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…
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48 results for “inverse limits”
Linear Flows on -Solenoidsmath.DS
Linear flows on inverse limits of tori are defined and it is shown that two linear flows on an inverse limit of tori are equivalent if and only if there is an automorphism of the inverse limit generating the equivalence.
We provide an easily verifiable condition for local -connectedness of an inverse limit of polyhedra.
Suppose that f and g are Markov surjections, each defined on a wedge of circles, each fixing the branch point and having the branch point as the only critical value. We show that if the points in the inverse limit spaces associated with f and g corresponding to the branch point are distinguished then these inverse limi…
Paper proposes IRL methods for limited interaction scenarios.
problem Learning with limited teacher interaction.
method Curriculum Inverse Reinforcement Learning (CIRL) and Self-Paced Inverse Reinforcement Learning (SPIRL).
result Training strategies can accelerate learning compared to random or batch methods.
Endowed with natural topologies, the fundamental group of the Hawaiian earring continuously injects into the inverse limit of free groups. This note shows the injection fails to have a continuous inverse. Such a phenomenon was unexpected and appears to contradict results of another author.
We show that the Bruschlinsky group with the winding order is a homeomorphism invariant for a class of one-dimensional inverse limit spaces. In particular we show that if a presentation of an inverse limit space satisfies the Simplicity Condition, then the Bruschlinsky group with the winding order of the inverse limit …
The paper characterizes -ANR spaces and their properties.
problem Characterizing -ANR spaces and their properties for compact groups.
method Proving conditions for a metrizable -space to be a -ANR.
result Conditions for a metrizable -space to be a -ANR are provided.
New flow expands hypersurfaces in hyperbolic space, showing round limiting shape for certain powers.
problem Understanding the limiting shape of hypersurfaces expanding in hyperbolic space.
method Introduced shifted inverse curvature flow with positive power for a smooth curvature function.
result For , limiting shape is always round as maximal existence time is approached.
Computational method approximates homology groups of compact metric spaces.
problem Computing homology groups of compact metric spaces.
method Inversely sequence of finite topological spaces, inverse limit, homeomorphic copy, strong deformation retract.
result Approximates homology groups of compact metric spaces.
Hausdorff reflection keeps space shape intact.
problem Preserving shape type in spaces.
method Hausdorff reflection method.
result Hausdorff reflection preserves shape type.
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…
Uncertainty Quantification in Seismic Inversion Through Integrated Importance Sampling and Ensemble Methodsphysics.geo-ph
This study improves uncertainty quantification in seismic inversion.
problem Uncertainty in seismic inversion due to limited data and model diversity.
method Integrates ensemble methods with importance sampling.
result More accurate uncertainty quantification in velocity models.
An inverse limit of a sequence of covering spaces over a given space is not, in general, a covering space over but is still a lifting space, i.e. a Hurewicz fibration with unique path lifting property. Of particular interest are inverse limits of finite coverings (resp. finite regular coverings), which yield fi…
The aim of this paper is to show how the homotopy type of compact metric spaces can be reconstructed by the inverse limit of an inverse sequence of finite approximations of the corresponding space. This recovering allows us to define inverse persistence as a new kind of persistence process.
Study transverse measures on infinite type hyperbolic surfaces.
problem Characterize the cone of transverse measures on infinite type hyperbolic surfaces.
method Use inverse limits and geodesic laminations to describe and construct cones of transverse measures.
result Explicit descriptions and bases of cones of transverse measures exist for many laminations.
Finite approximations help reconstruct countable metric and ultrametric spaces.
problem Reconstructing countable metric and ultrametric spaces.
method Topological reconstruction using inverse limits of finite spaces.
result Countable metric and ultrametric spaces can be reconstructed as finite approximations.
New method uses neural networks to identify sources from limited data in complex systems.
problem Identifying sources from noisy and limited data in high-dimensional systems.
method Calibrating deep neural network surrogates to ensemble simulations and using Bayesian optimization for source identification.
result Reliable source identification with uncertainty quantification using limited data and auxiliary processes.
