Browse
Submit Data
Databases
API
Help

Dataset Information

13 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

Local convergence of the boundary element method on polyhedral domains.

ABSTRACT: The local behavior of the lowest order boundary element method on quasi-uniform meshes for Symm's integral equation and the stabilized hyper-singular integral equation on polygonal/polyhedral Lipschitz domains is analyzed. We prove local a priori estimates in L2 for Symm's integral equation and in H1 for the hyper-singular equation. The local rate of convergence is limited by the local regularity of the sought solution and the sum of the rates given by the global regularity and additional regularity provided by the shift theorem for a dual problem.

SUBMITTER: Faustmann M

PROVIDER: S-EPMC6154049 | biostudies-other | 2018

REPOSITORIES: biostudies-other

ACCESS DATA

Json Xml

Publications

Local convergence of the boundary element method on polyhedral domains.

Faustmann Markus M Melenk Jens Markus JM

Numerische mathematik 20180629 3

The local behavior of the lowest order boundary element method on quasi-uniform meshes for Symm's integral equation and the stabilized hyper-singular integral equation on polygonal/polyhedral Lipschitz domains is analyzed. We prove local <i>a priori</i> estimates in L 2 for Symm's integral equation and in H 1 for the hyper-singular equation. The local rate of convergence is limited by the local regularity of the sought solution and the sum of the rates given by the global regularity and additi ...[more]

PMID: 30319152

Similar Datasets

Boundary element-associated factor 32B connects chromatin domains to the nuclear matrix.

Project description:Chromatin domain boundary elements demarcate independently regulated domains of eukaryotic genomes. While a few such boundary sequences have been studied in detail, only a small number of proteins that interact with them have been identified. One such protein is the boundary element-associated factor (BEAF), which binds to the scs' boundary element of Drosophila melanogaster. It is not clear, however, how boundary elements function. In this report we show that BEAF is associated with the nuclear matrix and map the domain required for matrix association to the middle region of the protein. This region contains a predicted coiled-coil domain with several potential sites for posttranslational modification. We demonstrate that the DNA sequences that bind to BEAF in vivo are also associated with the nuclear matrix and colocalize with BEAF. These results suggest that boundary elements may function by tethering chromatin to nuclear architectural components and thereby provide a structural basis for compartmentalization of the genome into functionally independent domains.

| S-EPMC1951503 | biostudies-literature

Boundary Element Fast Multipole Method for Enhanced Modeling of Neurophysiological Recordings.

Project description:ObjectiveA new numerical modeling approach is proposed which provides forward-problem solutions for both noninvasive recordings (EEG/MEG) and higher-resolution intracranial recordings (iEEG).MethodsThe algorithm is our recently developed boundary element fast multipole method or BEM-FMM. It is based on the integration of the boundary element formulation in terms of surface charge density and the fast multipole method originating from its inventors. The algorithm still possesses the major advantage of the conventional BEM - high speed - but is simultaneously capable of processing a very large number of surface-based unknowns. As a result, an unprecedented spatial resolution could be achieved, which enables multiscale modeling.ResultsFor non-invasive EEG/MEG, we are able to accurately solve the forward problem with approximately 1 mm anatomical resolution in the cortex within 1-2 min given several thousand cortical dipoles. Targeting high-resolution iEEG, we are able to compute, for the first time, an integrated electromagnetic response for an ensemble (2,450) of tightly packed realistic pyramidal neocortical neurons in a full-head model with 0.6 mm anatomical cortical resolution. The neuronal arbor is comprised of 5.9 M elementary 1.2 μm long dipoles. On a standard server, the computations require about 5 min.ConclusionOur results indicate that the BEM-FMM approach may be well suited to support numerical multiscale modeling pertinent to modern high-resolution and submillimeter iEEG.SignificanceBased on the speed and ease of implementation, this new algorithm represents a method that will greatly facilitate simulations at multi-scale across a variety of applications.

| S-EPMC7704617 | biostudies-literature

An Adaptive Fast Multipole Boundary Element Method for Poisson-Boltzmann Electrostatics.

