A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Paper tackles shape graph registration using neural networks.
A novel 3D shape registration method using spectral graph embedding and probabilistic matching.
New model for shape graph registration with partial matching constraints.
The paper presents a method for analyzing shape graphs using specific features.
Paper analyzes shapes of brain arterial networks using statistical methods.
Neural networks that compute over graph structures are a natural fit for problems in a variety of domains, including natural language (parse trees) and cheminformatics (molecular graphs). However, since the computation graph has a different shape and size for every input, such networks do not directly support batched t…
Estimates mean curvature, scalar curvature, shape operator in warped products.
Representing 3D shape deformations by linear models in high-dimensional space has many applications in computer vision and medical imaging, such as shape-based interpolation or segmentation. Commonly, using Principal Components Analysis a low-dimensional (affine) subspace of the high-dimensional shape space is determin…
Study efficient geodesics in curve complex using dot graphs.
SVarM uses varifold representations for shape classification and regression.
The paper classifies shapes of translating solitons from isoparametric graphs.
Random subsurfaces of hyperbolic surfaces equidistribute to ribbon graphs.
New algorithms detect outliers in high-dimensional data with arbitrary shapes.
We first show that the braid group over a graph topologically containing no -shape subgraph has a presentation related only by commutators. Then using discrete Morse theory and triple Massey products, we prove that a graph topologically contains none of four prescribed graphs if and only if its 4-braid groups is a r…
The paper classifies shapes of translating solitons for a specific flow.
In this work, we prove an optimal Penrose inequality for asymptotically locally hyperbolic manifolds which can be realized as graphs over Kottler space. Such inequality relies heavily on an optimal weighted Alexandrov-Fenchel inequality for the mean convex star shaped hypersurfaces in Kottler space.
New dataset and techniques detect money laundering patterns in crypto.
Robust GW distance improves graph data alignment.
We introduce a convolutional neural network that operates directly on graphs. These networks allow end-to-end learning of prediction pipelines whose inputs are graphs of arbitrary size and shape. The architecture we present generalizes standard molecular feature extraction methods based on circular fingerprints. We sho…
BIG Laplacians bridge combinatorial and Hodge Laplacians for discrete data.
We introduce and begin to explore the mean and median of finite sets of shapes represented as integral currents. The median can be computed efficiently in practice, and we focus most of our theoretical and computational attention on medians. We consider questions on the existence and regularity of medians. While the me…
The PageRank of a graph is a scalar function defined on the node set of the graph which encodes nodes centrality information of the graph. In this article, we use the PageRank function along with persistent homology to obtain a scalable graph descriptor and utilize it to compare the similarities between graphs. For a g…
New method learns high-quality Laplacian representations for reinforcement learning.
Study of Poincaré-Reeb graphs for algebraic domains.
In this paper, we use the inverse mean curvature flow to establish an optimal Minkowski type inquality, weighted Alexandrov-Fenchel inequality for the mean convex star shaped hypersurfaces in Reissner-Nordström-anti-deSitter manifold and Penrose type inequality for asymptotically locally hyperbolic manifolds in which c…
Study on anisotropic curvature flow for noncompact convex hypersurfaces.
This paper restricts efficient geodesics to non-separating curves.
Ring-reservoir networks simplify graph embeddings efficiently.
SHADOWCAST generates graphs with user-specified attributes.
A new graph signature invariant to graph automorphisms.
Spectral Graph Convolutional Networks (GCNs) are a generalization of convolutional networks to learning on graph-structured data. Applications of spectral GCNs have been successful, but limited to a few problems where the graph is fixed, such as shape correspondence and node classification. In this work, we address thi…
ES-VAE models skeletal pose trajectories by removing nuisance factors.
Study shapes of 3D bounded domains using Morse height functions and Reeb graphs.
Modular meta-learning is a new framework that generalizes to unseen datasets by combining a small set of neural modules in different ways. In this work we propose abstract graph networks: using graphs as abstractions of a system's subparts without a fixed assignment of nodes to system subparts, for which we would need …
Learning representation on graph plays a crucial role in numerous tasks of pattern recognition. Different from grid-shaped images/videos, on which local convolution kernels can be lattices, however, graphs are fully coordinate-free on vertices and edges. In this work, we propose a Gaussian-induced convolution (GIC) fra…
Graphs are ubiquitous data structures for representing interactions between entities. With an emphasis on the use of graphs to represent chemical molecules, we explore the task of learning to generate graphs that conform to a distribution observed in training data. We propose a variational autoencoder model in which bo…
The goal of this paper is to measure the non-convexity of compact and smooth connected components of real algebraic plane curves. We study these curves first in a general setting and then in an asymptotic one. In particular, we consider sufficiently small levels of a real bivariate polynomial in a small enough neighbou…
Classifies negative-twisting structures on Seifert fibred spaces using Heegaard Floer homology.
Recently many efforts have been made to incorporate persistence diagrams, one of the major tools in topological data analysis (TDA), into machine learning pipelines. To better understand the power and limitation of persistence diagrams, we carry out a range of experiments on both graph data and shape data, aiming to de…
From computational geometry comes the notion of a Gabriel graph of a point set in the plane. The Gabriel graph consists of those edges connecting two points of the point set such that the circle whose diameter is the edge does not contain any point of the point set in its interior. We define a generalization of the Gab…
A new deep learning framework for topological data.
New method constructs asymptotic convex hypersurfaces via equidistant hyperplanes.
Graph cross network improves graph classification accuracy.
Gromov-Hausdorff distances measure shape difference between the objects representable as compact metric spaces, e.g. point clouds, manifolds, or graphs. Computing any Gromov-Hausdorff distance is equivalent to solving an NP-Hard optimization problem, deeming the notion impractical for applications. In this paper we pro…
GCN and GPCA are mathematically connected, leading to improved node classification performance.
Given a matrix the seriation problem consists in permuting its rows in such way that all its columns have the same shape, for example, they are monotone increasing. We propose a statistical approach to this problem where the matrix of interest is observed with noise and study the corresponding minimax rate of estimatio…
EPFGNN models graph connections for better node classification.
In the series of our earlier papers on the subject, we proposed a novel statistical hypothesis testing method for detection of objects in noisy images. The method uses results from percolation theory and random graph theory. We developed algorithms that allowed to detect objects of unknown shapes in the presence of non…