The Experts below are selected from a list of 26574 Experts worldwide ranked by ideXlab platform
Juan F Pedraza - One of the best experts on this subject based on the ideXlab platform.
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bit threads einstein s equations and bulk locality
Journal of High Energy Physics, 2021Co-Authors: Cesar A Agon, Elena Caceres, Juan F PedrazaAbstract:In the context of holography, entanglement entropy can be studied either by i) extremal surfaces or ii) bit threads, i.e., divergenceless vector fields with a norm bound set by the Planck length. In this paper we develop a new method for metric reconstruction based on the latter approach and show the advantages over existing ones. We start by studying general linear perturbations around the vacuum state. Generic thread configurations turn out to encode the information about the metric in a highly nonlocal way, however, we show that for boundary regions with a local modular Hamiltonian there is always a canonical choice for the perturbed thread configurations that exploits bulk locality. To do so, we express the bit thread formalism in terms of differential forms so that it becomes manifestly background independent. We show that the Iyer-Wald formalism provides a natural candidate for a canonical local perturbation, which can be used to recast the problem of metric reconstruction in terms of the inversion of a particular linear differential Operator. We examine in detail the inversion problem for the case of spherical regions and give explicit expressions for the Inverse Operator in this case. Going beyond linear order, we argue that the Operator that must be inverted naturally increases in order. However, the inversion can be done recursively at different orders in the perturbation. Finally, we comment on an alternative way of reconstructing the metric non-perturbatively by phrasing the inversion problem as a particular optimization problem.
John W Belliveau - One of the best experts on this subject based on the ideXlab platform.
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assessing and improving the spatial accuracy in meg source localization by depth weighted minimum norm estimates
NeuroImage, 2006Co-Authors: Thomas Witzel, John W Belliveau, Seppo P Ahlfors, Steven M Stufflebeam, Matti HamalainenAbstract:Cerebral currents responsible for the extra-cranially recorded magnetoencephalography (MEG) data can be estimated by applying a suitable source model. A popular choice is the distributed minimum-norm estimate (MNE) which minimizes the l2-norm of the estimated current. Under the l2-norm constraint, the current estimate is related to the measurements by a linear Inverse Operator. However, the MNE has a bias towards superficial sources, which can be reduced by applying depth weighting. We studied the effect of depth weighting in MNE using a shift metric. We assessed the localization performance of the depth-weighted MNE as well as depth-weighted noise-normalized MNE solutions under different cortical orientation constraints, source space densities, and signal-to-noise ratios (SNRs) in multiple subjects. We found that MNE with depth weighting parameter between 0.6 and 0.8 showed improved localization accuracy, reducing the mean displacement error from 12 mm to 7 mm. The noise-normalized MNE was insensitive to depth weighting. A similar investigation of EEG data indicated that depth weighting parameter between 2.0 and 5.0 resulted in an improved localization accuracy. The application of depth weighting to auditory and somatosensory experimental data illustrated the beneficial effect of depth weighting on the accuracy of spatiotemporal mapping of neuronal sources.
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monte carlo simulation studies of eeg and meg localization accuracy
Human Brain Mapping, 2002Co-Authors: Arthur K Liu, Anders M Dale, John W BelliveauAbstract:Both electroencephalography (EEG) and magnetoencephalography (MEG) are currently used to localize brain activity. The accuracy of source localization depends on numerous factors, including the specific Inverse approach and source model, fundamental differences in EEG and MEG data, and the accuracy of the volume conductor model of the head (i.e., the forward model). Using Monte Carlo simulations, this study removes the effect of forward model errors and theoretically compares the use of EEG alone, MEG alone, and combined EEG/MEG data sets for source localization. Here, we use a linear estimation Inverse approach with a distributed source model and a realistic forward head model. We evaluated its accuracy using the crosstalk and point spread metrics. The crosstalk metric for a specified location on the cortex describes the amount of activity incorrectly localized onto that location from other locations. The point spread metric provides the complementary measure: for that same location, the point spread describes the mis-localization of activity from that specified location to other locations in the brain. We also propose and examine the utility of a “noise sensitivity normalized” Inverse Operator. Given our particular forward and Inverse models, our results show that 1) surprisingly, EEG localization is more accurate than MEG localization for the same number of sensors averaged over many source locations and orientations; 2) as expected, combining EEG with MEG produces the best accuracy for the same total number of sensors; 3) the noise sensitivity normalized Inverse Operator improves the spatial resolution relative to the standard linear estimation Operator; and 4) use of an a priori fMRI constraint universally reduces both crosstalk and point spread. Hum. Brain Mapping 16:47–62, 2002. © 2002 Wiley-Liss, Inc.
