arXiv research

Paper connects Painlevé VI equation to irregular systems, solving monodromy data.

The paper explores coalescent contractions in contractible spaces, providing criteria and examples.

We extend the analytic theory of Frobenius manifolds to semisimple points with coalescing eigenvalues of the operator of multiplication by the Euler vector field. We clarify which freedoms, ambiguities and mutual constraints are allowed in the definition of monodromy data, in view of their importance for conjectural re…

We propose a new algorithm to do posterior sampling of Kingman's coalescent, based upon the Particle Markov Chain Monte Carlo methodology. Specifically, the algorithm is an instantiation of the Particle Gibbs Sampling method, which alternately samples coalescent times conditioned on coalescent tree structures, and tree…

We introduce a new Bayesian model for hierarchical clustering based on a prior over trees called Kingman's coalescent. We develop novel greedy and sequential Monte Carlo inferences which operate in a bottom-up agglomerative fashion. We show experimentally the superiority of our algorithms over others, and demonstrate o…

New algorithms learn simple staged trees from data, improving model fit.

Linear-cost unbiased estimates for complex models via couplings.

Two oppositely charged droplets of (say) water in e.g. oil or air will tend to drift together under the influence of their charges. As they make contact, one might expect them to coalesce and form one large droplet, and this indeed happens when the charge difference is sufficiently small. However, Ristenpart et al disc…

Develops a variational method for ultrametric phylogenetic trees.

New definition of angular momentum avoids supertranslation ambiguity.

PipeDream-2BW accelerates large model training by 20x with minimal memory usage.

Study on kinetic Langevin diffusions and their couplings, showing subtle TV bounds and new non-Markovian couplings.

Bayesian Neural Networks detect gravitational wave events with high accuracy and real-time potential.

We propose a nonparametric Bayesian factor regression model that accounts for uncertainty in the number of factors, and the relationship between factors. To accomplish this, we propose a sparse variant of the Indian Buffet Process and couple this with a hierarchical model over factors, based on Kingman's coalescent. We…

Study models Indian stock market using hyperbolic geometry for market stability and volatility analysis.

We give a complete description of finite braid group orbits in Aff(C)-character varieties of the punctured Riemann sphere. This is performed thanks to a coalescence procedure and to the theory of finite complex reflection groups. We then derive consequences in the theory of differential equations. These concern algebra…

Extends ML fairness to handle minority groups over time.

New RL approach builds short ancestral recombination graphs.

In distributed function computation, each node has an initial value and the goal is to compute a function of these values in a distributed manner. In this paper, we propose a novel token-based approach to compute a wide class of target functions to which we refer as "Token-based function Computation with Memory" (TCM) …

Proposes a method to balance imbalanced image datasets using capsule-GAN.

Feature Squeezing is a recently proposed defense method which reduces the search space available to an adversary by coalescing samples that correspond to many different feature vectors in the original space into a single sample. It has been shown that feature squeezing defenses can be combined in a joint detection fram…

Study geodesic trees and exceptional directions in FPP on hyperbolic groups.

We introduce a compactification of the space of simple positive divisors on a Riemann surface, as well as a compactification of the universal family of punctured surfaces above this space. These are real manifolds with corners. We then study the space of constant curvature metrics on this Riemann surface with prescribe…

GrateTile optimizes CNN feature map storage for efficient data access.

We present an new sequential Monte Carlo sampler for coalescent based Bayesian hierarchical clustering. Our model is appropriate for modeling non-i.i.d. data and offers a substantial reduction of computational cost when compared to the original sampler without resorting to approximations. We also propose a quadratic co…

This paper is a tutorial for eigenvalue and generalized eigenvalue problems. We first introduce eigenvalue problem, eigen-decomposition (spectral decomposition), and generalized eigenvalue problem. Then, we mention the optimization problems which yield to the eigenvalue and generalized eigenvalue problems. We also prov…

The paper compares Steklov and Laplacian eigenvalues on graphs.

The paper proves convergence of WDVV potentials and semisimplicity of Frobenius manifolds.

In this paper, two interesting eigenvalue comparison theorems for the first non-zero Steklov eigenvalue of the Laplacian have been established for manifolds with radial sectional curvature bounded from above. Besides, sharper bounds for the first non-zero eigenvalue of the Wentzell eigenvalue problem of the weighted La…

Transforming cylindrical packings into bicontinuous surfaces.

The paper explores inequalities between eigenvalues on Riemannian manifolds.

Eigenvalues of Steklov eigenproblems change predictably with boundary tweaks.

Study compares eigenvalues on spherically symmetric manifolds to Euclidean balls.

The paper sets lower bounds for Laplacian eigenvalues and clamped plate problem eigenvalues.

Paper finds how Steklov eigenvalues change on graphs and trees.

Eigenvalue estimate for shrinkers in mean curvature flow.

In this paper we study eigenvalues of the closed eigenvalue problem of the Witten-Laplacian on an $n$-dimensional compact Riemannian manifold. Estimates for eigenvalues are given. As applications, we give a sharp upper bound for the $k^{\text{th}}$ eigenvalue and for isoparametric minimal hypersurfaces in the unit sphe…

For a bounded domain $Ω$ with a piecewise smooth boundary in an $n$-dimensional Euclidean space $\mathbf{R}^{n}$, we study eigenvalues of the Dirichlet eigenvalue problem of the Laplacian. First we give a general inequality for eigenvalues of the Laplacian. As an application, we study lower order eigenvalues of the Lap…

The paper provides estimates for eigenvalues of elliptic differential problems.

The paper compares eigenvalues of Dirichlet, Neumann, and Laplacian on graphs.

Sharp bounds derived for the first two Steklov eigenvalues of exterior domains.

We study first passage percolation (FPP) on a Gromov-hyperbolic group $G$ with boundary $\partial G$ equipped with the Patterson-Sullivan measure $ν$. We associate an i.i.d.\ collection of random passage times to each edge of a Cayley graph of $G$, and investigate classical questions about the asymptotics of first pass…

Let $\om $ be a bounded domain in an $n$-dimensional Euclidean space $\Bbb R^n$. We study eigenvalues of an eigenvalue problem of a system of elliptic equations: $$ \{\aligned &Δ{\mathbf u}+ α{\rm grad}(\text{div}{\mathbf u})=-σ{\mathbf u}, \ \text{in $Ω$}, &{\mathbf u}|_{\partial Ω}={\mathbf 0}. \aligned . $$ Estimate…

Improved lower bounds for poly-Laplacian eigenvalues in arbitrary dimensions.

Study eigenvalues of p-Laplacian on quaternionic Kähler manifolds.

We study the eigenvalue problem for the Riemannian Pucci operator on geodesic balls. We establish upper and lower bounds for the principal Pucci eigenvalues depending on the curvature, extending Cheng's eigenvalue comparison theorem for the Laplace-Beltrami operator. For manifolds with bounded sectional curvature, we p…

The paper studies eigenvalues of Xin-Laplacian on Riemannian manifolds.

The paper finds new inequalities for Laplacian and biharmonic eigenvalues on manifolds.