Improved 3D scene understanding from partial point sets using multiview fusion.
problem Challenging task of 3D scene semantic understanding from partial point clouds.
method Multiview representation of 360° point clouds and fusion with original data.
result Overall increase of 31.9% and 4.3% in segmentation accuracy for partial and complete scenes.
In this paper, we investigate the fixed-point set of an element of a CAT(0) group in its boundary. Suppose that a group G acts geometrically on a CAT(0) space X. Let g∈G and let Fg be the fixed-point set of g in the boundary ∂X. Then we show that Fg=L(Zg), where Zg is …
Given a hyperbolic subgroup H of a hyperbolic group G for which a Cannon-Thurston map $\hat i:\partial H \ra \partial G$ exists, we study the limit set ΛH of H with respect to its action on ∂G. We prove that the set of conical limit points is exactly the subset of ΛH consisting of the points to wh…
Extends Brouwer fixed point theorem with new conditions for continuous maps.
problem Existence of fixed points for continuous maps from an n-ball to itself.
method Using absolute retracts and blockading sets, and degree theory.
result Existence of fixed points under specific conditions.
We fully describe the horofunction boundary ∂hL2 with the word metric associated with the generating set {t,at} (i.e the metric arising in the Diestel-Leader graph DL(2,2)). The visual boundary ∂∞L2 with this metric is a subset of ∂hL2. Although $\partial_\infty L_2…
Clarifies when certain stochastic PDEs have affine state processes.
problem Characterizing stochastic PDEs with affine state processes.
method Characterization of initial points for affine realizations.
result Characterizes the set of initial points for affine realizations.
Develops piecewise visual, linearly connected metrics on group boundaries.
problem Creating metrics on group boundaries with cut points.
method Graph of groups decompositions and piecewise visual metrics.
result Linearly connected metrics on boundaries with cut points.
A new anomaly detection method using partial identification.
problem Detecting anomalies in large datasets.
method Partial Identification framework and PIDScore geometric anomaly measure.
result PIDForest outperforms other methods in anomaly detection.
This paper establishes the geometric structure of the lines of principal curvature of a hypersurface immersed in R4 in a neighborhood of the set S of its principal curvature singularities, consisting of the points at which atF least two principal curvatures are equal. Under generic conditions d…
We study the Hamiltonian vector field v=(−∂f/∂w,∂f/∂z) on C2, where f=f(z,w) is a polynomial in two complex variables, which is non-degenerate with respect to its Newton's polygon. We introduce coordinates in four-dimensional neighbourhoods of the "points at infinity", in …
Partial connections are (singular) differential systems generalizing classical connections on principal bundles, yielding analogous decompositions for manifolds with nonfree group actions. Connection forms are interpreted as maps determining projections of the tangent bundle onto the partial connection; this approach e…
Let X be a proper CAT(0) space and G a cocompact group of isometries of X without fixed point at infinity. We prove that if ∂X contains an invariant subset of circumradius π/2, then X contains a quasi-dense, closed convex subspace that splits as a product. Adding the assumption that the G-action…
Proves robust transitivity for geodesic flows from metrics with conjugate points.
problem Transitivity of geodesic flows from metrics with conjugate points.
method General criterion for robust transitivity of partially hyperbolic geodesic flows.
result First example of a C2 open set of Riemannian metrics with conjugate points and transitive geodesic flow. Extracts geometric information from point-clouds for multiclass classification.
problem Multiclass Classification with labeled point-clouds.
method Stochastic partial orderings and label embedding trees.
result Computes multiscale geometries for explainable prediction and error-free labeling.
The classical k-means algorithm for partitioning n points in Rd into k clusters is one of the most popular and widely spread clustering methods. The need to respect prescribed lower bounds on the cluster sizes has been observed in many scientific and business applications. In this paper, we present an…
PRNet registers partial 3D shapes using deep learning.
problem Partial-to-partial point cloud registration.
method Self-supervised deep learning network for non-convex alignment and partial correspondence.
result Outperforms existing methods on synthetic data.
Study solves optimal portfolio selection using HJB equation.
problem Optimal portfolio selection problem.
method Maximal monotone operator method, Banach fixed-point theorem, Fourier transform, monotone operators technique.
result Existence and uniqueness of solution to HJB equation.
