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 paper studies geometric properties of hydrodynamical density manifolds.
The density conjecture of Bers, Sullivan and Thurston predicts that each complete hyperbolic 3-manifold M with finitely generated fundamental group is an algebraic limit of geometrically finite hyperbolic 3-manifolds. We prove that the conjecture obtains for each complete hyperbolic 3-manifold with no cusps and incompr…
The paper analyzes geometric densities and compression radii for knot types.
We recently discovered a relationship between the volume density spectrum and the determinant density spectrum for infinite sequences of hyperbolic knots. Here, we extend this study to new quantum density spectra associated to quantum invariants, such as Jones polynomials, Kashaev invariants and knot homology. We also …
Study on packing links with geometric constraints.
Normal-bundle bootstrap generates new data preserving geometric structure.
Method flattens complex surfaces with consistent density and shape.
MCBP detects boundaries in high-dimensional data using curvature.
New method uses geometric properties for better density estimation.
Study recovers Riemannian quantities from noisy data densities.
Using the notion of vacuum pairs we show how the (square of the) mass matrix of the fermions can be considered geometrically as curvature. This curvature together with the curvature of space-time, defines the total curvature of the Clifford module bundle representing a ``free'' fermion within the geometrical setup of s…
The paper proposes methods for volumetric parameterization of 3D solid manifolds.
We prove a generalization of the fundamental inequality of Guivarc'h relating entropy, drift and critical exponent to Gibbs measures on geometrically finite quotients of CAT(-1) metric spaces. For random walks with finite superexponential moment, we show that the equality is achieved if and only if the Gibbs density is…
New Crofton formulae derived from existing ones.
Estimating dimension from sparse random geometric graphs.
In this paper we extend Thurston's hyperbolic Dehn surgery theorem to a class of geometrically infinite hyperbolic 3-manifolds. As an application we prove a modest density theorem for Kleinian groups. We also discuss hyperbolic Dehn surgery on geometrically finite hypebolic cone-manifolds.
We extend the geometric Hamilton-Jacobi formalism for hamiltonian mechanics to higher order field theories with regular lagrangian density. We also investigate the dependence of the formalism on the lagrangian density in the class of those yelding the same Euler-Lagrange equations.
The algebra of densities $\Den(M)$ is a commutative algebra canonically associated with a given manifold or supermanifold . We introduced this algebra earlier in connection with our studies of Batalin--Vilkovisky geometry. The algebra $\Den(M)$ is graded by real numbers and possesses a natural invariant scalar produ…
Properties of steady compressible flow for which geometric constraints have been placed on the potential function are derived, under hypotheses on the flow density and the singular set. Some related unconstrained problems are also considered, including the estimation of a class of fields having nonzero vorticity.
The paper defines and studies discrete p-density and compression-radius profiles of lattice knots.
We introduce a geometric framework to study Newton's equations on infinite-dimensional configuration spaces of diffeomorphisms and smooth probability densities. It turns out that several important PDEs of hydrodynamical origin can be described in this framework in a natural way. In particular, the Madelung transform be…
Skeleton clustering detects clusters in high-dimensional data without needing prototypes.
We suggest an algorithm allowing to obtain some new integral-geometric formulae from the existing formulae of Crofton type. These new formulae are applied to get smooth versions of BKK theorem. The algorithm is based on the calculations in the ring of normal densities on a manifold.
In this paper, we analyzed the physical meaning of scalar curvatures for a generalized Riemannian space. It is developed the Madsen's formulae for pressures and energy-densities with respect to the corresponding energy-momentum tensors. After that, the energy-momentum tensors, pressures, energy-densities and state-para…
Introduces q-paths for generalizing geometric annealing paths in machine learning.
A graph clustering method that moves nodes to highest-degree neighbors.
New geometric analysis of PWSPDs balances density and geometry in high-dimensional data.
The geometric approach to optimal transport and information theory has triggered the interpretation of probability densities as an infinite-dimensional Riemannian manifold. The most studied Riemannian structures are Otto's metric, yielding the -Wasserstein distance of optimal mass transport, and the Fisher--Rao me…
This paper proposes a geometric estimator of dependency between a pair of multivariate samples. The proposed estimator of dependency is based on a randomly permuted geometric graph (the minimal spanning tree) over the two multivariate samples. This estimator converges to a quantity that we call the geometric mutual inf…
A novel method compares 3D point clouds using information geometry.
Estimates mixing coefficients of geometrically ergodic Markov processes from a single sample path.
In this paper we investigate the geometry of the likelihood of the unknown parameters in a simple class of Bayesian directed graphs with hidden variables. This enables us, before any numerical algorithms are employed, to obtain certain insights in the nature of the unidentifiability inherent in such models, the way pos…
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…
We derive and analyze a generic, recursive algorithm for estimating all splits in a finite cluster tree as well as the corresponding clusters. We further investigate statistical properties of this generic clustering algorithm when it receives level set estimates from a kernel density estimator. In particular, we derive…
We prove that monotonicity of density and energy inequality imply the rectifiability of the singular sets for Yang-Mills flow.
Solves a general class of free boundary Monge-Ampère equations.
Introduces new info-geometric structure for dynamics on graphs and hypergraphs.
Stable solutions to a specific equation are one-dimensional.
SLS optimizes minimum-volume regions for conditional quantiles, bypassing density estimation.
G-GLN extends GLNs to multiple regression and density modeling.
New method clusters large datasets using geometric properties.
New method uses SoS densities and α-divergences for efficient sequential transport maps.
Study classifies mappings of bivariate normal densities, revealing three types with distinct geometric and statistical properties.
Markov Chain Monte Carlo methods become increasingly popular in applied mathematics as a tool for numerical integration with respect to complex and high-dimensional distributions. However, application of MCMC methods to heavy tailed distributions and distributions with analytically intractable densities turns out to be…
Paper proves stronger Penrose inequality with matter density.
New geometric interpretation of Amari-Cencov α-connections on probability densities.
A 3D space of hyperbolic manifolds is connected but not path-connected.
Topologically and geometrically engaging actions have proved to be useful to obtain rigidity results for semisimple Lie group actions. We show that the action of a simple noncompact Lie group on a compact manifold preserving a unimodular rigid geometric structure of algebraic type (e.g. a connection together with a vol…