Browse
Submit Data
Databases
API
Help

Dataset Information

0 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

Nonequilibrium Green's Functions for Functional Connectivity in the Brain.

ABSTRACT: A theoretical framework describing the set of interactions between neurons in the brain, or functional connectivity, should include dynamical functions representing the propagation of signal from one neuron to another. Green's functions and response functions are natural candidates for this but, while they are conceptually very useful, they are usually defined only for linear time-translationally invariant systems. The brain, instead, behaves nonlinearly and in a time-dependent way. Here, we use nonequilibrium Green's functions to describe the time-dependent functional connectivity of a continuous-variable network of neurons. We show how the connectivity is related to the measurable response functions, and provide two illustrative examples via numerical calculations, inspired from Caenorhabditis elegans.

SUBMITTER: Randi F

PROVIDER: S-EPMC8454901 | biostudies-literature | 2021 Mar

REPOSITORIES: biostudies-literature

ACCESS DATA

Json Xml

Publications

Nonequilibrium Green's Functions for Functional Connectivity in the Brain.

Randi Francesco F Leifer Andrew M AM

Physical review letters 20210301 11

A theoretical framework describing the set of interactions between neurons in the brain, or functional connectivity, should include dynamical functions representing the propagation of signal from one neuron to another. Green's functions and response functions are natural candidates for this but, while they are conceptually very useful, they are usually defined only for linear time-translationally invariant systems. The brain, instead, behaves nonlinearly and in a time-dependent way. Here, we use ...[more]

PMID: 33798383

Similar Datasets

Two-Dimensional Spectroscopy of Open Quantum Systems: Nonequilibrium Green's Function Formulation.

Project description:Two-dimensional spectroscopy is examined for open quantum systems featuring multiple simultaneously measurable fluxes. Specifically, we explore a junction where optical measurements of photon flux are paired with concurrent transport measurements of electron currents. The theory of two-dimensional spectroscopy for both fluxes is developed using a nonself-consistent nonequilibrium Green's function formulation. Theoretical derivations are demonstrated through numerical simulations within a generic junction model.

| S-EPMC11873975 | biostudies-literature

Green's functions for unsymmetric composite laminates with inclusions.

Project description:It is known that the stretching and bending deformations will be coupled together for the unsymmetric composite laminates under in-plane force and/or out-of-plane bending moment. Although Green's functions for unsymmetric composite laminates with elliptical elastic inclusions have been obtained by using Stroh-like formalism around 10 years ago, due to the ignoring of inconsistent rigid body movements of matrix and inclusion, the existing solution may lead to displacement discontinuity across the interface between matrix and inclusion. Due to the multi-valued characteristics of complex logarithmic functions appeared in Green's functions, special attention should be made on the proper selection of branch cuts of mapped variables. To solve these problems, in this study, the existing Green's functions are corrected and a simple way to correctly evaluate the mapped complex variable logarithmic functions is suggested. Moreover, to apply the obtained solutions to boundary element method, we also derive the explicit closed-form solution for Green's function of deflection. Since the continuity conditions along the interface have been satisfied in Green's functions, no meshes are required along the interface, which will save a lot of computational time and the results are much more accurate than any other numerical methods.

| S-EPMC7016552 | biostudies-literature

Diffusion in a disk with inclusion: Evaluating Green's functions.

Project description:We give exact Green's functions in two space dimensions. We work in a scaled domain that is a circle of unit radius with a smaller circular "inclusion", of radius a, removed, without restriction on the size or position of the inclusion. We consider the two cases where one of the two boundaries is absorbing and the other is reflecting. Given a particle with diffusivity D, in a circle with radius R, the mean time to reach the absorbing boundary is a function of the initial condition, given by the integral of Green's function over the domain. We scale to a circle of unit radius, then transform to bipolar coordinates. We show the equivalence of two different series expansions, and obtain closed expressions that are not series expansions.

| S-EPMC9009627 | biostudies-literature

Disambiguating brain functional connectivity.

