Bennequin invariant $n$ and rotation number $\pm(n-1)$. (Only one overt…

The paper connects Legendrian links to cluster theory and exact Lagrangian fillings.

Study tied links in various 3-manifolds, introducing new groups and proving theorems.

New techniques reveal tight contact manifolds with vanishing contact homology.

Digital Adherence Technologies (DATs) are an increasingly popular method for verifying patient adherence to many medications. We analyze data from one city served by 99DOTS, a phone-call-based DAT deployed for Tuberculosis (TB) treatment in India where nearly 3 million people are afflicted with the disease each year. T…

Two obstructions found to keep a foliation transverse.

A new model for defective media using two scales.

Single model learns physics from diverse data.

AI and HPC help screen millions of molecules for SARS-CoV-2 treatments.

We consider two principal bundles of embeddings with total space $Emb(M,N),$ with structure groups $Diff(M)$ and $Diff_+(M),$ where $Diff_+(M)$ is the groups of orientation preserving diffeomorphisms. The aim of this paper is to describe the structure group of the tangent bundle of the two base manifolds: $$ B(M,N) = E…

DS-TS adapts to abrupt and smooth changes in bandit problems.

Paper proposes a GPU-based system for training massive deep learning models in ads systems.