Inverts operator on hyperbolic surfaces, constructing invariant distributions.
problem Constructing explicit inversion formula for X-ray normal operator.
method First, inversion formula for attenuated normal operator on Poincaré disk and closed hyperbolic surfaces. Then, explicit construction of invariant distributions.
result Explicit construction of invariant distributions with prescribed pushforward.
New method uses CNN for seismic inversion uncertainty quantification.
problem Uncertainty quantification in seismic inversion for noisy data.
method Plug-and-Play Stein Variational Gradient Descent (PnP-SVGD) with CNN denoiser.
result High-resolution, trustworthy posterior samples for subsurface structures.
This note revisits the inverse mean curvature flow in the 3-dimensional hyperbolic space. In particular, we show that the limiting shape is not necessarily round after scaling, thus resolving an inconsistency in the literature.
Utilizing variational autoencoders in the Bayesian inverse problem of photoacoustic tomographyphysics.comp-ph
Study uses machine learning to solve photoacoustic tomography's inverse problem.
problem Solving the full inverse problem in photoacoustic tomography.
method Developed an approach using variational autoencoders for Bayesian estimation of the posterior distribution.
result Evaluated the approach with numerical simulations and compared it to a Bayesian solution.
Using an inverse system of metric graphs as in: J. Cheeger and B. Kleiner, "Inverse limit spaces satisfying a Poincaré inequality", we provide a simple example of a metric space that admits Poincaré inequalities for a continuum of mutually singular measures.
Paper presents a unique method to recover signals from their bispectrum.
problem Retrieving signals accurately from their bispectrum.
method Two-step trust region algorithm that minimizes a non-convex objective function.
result Signals with finite spectral or temporal support can be recovered from at least 3B measurements of their bispectrum.
In extension theory, in particular in dimension theory, it is frequently useful to represent a given compact metrizable space X as the limit of an inverse sequence of compact polyhedra. We are going to show that, for the purposes of extension theory, it is possible to replace such an X by a better metrizable compactum …
Study evaluates Tree-Ring Watermarking in rectified flow-based models, revealing detection and separability limitations.
problem Detecting and separating Tree-Ring Watermarks in rectified flow-based models.
method Extensive experimentation comparing SD 2.1 and FLUX.1-dev models with various text guidance configurations and augmentation attacks.
result Inversion limitations affect watermark recovery and statistical separation.
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.
We show, analytically and numerically, that wealth distribution in the Bouchaud-Mézard network model of the economy is described by a three-parameter generalized inverse gamma distribution. In the mean-field limit of a network with any two agents linked, it reduces to the inverse gamma distribution.
Optimal Insurance to Minimize the Probability of Ruin: Inverse Survival Function Formulationq-fin.RM
Optimal insurance minimizes ruin probability with non-decreasing functions.
problem Minimizing ruin probability with insurance premiums and non-decreasing functions.
method Reformulated problem with inverse survival function as control variable.
result Deductible insurance with maximum limit is optimal.
Improved inverse problem solving with data consistency in diffusion models.
problem Speed and data consistency issues in diffusion model-based inverse problems.
method Data Consistent Direct Diffusion Bridges (CDDB) that ensures data consistency without fine-tuning.
result CDDB outperforms inconsistent DDB in perception and distortion metrics.
Generative model creates frictional surfaces from friction laws.
problem Designing frictional interfaces with prescribed behavior is challenging.
method Uses Variational Autoencoders (VAEs) to infer surface topographies from friction laws.
result Efficiently generates candidate topographies without contact simulations.
We study the convergence behavior of the general inverse -flow on Kähler manifolds with initial metrics satisfying the Calabi Ansatz. The limiting metrics can be either smooth or singular. In the latter case, interesting conic singularities along negatively self-intersected sub-varieties are formed as a result of …
EnKG solves inverse problems without derivatives, using diffusion models.
problem Solving inverse problems with derivative-free methods.
method Ensemble Kalman Diffusion Guidance (EnKG) using diffusion models.
result EnKG can solve inverse problems with only forward model evaluations.
A new data-adaptive prior stabilizes kernel learning in operators.
problem Learning kernels in operators from data is ill-posed due to nonlocal dependence.
method Introduces a data-adaptive prior to stabilize the Bayesian posterior mean.
result The data-adaptive prior achieves a stable posterior with small noise limits.
