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.
A new method for clustering using graph connectivity centers.
problem Inappropriate scale leads to unreasonable cluster centers.
method Convert data similarity to graph connectivity, define connection center as cluster center, and use powers of similarity matrix for dynamic evolution.
result Cluster centers evolve naturally from local to global, suggesting appropriate scales and skipping unreasonable clusters.
Many pattern recognition methods rely on statistical information from centered data, with the eigenanalysis of an empirical central moment, such as the covariance matrix in principal component analysis (PCA), as well as partial least squares regression, canonical-correlation analysis and Fisher discriminant analysis. R…
This work analyzes centered binary Restricted Boltzmann Machines (RBMs) and binary Deep Boltzmann Machines (DBMs), where centering is done by subtracting offset values from visible and hidden variables. We show analytically that (i) centering results in a different but equivalent parameterization for artificial neural …
The paper analyzes k-means clustering for missing data, proving statistical guarantees under MCAR.
problem Statistical guarantees for k-means clustering with missing data, especially under Missing Completely at Random (MCAR).
method Established n-excess risk bound and consistency of cluster centers under general missing mechanisms; derived n-convergence rate and asymptotic normality for MCAR.
result Achieving n-rate and converging to true cluster centers requires distinct true cluster centers in every dimension under MCAR.
The classical notion of center of mass for an isolated system in general relativity is derived from the Hamiltonian formulation and represented by a flux integral at infinity. In contrast to mass and linear momentum which are well-defined for asymptotically flat manifolds, center of mass and angular momentum seem less …
We define the (total) center of mass for suitably asymptotically hyperbolic time-slices of asymptotically anti-de Sitter spacetimes in general relativity. We do so in analogy to the picture that has been consolidated for the (total) center of mass of suitably asymptotically Euclidean time-slices of asymptotically Minko…
Center identified in stated skein algebra for quantum traces.
problem Understanding the center of the stated skein algebra.
method Analyzing the algebra as a generalization of Kauffman bracket skein algebra, focusing on the case when the quantum parameter is a root of unity.
result Simple description and dimension calculation of the center over the center module.
We prove the existence and uniqueness of constant mean curvature foliations for initial data sets which are asymptotically flat satisfying the Regge-Teitelboim condition near infinity. It is known that the (Hamiltonian) center of mass is well-defined for manifolds satisfying this condition. We also show that the foliat…
Let f:M->M be a partially hyperbolic diffeomorphism such that all of its center leaves are compact. We prove that Sullivan's example of a circle foliation that has arbitrary long leaves cannot be the center foliation of f. This is proved by thorough study of the accessible boundaries of the center-stable and the center…
This paper presents eight PAC-Bayes bounds to analyze the generalization performance of multi-view classifiers. These bounds adopt data dependent Gaussian priors which emphasize classifiers with high view agreements. The center of the prior for the first two bounds is the origin, while the center of the prior for the t…
A flexible machine learning model infers the morphology of the Galactic Center Excess.
problem Inferring the unknown morphology of the Galactic Center Excess using Fermi gamma-ray data.
method Used a Gaussian process (GP) to model the Galactic Center Excess (GCE) as a flexible, non-parametric machine learning model.
result The best-fit GP contains morphological features not typically associated with traditional GCE studies, such as a localized bright source and a diagonal arm.