Quantitative susceptibility mapping (QSM) is a powerful MRI technique that has shown great potential in quantifying tissue susceptibility in numerous neurological disorders. However, the intrinsic ill-posed dipole inversion problem greatly affects the accuracy of the susceptibility map. We propose QSMGAN: a 3D deep con…
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48 results for “Quantitative Susceptibility Mapping”
NDI enables high-quality QSM without parameter tuning.
problem Quantitative Susceptibility Mapping (QSM) with regularization tuning issues.
method Nonlinear Dipole Inversion (NDI) using a physics-based forward model and a Variational Network (VN).
result NDI achieves high-quality QSM from as few as 2-direction data.
CycleQSM uses deep learning to accurately map tissue magnetic susceptibility without needing paired data.
problem Accurately mapping magnetic susceptibility values from phase images using QSM.
method Unsupervised deep learning approach using physics-informed cycleGAN.
result The method provides more accurate QSM maps compared to existing deep learning approaches.
Despite numerous attempts to defend deep learning based image classifiers, they remain susceptible to the adversarial attacks. This paper proposes a technique to identify susceptible classes, those classes that are more easily subverted. To identify the susceptible classes we use distance-based measures and apply them …
Overparameterized linear model shows strong classification but weak regression, susceptible to adversarial perturbations.
problem Adversarial vulnerability of overparameterized linear models.
method Lifted Fourier feature map, analyzing overparameterized linear ensemble.
result Spatial localization leads to adversarial vulnerability in an intermediate classification regime.
Study on stability of half-harmonic maps from R to S, proving non-degeneracy and quantitative stability.
problem Stability and non-degeneracy of half-harmonic maps from R to S.
method Analyzing the kernel of the linearized operator and using quantitative rigidity estimates.
result Uniform control of deviation for half-harmonic maps near Möbius transformations and Blaschke products.
Optimizes biharmonic map regularity using stratification methods.
problem Improving the known almost optimal regularity of biharmonic maps.
method Quantitative stratification method.
result Optimal regularity results for minimizing biharmonic maps.
MRI Parameter Mapping via Gaussian Mixture VAE: Breaking the Assumption of Independent Pixelseess.IV
New MRI method maps tissue parameters more accurately by ignoring voxel independence.
problem Voxel independence assumption limits model fitting reliability and repeatability.
method Self-supervised deep variational approach with Gaussian mixture prior.
result Our method outperforms current techniques in dMRI simulations and real data.
For harmonic maps of degree 2, a similar quantitative stability estimate does not hold uniformly.
problem Investigate the quantitative stability of harmonic maps of degree 2.
method Prove a local quantitative stability result for harmonic maps of degree 2, showing dependence on the given harmonic map.
result A uniformly quantitative stability estimate does not hold for degree 2 harmonic maps.
Recent results in Reinforcement Learning (RL) have shown that agents with limited training environments are susceptible to a large amount of overfitting across many domains. A key challenge for RL generalization is to quantitatively explain the effects of changing parameters on testing performance. Such parameters incl…
Convolutional neural networks (CNNs) are known for their good performance and generalization in vision-related tasks and have become state-of-the-art in both application and research-based domains. However, just like other neural network models, they suffer from a susceptibility to noise and adversarial attacks. An adv…
Proves polynomial injectivity of Fubini-Study map for ample line bundles.
problem Injectivity of Fubini-Study map for ample line bundles.
method Polynomial injectivity proof with polynomial dependence on ample line bundle exponent.
result Quantitative version of injectivity proved, polynomial in ample line bundle exponent.
Susceptibility Propagation by Using Diagonal Consistencycond-mat.stat-mech
A susceptibility propagation that is constructed by combining a belief propagation and a linear response method is used for approximate computation for Markov random fields. Herein, we formulate a new, improved susceptibility propagation by using the concept of a diagonal matching method that is based on mean-field app…
Analyzes empirical risk minimization in finance, showing effectiveness and generalization issues.
problem Analyzing empirical risk minimization in finance for optimal hedging and investment decisions.
method Classical statistical machine learning techniques and non-asymptotic estimates based on Rademacher complexity.
result Over-training leads to anticipative decisions, but non-asymptotic estimates show convergence for large training sets.
Sharp estimate shows maps with small energy defect are close to rational maps.
problem Quantitative rigidity of maps from to of general degree.
method Proved maps with small energy defect are essentially given by a collection of rational maps at different scales.
result Sharp quantitative rigidity estimate , sharpness shown.
The paper extends regularity for -minimizing maps using a Reifenberg Theorem.
problem Quantitative regularity of -minimizing maps between Riemannian manifolds.
method Stratification of singular points based on almost-symmetries, followed by application of a Reifenberg-type Theorem.
result Upper bound on the Minkowski content of the singular set, and -rectifiability of the singular set.
