Paper proves stability of positive mass theorem for specific types of manifolds.
problem Stability of positive mass theorem for compact graphical manifolds.
method Used Federer--Fleming flat distance and static quasi-local Brown-York energy.
result Proved stability of positive mass theorem for compact (locally) hyperbolic graphical manifolds.
Extends Brakke's local regularity theorem to longer time intervals.
problem Proving smoothness and graphicality of Brakke flows over extended time periods.
method Proving graphicality of Brakke flows with small gradient over time.
result Brakke flows remain graphical for some extended time intervals.
Method solves Gaussian graphical models on ladder graphs efficiently.
problem Solving Gaussian graphical models on ladder graphs efficiently.
method Proposes a method that depends on the position of zeros in local covariance matrices.
result Efficiently solves Gaussian graphical models on ladder graphs under certain conditions.
Localized inference for large graphs with error bounds.
problem Efficiently answering queries in large graphical models.
method Localized algorithm with error bounds based on Dobrushin's theorem.
result Localized inference provides fast and accurate approximations for large models.
Study on 2D self-shrinkers, proving their local behavior and boundedness.
problem Understanding the geometry and behavior of 2D self-shrinkers.
method Local graphical theorem, asymptotic behavior analysis, boundedness proof.
result Uniform boundedness of second fundamental form for noncompact self-shrinkers.
The paper proves stability of a quasi-local positive mass theorem for graphical hypersurfaces.
problem Stability of a quasi-local positive mass theorem for graphical hypersurfaces.
method Worked with the Brown--York quasi-local mass, considering compact n-manifolds with boundary as graphs in R^(n+1).
result If the Brown--York mass of the boundary of a compact manifold is small, then the manifold is close to a Euclidean hyperplane.
The paper extends Bernstein Theorem for minimal spacelike surfaces in 4D Minkowski space.
problem Analyzing Bernstein property for minimal spacelike surfaces in 4D Minkowski space.
method Study of an extension of the Bernstein Theorem for minimal spacelike surfaces in R^4_1.
result The Bernstein property does not hold in general for graphic spacelike surfaces in R^4_1.
We find a closed-form determinant for a specific sparse covariance matrix model.
problem Finding the determinant of a specific class of sparse positive definite matrices.
method Using Fourier transform of local factors, Normal Factor Graph Duality Theorem, and Matrix Determinant Lemma.
result We derive a closed-form expression for the determinant.
Proves smoothness of minimal surfaces near polyhedral boundaries.
problem Smoothness of free-boundary minimal surfaces near polyhedral domains.
method Allard-type regularity theorem for minimal surfaces in convex polyhedra.
result Minimal surfaces are C1,α graphical over a free-boundary plane if close to it. New inequality shows energy growth and decay in geometric problems.
problem Understanding energy behavior in geometric problems.
method Introduced a symmetric (log-)epiperimetric inequality.
result Energy growth and decay observed in geometric problems.
In this paper, we prove a generalization of Rado's Theorem, a fundamental result of minimal surface theory, which says that minimal surfaces over a convex domain with graphical boundaries must be disks which are themselves graphical. We will show that, for a minimal surface of any genus, whose boundary is "almost graph…
Graphical hypersurfaces inside a cylinder become almost graphical after a period.
problem Dealing with mean curvature flow of hypersurfaces inside a cylinder that are initially graphical except for a small set.
method Using White's regularity theorem, proving a lower bound on the period during which the flow remains graphical inside a cylinder of half the radius.
result A mean curvature flow that lies inside a slab and is initially graphical inside a cylinder except for a small set will become graphical inside the cylinder of half the radius.
Formula for mass in higher-dimensional graphs proves mass theorems.
problem Proving mass theorems for higher-dimensional graphs.
method Explicit formula for Gauss-Bonnet-Chern mass, applied to asymptotically flat graphical manifolds.
result Proves positive mass theorem and Penrose inequality for graphs with flat normal bundle.
Survey Bernstein-type theorems for graphical surfaces in Euclidean and Lorentz-Minkowski spaces.
problem Proving theorems for minimal and constant mean curvature graphs in Euclidean and Lorentz-Minkowski spaces.
method Explains several proofs and provides mean curvature estimates for graphs in Euclidean and Lorentz-Minkowski spaces.
result Bernstein-type theorems for constant mean curvature graphs in Euclidean 3-space and space-like graphs in Lorentz-Minkowski 3-space.
