arXiv research

Deep learning models predict postoperative complications more accurately than random forests.

Solar improves variable selection in high-dimensional data with complicated dependence structures.

Paper proposes a multi-task learning approach to predict multiple diabetes complications.

New model detects postoperative complications early after surgery.

Let M_1 and M_2 be compact, orientable 3-manifolds with incompressible boundary, and M the manifold obtained by gluing with a homeomorphism $φ:\bdy M_1 \to \bdy M_2$. We analyze the relationship between the sets of low genus Heegaard splittings of M_1, M_2, and M, assuming the map φis "sufficiently complicated." This a…

Study describes severe dengue ICU patients in Brazil, 2012-2024.

We describe the fundamental groups of ordered and unordered k point sets in complex projective space of dimension n generating a projective subspace of dimension i. We apply these to study connectivity of more complicated configurations of points.

Authors construct an example of a Schottky group of rank three.

AI identifies patient clusters for diabetes case management.

Structured missing data complicates machine learning, presenting new challenges.

Dehn surgery on complicated fibered knots doesn't yield lens spaces.

We introduce a new operation, double point surgery, on immersed surfaces in a 4-manifold, and use it to construct knotted configurations of surfaces in many 4-manifolds. Taking branched covers, we produce smoothly exotic actions of Z/m x Z/n on simply connected 4-manifolds with complicated fixed-point sets.

We construct families of manifolds that have pairs of genus $g$ Heegaard splittings that must be stabilized roughly $g$ times to become equivalent. We also show that when two unstabilized, boundary-unstabilized Heegaard splittings are amalgamated by a "sufficiently complicated" map, the resulting splitting is unstabili…

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

Let $M$ be a 3-manifold with torus boundary components $T_1$ and $T_2$. Let $φ\colon T_1 \to T_2$ be a homeomorphism, $M_φ$ the manifold obtained from $M$ by gluing $T_1$ to $T_2$ via the map $φ$, and $T$ the image of $T_1$ in $M_φ$. We show that if $φ$ is "sufficiently complicated" then any incompressible or strongly …

Simple math predicts growth trends.

VAEs are a neural network approach to unsupervised learning.

A new method improves maximum margin criterion for better pattern analysis.

The paper explores non-classical Schottky groups and their properties.

We sharply characterize the performance of different penalization schemes for the problem of selecting the relevant variables in the multi-task setting. Previous work focuses on the regression problem where conditions on the design matrix complicate the analysis. A clearer and simpler picture emerges by studying the No…

The study predicts surgical complications in Crohn's disease patients using machine learning.

Improved online convex optimization with long-term constraints achieving low regret and constraint violations.

Develops a data-driven fault diagnosis framework for time-series data.

A simple framework improves deep metric learning performance.

Fast and efficient homology algorithms are in demand in the applied sciences for analyzing solid materials and proteins, processing digital imaging data, or pattern classification among others. Recent advances employ discrete Morse theory as a preprocessor. Research in this area has lead to the need to find complicated…

This study predicts diabetes complications using financial records and neural networks.

New method trims network data to resist adversarial contamination.

Model improves surgical complication prediction using latent factor learning.

Proposes a deep structured generative model for complex scenes.

SynthETIC simulates insurance claims with customizable features.

EI-MTD defends edge intelligence against adversarial attacks with dynamic scheduling.

CDANs classify unordered feature sets efficiently and invariantly.

New surfaces show horocyclic flow isn't always minimal.

Machine learning faces challenges in healthcare data, but offers opportunities.

Flexible variable selection handles missing data for better biomarker panels.

Eigenfunctions of the Dirac operator on spheres reveal complex nodal structures.

New CapsNet and NLSTM framework improves traffic forecasting accuracy.

This work introduces a noise-adaptive conformal inference method for better prediction sets in noisy data.

Our goal is to build robust optimization problems for making decisions based on complex data from the past. In robust optimization (RO) generally, the goal is to create a policy for decision-making that is robust to our uncertainty about the future. In particular, we want our policy to best handle the the worst possibl…

Eigenfunctions on spheres and tori with complex nodal sets.

Let M_1 and M_2 be compact, orientable 3-manifolds, and M the manifold obtained by gluing some component F of \bdy M_1 to some component of \bdy M_2 by a homeomorphism φ. We show that when φis "sufficiently complicated" then (1) the amalgamation of low genus, unstabilized, boundary-unstabilized Heegaard splittings of M…

Motivated by the algorithmic study of 3-dimensional manifolds, we explore the structural relationship between the JSJ decomposition of a given 3-manifold and its triangulations. Building on work of Bachman, Derby-Talbot and Sedgwick, we show that a "sufficiently complicated" JSJ decomposition of a 3-manifold enforces a…

We present a short proof of the following Pontryagin theorem, whose original proof was complicated and has never been published in details: {\bf Theorem.} Let $M$ be a connected oriented closed smooth 3-manifold. Let $L_1(M)$ be the set of framed links in $M$ up to a framed cobordism. Let $°:L_1(M)\to H_1(M;\Z)$ be the…

Smooth isotopy on cube saves energy with extra dimensions.

Based on recent work by Futer, Kalfagianni and Purcell, we prove that the volume of sufficiently complicated positive braid links is proportional to the signature defect $Δσ=2g-σ$.

New differential equation generates more doubly periodic minimal surfaces.

Paper proposes a machine learning framework for VLSI mask optimization.

Unified approach for robust and heavy-tailed mean estimation in high dimensions.