Estimates point counts in Teichmüller space for mapping class groups.
problem Counting points in Teichmüller space under mapping class group actions.
method Quantitative estimates with power saving error terms for Teichmüller metric balls.
result Effectivizes asymptotic counting results of Athreya et al.
In this paper we prove quantitative regularity results for stationary and minimizing extrinsic biharmonic maps. As an application, we determine sharp, dimension independent bounds for that do not require a small energy hypothesis. In particular, every minimizing biharmonic map is in for all…
In this paper, we prove estimates and quantitative regularity results for the harmonic map flow. First, we consider H^1_loc-maps u defined on a parabolic ball P\subset M\times R and with target manifold N, that have bounded Dirichlet-energy and Struwe-energy. We define a quantitative stratification, which groups togeth…
Unified view of SOMs and SNE from a common framework.
problem Comparing and understanding SOMs and SNE.
method Unified mathematical framework, quantitative comparison on datasets.
result SOMs and SNE can be derived from a common framework.
In this article, we study the regularity of minimizing and stationary -harmonic maps between Riemannian manifolds. The aim is obtaining Minkowski-type volume estimates on the singular set , as opposed to the weaker and non quantitative Hausdorff dimension bo…
Sharp stability result for maps near infinitely concentrated minimisers.
problem Stability of maps near minimisers with infinite concentration.
method Dynamic approach to deform maps into harmonic maps, controlling topology changes.
result Sharp quantitative estimates on map distance to infinitely concentrated minimisers.
Sharp quantitative stability of the Möbius group among sphere-valued maps in arbitrary dimensionmath.AP
Sharp stability of Möbius group among sphere-valued maps proved in arbitrary dimensions.
problem Proving a sharp quantitative form of Liouville's theorem for sphere-valued maps.
method New arguments and an inequality from Sobolev inequality proof.
result Sharp stability estimate for weakly conformal maps of arbitrary dimensions.
Quantifies uniqueness of conformal-harmonic maps on 4-manifolds.
problem Quantifying uniqueness of conformal-harmonic maps on 4-manifolds.
method Proves a quantitative uniqueness result using convexity and second order Hardy inequality.
result Proves a version of second order Hardy inequality on manifolds.
We show that uniform lattices in some semi-simple groups (notably complex ones) admit Anosov surface subgroups. This result has a quantitative version: we introduce a notion, called -Sullivan maps, which generalizes the notion of -quasi-circles in hyperbolic geometry, and show in particular that Sullivan maps are…
Softmax and k-means clustering are mathematically linked, improving neural network robustness.
problem Improving neural network robustness against adversarial attacks.
method Formally proving the connection between softmax and k-means, proposing Centroid Based Tailoring.
result The proposed Gauss network is less susceptible to one-pixel attacks.
LIME outperforms other explainers in identifying adversarial attack regions.
problem Evaluating explainers for detecting adversarial attacks in neural networks.
method Quantitative and qualitative investigation of three explainers on adversarial examples.
result LIME outperforms classic salience and guided backpropagation in identifying adversarial attack regions.
Extends scaling maps theory to manifolds with boundary.
problem Quantitative study of Carnot-Carathéodory balls on manifolds with boundary.
method Introduction of scaling maps adapted to Carnot-Carathéodory balls and Hörmander vector fields on manifolds with boundary.
result First paper in a series studying maximally subelliptic boundary value problems.
Improved Yang-Yau inequality for all orientable surfaces except for specific genera.
problem Bounding the first eigenvalue of the Laplacian on orientable surfaces.
method Using holomorphic maps to CP^n to improve the Yang-Yau inequality.
result Quantitative improvement of the Yang-Yau inequality for all genera except 4, 6, 8, 10, and 14.
LMGPs extend GPs to handle mixed data, offering better accuracy and interpretability.
problem Handling mixed data types (quantitative and qualitative) in metamodeling.
method Introduce LMGPs that learn a latent manifold for qualitative inputs, using a low-rank linear map.
result LMGPs outperform existing methods in accuracy and versatility.
The paper studies constraint maps with singularities and free boundaries, proving continuity near singularities and optimality.
problem Analyzing the structure of constraint maps with singularities and free boundaries.
method Establish continuity near singularities using a new quantitative unique continuation principle, and investigate the presence of branch points leading to new singularities.
result Topological singularities can only lie in the interior of the contact set in the uniformly convex setting, and the optimality of this result is proven.
Riemannian stochastic gradient descent approximates a diffusion process called Riemannian stochastic modified flow.
problem Improving convergence rate of Riemannian stochastic gradient descent.
method Using stochastic differential geometry, the paper shows RSGD can be approximated by the Riemannian stochastic modified flow (RSMF).
result RSGD can be approximated by the solution to the RSMF driven by an infinite-dimensional Wiener process, increasing the order of approximation.
