arXiv research

New measures for prediction validity and consonant plausibility introduced.

No minimal chart of type (2,3,2) exists.

In this paper we give sufficient conditions that guarantee the meancurvature flow with free boundary on an embedded rotationally symmetric double cone develops a Type 2 curvature singularity. We additionally prove that Type 0 singularities may only occur at infinity.

Quaternionic curves with specific torsion properties don't exist.

Objective: To evaluate unsupervised clustering methods for identifying individual-level behavioral-clinical phenotypes that relate personal biomarkers and behavioral traits in type 2 diabetes (T2DM) self-monitoring data. Materials and Methods: We used hierarchical clustering (HC) to identify groups of meals with simila…

The paper defines a new equivalence relation for knot projections and finds an infinite number of distinct classes.

New method interprets deep embeddings for diabetes patient clustering.

We study Veech surfaces of genus 2 arising from quadratic differentials that are not squares of abelian differentials. We prove that all such surfaces of type (2,2) and (2,1,1) are arithmetic. In (1,1,1,1) case, we reduce the question to abelian differentials of type (2,2) on hyperelliptic genus 3 surfaces with singula…

The paper introduces a new model to correct bias in treatment effect estimates due to sample selection.

Two constructions link path geometries to almost Grassmann structures.

Enhanced fuzzy system predicts chaotic time series with improved accuracy.

In this paper, we study the problem of finding the affine factorable surfaces in a 3-dimensional isotropic space with prescribed Gaussian (K) and mean (H) curvature. Because the absolute figure two different types of these surfaces appear by permutation of coordinates. We firstly classify the affine factorable surfaces…

We establish that, for every hyperbolic orbifold of type (2, q, $\infty$) and for every orbifold of type (2, 3, 4g+2), the geodesic flow on the unit tangent bundle is left-handed. This implies that the link formed by every collection of periodic orbits (i) bounds a Birkhoff section for the geodesic flow, and (ii) is a …

This paper provides a ML framework for diabetes prediction and care management.

This paper determines the braid indices for non-alternating pretzel links.

We prove that non-compact finite volume hyperbolic 3-manifolds that satisfy a mild cohomological condition (infinitesimal rigidity) admit a family of properly convex deformations of their complete hyperbolic structure where the ends become generalized cusps of type 1 or type 2. We also discuss methods for controlling w…

Background: Predictive modeling is a key component of solutions to many healthcare problems. Among all predictive modeling approaches, machine learning methods often achieve the highest prediction accuracy, but suffer from a long-standing open problem precluding their widespread use in healthcare. Most machine learning…

Paper extends Bayes Theorem for interval probability estimates.

According to the American Diabetes Association(ADA), 30.3 million people in the United States have diabetes, but only 7.2 million may be undiagnosed and unaware of their condition. Type 2 diabetes is usually diagnosed for most patients later on in life whereas the less common Type 1 diabetes is diagnosed early on in li…

HAD-Net forecasts glucose levels with insights into insulin and carbs diffusion.

New examples of hyperbolic links with generalized torsion elements found.

A new algorithm discovers causal factors between T2DM and bone mineral density.

In this note we present a short proof that the 4 oriented Reidemeister moves of type 2 together with any one of the 8 oriented Reidemeister moves of type 3 are sufficient to imply the other 7.

PseudoH-type is a natural generalization of H-type to geometries with indefinite metric tensors. We give a complete determination of the conjugate locus including multiplicities. We also obtain a partial characterization in terms of the abundance of totally geodesic, 3-dimensional submanifolds.

A new GP framework for discovering unknown functions and hypergraph structure.

New method targets relative risk heterogeneity in clinical trials.

Given an almost complex manifold (M, J), we study complex connections with trivial holonomy and such that the corresponding torsion is either of type (2,0) or of type (1,1) with respect to J. Such connections arise naturally when considering Lie groups, and quotients by discrete subgroups, equipped with bi-invariant an…

The paper examines how calibration affects the interpretability of ML models in diabetes screening.

We present a combinatorial method for a calculation of knot Floer homology with Z-coefficient of (1,1)-knots, and then demonstrate it for non-alternating (1,1)-knots with ten crossings and the pretzel knots of type (-2,m,n). Our calculations determine the unknotting numbers and 4-genera of the pretzel knots of this typ…

Almost para-quaternionic structures on smooth manifolds of dimension $2n$ are equivalent to almost Grassmannian structures of type $(2,n)$. We remind the equivalence and exhibit some interrelations between subjects that were previously studied independently from the para-quaternionic and the Grassmannian point of view.…

Type 2 Diabetes (T2D) is a chronic metabolic disorder that can lead to blindness and cardiovascular disease. Information about early stage T2D might be present in retinal fundus images, but to what extent these images can be used for a screening setting is still unknown. In this study, deep neural networks were employe…

Study completes braid index determination for all pretzel links.

Fuzzy eIX method evolves classifiers for online data streams.

Data augmentation improves microbiome disease prediction.

2 Diabetes is a leading worldwide public health concern, and its increasing prevalence has significant health and economic importance in all nations. The condition is a multifactorial disorder with a complex aetiology. The genetic determinants remain largely elusive, with only a handful of identified candidate genes. G…

New method improves PCA robustness using Wasserstein distances.

Develops methods for near-optimal personalized treatment recommendations.

Minimizes indecisions in selective classification to control misclassification rates.

This paper gives an alternate definition of the Affine Index Polynomial (called the Wriggle Polynomial) using virtual linking numbers and explores applications of this polynomial. In particular, it proves the Cosmetic Crossing Change Conjecture for odd virtual knots and pure virtual knots. It also demonstrates that the…

Develops a SAS approach for high-dimensional risk prediction using unlabeled data.

We give a complete description of exceptional surgeries on pretzel knots of type $(-2, p, p)$ with $p \ge 5$. It is known that such a knot admits a unique toroidal surgery yielding a toroidal manifold with a unique incompressible torus. By cutting along the torus, we obtain two connected components, one of which is a t…

Study bihamiltonian structures and Frobenius manifolds for specific Toda hierarchies.

We determine the Fukaya Floer homology of the three-manifold which is the product of a Riemann surface of genus $g\geq 1$ times the circle. This sets up the groundwork for finding the structure of the Donaldson invariants of four-manifolds not of simple type in the future. We give the following applications: 1) We show…

Let $M$ be a compact manifold. and $D$ a Dirac type differential operator on $M$. Let $A$ be a $C^*$-algebra. Given a bundle $W$ of $A$-modules over $M$ (with connection), the operator $D$ can be twisted with this bundle. One can then use a trace on $A$ to define numerical indices of this twisted operator. We prove an …

The paper studies cylindrical handlebody-knots of genus two with unique unknotting annuli and finds trivial symmetry groups.

Study on 2-ruled hypersurfaces in a Walker 4-manifold.

In this paper we study the stochastic evolution equation (1.1) in martingale-type 2 Banach spaces (with the linear part of the drift being only a generator of a C0-semigroup). We prove the existence and the uniqueness of solutions to this equation. We apply the abstract results to the Heath-Jarrow-Morton-Musiela (HJMM)…

Study $Θ$-invariants for spherical 3-manifolds via $\mathbb{Z}π$-homology equivalences.