Evoked pain intensity representation is distributed across brain systems: A multistudy mega-analysis

ABSTRACTInformation is coded in the brain at different scales for different phenomena: locally, distributed across regions and networks, and globally. For pain, the scale of representation is controversial. Although generally believed to be an integrated cognitive and sensory phenomenon implicating diverse brain systems, quantitative characterizations of which regions and networks are sufficient to represent pain are lacking. In this meta-analysis (or mega-analysis) using data from 289 participants across 10 studies, we use model comparison combined with multivariate predictive models to investigate the spatial scale and location of acute pain representation. We compare models based on (a) a single most pain-predictive module, either previously identified elementary regions or a single best large-scale cortical resting-state network module; (b) selected cortical-subcortical systems related to evoked pain in prior literature (‘multi-system models’); and (c) a model spanning the full brain. We estimate the accuracy of pain intensity predictions using cross validation (7 studies) and subsequently validate in three independent holdout studies. All spatial scales convey information about pain intensity, but distributed, multi-system models better characterize pain representations than any individual region or network (e.g. multisystem models explain >20% more of individual subject pain ratings than the best elementary region). Full brain models showed no predictive advantage over multi-system models. These findings quantify the extent that representation of evoked pain experience is distributed across multiple cortical and subcortical systems, show that pain representation is not circumscribed by any elementary region or conical network, and provide a blueprint for identifying the spatial scale of information in other domains.Significance StatementWe define modular, multisystem and global views of brain function, use multivariate fMRI decoding to characterize pain representations at each level, and provide evidence for a multisystem representation of evoked pain. We further show that local views necessarily exclude important components of pain representation, while a global full brain representation is superfluous, even though both are viable frameworks for representing pain. These findings quantitatively juxtapose and reconcile divergent conclusions from evoked pain studies within a generalized neuroscientific framework, and provide a blueprint for investigating representational architecture for diverse brain processes.Author NoteData storage supported by the University of Colorado Boulder “PetaLibrary”. Research funded by NIMH R01 MH076136, NIDA R01 DA046064 and NIDA R01 DA035484. Lauren Atlas is supported in part by funding from the Intramural Research Program of the National Center for Complementary and Integrative Health, National Institutes of Health (ZIA-AT000030). Marina Lopez-Sola is supported by a Serra Hunter fellow lecturer program. We would like to thank Dr. Christian Buchel for contributing data to this project, and Dr. Marta Čeko for comments and feedback on the manuscript.

An inverse problem of synthesis of nanooptical security elements for visual and automated authenticity verification

Статья посвящена решению обратных задач синтеза нанооптических защитных элементов. Синтез нанооптического элемента включает в себя как решение обратной задачи расчета его фазовой функции, так и прецизионное формирование микрорельефа. При освещении микрорельефа в любой точке нанооптического элемента когерентным излучением в фокальной плоскости, параллельной плоскости оптического элемента, формируется изображение, используемое для автоматизированного контроля. Область оптического элемента разбивается на элементарные области. Изображение в элементарных областях формируется с помощью бинарных киноформов, фазовая функция которых рассчитывается с помощью решения нелинейного интегрального уравнения Фредгольма первого рода. Глубина микрорельефа в каждой элементарной области постоянна и определяет цвет элементарной области при освещении оптического элемента белым светом. Разработанные элементы могут быть использованы для защиты документов, акцизных марок, брендов и др. This paper is concerned with solving inverse problems of the synthesis of nanooptical security elements. The synthesis of a nanooptical element involves calculating its phase function via solving an inverse problem and fabricating the microrelief with high precision. The microrelief of the nanooptical element illuminated at any point with coherent radiation produces an image in the focal plane parallel to the plane of the optical element. This image is used for the automated authenticity verification. The area of the optical element is divided into elementary regions. In each elementary region, the image is formed using binary kinoforms whose phase function is calculated via solving a nonlinear Fredholm integral equation of the first kind. The depth of the microrelief is constant in each elementary region and determines the color of that region when the optical element is illuminated with white light. The developed elements can be used to protect documents, excise stamps, and brands.

Asymptotic optimal control over elliptic system with special characteristics

We construct and substantiate the solution of two-dimensional problem of the optimal distributed control over elliptic system with small parameter at higher derivative in an elementary region - in a square. We assume that the characteristics of limit control coincide with part of region boundary, and the control is unbounded.We show that the solutions of this problem have increasing singularities on some internal sets and, therefore, that the problem is bisingular.