The study classifies branched Willmore spheres in 3- and 4-spheres.
problem Classifying branched Willmore spheres in 3- and 4-spheres.
method Analyzing variational branched Willmore spheres and their projections onto R3 and R4. result Improved C1,1 regularity of unit normals and integer multiples of width in sphere eversion. BSVGD improves sampling for multimodal distributions using branching.
problem Sampling from multimodal distributions.
method Random branching in Stein Variational Gradient Descent (SVGD).
result Theoretical convergence guarantee and empirical validation.
Study continuous deformations of branched projective structures on surfaces, preserving holonomy and branch points.
problem Continuous deformations of branched projective structures on closed surfaces of genus g≥2. method Schiffer variations and analysis of canonical divisors.
result Branch points are necessarily arranged on a canonical divisor when the underlying complex structure is infinitesimally preserved.
Improved phylogenetic tree reconstruction using flexible branch length distributions.
problem Inefficient Markov chain Monte Carlo methods for large sequence datasets.
method Variational Bayesian phylogenetic inference with semi-implicit branch length distributions.
result Proposed method improves marginal likelihood estimation and branch length posterior approximation.
Improved phylogenetic inference with normalizing flows.
problem Limitations of current diagonal Lognormal branch length approximation in VBPI.
method Proposes VBPI-NF using normalizing flows to handle non-Euclidean branch length space.
result Significantly improves phylogenetic posterior estimation on real data.
The paper bounds the index of CMC surfaces with capillary boundary.
problem Bounding the index of CMC surfaces with capillary boundary.
method Comparison of second variations of area and energy, derived second variation formulae.
result The index is bounded linearly by genus, boundary components, and contact angle.
Improved phylogenetic inference using VBPI-Mixtures for tree topology and branch length.
problem Multimodality of tree-topology posterior distributions in phylogenetic inference.
method VBPI-Mixtures algorithm that uses mixture learning within the BBVI framework.
result VBPI-Mixtures captures tree-topology distributions better than VBPI.
Optimal regularity for 2D stationary varifolds proved.
problem Regularity of parametrized integer stationary varifolds in 2D.
method Established optimal regularity result for stationary varifolds.
result Smooth minimal branched immersion and constant multiplicity function.
New algorithm improves solving constraint satisfaction problems by avoiding contradictory estimates.
problem Improving solving efficiency for constraint satisfaction problems with approximate marginals.
method Introducing a streamlined branching strategy based on streamlining constraints.
result Streamlined solvers outperform decimation-based solvers on random k-SAT instances, reducing the gap in performance by 16.3% on average.
VLBM learns MDP transitions from limited data, improving OPE performance.
problem Limited coverage of state and action space in offline trajectories.
method VLBM uses variational inference with RSA and branching architecture.
result VLBM outperforms existing OPE methods on deep OPE benchmark.
Proves sufficiency of countable test plans for BV functions on metric spaces.
problem Recovering BV functions and their measures on arbitrary metric spaces.
method Proves sufficiency of countable test plans on arbitrary metric measure spaces and geodesics on CD(K,N) spaces. result Countable test plans are sufficient for BV functions and their measures on metric spaces.
A new variational method speeds up Bayesian phylogenetic inference.
problem Slow and inefficient MCMC methods in Bayesian phylogenetic inference.
method Combining subsplit Bayesian networks with variational inference for efficient tree topology and branch length estimation.
result Variational approach provides competitive performance with significantly fewer iterations.
New method for ancestral inference in branching processes with random environments.
problem Determining ancestor distribution parameters in branching processes with random environments.
method Generalized method of moments for ancestral inference.
result Limiting distribution of ancestor and offspring estimators decouple and converge to independent Gaussian variables under certain conditions.
Bayesian nonparametric Hawkes process model with EM-variational inference.
problem Limited model flexibility in classical Hawkes processes.
method Gaussian process modulated Hawkes process with EM-variational inference.
result Recover underlying baseline intensity and triggering kernel without parametric restriction.
Study on geometric variational problems for existence, regularity, and uniqueness of solutions.
problem Geometric variational problems, focusing on existence, regularity, and uniqueness of solutions.
method Formulated in Federer and Fleming's theory of currents, discussed the existence theory, and presented core ideas of the (interior) regularity theory for area-minimizing currents and optimal transport paths. Two original results on generic uniqueness of solutions were presented.
result Generic uniqueness of solutions for both Plateau's problem and optimal branched transport problem.
