arXiv research

One-hot CNN (convolutional neural network) has been shown to be effective for text categorization (Johnson & Zhang, 2015). We view it as a special case of a general framework which jointly trains a linear model with a non-linear feature generator consisting of `text region embedding + pooling'. Under this framework, we…

Improved object detection for scientific document images.

This paper presents a new semi-supervised framework with convolutional neural networks (CNNs) for text categorization. Unlike the previous approaches that rely on word embeddings, our method learns embeddings of small text regions from unlabeled data for integration into a supervised CNN. The proposed scheme for embedd…

3-manifolds with two abelian-filled spaces.

The study proves the existence of free boundary minimal disks in convex regions.

The study explores how 3-manifolds embed locally flatly in $S^4$.

ViCE uses superpixels to enhance self-supervised learning for better dense visual embeddings.

We consider embeddings of 3-manifolds in $S^4$ such that each of the two complementary regions has an abelian fundamental group. In particular, we show that an homology handle $M$ has such an embedding if and only if $π_1(M)'$ is perfect, and that the embedding is then essentially unique.

An embedding of a metric graph $(G, d)$ on a closed hyperbolic surface is \emph{essential}, if each complementary region has a negative Euler characteristic. We show, by construction, that given any metric graph, its metric can be rescaled so that it admits an essential and isometric embedding on a closed hyperbolic su…

We introduce a new multi-dimensional nonlinear embedding -- Piecewise Flat Embedding (PFE) -- for image segmentation. Based on the theory of sparse signal recovery, piecewise flat embedding with diverse channels attempts to recover a piecewise constant image representation with sparse region boundaries and sparse clust…

Given a smooth polarized Riemann surface (X, L) endowed with a hyperbolic metric $ω$ with cusp singularities along a divisor D, we show the L^2 projective embedding of (X, D) defined by L^k is asymptotically almost balanced in a weighted sense. The proof depends on sufficiently precise understanding of the behavior of …

In this paper, we propose a new pooling method called spatial pyramid encoding (SPE) to generate speaker embeddings for text-independent speaker verification. We first partition the output feature maps from a deep residual network (ResNet) into increasingly fine sub-regions and extract speaker embeddings from each sub-…

Graph embeddings from commute networks identify socioeconomic disparities in urban areas.

In this paper we provide a large new family of embedded capillary surfaces inside polyhedral regions in the Euclidean space. The angle of contact of the examples we furnish is prescribed to be any value in $(\fracπ{2}, π]$ and it is allowed to vary from one boundary component to the other.

We measure, in two distinct ways, the extent to which the boundary region of moduli space contributes to the ``simple type'' condition of Donaldson theory. Using a geometric representative of μ(pt), the boundary region of moduli space contributes 6/64 of the homology required for simple type, regardless of the topology…

A leveraged exchange traded fund (LETF) is an exchange traded fund that uses financial derivatives to amplify the price changes of a basket of goods. In this paper, we consider the robust hedging of European options on a LETF, finding model-free bounds on the price of these options. To obtain an upper bound, we establi…

Diffusion maps are a commonly used kernel-based method for manifold learning, which can reveal intrinsic structures in data and embed them in low dimensions. However, as with most kernel methods, its implementation requires a heavy computational load, reaching up to cubic complexity in the number of data points. This l…

LASE improves local network structure visualization by targeting locally low-dimensional regions.

Significant progress has been made using fMRI to characterize the brain changes that occur in ASD, a complex neuro-developmental disorder. However, due to the high dimensionality and low signal-to-noise ratio of fMRI, embedding informative and robust brain regional fMRI representations for both graph-level classificati…

New method predicts AD progression using MEG brain networks.

New algorithm quantifies uncertainty in regression models for complex data types.

