Proves rigidity of circle packings in the plane, generalizing previous work.
problem Rigidity of infinite inversive distance circle packings in the plane.
method Maximal principle for generic weighted Delaunay inversive distance circle packings and ring lemma for inversive distance circle packings in hexagonal triangulated plane.
result Proves Bowers-Stephenson's conjecture for inversive distance circle packings.
Proof of existence and uniqueness of weighted Voronoi-Delaunay on polyhedral surfaces.
problem Existence and uniqueness of weighted Voronoi-Delaunay on polyhedral surfaces.
method Construct an isotopic map instead of edge-flipping algorithm, generalizing Dyer et al's method.
result Strict proof of existence and uniqueness of weighted Voronoi-Delaunay on polyhedral surfaces.
The paper extends the Discrete Schwarz-Pick Lemma to circle packings with obtuse intersections and disjoint packings.
problem Proving the Discrete Schwarz-Pick Lemma for circle packings with various inversive distances.
method Using a variational principle for circle packings with inversive distances, the paper extends the lemma to a broader range of packings.
result The Discrete Schwarz-Pick Lemma holds for circle packings with inversive distances in (−1,1], provided an additional condition on triangle weights. The paper proves the existence of a unique circle packing on hyperbolic surfaces.
problem Proving the existence of a unique inversive distance circle packing on hyperbolic polyhedral surfaces.
method Deforming the surface by discrete Ricci flow, doing surgery by edge flipping, and using a variational principle of a convex Ricci potential.
result There exists a unique inversive distance circle packing that is discrete conformal to the original one.
Hierarchical clustering uses OWA operators to generalize linkage methods and avoid dendrogram inversions.
problem Avoiding unaesthetic inversions in hierarchical clustering dendrograms.
method OWA-based linkages combined with the Lance-Williams formula and conditions on weight generators.
result Conditions for weight generators to produce dendrograms without inversions.
Fundamental weight systems identified as quantum states.
problem Identifying which weight systems are quantum states.
method Analyzing the Cayley distance kernel on the symmetric group and its positivity.
result All fundamental gl(n)-weight systems are quantum states.
Global optimization problems whose objective function is expensive to evaluate can be solved effectively by recursively fitting a surrogate function to function samples and minimizing an acquisition function to generate new samples. The acquisition step trades off between seeking for a new optimization vector where the…
New theorem proves rigidity of circle packings in hyperbolic geometry.
problem Rigidity of circle packings in hyperbolic geometry.
method Established maximum principles and applied them to prove rigidity.
result Proved infinite rigidity of weighted Delaunay triangulations in the Poincaré disk.
IDA adapts to non-iid data in federated learning for medical imaging.
problem Statistical heterogeneity in federated learning data, especially in medical imaging.
method IDA (Inverse Distance Aggregation) is a novel adaptive weighting approach for clients based on meta-information.
result IDA outperforms Federated Averaging in handling unbalanced and non-iid data in federated learning.
A new framework enhances IDW models for complex industrial datasets.
problem Low performance of IDW models in complex industrial datasets.
method Deep reinforcement learning network to enhance IDW models and learn hyperparameters.
result The proposed framework achieves differential spatial prediction and is more accurate than current IDW models.
Inversive distance circle packing metric was introduced by P Bowers and K Stephenson \cite{BS} as a generalization of Thurston's circle packing metric \cite{T1}. They conjectured that the inversive distance circle packings are rigid. For nonnegative inversive distance, Guo \cite{Guo} proved the infinitesimal rigidity a…
We give a counterexample of Bowers-Stephenson's conjecture in the spherical case: spherical inversive distance circle packings are not determined by their inversive distances.
Paper proves circle packings converge to Riemann mapping for Jordan domains.
problem Proving discrete conformal maps converge to Riemann mapping.
method Establishing solvability theorem for inversive distance circle packings.
result Bowers-Stephenson's conjecture for Jordan domains is proven.
New method finds metrics on surfaces with prescribed curvatures using circle packings and surgery.
problem Finding piecewise Euclidean metrics on surfaces with prescribed combinatorial curvatures.
method Combinatorial curvature flows with surgery for inversive distance circle packings.
result Longtime existence and global convergence of combinatorial curvature flows with surgery.
Inversive distance circle packing on surfaces was introduced by Bowers-Stephenson as a generalization of Thurston's circle packing and conjectured to be rigid. The infinitesimal and global rigidity of circle packing with nonnegative inversive distance were proved by Guo and Luo respectively. The author proved the globa…
This work characterizes, analytically and numerically, two major effects of the quadratic Wasserstein (W2) distance as the measure of data discrepancy in computational solutions of inverse problems. First, we show, in the infinite-dimensional setup, that the W2 distance has a smoothing effect on the inversion pro…
Study Gaussian-process limits of neural networks using tensor programs.
problem Understanding the behavior of neural networks as they approach infinite width.
method Quantitative analysis through tensor programs and Wasserstein distance.
result Explicit finite-width error bounds, showing convergence to Gaussian-process limits.