Minimal surfaces in a Riemannian manifold Mn are surfaces which are stationary for area: the first variation of area vanishes. In this paper we focus on surfaces of the topological type of the real projective plane RP2. We show that a minimal surface f:RP2→M3 which has the smallest area, among those ma…
Paper develops a new method to analyze 3D tree-like objects.
problem Analyzing complex geometrical and topological variations in 3D tree-like objects.
method Extended SRVF representation and new metric for tree-shaped 3D objects.
result Captures full elasticity and topological variations of branches.
In this work we present new fundamental tools for studying the variations of the Willmore functional of immersed surfaces into Rm. This approach gives for instance a new proof of the existence of a Willmore minimizing embedding of an arbitrary closed surface in arbitrary codimension. We explain how the same approach…
This paper extends FP's method to complex hyperbolic branched covers to find Einstein metrics.
problem Finding Einstein metrics on non-locally symmetric manifolds.
method Generalized FP's construction to complex hyperbolic branched covers.
result Yields a negatively curved Einstein metric that asymptotically approaches GH's metric.
Several models of stock trading [P. Bak et al, Physica A {\bf 246}, 430 (1997)] are analyzed in analogy with one-dimensional, two-species reaction-diffusion-branching processes. Using heuristic and scaling arguments, we show that the short-time market price variation is subdiffusive with a Hurst exponent H=1/4. Biase…
The paper is devoted to the variational analysis of the Willmore, and other L^2 curvature functionals, among immersions of 2-dimensional surfaces into a compact riemannian m-manifold (M^m,h) with m>2. The goal of the paper is twofold, on one hand, we give the right setting for doing the calculus of variations (includin…
RWS outperforms current methods in learning SCFMs.
problem Learning models with stochastic control flow is challenging.
method Revisited reweighted wake-sleep algorithm for SCFMs.
result RWS learns better models and inference networks with more particles.
The study presents examples of CD(0,N) spaces with varying dimensions and discusses the limitations of the CD(0,N) condition.
problem Exploring the properties and limitations of CD(0,N) spaces with varying dimensions. method Generalizing results from previous work, presenting examples and analyzing the conditions under which the CD(0,N) condition fails. result The CD(0,N) condition is not stable under measured Gromov-Hausdorff convergence and may fail in various ways. Study improves oracle inequality for tree graphs using total variation regularization.
problem Improving oracle inequality for tree graphs with total variation regularization.
method Generalized Fused Lasso result to tree graphs, using harmonic mean of distances.
result Proved a lower bound on compatibility constant for total variation penalty.
In this paper, we build up a min-max theory for minimal surfaces using sweepouts of surfaces of genus g≥2. We develop a direct variational methods similar to the proof of the famous Plateau problem by J. Douglas and T. Rado. As a result, we show that the min-max value for the area functional can be achieved by a …
Framework separates chemical and structural contributions to aqueous solubility.
problem Merging chemical and structural information in solubility models obscures their relative importance.
method Additive MLP-GNN framework with separate chemical and structural branches.
result Framework reveals distinct roles of chemical and structural information in solubility.
Model captures both slow and fast time variations in financial data.
problem Analyzing high-frequency financial data with varying background rates.
method Developed a Hawkes process with a time-varying background rate using Bayesian estimation.
result Model significantly improves goodness-of-fit to financial data, especially during fluctuating background rates.
A framework separates chemical and structural contributions to aqueous solubility.
problem Merging chemical and structural information in solubility models obscures their relative contributions.
method Additive MLP-GNN framework with separate chemical and structural branches.
result Framework reveals distinct roles of chemical and structural information in solubility.
We consider the Dirichlet problem for semilinear elliptic equations on a bounded domain which is diffeomorphic to a ball and investigate bifurcation from a given (trivial) branch of solutions, where the radius of the ball serves as bifurcation parameter. Our methods are based on well known results from variational bifu…
We consider a parallelizable 2n-manifold F which has the homotopy type of the wedge product of n-spheres and show that the group of pseudo-isotopy classes of orientation preserving diffeomorphisms that keep the boundary ∂F pointwise fixed and induce the trivial variation operator is a central extension …
Study on moduli spaces of branched projective structures on surfaces.
problem Characterizing and understanding moduli spaces of branched projective structures.
method Analytic and geometric methods to study the moduli spaces of branched projective structures.
result The moduli space of marked branched projective structures is a complex analytic space with specific dimensions and singular points.