Project description:Functional connectivity (FC) analyses of correlations of neural activity are used extensively in neuroimaging and electrophysiology to gain insights into neural interactions. However, analyses assessing changes in correlation fail to distinguish effects produced by sources as different as changes in neural signal amplitudes or noise levels. This ambiguity substantially diminishes the value of FC for inferring system properties and clinical states. Network modelling approaches may avoid ambiguities, but require specific assumptions. We present an enhancement to FC analysis with improved specificity of inferences, minimal assumptions and no reduction in flexibility. The Additive Signal Change (ASC) approach characterizes FC changes into certain prevalent classes of signal change that involve the input of additional signal to existing activity. With FMRI data, the approach reveals a rich diversity of signal changes underlying measured changes in FC, suggesting that it could clarify our current understanding of FC changes in many contexts. The ASC method can also be used to disambiguate other measures of dependency, such as regression and coherence, providing a flexible tool for the analysis of neural data.

| S-EPMC5929905 | biostudies-literature

Energetic cost of brain functional connectivity.

Project description:The brain's functional connectivity is complex, has high energetic cost, and requires efficient use of glucose, the brain's main energy source. It has been proposed that regions with a high degree of functional connectivity are energy efficient and can minimize consumption of glucose. However, the relationship between functional connectivity and energy consumption in the brain is poorly understood. To address this neglect, here we propose a simple model for the energy demands of brain functional connectivity, which we tested with positron emission tomography and MRI in 54 healthy volunteers at rest. Higher glucose metabolism was associated with proportionally larger MRI signal amplitudes, and a higher degree of connectivity was associated with nonlinear increases in metabolism, supporting our hypothesis for the energy efficiency of the connectivity hubs. Basal metabolism (in the absence of connectivity) accounted for 30% of brain glucose utilization, which suggests that the spontaneous brain activity accounts for 70% of the energy consumed by the brain. The energy efficiency of the connectivity hubs was higher for ventral precuneus, cerebellum, and subcortical hubs than for cortical hubs. The higher energy demands of brain communication that hinges upon higher connectivity could render brain hubs more vulnerable to deficits in energy delivery or utilization and help explain their sensitivity to neurodegenerative conditions, such as Alzheimer's disease.

| S-EPMC3746878 | biostudies-other

DeepGreen: deep learning of Green's functions for nonlinear boundary value problems.

Project description:Boundary value problems (BVPs) play a central role in the mathematical analysis of constrained physical systems subjected to external forces. Consequently, BVPs frequently emerge in nearly every engineering discipline and span problem domains including fluid mechanics, electromagnetics, quantum mechanics, and elasticity. The fundamental solution, or Green's function, is a leading method for solving linear BVPs that enables facile computation of new solutions to systems under any external forcing. However, fundamental Green's function solutions for nonlinear BVPs are not feasible since linear superposition no longer holds. In this work, we propose a flexible deep learning approach to solve nonlinear BVPs using a dual-autoencoder architecture. The autoencoders discover an invertible coordinate transform that linearizes the nonlinear BVP and identifies both a linear operator L and Green's function G which can be used to solve new nonlinear BVPs. We find that the method succeeds on a variety of nonlinear systems including nonlinear Helmholtz and Sturm-Liouville problems, nonlinear elasticity, and a 2D nonlinear Poisson equation and can solve nonlinear BVPs at orders of magnitude faster than traditional methods without the need for an initial guess. The method merges the strengths of the universal approximation capabilities of deep learning with the physics knowledge of Green's functions to yield a flexible tool for identifying fundamental solutions to a variety of nonlinear systems.

| S-EPMC8566504 | biostudies-literature

Data-driven discovery of Green's functions with human-understandable deep learning.

Project description:There is an opportunity for deep learning to revolutionize science and technology by revealing its findings in a human interpretable manner. To do this, we develop a novel data-driven approach for creating a human-machine partnership to accelerate scientific discovery. By collecting physical system responses under excitations drawn from a Gaussian process, we train rational neural networks to learn Green's functions of hidden linear partial differential equations. These functions reveal human-understandable properties and features, such as linear conservation laws and symmetries, along with shock and singularity locations, boundary effects, and dominant modes. We illustrate the technique on several examples and capture a range of physics, including advection-diffusion, viscous shocks, and Stokes flow in a lid-driven cavity.

| S-EPMC8940897 | biostudies-literature

Whole-brain functional connectivity identification of functional dyspepsia.