The paper introduces a new Wasserstein distance for approximating posteriors in inverse problems.
problem Approximating posterior measures in inverse problems using conditional Wasserstein distances.
method Introduces a conditional Wasserstein distance with restricted couplings and derives its dual.
result Shows that conditional Wasserstein GANs can yield favorable properties for posterior sampling.
Proposes stabilized weights for causal inference using isotonic calibration.
problem Stability and bias issues in inverse propensity weighting.
method Post-hoc isotonic calibration of inverse propensity weights.
result Improves performance of doubly robust estimators of average treatment effect.
This paper investigates several global rigidity issues for polyhedral surfaces including inversive distance circle packings. Inversive distance circle packings are polyhedral surfaces introduced by P. Bowers and K. Stephenson as a generalization of Andreev-Thurston's circle packing. They conjectured that inversive dist…
A Euclidean (or hyperbolic) circle packing on a closed triangulated surface with prescribed inversive distance is locally determined by its cone angles. We prove this by applying a variational principle.
Sharp upper bounds derived for Alexandrov-Fenchel deficit using weighted Minkowski integral formulas.
problem Deriving upper bounds for the Alexandrov-Fenchel deficit.
method Using weighted Minkowski integral formulas and an integral formula for the deficit in Jensen's inequality.
result Quantitative estimates under weaker convexity assumptions, including a distance term.
In this paper, we generalize Chow-Luo's combinatorial Ricci flow to inversive distance circle packing setting. Although the solution to the generalized flow may develop singularities in finite time, we can always extend the solution so as it exists for all time and converges exponentially fast. Thus the generalized flo…
R-Learning uses inverse-variance weights to estimate treatment effects more accurately.
problem Estimating heterogeneous treatment effects (CATEs) with stable and accurate methods.
method R-Learning with inverse-variance weights (IVWs) for pseudo-outcome regression.
result IVWs improve the stability and accuracy of CATE estimation.
A method for optimal Bayesian filtering using progressive particle flow and optimal transport maps.
problem Optimizing Bayesian filtering with deterministic particles to avoid degeneration.
method Progressive flow of particles through a sequence of sub-steps, each using an optimal transport map to replace non-equally weighted particles with equally weighted ones.
result The method avoids particle degeneration and simplifies the filtering process by not requiring inversions or monotonicity constraints.
The subject of this article is the introduction of a new concept of well-posedness of Bayesian inverse problems. The conventional concept of (Lipschitz, Hellinger) well-posedness in [Stuart 2010, Acta Numerica 19, pp. 451-559] is difficult to verify in practice and may be inappropriate in some contexts. Our concept sim…
Improves deep learning performance on noisy datasets using inverse-variance weighting.
problem Heteroscedastic regression with varying noise levels.
method Batch Inverse-Variance (BIV) loss function for neural networks.
result Significantly improves network performance on noisy datasets compared to other methods.
Given a triangulated surface M, we use Ge-Xu's α-flow \cite{Ge-Xu1} to deform any initial inversive distance circle packing metric to a metric with constant α-curvature. More precisely, we prove that the inversive distance circle packing with constant α-curvature is unique if αχ(M)≤0, which generalize And…
The aim of the paper is to investigate the relation between inverse limit of branched manifolds and codimension zero laminations. We give necessary and sufficient conditions for such an inverse limit to be a lamination. We also show that codimension zero laminations are inverse limits of branched manifolds. The inverse…
New nonparametric estimators improve causal effect estimation.
problem Estimation of causal effects with selection bias.
method Undersmoothing of the highly adaptive lasso for estimating the weighting mechanism.
result Asymptotic efficiency and convergence to nonparametric efficiency bound.
In this article we consider the anisotropic Calderon problem and related inverse problems. The approach is based on limiting Carleman weights, introduced in Kenig-Sjoestrand-Uhlmann (Ann. of Math. 2007) in the Euclidean case. We characterize those Riemannian manifolds which admit limiting Carleman weights, and give a c…
The MEM method uses data-driven priors for linear inverse problems, proving convergence and estimating differences.
problem Linear inverse problems with approximate priors.
method Maximum Entropy on the Mean (MEM) method with data-driven priors.
result Empirical mean convergence and estimates for prior differences based on epigraphical distance.
Reconstructing manifolds from partial distance and heat kernel data.
problem Reconstructing a manifold from noisy distance measurements and heat kernel data.
method Approximate reconstruction of a manifold from partial distance and heat kernel data with noise.
result A stable reconstruction of the manifold can be achieved from noisy heat kernel data.