We define a laminar branched surface to be a branched surface satisfying the following conditions: (1) Its horizontal boundary is incompressible; (2) there is no monogon; (3) there is no Reeb component; (4) there is no sink disk (after eliminating trivial bubbles in the branched surface). The first three conditions are…
GeoPhy uses geometric gradients to efficiently infer phylogenetic trees from molecular data.
problem Challenges in accurately inferring species relationships from molecular data due to combinatorially vast tree topologies.
method Introduces a novel, fully differentiable formulation of phylogenetic inference using geometric spaces and variational Bayesian methods.
result Significantly outperforms other approximate Bayesian methods in inferring phylogenetic trees.
Proper branched coverings are homeomorphisms on 3D balls or when branch set is empty.
problem Global injectivity of proper branched coverings on Euclidean balls.
method Analyzing the global injectivity of proper branched coverings defined on the Euclidean n-ball. result Proper branched coverings are homeomorphisms on 3D balls or when branch set is empty.
New criterion for branched covers between 2-spheres.
problem Existence of specific types of branched covers between 2-spheres.
method Combining complex analysis and topology techniques.
result Established a complete criterion for the existence of branched covers.
Given a branched covering of degree d between closed surfaces, it determines a collection of partitions of d, the branch data. In this work we show that any branch data are realized by an indecomposable primitive branched covering on a connected close surface N with Euler's characteristic less than or equal to 0. This …
In this note we continue the analysis of metric measure space with variable ricci curvature bounds. First, we study (κ,N)-convex functions on metric spaces where κ is a lower semi-continuous function, and gradient flow curves in the sense of a new evolution variational inequality that captures the information that …
For surface-knots, branched covers with degree 3 have simplifying numbers <3.
problem Understanding numerical invariants of branched covering surface-knots.
method Analyzing numerical invariant (simplifying number) of branched covering surface-knots with degree 3.
result Branched covering surface-knots with degree 3 have simplifying numbers less than 3.
Ideal triangulations of 3-manifolds are shown equivalent up to certain moves.
problem Equivalence of ideal triangulations in 3-manifolds.
method Using branched triangulations and transit equivalences, the paper shows that ideal triangulations are equivalent up to certain moves.
result Ideal triangulations of 3-manifolds are equivalent up to certain moves.
Open and discrete maps with specific branch set images are equivalent to PL branched covers.
problem Understanding the equivalence of open and discrete maps and PL branched covers.
method Demonstrated that an open and discrete map f:SnoSn with a specific branch set image is equivalent to a PL branched cover up to homeomorphism. result Open and discrete maps with a specific branch set image are equivalent to PL branched covers.
Criteria found for knots not determined by their double branched covers.
problem Determining knots from their double branched covers.
method Criteria based on tunnel number one knots and their double branched covers.
result Provided criteria for knots not determined by their double branched covers.
Uniformly branching trees are equivalent to certain metric spaces.
problem Characterizing metric spaces equivalent to uniformly branching trees.
method Proving equivalence between trivalent quasiconformal trees and uniformly branching trees.
result Any two uniformly branching trees are quasisymmetrically equivalent.
Study of geodesic branching in 2D sub-Riemannian manifolds.
problem Branching of geodesics in sub-Riemannian manifolds of rank two.
method Analysis of geodesic behavior in sub-Riemannian geometry.
result Continuous families of strictly abnormal branching geodesics and accumulation of branching points.
The paper studies which branched covers can be lifted to braided embeddings.
problem Which branched covers lift to braided embeddings?
method Analyzes conditions for liftability using Hansen's criterion and examples in different dimensions.
result Not all branched covers lift to braided embeddings; examples are provided in various dimensions.
New method finds unrealizable branched cover data.
problem Existence of branched covers between Riemann surfaces.
method Connecting spherical conic metrics to combinatorial constraints.
result New infinite sets of exceptional branching data found.
The paper details folding of branched covers of the 3-sphere over knots.
problem Understanding folding of branched covers of the 3-sphere over knots.
method Presenting detailed foldings of dihedral covers of the 3-sphere branched over torus knots.
result Detailed foldings of dihedral covers of the 3-sphere branched over torus knots are presented.
New method learns better branching policies for MILP problems.
problem Improving branch and bound search for solving MILP problems.
method Imitates strong branching rule with parameterized state of B&B search tree.
result Generalized policies outperform current state-of-the-art.
Simplifies surface-knots using chart moves involving black vertices.
problem Simplifying branched covering surface-knots.
method Chart moves involving black vertices to simplify surface-knots.
result Properties of simplified branched covering surface-knots with branch points.