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.
The CN matrix of a pure braid projection is characterized and applied.
New algorithms for neural bandits learn from context and arm features.
CN normalizes channels for better time series model performance.
CN-SBM clusters cancer samples and regions based on copy number variants.
In this paper we revisit the anisotropic isoperimetric and the Brunn-Minkowski inequalities for convex sets. The best known constant depending on the space dimension in both inequalities is due to Segal [\ref{bib:Seg.}]. We improve that constant to for convex sets and to for centrally sy…
The study constructs minimal submanifolds in complex and quaternionic projective spaces.
Capsule Networks (CN) offer new architectures for Deep Learning (DL) community. Though its effectiveness has been demonstrated in MNIST and smallNORB datasets, the networks still face challenges in other datasets for images with distinct contexts. In this research, we improve the design of CN (Vector version) namely we…
Two large medical dialogue datasets for improving healthcare.
We give a necessary complex geometric condition for a bounded smooth convex domain in Cn, endowed with the Kobayashi distance, to be Gromov hyperbolic. More precisely, we prove that if a smooth bounded convex domain contains an analytic disk in its boundary, then the domain is not Gromov hyperbolic for the Kobayashi di…
Protein interaction networks are a promising type of data for studying complex biological systems. However, despite the rich information embedded in these networks, they face important data quality challenges of noise and incompleteness that adversely affect the results obtained from their analysis. Here, we explore th…
The paper analyzes the robustness of a minimum interpolator in high-dimensional linear regression.
New model for Witten-Reshetikhin-Turaev invariants using Lagrangian intersections.
Study Lie algebras with complex structures, focusing on degenerations and deformations.
A new method for estimating uncertainty intervals in regression.
For a semisimple Lie group with parabolic subgroups , we associate to a parabolic geometry of type on a smooth manifold the correspondence space $\Cal CN$, which is the total space of a fiber bundle over with fiber a generalized flag manifold, and construct a canonical parabolic…
Smile-GANs clusters brain MRI scans to reveal disease subtypes and progression.
Estimates for graph embeddings into symmetric spaces derived from coarse geometry.
EPGP surrogate outperforms finite elements in solving wave equations.
Deep learning has demonstrated abilities to learn complex structures, but they can be restricted by available data. Recently, Consensus Networks (CNs) were proposed to alleviate data sparsity by utilizing features from multiple modalities, but they too have been limited by the size of labeled data. In this paper, we ex…
1. Translated by Thomas E. Cecil, Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, MA 01610, USA; E-mail address: cecil@mathcs.holycross.edu 2. Typed by Wenjiao Yan, School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing 10…
In recent years, the number of papers on Alzheimer's disease classification has increased dramatically, generating interesting methodological ideas on the use machine learning and feature extraction methods. However, practical impact is much more limited and, eventually, one could not tell which of these approaches are…
Pseudo-marginal Metropolis-Hastings (pmMH) is a powerful method for Bayesian inference in models where the posterior distribution is analytical intractable or computationally costly to evaluate directly. It operates by introducing additional auxiliary variables into the model and form an extended target distribution, w…
Despite the growing interest in continual learning, most of its contemporary works have been studied in a rather restricted setting where tasks are clearly distinguishable, and task boundaries are known during training. However, if our goal is to develop an algorithm that learns as humans do, this setting is far from r…
Graph matching involves combinatorial optimization based on edge-to-edge affinity matrix, which can be generally formulated as Lawler's Quadratic Assignment Problem (QAP). This paper presents a QAP network directly learning with the affinity matrix (equivalently the association graph) whereby the matching problem is tr…
The present article is the final part of a series on the classification of the totally geodesic submanifolds of the irreducible Riemannian symmetric spaces of rank 2. After this problem has been solved for the 2-Grassmannians in my previous papers cited in the present paper as [K1] and [K2], and for the space SU(3)/SO(…
Proves Hölder continuity of complex Monge-Ampère solutions.
Proposes a VAE for HDLSS data augmentation.
