In this paper we consider the geodesic X-ray transform with attenuation coefficient as a combination of smooth complex function and 1-form. We show that attenuated X-ray transform applied to the pair of tensors is injective modulo the natural obstruction.
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For a two-dimensional simple magnetic system, we study the attenuated magnetic ray transform , with attenuation given by a unitary connection and a skew-Hermitian Higgs field . We give a description for the range of acting on -valued tensor fields.
We show that the attenuated geodesic ray transform on two dimensional simple surfaces is injective. Moreover we give a stability estimate and develop a reconstruction procedure.
It has been shown in [Pa1] that on a simple, compact Riemannian 2-manifold the attenuated geodesic ray transform, with attenuation given by a connection and Higgs field, is injective on functions and 1-forms modulo the natural obstruction. Furthermore, the scattering relation determines the connection and Higgs field m…
For a compact Riemannian surface with boundary we study attenuated geodesic transform of functions and differential forms. We generalize several known results on uniqueness and stability of this transform dropping condition of absence of conjugate points.
Causal forests underestimate treatment effect heterogeneity, a correction is proposed.
problem Causal forests underestimate treatment effect heterogeneity in fixed-effects panel settings.
method Cross-fitted correction to estimate and restore the spread of conditional average treatment effects.
result The correction reduces mean-squared error by 25-42% in simulations and restores heterogeneity in a real-world panel study.
Attenuation correction for brain PET imaging using deep neural network based on dixon and ZTE MR imagesphysics.med-ph
Positron Emission Tomography (PET) is a functional imaging modality widely used in neuroscience studies. To obtain meaningful quantitative results from PET images, attenuation correction is necessary during image reconstruction. For PET/MR hybrid systems, PET attenuation is challenging as Magnetic Resonance (MR) images…
We describe the range of the attenuated ray transform of a unitary connection on a simple surface acting on functions and 1-forms. We use this to determine the range of the ray transform acting on symmetric tensor fields.
LatentNN corrects neural network attenuation bias in astronomical data.
problem Neural networks underestimate extreme values due to measurement errors.
method Jointly optimizes network parameters and latent input values.
result LatentNN reduces attenuation bias across various signal-to-noise ratios.
We study the problem of recovery both the attenuation and the source in the attenuated X-ray transform in the plane. We study the linearization as well. It turns out that there are natural Hamiltonian flow that determines which singularities we can recover. If the perturbations , are supported in a com…
Framework predicts and prepares for rain-induced microwave link attenuation.
problem Severe signal attenuation due to weather conditions degrades network performance.
method Predictive Network Reconfiguration (PNR) framework using LSTM for attenuation prediction and MSNR for dynamic routing.
result Framework improves network utilization by more than 200% compared to reactive algorithms.
Deep Boosted Regression for MR to CT Synthesisphysics.med-ph
Attenuation correction is an essential requirement of positron emission tomography (PET) image reconstruction to allow for accurate quantification. However, attenuation correction is particularly challenging for PET-MRI as neither PET nor magnetic resonance imaging (MRI) can directly image tissue attenuation properties…
We present two range characterizations for the attenuated geodesic X-ray transform defined on pairs of functions and one-forms on simple surfaces. Such characterizations are based on first isolating the range over sums of functions and one-forms, then separating each sub-range in two ways, first by implicit conditions,…
We derive explicit reconstruction formulas for the attenuated geodesic X-ray transform over functions and, in the case of non-vanishing attenuation, vector fields, on a class of simple Riemannian surfaces with boundary. These formulas partly rely on new explicit approaches to construct continuous right-inverses for bac…
Solves open problem on simple surfaces with novel twistor correspondence.
problem Existence of nontrivial holomorphic vector bundles on simple surfaces.
method Novel twistor correspondence, Nash-Moser inverse function theorem, and microlocal analysis.
result Simple surface twistor space supports no nontrivial holomorphic vector bundles.
We show that for a simple surface with boundary the attenuated ray transform in the presence of a unitary connection and a skew-Hermitian Higgs field is injective modulo the natural obstruction for functions and vector fields. We also show that the connection and the Higgs field are uniquely determined by the scatterin…
The paper reviews machine learning methods in PET imaging.
problem Improving accuracy in PET attenuation correction and reconstruction.
method Summarizes recent machine learning-based studies in PET imaging.
result Discusses the performance and challenges of current methods.
