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 identifies latent factors from noisy measurements using tensor decomposition.
Improved algorithm for multidimensional scaling reduces stress.
Study on identifiability of deep polynomial neural networks.
New approach confirms Kruskal-Szekeres extension for Schwarzschild spacetime.
A multi-way factor analysis model is introduced for tensor-variate data of any order. Each data item is represented as a (sparse) sum of Kruskal decompositions, a Kruskal-factor analysis (KFA). KFA is nonparametric and can infer both the tensor-rank of each dictionary atom and the number of dictionary atoms. The model …
Enhances tensor regression for interpretability and performance.
By considering suitable axially symmetric slices on the Kruskal spacetime, we construct counterexamples to a recent version of the Penrose inequality in terms of so-called generalized apparent horizons.
New CSC model extracts EEG signals with low noise sensitivity.
Tensor decompositions have rich applications in statistics and machine learning, and developing efficient, accurate algorithms for the problem has received much attention recently. Here, we present a new method built on Kruskal's uniqueness theorem to decompose symmetric, nearly orthogonally decomposable tensors. Unlik…
We solve spacelike spherically symmetric constant mean curvature (SS-CMC) hypersurfaces in Schwarzschild spacetimes and analyze their asymptotic behavior near the coordinate singularity r = 2M. Furthermore, we join SS-CMC hypersurfaces in the Kruskal extension to obtain complete ones and discuss the smooth properties.
We first summarize the characterization of smooth spacelike spherically symmetric constant mean curvature (SS-CMC) hypersurfaces in the Schwarzschild spacetime and Kruskal extension. Then use the characterization to prove special SS-CMC foliation property, and verify part of the conjecture by Malec and Ó Murchadha in t…
We construct a -axisymmetric, spacelike, spherically symmetric, constant mean curvature hypersurfaces foliation in the Kruskal extension with properties that the mean curvature varies in each slice and ranges from minus infinity to plus infinity. This family of hypersurfaces extends the CMC foliation discussions pos…
We construct a Kruskal-Szekeres-type analytic extension of the Emparan-Reall black ring, and investigate its geometry. We prove that the extension is maximal, globally hyperbolic, and unique within a natural class of extensions. The key to those results is the proof that causal geodesics are either complete, or approac…
The geometry of five-dimensional Kerr black holes is discussed based on geodesics and Weyl curvatures. Kerr-Star space, Star-Kerr space and Kruskal space are naturally introduced by using special null geodesics. We show that the geodesics of AdS Kerr black hole are integrable, which generalizes the result of Frolov and…
Study measures uncertainty in MST identification across different correlation networks.
This paper introduces a new multivariate convolutional sparse coding based on tensor algebra with a general model enforcing both element-wise sparsity and low-rankness of the activations tensors. By using the CP decomposition, this model achieves a significantly more efficient encoding of the multivariate signal-partic…
We prove several results about chordal graphs and weighted chordal graphs by focusing on exposed edges. These are edges that are properly contained in a single maximal complete subgraph. This leads to a characterization of chordal graphs via deletions of a sequence of exposed edges from a complete graph. Most interesti…
When response variables are nominal and populations are cross-classified with respect to multiple polytomies, questions often arise about the degree of association of the responses with explanatory variables. When populations are known, we introduce a nominal association vector and matrix to evaluate the dependence of …
We present a framework for incorporating prior information into nonparametric estimation of graphical models. To avoid distributional assumptions, we restrict the graph to be a forest and build on the work of forest density estimation (FDE). We reformulate the FDE approach from a Bayesian perspective, and introduce pri…
This paper is an expository account of the development of soliton mathematics, from its inception in famous numerical experiments of Fermi-Pasta-Ulam and Zabusky-Kruskal to the recent synthesis of Terng-Uhlenbeck (dg-ga/9707004) that explains hidden symmetries of soliton equations in terms of loop-groups acting by dres…
The existence, established over the past number of years and supporting earlier work of Ori [14], of physically relevant black hole spacetimes that admit metric extensions beyond the future Cauchy horizon, while being -inextendible, has focused attention on fundamental issues concerning the strong cosmic cen…
We study graph estimation and density estimation in high dimensions, using a family of density estimators based on forest structured undirected graphical models. For density estimation, we do not assume the true distribution corresponds to a forest; rather, we form kernel density estimates of the bivariate and univaria…
In this paper we adopted state-of-the-art machine learning algorithms, namely: random forest (RF) and least squares boosting, to model crash data and identify the optimum model to study the impact of narrow lanes on the safety of arterial roads. Using a ten-year crash dataset in four cities in Nebraska, two machine lea…
This paper identifies and estimates the label noise transition matrix without ground truth labels.
Study shows nonextendibility of warped spacelike singularities in specific spacetimes.
Portfolio allocation and risk management make use of correlation matrices and heavily rely on the choice of a proper correlation matrix to be used. In this regard, one important question is related to the choice of the proper sample period to be used to estimate a stable correlation matrix. This paper addresses this qu…
The Rectified Linear Unit (ReLU) is a foundational activation function in artficial neural networks. Recent literature frequently misattributes its origin to the 2018 (initial) version of this paper, which exclusively investigated ReLU at the classification layer. This paper formally corrects the citation record by tra…
Continuous MDS embeds sequences of dissimilarities in Euclidean space.
AI generates theorems and proofs for training theorem provers.
Global inverse function theorem proved easily using Riemannian geometry.
A new comparison theorem for geometric spaces.
Paper develops formulas and theorems in Hermitian geometry.
The paper proves three circles theorems and Liouville type theorems for subharmonic and holomorphic functions.
Revises a theorem by Thurston, finding a counter-example and a weaker version.
Proofs for Moon's theorem and its generalization.
Analyzes Saito vanishing theorem using methods.
Investigates proving geometric theorems over complex and real numbers using tilings.
Extends symplectic reduction and theorem to Lie algebroids.
Paper generalizes complex Brunn-Minkowski theory and proves new extension theorems.
Proves Thurston's bounded image theorem for Haken manifolds.
Method upgrades limit theorems to mixing limit theorems for dynamical systems.
Formulates Index III lemma and Rauch III theorem with applications.
In LM, we proved a family version of the famous Witten rigidity theorems and several family vanishing theorems for elliptic genera. In this paper, we gerenalize our theorems LM in two directions. First we establish a family rigidity theorem for the Dirac operator on loop space twisted by general positive energy loop gr…
The paper explains the topological origin of the distinction between incidence theorems over division rings and fields.
Proves two theorems on odd-dimensional manifolds with boundary.
Sharp convergence theorem for sphere submanifolds proved.
INT benchmark tests theorem proving agents' ability to generalize to unseen theorems.
A homological selection theorem for C-spaces, as well as, a finite-dimensional homological selection theorem is established. We apply the finite-dimensional homological selection theorem to obtain fixed-point theorems for usco homologically UV^n set-valued maps.