CNNs can develop blind spots due to uneven padding in feature maps.
problem Spatial bias in convolutional networks leads to blind spots in certain tasks.
method Identified and analyzed the role of padding in convolutional networks, proposing solutions to mitigate bias.
result Mitigating spatial bias improves model accuracy, especially in tasks like small object detection.
Classifies low energy maps from curved surfaces into spheres.
problem Classifying maps from surfaces of constant curvature into spheres.
method Analyzes maps with low energy and degree ±1, focusing on bubble configurations.
result Maps are quantitively close to a bubble configuration with specific radii.
Stability of the positive mass theorem and torus rigidity theorems under integral curvature boundsmath.DG
The paper analyzes harmonic maps to flat model spaces to prove geometric stability of the positive mass theorem.
problem Geometric stability of the positive mass theorem and related conjectures.
method Analysis of harmonic maps to flat model spaces under integral curvature bounds.
result Upgrading harmonic maps to diffeomorphisms when conditions are met, proving quantitative closeness to model spaces.
In this paper, we will show the Yau's gradient estimate for harmonic maps into a metric space with curvature bounded above by a constant , , in the sense of Alexandrov. As a direct application, it gives some Liouville theorems for such harmonic maps. This extends the works of S. Y. Cheng [4] and H.…
We prove a quantitative openness theorem for submersions under suitable assumptions on the differential. We then apply our result to a class of exponential maps appearing in Carnot-Carathéodory spaces and we improve a classical completeness result by Palais.
We introduce a technique for proving quantitative representation stability theorems for sequences of representations of certain finite linear groups over a field of characteristic zero. In particular, we prove a vanishing result for higher syzygies of VIC- and SI-modules, which can be thought of as a weaker version of …
Optimally stabilizes Möbius group maps in spheres across dimensions.
problem Ensuring optimal stability of Möbius group maps in spheres of all dimensions.
method Proves stability estimate involving optimal λ and φ transformations.
result Compact sequences with vanishing deficit under Möbius group action.
The contour map of estimation error of Expected Shortfall (ES) is constructed. It allows one to quantitatively determine the sample size (the length of the time series) required by the optimization under ES of large institutional portfolios for a given size of the portfolio, at a given confidence level and a given esti…
We study in this paper the maximal version of the coarse Baum-Connes assembly map for families of expanding graphs arising from residually finite groups. Unlike for the usual Roe algebra, we show that this assembly map is closely related to the (maximal) Baum-Connes assembly map for the group and is an isomorphism for …
The study of genetic variants can help find correlating population groups to identify cohorts that are predisposed to common diseases and explain differences in disease susceptibility and how patients react to drugs. Machine learning algorithms are increasingly being applied to identify interacting GVs to understand th…
Stability estimates in determination of non-orientable surface from its Dirichlet-to-Neumann mapmath.DG
Study shows continuity of non-orientable surface determination from Dirichlet-to-Neumann map.
problem Determining non-orientable surfaces from Dirichlet-to-Neumann map.
method Proving closeness of Dirichlet-to-Neumann maps implies near-conformal diffeomorphism.
result Established continuity of determination and quantitative estimates of .
We show that any closed n-dimensional Riemannian manifold can be embedded by a map constructed from heat kernels at a certain time from a finite number of points. Both this time and this number can be bounded in terms of the dimension, a lower bound on the Ricci curvature, the injectivity radius and the volume. It foll…
Harmonic maps to Euclidean buildings have rectifiable singular strata.
problem Understanding the structure of singular points for harmonic maps.
method Defining singular strata and proving rectifiability using the rectifiable Reifenberg program.
result Rectifiability of singular strata for harmonic maps into -connected complexes.
Framework combines machine learning and inverse methods to quantify uncertainties in model parameters.
problem Combining aleatoric and epistemic uncertainties in engineered systems modeling.
method Develops a robust filtering step in LUQ to learn useful QoI maps from noisy datasets, iterates over time, and uses sufficiency tests.
result Transforms datasets into distributions for DC-based inversion, improving parameter quantification.
Generative Neural Samplers for the Quantum Heisenberg Chaincond-mat.stat-mech
Generative neural samplers estimate quantum spin system properties.
problem Estimating observables for quantum spin systems.
method Autoregressive models using Suzuki-Trotter transformation.
result Results for energy, specific heat, and susceptibility are in good agreement with Monte Carlo methods.
New method bounds membership inference attack success using mutual information.
problem Vulnerability of deep neural networks to membership inference attacks.
method Extended Fano's inequality to measure mutual information between inputs and activations.
result Empirical evaluation shows strong correlation between mutual information and model susceptibility.