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monte carlo simulation studies of eeg and meg localization accuracy
Human Brain Mapping, 2002Co-Authors: Arthur K Liu, Anders M Dale, John W BelliveauAbstract:Both electroencephalography (EEG) and magnetoencephalography (MEG) are currently used to localize brain activity. The accuracy of source localization depends on numerous factors, including the specific Inverse approach and source model, fundamental differences in EEG and MEG data, and the accuracy of the volume conductor model of the head (i.e., the forward model). Using Monte Carlo simulations, this study removes the effect of forward model errors and theoretically compares the use of EEG alone, MEG alone, and combined EEG/MEG data sets for source localization. Here, we use a linear estimation Inverse approach with a distributed source model and a realistic forward head model. We evaluated its accuracy using the crosstalk and point spread metrics. The crosstalk metric for a specified location on the cortex describes the amount of activity incorrectly localized onto that location from other locations. The point spread metric provides the complementary measure: for that same location, the point spread describes the mis-localization of activity from that specified location to other locations in the brain. We also propose and examine the utility of a "noise sensitivity normalized" Inverse Operator. Given our particular forward and Inverse models, our results show that 1) surprisingly, EEG localization is more accurate than MEG localization for the same number of sensors averaged over many source locations and orientations; 2) as expected, combining EEG with MEG produces the best accuracy for the same total number of sensors; 3) the noise sensitivity normalized Inverse Operator improves the spatial resolution relative to the standard linear estimation Operator; and 4) use of an a priori fMRI constraint universally reduces both crosstalk and point spread.
Arthur K Liu - One of the best experts on this subject based on the ideXlab platform.
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monte carlo simulation studies of eeg and meg localization accuracy
Human Brain Mapping, 2002Co-Authors: Arthur K Liu, Anders M Dale, John W BelliveauAbstract:Both electroencephalography (EEG) and magnetoencephalography (MEG) are currently used to localize brain activity. The accuracy of source localization depends on numerous factors, including the specific Inverse approach and source model, fundamental differences in EEG and MEG data, and the accuracy of the volume conductor model of the head (i.e., the forward model). Using Monte Carlo simulations, this study removes the effect of forward model errors and theoretically compares the use of EEG alone, MEG alone, and combined EEG/MEG data sets for source localization. Here, we use a linear estimation Inverse approach with a distributed source model and a realistic forward head model. We evaluated its accuracy using the crosstalk and point spread metrics. The crosstalk metric for a specified location on the cortex describes the amount of activity incorrectly localized onto that location from other locations. The point spread metric provides the complementary measure: for that same location, the point spread describes the mis-localization of activity from that specified location to other locations in the brain. We also propose and examine the utility of a “noise sensitivity normalized” Inverse Operator. Given our particular forward and Inverse models, our results show that 1) surprisingly, EEG localization is more accurate than MEG localization for the same number of sensors averaged over many source locations and orientations; 2) as expected, combining EEG with MEG produces the best accuracy for the same total number of sensors; 3) the noise sensitivity normalized Inverse Operator improves the spatial resolution relative to the standard linear estimation Operator; and 4) use of an a priori fMRI constraint universally reduces both crosstalk and point spread. Hum. Brain Mapping 16:47–62, 2002. © 2002 Wiley-Liss, Inc.