Project description:Recent neuroimaging studies have shown local brain aberrations in functional dyspepsia (FD) patients, yet little attention has been paid to the whole-brain resting-state functional network abnormalities. The purpose of this study was to investigate whether FD disrupts the patterns of whole-brain networks and the abnormal functional connectivity could reflect the severity of the disease. The dysfunctional interactions between brain regions at rest were investigated in FD patients as compared with 40 age- and gender- matched healthy controls. Multivariate pattern analysis was used to evaluate the discriminative power of our results for classifying patients from controls. In our findings, the abnormal brain functional connections were mainly situated within or across the limbic/paralimbic system, the prefrontal cortex, the tempo-parietal areas and the visual cortex. About 96% of the subjects among the original dataset were correctly classified by a leave one-out cross-validation approach, and 88% accuracy was also validated in a replication dataset. The classification features were significantly associated with the patients' dyspepsia symptoms, the self-rating depression scale and self-rating anxiety scale, but it was not correlated with duration of FD patients (p>0.05). Our results may indicate the effectiveness of the altered brain functional connections reflecting the disease pathophysiology underling FD. These dysfunctional connections may be the epiphenomena or causative agents of FD, which may be affected by clinical severity and its related emotional dimension of the disease rather than the clinical course.

| S-EPMC3684590 | biostudies-literature

Brain Modulyzer: Interactive Visual Analysis of Functional Brain Connectivity.

Project description:We present Brain Modulyzer, an interactive visual exploration tool for functional magnetic resonance imaging (fMRI) brain scans, aimed at analyzing the correlation between different brain regions when resting or when performing mental tasks. Brain Modulyzer combines multiple coordinated views-such as heat maps, node link diagrams and anatomical views-using brushing and linking to provide an anatomical context for brain connectivity data. Integrating methods from graph theory and analysis, e.g., community detection and derived graph measures, makes it possible to explore the modular and hierarchical organization of functional brain networks. Providing immediate feedback by displaying analysis results instantaneously while changing parameters gives neuroscientists a powerful means to comprehend complex brain structure more effectively and efficiently and supports forming hypotheses that can then be validated via statistical analysis. To demonstrate the utility of our tool, we present two case studies-exploring progressive supranuclear palsy, as well as memory encoding and retrieval.

| S-EPMC5585064 | biostudies-literature

Excited-State Geometry Optimization of Small Molecules with Many-Body Green's Functions Theory.

Project description:We present a benchmark study of gas phase geometry optimizations in the excited states of carbon monoxide, acetone, acrolein, and methylenecyclopropene using many-body Green's functions theory within the GW approximation and the Bethe-Salpeter equation (BSE) employing numerical gradients. We scrutinize the influence of several typical approximations in the GW-BSE framework; we used one-shot G0W0 or eigenvalue self-consistent evGW, employing a fully analytic approach or plasmon-pole model for the frequency dependence of the electron self-energy, or performing the BSE step within the Tamm-Dancoff approximation. The obtained geometries are compared to reference results from multireference perturbation theory (CASPT2), variational Monte Carlo (VMC) method, second-order approximate coupled cluster (CC2) method, and time-dependent density-functional theory (TDDFT). We find overall a good agreement of the structural parameters optimized with the GW-BSE calculations with CASPT2, with an average relative error of around 1% for the G0W0 and 1.5% for the evGW variants based on a PBE0 ground state, respectively, while the other approximations have negligible influence. The relative errors are also smaller than those for CC2 and TDDFT with different functionals and only larger than VMC, indicating that the GW-BSE method does not only yield excitation energies but also geometries in good agreement with established higher-order wave function methods.

| S-EPMC7876808 | biostudies-literature

OmicsDI is part of the ELIXIR infrastructure

OmicsDI is an Elixir interoperability service. Learn more ›

Tweets

OmicsDI Databases

PRIDE
PeptideAtlas
MassIVE
JPOST Repository
Physiome Model Repository

EGA
EVA
ENA
LINCS
PAXDB
Cell Collective

MetaboLights
Metabolomics Workbench
MetabolomeExpress
GNPS
BioModels
FAIRDOMHub

ArrayExpress
dbGaP
ExpressionAtlas
GEO
NODE

Information

Databases
Help
API
Contact us
Code on GitHub
Terms of use
Submit Data