We give, via elementary methods, explicit formulas for the ADM mass which allow us to conclude the positive mass theorem and Penrose inequality for a class of graphical manifolds which includes, for instance, that ones with flat normal bundle.
We study minimal graphic functions on complete Riemannian manifolds $\Si$ with non-negative Ricci curvature, Euclidean volume growth and quadratic curvature decay. We derive global bounds for the gradients for minimal graphic functions of linear growth only on one side. Then we can obtain a Liouville type theorem with …
Proves a Bernstein theorem for 2D surfaces in 4D space.
problem Understanding properties of self-shrinkers in higher dimensions.
method Derives structure equations and uses Jacobian conditions.
result Graphical self-shrinkers in 4D are affine linear under certain conditions.
Develops a graphical calculus for stable curvature invariants.
problem Calculating stable curvature invariants of Riemannian manifolds.
method Graphical calculus based on trivalent graphs with colored edges.
result Derives a curvature identity for compact Einstein manifolds.
Stability of positive mass theorem for hyperbolic manifolds studied.
problem Stability of the positive mass theorem for asymptotically hyperbolic manifolds.
method Adapted intrinsic flat distance approach to show stability for a class of manifolds.
result Stability of the positive mass theorem for a class of asymptotically hyperbolic graphical manifolds.
In this paper, we prove a positive mass theorem and Penrose-type inequality of the Gauss-Bonnet-Chern mass m2 for the graphic manifold with flat normal bundle.
Graphically discrete groups have strong rigidity properties.
problem Understanding the rigidity of group actions on graphs.
method Introducing graphical discreteness and proving rigidity properties.
result Free products of graphically discrete groups are action rigid.
Extends a theorem for first-order elliptic operators on manifolds.
problem Proving the relative index theorem for general first-order elliptic operators.
method Using boundary value problems and graphical decomposition of elliptically regular boundary conditions.
result Proves the relative index theorem for general first-order elliptic operators.
Paper introduces new cluster-based graphical models for high-dimensional data.
problem Inference for high-dimensional graphical models with many features.
method Cluster-based model with model-assisted clustering; likelihood-based estimation and inference strategies.
result Developed estimators for precision matrix of latent vector, with asymptotic central limit theorems.
New method controls error in low-dimensional marginals of spatial models.
problem Inaccurate approximation of low-dimensional marginals in spatial models.
method Stein's method with δ-locality condition for spatial models.
result Uniform error bound for marginals of approximate distributions.
In this note we will prove that an n dimensional graphic self-shrinker in Rn+m with flat normal bundle is a linear subspace. This result is a generalization of the corresponding result of Lu Wang in codimension one case.
A new algorithm combines SVGD with local kernels for efficient inference in continuous graph models.
problem Efficient inference in high-dimensional continuous graphical models.
method Stein variational gradient descent extended with local kernels.
result Local kernels improve approximation and enable distributed inference.
Efficiently estimates graph models across multiple machines.
problem Estimating graph models in high-dimensional data with limited communication.
method Distributed estimation and inference for transelliptical graphical models.
result Aggregated estimator achieves same statistical rate as centralized estimator.
We introduce and study graphic lambda calculus, a visual language which can be used for representing untyped lambda calculus, but it can also be used for computations in emergent algebras or for representing Reidemeister moves of locally planar tangle diagrams.
Local method identifies causal relations in Markov equivalent DAGs.
problem Identifying causal relations when multiple DAGs are Markov equivalent.
method Graphical condition and local criteria for identifying causal paths.
result Local learning algorithm efficiently identifies causal variables.
This paper presents foundational theoretical results on distributed parameter estimation for undirected probabilistic graphical models. It introduces a general condition on composite likelihood decompositions of these models which guarantees the global consistency of distributed estimators, provided the local estimator…
The rigidity of the Positive Mass Theorem states that the only complete asymptotically flat manifold of nonnegative scalar curvature and zero mass is Euclidean space. We study the stability of this statement for spaces that can be realized as graphical hypersurfaces in Euclidean space. We prove (under certain technical…
We provide a classification of graphical models according to their representation as subfamilies of exponential families. Undirected graphical models with no hidden variables are linear exponential families (LEFs), directed acyclic graphical models and chain graphs with no hidden variables, including Bayesian networks …
Dynamic sampling from changing graphical models.
problem Sampling from a changing graphical model.
method Parallel Las Vegas algorithm for dynamic sampling.
result First dynamic sampling algorithms for Ising and hardcore models.