Generative models improve inverse problems by providing tailored priors.
problem Analyzing the error in inverse problems solved with generative priors.
method Quantitative error bounds for minimum Wasserstein-2 generative models.
result The error in the posterior due to the generative prior is bounded by the prior's error in Wasserstein-1 distance.
Innovative game theory approach optimizes survival analysis metrics.
problem Survival analysis models trained with maximum likelihood do not directly optimize criteria like Brier score or Bernoulli log likelihood.
method Inverse-Weighted Survival Games: Construct objectives from re-weighted estimates featuring the other model, holding the latter fixed during training.
result Games optimize Brier score on simulations and real-world data.
Graph curvature measured by inverse resistance distance.
problem Defining and analyzing curvature in graphs.
method Defining curvature via inverse resistance distance and proving properties.
result Graphs with positive curvature have controlled diameter and spectral properties.
Study shows refugee matching gains are robust to different evaluation methods.
problem Stability of refugee matching gains under various evaluation methods.
method Used multiple off-policy evaluation methods including IPW and AIPW.
result Impact estimates remain consistent in magnitude and statistically significant.
Unified framework recovers exact input from SOM activation patterns.
problem Generating high-dimensional data from Self-Organizing Maps (SOMs).
method Inverting SOM activation patterns to recover input, using linear system and Tikhonov regularization.
result MUSIC framework produces coherent semantic transitions and maintains high classifier confidence.
The original Broad Learning System (BLS) on new added nodes and its existing efficient implementation both assume the ridge parameter lambda -> 0 in the ridge inverse to approximate the generalized inverse, and compute the generalized inverse solution for the output weights. In this paper, we propose two ridge solution…
We study the inverse spectral problem for weighted projective spaces using wave-trace methods. We show that in many cases one can "hear" the weights of a weighted projective space.
Wide deep neural networks with Gaussian weights approximate Gaussian processes closely.
problem Understanding the approximation of deep neural networks with Gaussian weights to Gaussian processes.
method Established novel rates for the Gaussian approximation of random deep neural networks with Gaussian parameters and Lipschitz activation functions in the wide limit.
result The distance between the network output and the Gaussian approximation scales inversely with the width of the network.
New method calculates Ricci curvature from distances between weighted volumes.
problem Calculating Ricci curvature for weighted Riemannian manifolds.
method Asymptotic retrieval of generalized Ricci tensor from scaled metric derivatives of Wasserstein 1-distances.
result Limiting coarse curvature of random graphs converges to generalized Ricci tensor.
ROTS improves sentence similarity by incorporating structural information.
problem Measuring sentence similarity with theoretical insights and structural awareness.
method Recursive Optimal Transport (ROT) framework to incorporate structural information.
result ROTS outperforms weakly supervised approaches in sentence similarity tasks.
Unified framework evaluates different nearest neighbor classification methods.
problem Evaluating and comparing classical, fuzzy, and fuzzy rough nearest neighbor classification methods.
method Standardized nearest neighbor weighting with kernel functions applied to distance and/or rank values of nearest neighbors.
result NN, FNN, and FRNN perform best with Boscovich distance, and NN and FRNN perform best with specific combinations of weights and scaling measures.
Unified framework for Bayesian PDE-constrained inversion using physics-informed neural networks.
problem Incorporating prior distributions in function space into Bayesian PINN-based inversion.
method Functional-prior-based approaches (fpBPINN) to Bayesian PDE-constrained inversion using physics-informed neural networks (PINNs). Two complementary approaches: FPI-BPINN and fParVI-PINN.
result Accurate estimation of posterior distributions in seismic traveltime tomography and Darcy-flow permeability inversion.
Transformer learns context and regularization for ICL in inverse problems.
problem Learning context and effective regularization for transformer-based in-context learning (ICL) in inverse problems.
method Introduced a linear transformer to learn inverse mapping from contextual examples to weight vectors, addressing rank-deficient problems.
result Transformer implicitly learns a prior distribution and effective regularization strategy, outperforming traditional methods.
Efficient algorithm removes redundant nodes and obsolete samples in machine learning.
problem Pruning redundant nodes and removing obsolete training samples in machine learning.
method Deduced decremented learning algorithms from incremental learning algorithms, using inverse Cholesterol factor and unitary transformation.
result Proposed decremented learning algorithms efficiently prune redundant nodes and remove obsolete training samples.
Study improves estimation of functions from noisy data using convex penalties.
problem Estimating functions from noisy point evaluations of linear operators.
method Tikhonov regularization with convex and p-homogeneous penalty functionals. result Derives concentration rates for regularized solutions in symmetric Bregman distance.