Let $\1$ and $\2$ be $\s$ domains in $\Cn$ and $f: \1 \rt \2$ an isometry for the Kobayashi or Carathéodory metrics. Suppose that extends as a map to $ \bar \om_1$. We then prove that $f|_{\partial \1}: \partial \1 \rt \partial \2$ is a CR or anti-CR diffeomorphism. It follows that $\1$ and $\2$ must be bihol…
Correlation Networks (CNs) inherently suffer from redundant information in their network topology. Bayesian Networks (BNs), on the other hand, include only non-redundant information (from a probabilistic perspective) resulting in a sparse topology from which generalizable physical features can be extracted. We advocate…
We develop the first steps of a parabolic pluripotential theory in bounded strongly pseudo-convex domains of Cn. We study certain degenerate parabolic complex Monge-Amp{è}re equations, modelled on the K{ä}hler-Ricci flow evolving on complex algebraic varieties with Kawamata log-terminal singularities. Under natural ass…
In this paper we prove a new matrix Li-Yau-Hamilton estimate for Kähler-Ricci flow. The form of this new Li-Yau-Hamilton estimate is obtained by the interpolation consideration originated in \cite{Ch1}. This new inequality is shown to be connected with Perelman's entropy formula through a family of differential equalit…
New algorithm for computing Gaussian mixtures with guaranteed accuracy and efficiency.
A curve of minimum length to enclose a unit sphere in 3D is at least 4π.
Random covers of hyperbolic surfaces have a spectral gap with polynomial rate.
We present a short exposition of the following results by S. Parsa. Let be a graph such that the join (i.e. the union of three cones over along their common bases) piecewise linearly (PL) embeds into . Then admits a PL embedding into such that any two disjoint cycles…
The paper tackles causal bandits with unknown SCMs and soft interventions, providing upper and lower bounds on regret.
Ensemble model predicts AD progression from CN status with high accuracy.
Addressing a question of Gromov, we give a rate in Pansu's theorem about the convergence in Gromov-Hausdorff metric of a finitely generated nilpotent group equipped with a left-invariant word metric scaled by a factor 1/n towards its asymptotic cone. We show that due to the possible presence of abnormal geodesics in th…
We describe some buildings related to complex Kac-Moody groups. First we describe the spherical building of SLn(C) (i.e. the projective geometry PG(Cn)) and its Veronese representation. Next we recall the construction of the affine building associated to a discrete valuation on the rational function field . Then …
Unified proof of smooth fibration theorems for collapsed manifolds.
In this paper we complete the study of the normal holonomy groups of complex submanifolds (non nec. complete) of Cn or CPn. We show that irreducible but non transitive normal holonomies are exactly the Hermitian s-representations of [CD09, Table 1] (see Corollary 1.1). For each one of them we construct a non necessaril…
A new clustering method uses nonparametric smoothing to estimate cluster membership functions.
The paper defines cross-section continuity for angular momentum definitions and finds the CWY definition valid.
A rack of order is a binary operation $\rack$ on a set of cardinality , such that right multiplication is an automorphism. More precisely, $(X,\rack)$ is a rack provided that the map $x\mapsto x\rack y$ is a bijection for all , and $(x\rack y)\rack z=(x\rack z)\rack (y\rack z)$ for all . …
Multiple sclerosis (MS) is an inflammatory demyelinating disease of the central nervous system (CNS) that results in focal injury to the grey and white matter. The presence of white matter lesions biases morphometric analyses such as registration, individual longitudinal measurements and tissue segmentation for brain v…
It is now well known that deep neural networks (DNNs) are vulnerable to adversarial attack. Adversarial samples are similar to the clean ones, but are able to cheat the attacked DNN to produce incorrect predictions in high confidence. But most of the existing adversarial attacks have high success rate only when the inf…
WeSinger improves singing voice synthesis with data augmentation and specialized modules.
Multiple modalities of biomarkers have been proved to be very sensitive in assessing the progression of Alzheimer's disease (AD), and using these modalities and machine learning algorithms, several approaches have been proposed to assist in the early diagnosis of AD. Among the recent investigated state-of-the-art appro…