The rigidity of the positive mass theorem states that the only complete asymptotically flat manifold of nonnegative scalar curvature and zero mass is Euclidean space. We prove a corresponding stability theorem for spaces that can be realized as graphical hypersurfaces in Rn+1. Specifically, for an asympto…
We describe algorithms for finding harmonic cochains, an essential ingredient for solving elliptic partial differential equations in exterior calculus. Harmonic cochains are also useful in computational topology and computer graphics. We focus on finding harmonic cochains cohomologous to a given cocycle. Amongst other …
Calabi surgery modifies Z/2 harmonic 1-forms using 2-valued 1-forms.
problem Modifying Z/2 harmonic 1-forms under weak regularity assumptions.
method Calabi surgery method, involving cutting and pasting closed 2-valued 1-forms.
result Flexible construction and modification of Z/2 harmonic 1-forms.
New method aggregates nodes in sparse graphical models.
problem Estimating edge-sparse graphical models.
method Tree-aggregated graphical lasso (tag-lasso) method.
result Aggregates nodes in a data-driven fashion using a tree.
Let S be a C^2 H-minimal noncharacteristic hypersurface in the first Heisenberg group. We show that if S contains a graphical strip, then it is not a stable minimal surface. Moreover, we show that if S is a C^2 H-minimal noncharacteristic entire graph which is not itself a vertical plane, then S contains a graphical st…
We derive pointwise curvature estimates for graphical mean curvature flows in higher codimensions. To the best of our knowledge, this is the first such estimates without assuming smallness of first derivatives of the defining map. An immediate application is a convergence theorem of the mean curvature flow of the graph…
Layered graphical models improve discriminative learning efficiency.
problem Improving discriminative learning efficiency in graphical models.
method Designing layered graphical models (LGMs) in analogy to neural networks, using tensorized truncated variational inference and backpropagation.
result LGMs achieve competitive results in image classification, comparable to neural networks.
Local approach identifies non-existence of maximum likelihood estimates in sparse discrete models.
problem Non-existence of maximum likelihood estimates in high-dimensional discrete graphical models with sparse data.
method Local approach to identifying faces of marginal cones and composite maximum likelihood estimation.
result Local faces of marginal cones can be identified by examining induced subgraphs.
Liouville theorem for minimal graphs on manifolds with specific properties.
problem Characterizing positive minimal graphic functions on specific Riemannian manifolds.
method Using volume doubling property and uniform Neumann-Poincaré inequality.
result Positive minimal graphic functions on the manifold are constants.
Simple proof for graph curvature in Gauss space leads to new theorems.
problem Proving curvature bounds for graphs in Gauss space.
method Simple proof using weighted area estimates.
result Bernstein type theorems for self-shrinkers and graphic hypersurfaces.
Delta-AI speeds up inference in sparse PGMs by local credit assignment.
problem Efficient inference in sparse probabilistic graphical models.
method Local credit assignment in agent's policy learning objective.
result Trained sampler recovers marginals and conditional distributions.
A new method combines Gaussian graphical models for better distributed Gaussian process predictions.
problem Poor results from traditional DGP due to violated conditional independence assumption.
method Proposes using Gaussian graphical models to aggregate local predictions from subsets of data.
result Our method outperforms other state-of-the-art DGP approaches on both synthetic and real datasets.
New graph model relaxes acyclic constraint for better flexibility.
problem Graphical model constraints limit flexibility.
method Introduces new graphical models with relaxed constraints.
result New models allow directed cycles and up to two edges between nodes.
Two algorithms learn Gaussian graphical models from Glauber dynamics trajectories.
problem Learning Gaussian graphical models from dependent data.
method Two complementary approaches: local edge-testing and burn-in/thinning reduction.
result Both approaches provide finite-sample recovery guarantees and empirical comparisons.
Graphical potential games extend game theory to networks and machine learning.
problem Extending potential games to network settings.
method Characterizing graphical potential games using probabilistic graphical models.
result Game-playing rules imply agents are in a graphical potential game.