We prove that every function f:Rn→R satisfies that the image of the set of critical points at which the function f has Taylor expansions of order n−1 and non-empty subdifferentials of order n is a Lebesgue-null set. As a by-product of our proof, for the proximal subdifferential $\partial_{…
Clarifies when solutions to stochastic PDEs stay near given subsets.
problem Understanding the proximity of solutions to stochastic PDEs to given subsets.
method Analyzes distance between closed sets and solutions to stochastic PDEs.
result Clarifies conditions for solutions to stay near given subsets.
For any atoroidal iwip φ∈Out(FN) the mapping torus group Gφ=FN⋊φ<t>e is hyperbolic, and the embedding ι:FN⟶⊲Gφ induces a continuous, FN-equivariant and surjective {\em Cannon-Thurston map} ι^:∂FN→∂Gφ. We prove that for any φ as above…
We consider a locally trivial fiber bundle π:E→M over a compact oriented two-dimensional manifold M, and a section s of this bundle defined over M∖Σ, where Σ is a discrete subset of M. We call the set Σ the set of singularities of the section s:M∖Σ→E. We assume that the beh…
Paper tackles distribution matching by partially matching distributions, achieving robust results.
problem Robustly aligning two probability distributions.
method Developed a partial Wasserstein adversarial network (PWAN) to efficiently approximate the partial Wasserstein-1 (PW) discrepancy.
result The PWAN effectively produces highly robust matching results, outperforming state-of-the-art methods.
A new boundary for geodesic spaces defined and studied.
problem Understanding boundaries of geodesic spaces.
method Definition and study of quasi-geometric boundary ∂QGX. result The quasi-geometric boundary ∂QGX is compact and invariant under quasi-isometric equivalences. Paper proposes a method to recover point configurations from noisy distance data.
problem Recovering point configurations from noisy distance data.
method Robust Euclidean Distance Geometry via Dual Basis (RoDEoDB) algorithm.
result Exact recovery guarantees for point configuration and Gram matrix under mild conditions.
DAS-PINNs uses deep learning to solve complex PDEs more accurately.
problem Solving high-dimensional PDEs with high accuracy.
method Deep neural networks and generative models for adaptive sampling.
result DAS-PINNs significantly improves solution accuracy for low regularity and high-dimensional problems.
Paper introduces efficient methods for estimating cross-partial derivatives and sensitivity indices.
problem Efficiently estimating cross-partial derivatives and sensitivity indices in complex models.
method Using randomized points and constraints, the paper develops estimators with optimal convergence rates and low bias.
result The estimators achieve optimal rates of convergence and do not suffer from the curse of dimensionality.
We obtain in this paper bounds for the capacity of a compact set K. If K is contained in an (n+1)-dimensional Cartan-Hadamard manifold, has smooth boundary, and the principal curvatures of ∂K are larger than or equal to H0>0, then Cap(K)≥(n−1)H0vol(∂K). When K is contai…
We study n-dimensional area-minimizing currents T in Rn+1, with boundary ∂T satisfying two properties: ∂T is locally a finite sum of (n−1)-dimensional C1,α orientable submanifolds which only meet tangentially and with same orientation, for some α∈(0,1]; ∂T has…
We consider the question of efficient estimation in the tails of Gaussian copulas. Our special focus is estimating expectations over multi-dimensional constrained sets that have a small implied measure under the Gaussian copula. We propose three estimators, all of which rely on a simple idea: identify certain \emph{dom…
The paper proves smoothness of almost-minimizers' boundaries near the free boundary.
problem Minimizing degenerate area functionals with weighted boundary conditions.
method Epsilon-regularity theorem applied to almost-minimizers.
result Almost-minimizers' boundaries are C1,γ0-smooth, orthogonal to the boundary Ω. Artemis framework improves distributed learning with bidirectional compression and partial participation.
problem Learning in distributed or federated settings with communication constraints and device partial participation.
method Artemis framework using bidirectional compression, memory mechanism, and Polyak-Ruppert averaging.
result Fast rates of convergence (linear up to a threshold) under weak assumptions on stochastic gradients.
New method for partial matching of shapes with Varifolds.
problem Matching structures with topological or shape differences.
method Varifold shape representation and LDDMM framework.
result Effective partial matching despite topological differences.
New concept of partial comonotonicity connects riskmetrics and dependence.
problem Understanding and quantifying risk metrics under partial comonotonicity.
method Developed a new notion of partial comonotonicity and established its connection to distortion riskmetrics.
result Partial comonotonicity uniquely characterizes a class of distortion riskmetrics through additivity.