This is an expository article, explaining recent work by D. Groisser and myself [GS] on the extent to which the boundary region of moduli space contributes to the ``simple type'' condition of Donaldson theory. The presentation is intended to complement [GS], presenting the essential ideas rather than the analytical det…

We give several generalizations of the Kodaira vanishing and embedding theorems for Kähler manifolds to the case where the relevent line bundle has a small region of negative curvature. To prove the vanishing theorems we adapt techniques of Elworthy-Rosenberg for vanishing theorems in Riemannian geometry. For the embed…

Study embeddings of 3-manifolds in $S^4$ with nilpotent fundamental groups.

Paper shows any link can be diagrammed with only triangles and quadrilaterals.

The paper divides minimal hypersurfaces in a ball into two parts.

We prove a comparison theorem for the isoperimetric profiles of simple closed curves evolving by the normalized curve shortening flow: If the isoperimetric profile of the region enclosed by the initial curve is greater than that of some `model' convex region with exactly four vertices and with reflection symmetry in bo…

Study integrates reliability constraints into generation planning models.

Proposes a text perturbation method using a Mahalanobis metric to balance privacy and utility.

sBayFDNN bridges deep learning and functional data analysis for complex, structured data.

The paper forecasts joint electricity demand across 14 British regions using additive models.

End-to-end pipeline for data-driven decision making in mixed-integer optimization.

DBGDGM models dynamic brain graphs for better understanding brain function.

Donor-aware scRNA-seq benchmarks improve classification accuracy in inflammatory bowel disease.

Deep metric learning algorithms have been utilized to learn discriminative and generalizable models which are effective for classifying unseen classes. In this paper, a novel noise tolerant deep metric learning algorithm is proposed. The proposed method, termed as Density Aware Metric Learning, enforces the model to le…

We prove that every plane passing through the origin divides an embedded compact free boundary minimal surface of the euclidean $3$-ball in exactly two connected surfaces. We also show that if a region in the ball has mean convex boundary and contains a nullhomologous diameter, then this region is a closed halfball. Mo…

New curvature condition helps organize high-curvature regions in geometric flows.

Instance segmentation on 3D point clouds is one of the most extensively researched areas toward the realization of autonomous cars and robots. Certain existing studies have split input point clouds into small regions such as 1m x 1m; one reason for this is that models in the studies cannot consume a large number of poi…

The study embeds graphs on translation surfaces, proving essential-systolic embeddings and estimating surface genera.

In order to model entanglements of polymers in a confined region, we consider the linking numbers and writhes of cycles in random linear embeddings of complete graphs in a cube. Our main results are that for a random linear embedding of $K_n$ in a cube, the mean sum of squared linking numbers and the mean sum of square…

In this short article we investigate the topology of the moduli space of two-convex embedded tori $S^{n-1}\times S^1\subset \mathbb{R}^{n+1}$. We prove that for $n \geq 3$ this moduli space is path-connected, and that for $n = 2$ the connected components of the moduli space are in bijective correspondence with the knot…

In this paper we study the mean curvature flow of embedded disks with free boundary on an embedded cylinder or generalised cone of revolution, called the support hypersurface. We determine regions of the interior of the support hypersurface such that initial data is driven to a curvature singularity in finite time or e…

New analysis shows rational actors will deploy AGI despite negative social value due to catastrophic risk.

BN refines local partition geometry in piecewise-affine networks during training.

SOCP uses SOM to find groups and local calibration buffers for better regional coverage.

We propose the Graph Space Embedding (GSE), a technique that maps the input into a space where interactions are implicitly encoded, with little computations required. We provide theoretical results on an optimal regime for the GSE, namely a feasibility region for its parameters, and demonstrate the experimental relevan…

We study the quasi-local energy (QLE) and the surface geometry for Kerr spacetime in the Boyer-Lindquist coordinates without taking the slow rotation approximation. We also consider in the region $r\leq2m$, which is inside the ergosphere. For a certain region, $r>r_{k}(a)$, the Gaussian curvature of the surface with co…

Develops methods to analyze feature-outcome associations in subpopulations.