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monte carlo simulation studies of eeg and meg localization accuracy
Human Brain Mapping, 2002Co-Authors: Arthur K Liu, Anders M Dale, John W BelliveauAbstract:Both electroencephalography (EEG) and magnetoencephalography (MEG) are currently used to localize brain activity. The accuracy of source localization depends on numerous factors, including the specific Inverse approach and source model, fundamental differences in EEG and MEG data, and the accuracy of the volume conductor model of the head (i.e., the forward model). Using Monte Carlo simulations, this study removes the effect of forward model errors and theoretically compares the use of EEG alone, MEG alone, and combined EEG/MEG data sets for source localization. Here, we use a linear estimation Inverse approach with a distributed source model and a realistic forward head model. We evaluated its accuracy using the crosstalk and point spread metrics. The crosstalk metric for a specified location on the cortex describes the amount of activity incorrectly localized onto that location from other locations. The point spread metric provides the complementary measure: for that same location, the point spread describes the mis-localization of activity from that specified location to other locations in the brain. We also propose and examine the utility of a "noise sensitivity normalized" Inverse Operator. Given our particular forward and Inverse models, our results show that 1) surprisingly, EEG localization is more accurate than MEG localization for the same number of sensors averaged over many source locations and orientations; 2) as expected, combining EEG with MEG produces the best accuracy for the same total number of sensors; 3) the noise sensitivity normalized Inverse Operator improves the spatial resolution relative to the standard linear estimation Operator; and 4) use of an a priori fMRI constraint universally reduces both crosstalk and point spread.
Semyon Yakubovich - One of the best experts on this subject based on the ideXlab platform.
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new inversion convolution and titchmarsh s theorems for the half hilbert transform
Integral Transforms and Special Functions, 2014Co-Authors: Semyon YakubovichAbstract:While exploiting the generalized Parseval equality for the Mellin transform, we derive the reciprocal Inverse Operator in the weighted L2-space related to the Hilbert transform on the nonnegative half-axis. Moreover, employing the convolution method, which is based on the Mellin–Barnes integrals, we prove the corresponding convolution and Titchmarsh's theorems for the half-Hilbert transform. Some applications to the solvability of a new class of singular integral equations are demonstrated. Our technique does not require the use of methods of the Riemann–Hilbert boundary value problems for analytic functions. The same approach is applied recently to invert the half-Hartley transform and to establish its convolution theorem.
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the plancherel titchmarsh and convolution theorems for the half hartley transform
Integral Transforms and Special Functions, 2014Co-Authors: Semyon YakubovichAbstract:The generalized Parseval equality for the Mellin transform is employed to prove the Plancherel-type theorem in L2 with the respective Inverse Operator related to the Hartley transform on the nonnegative half-axis (the half-Hartley transform). Moreover, involving the convolution method, which is based on the double Mellin–Barnes integrals, the corresponding convolution and Titchmarsh's theorems for the half-Hartley transform are established. As an application, we consider solvability conditions for a homogeneous integral equation of the second kind involving the Hartley kernel.
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new inversion convolution and titchmarsh s theorems for the half hartley transform
arXiv: Classical Analysis and ODEs, 2014Co-Authors: Semyon YakubovichAbstract:The generalized Parseval equality for the Mellin transform is employed to prove the inversion theorem in L_2 with the respective Inverse Operator related to the Hartley transform on the nonnegative half-axis (the half-Hartley transform). Moreover, involving the convolution method, which is based on the double Mellin-Barnes integrals, the corresponding convolution and Titchmarsh's theorems for the half-Hartley transform are established. As an application, we consider solvability conditions for a homogeneous integral equation of the second kind involving the Hartley kernel.
T A Bolokhov - One of the best experts on this subject based on the ideXlab platform.
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Properties of the Radial Part of the Laplace Operator for l=1 in a Special Scalar Product
Journal of Mathematical Sciences, 2016Co-Authors: T A BolokhovAbstract:We develop self-adjoint extensions of the radial part of the Laplace Operator for l = 1 in a special scalar product. The product arises under the passage of the standard product from ℝ^3 to the set of functions parametrizing one of two components of the transverse vector field. Similar extensions are treated for the square of the Inverse Operator of the radial part in question. Bibliography: 8 titles.
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properties of the l 1 radial part of the laplace Operator in a special scalar product
arXiv: Spectral Theory, 2015Co-Authors: T A BolokhovAbstract:We develop self-adjoint extensions of the l=1 radial part of the Laplace Operator in a special scalar product. The product arises as the transfer of the plain product from R^3 into the set of functions parametrizing one of the two components of the transverse vector field. The similar extensions are treated for the square of Inverse Operator of the radial part in question.
