Search results for "problems"
showing 10 items of 620 documents
Partial data inverse problems for the Hodge Laplacian
2017
We prove uniqueness results for a Calderon type inverse problem for the Hodge Laplacian acting on graded forms on certain manifolds in three dimensions. In particular, we show that partial measurements of the relative-to-absolute or absolute-to-relative boundary value maps uniquely determine a zeroth order potential. The method is based on Carleman estimates for the Hodge Laplacian with relative or absolute boundary conditions, and on the construction of complex geometric optics solutions which reduce the Calderon type problem to a tensor tomography problem for 2-tensors. The arguments in this paper allow to establish partial data results for elliptic systems that generalize the scalar resu…
The Geodesic Ray Transform on Spherically Symmetric Reversible Finsler Manifolds
2023
We show that the geodesic ray transform is injective on scalar functions on spherically symmetric reversible Finsler manifolds where the Finsler norm satisfies a Herglotz condition. We use angular Fourier series to reduce the injectivity problem to the invertibility of generalized Abel transforms and by Taylor expansions of geodesics we show that these Abel transforms are injective. Our result has applications in linearized boundary rigidity problem on Finsler manifolds and especially in linearized elastic travel time tomography.
Pestov identities and X-ray tomography on manifolds of low regularity
2021
We prove that the geodesic X-ray transform is injective on scalar functions and (solenoidally) on one-forms on simple Riemannian manifolds $(M,g)$ with $g \in C^{1,1}$. In addition to a proof, we produce a redefinition of simplicity that is compatible with rough geometry. This $C^{1,1}$-regularity is optimal on the H\"older scale. The bulk of the article is devoted to setting up a calculus of differential and curvature operators on the unit sphere bundle atop this non-smooth structure.
The method of moving planes: a quantitative approach
2018
We review classical results where the method of the moving planes has been used to prove symmetry properties for overdetermined PDE's boundary value problems (such as Serrin's overdetermined problem) and for rigidity problems in geometric analysis (like Alexandrov soap bubble Theorem), and we give an overview of some recent results related to quantitative studies of the method of moving planes, where quantitative approximate symmetry results are obtained.
A symmetrization result for Monge–Ampère type equations
2007
In this paper we prove some comparison results for Monge–Ampere type equations in dimension two. We also consider the case of eigenfunctions and we derive a kind of “reverse” inequalities. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Critical points for nondifferentiable functions in presence of splitting
2006
A classical critical point theorem in presence of splitting established by Brézis-Nirenberg is extended to functionals which are the sum of a locally Lipschitz continuous term and of a convex, proper, lower semicontinuous function. The obtained result is then exploited to prove a multiplicity theorem for a family of elliptic variational-hemivariational eigenvalue problems. © 2005 Elsevier Inc. All rights reserved.
A matheuristic for the Team Orienteering Arc Routing Problem
2015
In the Team OrienteeringArc Routing Problem (TOARP) the potential customers are located on the arcs of a directed graph and are to be chosen on the basis of an associated profit. A limited fleet of vehicles is available to serve the chosen customers. Each vehicle has to satisfy a maximum route duration constraint. The goal is to maximize the profit of the served customers. We propose a matheuristic for the TOARP and test it on a set of benchmark instances for which the optimal solution or an upper bound is known. The matheuristic finds the optimal solutions on all, except one, instances of one of the four classes of tested instances (with up to 27 vertices and 296 arcs). The average error o…
Internalizing problems as a mediator in the relationship between low effortful control and internet abuse in adolescence: A three-wave longitudinal s…
2019
Abstract The aim of the study is to examine the relationships between early adolescents' low effortful control, middle adolescents' internalizing problems and late adolescents' Internet abuse, focusing on the mediating role that middle adolescents' internalizing problems may play in the relationship between early adolescents' low effortful control and late adolescents' Internet abuse. The study followed a sample of 482 adolescents (245 boys and 237 girls) from early adolescence (wave 1; mean age = 14.76, SD = 0.63), through middle adolescence (wave 2; mean age = 15.77, SD = 0.61), to late adolescence (wave 3; mean age = 17.88, SD = 0.57). The participants completed self-report questionnaire…
Developmental dynamics between children’s externalizing problems, task-avoidant behavior, and academic performance in early school years: A 4-year fo…
2015
This longitudinal study investigated the associations among children’s externalizing problems, task-avoidant behavior, and academic performance in early school years. The participants were 586 children (43% girls, 57% boys). Data pertaining to externalizing problems (teacher ratings) and task-avoidant behaviors (mother and teacher ratings) were gathered, and the children were tested yearly on their academic performance in Grades 1–4. The results were similar for both genders. The analyses supported a mediation model: high externalizing problems in Grades 1 and 2 were linked with low academic performance in Grades 3 and 4 through increases in task-avoidant behavior in Grades 2 and 3. The res…
Using Artificial Intelligence to Enhance Ongoing Psychological Interventions for Emotional Problems in Real- or Close to Real-Time: A Systematic Revi…
2022
Emotional disorders are the most common mental disorders globally. Psychological treatments have been found to be useful for a significant number of cases, but up to 40% of patients do not respond to psychotherapy as expected. Artificial intelligence (AI) methods might enhance psychotherapy by providing therapists and patients with real- or close to real-time recommendations according to the patient’s response to treatment. The goal of this investigation is to systematically review the evidence on the use of AI-based methods to enhance outcomes in psychological interventions in real-time or close to real-time. The search included studies indexed in the electronic databases Scopus, Pubmed, W…