AUCRSS detects change points in partially observed multivariate autocorrelated data.
problem Detecting change points in multivariate autocorrelated data with limited sensing resources.
method Adaptive Upper Confidence Region (AUCRSS) with state space model (SSM), adaptive sampling policy, and generalized likelihood ratio test.
result The method outperforms existing approaches in detecting change points efficiently.
The objective is to study an on-line Hidden Markov model (HMM) estimation-based Q-learning algorithm for partially observable Markov decision process (POMDP) on finite state and action sets. When the full state observation is available, Q-learning finds the optimal action-value function given the current action (Q func…
Method uses NMF for clustering with partial distance measurements.
problem Proximity clustering with partial distance measurements.
method Nyström approximation with Nonnegative Matrix Factorization.
result Find nearly optimal clustering quality on synthetic and real-world data.
In this article, we prove several results about the extension to the boundary of conformal immersions from an open subset Ω of a Riemannian manifold L, into another Riemannian manifold N of the same dimension. In dimension n≥3, and when the (n−1)-dimensional Hausdorff measure of ∂Ω is zero, we …
Meta-learners estimate CATE from multiple environments with partial identification.
problem Estimating CATE from observational data across multiple environments with violations of causal assumptions.
method Adapt IV literature for partial identification, propose model-agnostic meta-learners.
result Meta-learners effectively estimate CATE bounds across various experiments.
New subgroup properties proven based on boundary compactness.
problem Characterizing acylindrically hyperbolic subgroups.
method Analyzing the contracting boundary and action on space of triples.
result Subgroups with certain boundary properties are acylindrically hyperbolic.
PILNO uses neural operators to solve PDEs efficiently on point clouds.
problem Solving partial differential equations (PDEs) on point cloud data efficiently.
method Physics-informed low-rank neural operator framework combining low-rank kernel approximations and an encoder-decoder architecture.
result PILNO efficiently approximates solution operators of PDEs on point cloud data, satisfying PDE constraints and boundary conditions.
New rigidity result for CAT(0) spaces of higher rank.
problem Rigidity of CAT(0) spaces of rank at least 2.
method Study of Morse flats and their Tits boundaries.
result CAT(0) spaces of rank at least n contain a regular point in their Tits boundary.
The paper develops methods to estimate POMDPs from partial information.
problem Making decisions under partial information about state variables.
method Structural estimation of POMDP primitives using observable history.
result Conditions for model identifiability without state dynamics knowledge.
Partial convexification improves tractability of low-rank spectral optimization problems.
problem Minimizing linear objectives subject to matrix inequalities and low-rank constraints.
method Partial convexification of the domain set, deriving rank bounds, and developing a column generation algorithm.
result The partial convexification LSOP-R is equivalent to the original LSOP under certain conditions and yields high-quality solutions.
We prove the statistical consistency of kernel Partial Least Squares Regression applied to a bounded regression learning problem on a reproducing kernel Hilbert space. Partial Least Squares stands out of well-known classical approaches as e.g. Ridge Regression or Principal Components Regression, as it is not defined as…
Complete list of solvable BS groups' actions on hyperbolic spaces.
problem Characterizing actions of solvable Baumslag-Solitar groups on hyperbolic metric spaces.
method Complete enumeration and classification of actions up to equivalence.
result Finitely many equivalence classes of actions, each containing a point, tree, or hyperbolic plane action.
In this paper we consider the lens rigidity problem with partial data for conformal metrics in the presence of a magnetic field on a compact manifold of dimension ≥3 with boundary. We show that one can uniquely determine the conformal factor and the magnetic field near a strictly convex (with respect to the magne…
A \emph{generalized dunce hat} is a 2-dimensional polyhedron created by attaching the boundary of a disk Δ to a circle J via a map f:∂Δ→J with the property that there is a point v∈J such that f−1({v}) is a finite set containing at least 3 points and f maps each component of $\partial Δ- …
The paper proves bounds on the Morse index of free boundary minimal hypersurfaces.
problem Finding bounds on the Morse index of free boundary minimal hypersurfaces.
method Min-max theory applied to (n+1)-dimensional compact manifolds with boundary. result Establishes general upper bounds for the Morse index of free boundary minimal hypersurfaces.