In this paper, a geometric function is introduced to reflect the attenuation speed of impact of one firm's default to its partner. If two firms are competitions (copartners), the default intensity of one firm will decrease (increase) abruptly when the other firm defaults. As time goes on, the impact will decrease gradu…
This article deals with stability issues related to geodesic X-ray transforms, where an interplay between the (attenuation type) weight in the transform and the underlying geometry strongly impact whether the problem is stable or unstable. In the unstable case, we also explain what types of artifacts are expected in te…
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.
L2F learns to forget, improving few-shot learning performance.
problem Few-shot learning challenges in adapting to unseen tasks.
method Task-and-layer-wise attenuation on compromised initialization to reduce prior knowledge influence.
result Faster adaptation and improved performance demonstrated experimentally.
LAWN normalizes logits to improve deep network adaptability and generalization.
problem Large logits and weights lead to overfitting in deep networks.
method Logit Attenuating Weight Normalization (LAWN) constrains weight norms in the final sub-network.
result LAWN improves generalization and adaptability of deep networks.
A deep learning model improves seismic noise reduction.
problem Seismic noise attenuation in pre-stack data processing.
method N2N-Seismic model based on residual neural networks.
result The model significantly outperforms conventional approaches in noise reduction metrics.
We study the geodesic X-ray transform on compact Riemannian surfaces with conjugate points. Regardless of the type of the conjugate points, we show that we cannot recover the singularities and therefore, this transform is always unstable (ill-posed). We describe the microlocal kernel of and relate it to the con…
New method prevents gradient attenuation in Lipschitz constrained convolutional networks.
problem Gradient norm attenuation in Lipschitz constrained convolutional networks.
method Block Convolution Orthogonal Parameterization (BCOP) to train scalable, expressive, provably Lipschitz convolutional networks.
result Empirically, BCOP parameterization is competitive with existing approaches to provable adversarial robustness and Wasserstein distance estimation.
Modelling long-term dependencies is a challenge for recurrent neural networks. This is primarily due to the fact that gradients vanish during training, as the sequence length increases. Gradients can be attenuated by transition operators and are attenuated or dropped by activation functions. Canonical architectures lik…
Proposes a method to improve classification robustness against label noise.
problem Improving classification robustness against label noise.
method Extends a simple regression approach to classification, modeling labels as samples from a logistic-normal distribution.
result The method improves robustness against label noise in classification.
The paper studies ray transforms on surfaces with negative curvature, proving injectivity and determining connections and Higgs fields.
problem Injectivity of ray transforms on surfaces with negative curvature and determination of connections and Higgs fields.
method Analysis of Gaussian thermostats on compact Riemannian surfaces with negative curvature, proving injectivity and determining connections and Higgs fields.
result Injectivity of the thermostat ray transform and determination of connections and Higgs fields.
Financial system being the place of metting capital flows (equality between saving and investment), a volatility of capital flows can destroy the robustness and good working of financial system, it means subvert financial stability. The same a weak financial system, few regulated and bad manage can exacerbate volatilit…
New methods reduce bias in machine learning predictions for causal inference without extra data.
problem Machine learning predictions from satellite data shrink toward the mean, leading to biased causal estimates.
method Two post-hoc correction methods: Linear Calibration Correction (LCC) and Tweedie's approach, reduce shrinkage-induced bias.
result Tweedie's method yields nearly unbiased treatment-effect estimates, enabling multiple trials with a single map.
In this paper, we reveal the attenuation mechanism of anchor of the commodity money from the perspective of logistics warehousing costs, and propose a novel Decayed Commodity Money (DCM) for the store of value across time and space. Considering the logistics cost of commodity warehousing by the third financial institut…
The Critical Horizon: Inspection Design Principles for Multi-Stage Operations and Deep Reasoningstat.ML
New insights into how to inspect and learn from multi-stage processes and AI reasoning.
problem Understanding how to attribute outcomes to early stages in multi-stage operations and AI reasoning.
method Information-theoretic analysis and mathematical proofs of four key results.
result Uniform checkpoint spacing is minimax-optimal for inspection design under homogeneous signal attenuation.
