arXiv research

LatentNN corrects neural network attenuation bias in astronomical data.

New methods reduce bias in machine learning predictions for causal inference without extra data.

The study examines methods to correct measurement error in nutritional epidemiology studies.

The study examines when to trust confidence thresholding in pseudo-labelling regression.

This study quantifies uncertainty in comparing treatments using RCTs with before-and-after measures.

New EiV models correct bias in operator learning with noisy data.

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.

For a two-dimensional simple magnetic system, we study the attenuated magnetic ray transform $I_{A,Φ}$, with attenuation given by a unitary connection $A$ and a skew-Hermitian Higgs field $Φ$. We give a description for the range of $I_{A,Φ}$ acting on $\mathbb C^n$-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.

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.

We study the problem of recovery both the attenuation $a$ and the source $f$ 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 $δa$, $δf$ are supported in a com…

Framework predicts and prepares for rain-induced microwave link attenuation.

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…

Develops a GMM method to estimate roughness in stochastic volatility models.

Solves open problem on simple surfaces with novel twistor correspondence.

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.

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.

LAWN normalizes logits to improve deep network adaptability and generalization.

A deep learning model improves seismic noise reduction.

We study the geodesic X-ray transform $X$ 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 $X$ and relate it to the con…

New method prevents gradient attenuation in Lipschitz constrained convolutional networks.

A new method lifts training of input-convex neural networks to avoid dead weights and plateaued loss.

Transfer learning improves causal model estimates in small samples.

New method estimates treatment effects over time for survival data, improving accuracy and smoothness.

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.

This study shows ESG ratings reduce equity crash risk during market downturns.

The paper studies ray transforms on surfaces with negative curvature, proving injectivity and determining connections and Higgs fields.

Few-shot learning is a challenging problem where the goal is to achieve generalization from only few examples. Model-agnostic meta-learning (MAML) tackles the problem by formulating prior knowledge as a common initialization across tasks, which is then used to quickly adapt to unseen tasks. However, forcibly sharing an…

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…

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…

New insights into how to inspect and learn from multi-stage processes and AI reasoning.

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 $Γ$. 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…

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.

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…

SFP prunes ID features to improve OOD generalization without domain data.

Let $(X,ω)$ be a compact Kähler manifold. We introduce and study the largest set $DMA(X,ω)$ of $ω$-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.