Inverse Particle Filtermath.OC
Develops an inverse particle filter for cognitive systems.
problem Tracking cognitive adversaries in counter-adversarial applications.
method Global filtering approach using Monte Carlo methods and differentiable I-PF.
result Demonstrates convergence to optimal inverse filter and improved estimation performance.
We consider the geometric inverse problem of determining a closed Riemannian manifold from measurements of the heat kernel in an open subset of the manifold. In this paper we analyze the stability of this problem in the class of -dimensional Riemannian manifolds with bounded diameter and sectional curvature. It is w…
Identification of a groundwater contaminant source simultaneously with the hydraulic conductivity in highly-heterogeneous media often results in a high-dimensional inverse problem. In this study, a deep autoregressive neural network-based surrogate method is developed for the forward model to allow us to solve efficien…
If pricing kernels are assumed non-negative then the inverse problem of finding the pricing kernel is well-posed. The constrained least squares method provides a consistent estimate of the pricing kernel. When the data are limited, a new method is suggested: relaxed maximization of the relative entropy. This estimator …
SINGD improves KFAC for memory-efficiency and stability in low-precision training.
problem Memory inefficiency and numerical instability of KFAC in low-precision training.
method Formulated inverse-free KFAC update and imposed structures in Kronecker factors.
result SINGD is memory-efficient and numerically robust, often outperforming AdamW in half precision.
On absence of steady state in the Bouchaud-Mézard network modelcond-mat.stat-mech
In the limit of infinite number of nodes (agents), the Itô-reduced Bouchaud-Mézard network model of economic exchange has a time-independent mean and a steady-state inverse gamma distribution. We show that for a finite number of nodes the mean is actually distributed as a time-dependent lognormal and inverse gamma is q…
The flow of a torus by inverse mean curvature keeps total curvature bounded until singularity.
problem Understanding the behavior of a torus under inverse mean curvature flow until singularity.
method Analyzing the evolution of a rotationally symmetric embedded torus in by inverse mean curvature flow.
result The total curvature remains bounded until the singular time .
Solenoids are ``inverse limits'' of the circle, and the classical knot theory is the theory of tame embeddings of the circle into the 3-space. We give some general study, including certain classification results, of tame embeddings of solenoids into the 3-space as the ``inverse limits'' of the tame embeddings of the ci…
p-adic framed braidsmath.GR
In this paper we define the -adic framed braid group , arising as the inverse limit of the modular framed braids and we give topological generators for . We also give geometric interpretations for the -adic framed braids. We then construct a -adic Yokonuma-Hec…
Paper introduces variational inference for Bayesian inverse problems with gamma hyperpriors.
problem Bayesian inverse problems with sparse solutions.
method Variational iterative alternating scheme for hierarchical models with gamma hyperpriors.
result Accurate reconstruction and meaningful uncertainty quantification.
Bayesian framework learns prior from data to quantify uncertainty in MRI reconstruction.
problem Quantifying uncertainty in deep learning solutions for inverse problems.
method Adopting denoising score matching to learn prior from data, using it in an annealed Hamiltonian Monte-Carlo scheme.
result The approach yields high-quality reconstructions and assesses uncertainty on specific features.
Deep learning methods improve subsurface flow modeling efficiency.
problem Efficiently modeling subsurface flow with uncertain parameters.
method Two categories of deep-learning based inverse modeling methods: surrogate-based and direct.
result Deep-learning methods significantly accelerate subsurface flow modeling.
In this paper we construct a compactification for the parameter space of convex projective structures on a fixed n-manifold M. This parameter space is a closed semi-algebraic subset of the variety of characters of representations of the fundamental group of M in SL_{n+1}(R). The boundary is the inverse limit of an inve…
This paper tackles regularization parameter learning in inverse problems using data-driven bilevel optimization.
problem Finding optimal regularization parameters in inverse problems.
method Data-driven bilevel optimization approach, analyzing performance in large data samples.
result The approach can reduce computational cost through online numerical schemes based on stochastic gradient descent.