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 absolute Galois group of 3-manifolds determines their structure up to homeomorphism.
We prove that every lens space contains a genus one homologically fibered knot, which is contrast to the fact that some lens spaces contain no genus one fibered knot. In the proof, the Chebotarev density theorem and binary quadratic forms in number theory play a key role. We also discuss the Alexander polynomial of hom…
Modular knots follow Chebotarev law from surgeries on hyperbolic fibered links.
Extends Floquet-Bloch theory to nilpotent groups for geometric applications.
We determine the condition on a given lens space having a realization as a closure of homology cobordism over a planar surface with a given number of boundary components. As a corollary, we see that every lens space is represented as a closure of homology cobordism over a planar surface with three boundary components. …
We discuss the relationship between two analogues in a 3-manifold of the set of prime ideals in a number field. We prove that if is a sequence of knots obeying the Chebotarev law in the sense of Mazur and McMullen, then is a stably generic link in the sense of Mih…
In 1992, Reid asked whether hyperbolic 3-manifolds with the same geodesic length spectra are necessarily commensurable. While this is known to be true for arithmetic hyperbolic 3-manifolds, the non-arithmetic case is still open. Building towards a negative answer to this question, Futer and Millichap recently construct…
The paper calculates heat kernel and closed geodesic asymptotics for nilpotent coverings.
Proves section conjecture for curves and surface bundles over various fields.
MCD reformulates conditional density estimation into binary classification.
Paper proposes MMC to avoid high-density bias in clustering.
New method minimizes robust density power-based divergences for general parametric densities.
Modes and ridges of the probability density function behind observed data are useful geometric features. Mode-seeking clustering assigns cluster labels by associating data samples with the nearest modes, and estimation of density ridges enables us to find lower-dimensional structures hidden in data. A key technical cha…
Normalizing flows improve density estimation from noisy data.
Study exact minimax rates for density estimation over convex classes, extending previous work.
New method uses SoS densities and α-divergences for efficient sequential transport maps.
The volume density of a hyperbolic link is defined as the ratio of hyperbolic volume to crossing number. We study its properties and a closely-related invariant called the determinant density. It is known that the sets of volume densities and determinant densities of links are dense in the interval [0,v_{oct}]. We cons…
TAKDE optimizes kernel density estimation for real-time dynamic processes.
Most density-based clustering methods largely rely on how well the underlying density is estimated. However, density estimation itself is also a challenging problem, especially the determination of the kernel bandwidth. A large bandwidth could lead to the over-smoothed density estimation in which the number of density …
Optimizes kernel density ratios for better predictions and information measures.
Study finds a linear lower bound on conformal dimension for random hyperbolic groups.
Chia and Nakano (2009) introduced the concept of M-decomposability of probability densities in one-dimension. In this paper, we generalize M-decomposability to any dimension. We prove that all elliptical unimodal densities are M-undecomposable. We also derive an inequality to show that it is better to represent an M-de…
We introduce a novel conditional density estimation model termed the conditional density operator (CDO). It naturally captures multivariate, multimodal output densities and shows performance that is competitive with recent neural conditional density models and Gaussian processes. The proposed model is based on a novel …
Quantum method improves neural density estimation in high dimensions.
Roundtrip uses deep generative models for flexible density estimation.
Explains BV Laplacian on half-densities in simple terms.
Fully augmented links have dense volume densities but discrete in certain ranges.
The study proves optimal isoperimetric regions in manifolds with density.
Log-density gradient estimation is a fundamental statistical problem and possesses various practical applications such as clustering and measuring non-Gaussianity. A naive two-step approach of first estimating the density and then taking its log-gradient is unreliable because an accurate density estimate does not neces…
Defines hierarchical clustering axioms for various densities.
The paper analyzes kNN density estimation's convergence rates under different conditions.
Estimation of density derivatives is a versatile tool in statistical data analysis. A naive approach is to first estimate the density and then compute its derivative. However, such a two-step approach does not work well because a good density estimator does not necessarily mean a good density-derivative estimator. In t…
Develops spherical density-equalizing maps for closed surfaces.
Adapts RKHS methods to estimate density ratios with optimal error.
Method uses normalizing flows to efficiently sample from complex target densities.
Develops a new density ratio estimator for causal inference.
New density estimator from Markov Chains outperforms KDE.
Density-based spatial clustering of applications with noise (DBSCAN) is a data clustering algorithm which has the high-performance rate for dataset where clusters have the constant density of data points. One of the significant attributes of this algorithm is noise cancellation. However, DBSCAN demonstrates reduced per…
We find that cusp densities of hyperbolic knots in the 3-sphere are dense in [0,0.6826...] and those of links are dense in [0,0.853...]. We define a new invariant associated with cusp volume, the cusp crossing density, as the ratio between the cusp volume and the crossing number of a link, and show that cusp crossing d…
This paper introduces a probability density estimator based on Green's function identities. A density model is constructed under the sole assumption that the probability density is differentiable. The method is implemented as a binary likelihood estimator for classification purposes, so issues such as mis-modeling and …
Meta-learning improves relative density-ratio estimation from limited data.
Machine learning is used to approximate density functionals. For the model problem of the kinetic energy of non-interacting fermions in 1d, mean absolute errors below 1 kcal/mol on test densities similar to the training set are reached with fewer than 100 training densities. A predictor identifies if a test density is …
New model for density estimation using tensor trains.
We investigate the ability of popular flow based methods to capture tail-properties of a target density by studying the increasing triangular maps used in these flow methods acting on a tractable source density. We show that the density quantile functions of the source and target density provide a precise characterizat…
Data analysis in high-dimensional spaces aims at obtaining a synthetic description of a data set, revealing its main structure and its salient features. We here introduce an approach providing this description in the form of a topography of the data, namely a human-readable chart of the probability density from which t…
LGKDE learns graph density using neural networks and perturbations.
The two most extended density-based approaches to clustering are surely mixture model clustering and modal clustering. In the mixture model approach, the density is represented as a mixture and clusters are associated to the different mixture components. In modal clustering, clusters are understood as regions of high d…
New framework quantifies uncertainty in flexible density-based clustering.