We reduce boundary determination of an unknown function and its normal derivatives from the (possibly weighted and attenuated) broken ray data to the injectivity of certain geodesic ray transforms on the boundary. For determination of the values of the function itself we obtain the usual geodesic ray transform, but for…
We consider the tomography problem of recovering a covector field on a simple Riemannian manifold based on its weighted Doppler transformation over a family of curves . This is a generalization of the attenuated Doppler transform. Uniqueness is proven for a generic set of weights and families of curves under a condi…
This study quantifies uncertainty in comparing treatments using RCTs with before-and-after measures.
problem Uncertainty in comparing treatments using RCTs with before-and-after measures.
method New statistical modeling principle called ETZ enables counterfactual uncertainty quantification (CUQ) in RCTs with Before-and-After Repeated Measures.
result CUQ typically has lower variability than factual uncertainty quantification and can be achieved in RCTs.
We first give a constructive answer to the attenuated tensor tomography problem on simple surfaces. We then use this result to propose two approaches to produce vector-valued integral transforms which are fully injective over tensor fields. The first approach is by construction of appropriate weights which vary along t…
A quantum memory model for Kelly betting with amplified or attenuated outcomes.
problem Optimizing Kelly betting strategies with quantum memory elements.
method Semi-classical model using quantum memory to encode payoff, modeled as random lasing dynamics.
result Best strategy is to invest all capital in coherent state amplitude for optimal performance.
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…
When to Trust Confidence Thresholding: Calibration Diagnostics for Pseudo-Labelled Regressionstat.ME
The study examines when to trust confidence thresholding in pseudo-labelling regression.
problem Calibrated probabilities from classifiers used for pseudo-labelling need careful handling to avoid bias in downstream regression.
method Developed a diagnostic apparatus to predict and bound the bias induced by confidence thresholding, derived a closed-form expression for the attenuation bias.
result The bias can be predicted from the residual score variance , motivating a structural separation between classifier features and downstream controls.
Let be a compact Kähler manifold. We introduce and study the largest set of -plurisubharmonic (psh) functions on which the complex Monge-Ampère operator is well defined. It is much larger than the corresponding local domain of definition, though still a proper subset of the set $PSH(X,\om)$ of all…
The paper introduces a method to make neural networks more robust to adversarial attacks.
problem Vulnerability of deep neural networks to small, adversarially designed perturbations.
method A bottom-up strategy using a nonlinear front end that polarizes and quantizes data.
result The approach can completely eliminate adversarial perturbations on MNIST and Fashion MNIST datasets.
The paper shows that causal identification is not essential for efficient portfolios, focusing on geometric sufficiency conditions.
problem The necessity of causal identification for efficient portfolios.
method Re-examination of predictive signals and their impact on portfolio efficiency under structural misspecification.
result Efficiency is governed by geometric sufficiency conditions (directional alignment, ranking preservation, and calibration) rather than causal identification.
Parts of Texas, Oklahoma, and Kansas have experienced increased rates of seismicity in recent years, providing new datasets of earthquake recordings to develop ground motion prediction models for this particular region of the Central and Eastern North America (CENA). This paper outlines a framework for using Artificial…
The study examines methods to correct measurement error in nutritional epidemiology studies.
problem Measurement error in nutritional studies leads to biased and underconfident estimates.
method The article reviews various bias-correction models for exposure variables in nutritional epidemiology.
result Bias-correction methods are essential for accurate inference in nutritional studies.
New defense method reduces adversarial attacks on neural networks.
problem Vulnerability of deep neural networks to adversarial attacks.
method Sparse coding frontend trained on clean images.
result Significantly attenuates adversarial attacks before reaching classifier.
Over the past few years, neural networks were proven vulnerable to adversarial images: targeted but imperceptible image perturbations lead to drastically different predictions. We show that adversarial vulnerability increases with the gradients of the training objective when viewed as a function of the inputs. Surprisi…
New method improves estimation of neural network aleatoric uncertainty.
problem Existing methods overestimate aleatoric uncertainty in neural networks.
method Proposes a new de-noising method to estimate data uncertainty more accurately.
result Demonstrates better approximation of actual data uncertainty.
New EiV models correct bias in operator learning with noisy data.
problem Bias in operator learning due to noisy independent variables.
method Developed EiV models for MOR-Physics and DeepONet.
result EiV models reduce bias in noisy operator learning.