Project description:The numerical solution of the Poisson-Boltzmann (PB) equation is a useful but a computationally demanding tool for studying electrostatic solvation effects in chemical and biomolecular systems. Recently, we have described a boundary integral equation-based PB solver accelerated by a new version of the fast multipole method (FMM). The overall algorithm shows an order N complexity in both the computational cost and memory usage. Here, we present an updated version of the solver by using an adaptive FMM for accelerating the convolution type matrix-vector multiplications. The adaptive algorithm, when compared to our previous nonadaptive one, not only significantly improves the performance of the overall memory usage but also remarkably speeds the calculation because of an improved load balancing between the local- and far-field calculations. We have also implemented a node-patch discretization scheme that leads to a reduction of unknowns by a factor of 2 relative to the constant element method without sacrificing accuracy. As a result of these improvements, the new solver makes the PB calculation truly feasible for large-scale biomolecular systems such as a 30S ribosome molecule even on a typical 2008 desktop computer.

| S-EPMC2693949 | biostudies-other

The scs' boundary element: characterization of boundary element-associated factors.

Project description:Boundary elements are thought to define the peripheries of chromatin domains and to restrict enhancer-promoter interactions to their target genes within their domains. We previously characterized a cDNA encoding the BEAF-32A protein (32A), which binds with high affinity to the scs' boundary element from the Drosophila melanogaster 87A7 hsp70 locus. Here, we report a second protein, BEAF-32B, that differs from 32A only in its amino terminus. Unlike 32A, it has the same DNA binding specificity as the complete BEAF activity affinity purified from Drosophila. We characterize three domains in these proteins. Heterocomplex formation is mediated by their identical carboxy-terminal domains, and DNA binding is mediated by their unique amino-terminal domains. The identical middle domains of 32A and 32B are dispensable for the functions described here, although they may be important for boundary element function. 32A and 32B apparently form trimers, and the ratio of 32A to 32B varies at different loci on polytene chromosomes as judged by immunofluorescence. The scs' element contains a high- and low-affinity binding site for BEAF. We observed that interaction with the low-affinity site is facilitated by binding to the high-affinity site some 200 bp distant.

| S-EPMC231825 | biostudies-other

Comparative performance of the finite element method and the boundary element fast multipole method for problems mimicking transcranial magnetic stimulation (TMS).

Project description:OBJECTIVE:A study pertinent to the numerical modeling of cortical neurostimulation is conducted in an effort to compare the performance of the finite element method (FEM) and an original formulation of the boundary element fast multipole method (BEM-FMM) at matched computational performance metrics. APPROACH:We consider two problems: (i) a canonic multi-sphere geometry and an external magnetic-dipole excitation where the analytical solution is available and; (ii) a problem with realistic head models excited by a realistic coil geometry. In the first case, the FEM algorithm tested is a fast open-source getDP solver running within the SimNIBS 2.1.1 environment. In the second case, a high-end commercial FEM software package ANSYS Maxwell 3D is used. The BEM-FMM method runs in the MATLAB® 2018a environment. MAIN RESULTS:In the first case, we observe that the BEM-FMM algorithm gives a smaller solution error for all mesh resolutions and runs significantly faster for high-resolution meshes when the number of triangular facets exceeds approximately 0.25 M. We present other relevant simulation results such as volumetric mesh generation times for the FEM, time necessary to compute the potential integrals for the BEM-FMM, and solution performance metrics for different hardware/operating system combinations. In the second case, we observe an excellent agreement for electric field distribution across different cranium compartments and, at the same time, a speed improvement of three orders of magnitude when the BEM-FMM algorithm used. SIGNIFICANCE:This study may provide a justification for anticipated use of the BEM-FMM algorithm for high-resolution realistic transcranial magnetic stimulation scenarios.

| S-EPMC6546501 | biostudies-other

An analysis on local convergence of inexact newton-gauss method for solving singular systems of equations.

Project description:We study the local convergence properties of inexact Newton-Gauss method for singular systems of equations. Unified estimates of radius of convergence balls for one kind of singular systems of equations with constant rank derivatives are obtained. Application to the Smale point estimate theory is provided and some important known results are extended and/or improved.

| S-EPMC3984777 | biostudies-other

Example of Steady-State Electric-Current Modeling of a Complicated Cellular Topology with Boundary Element Fast Multipole Method

Project description:In this study, we demonstrate the ability of the boundary element fast multipole method (BEM-FMM) to perform electrical modeling of a rather complicated microbiological surface topology in a reasonable amount of time. As an example, we consider a Computer Aided Design (CAD)-based SARS-CoV-2 spike glycoprotein structure. This structure is crucial to the mechanism by which the coronavirus attaches to a target object. Only classic DC steady-state modeling has been performed, in an isotropic continuous medium.

| S-EPMC7403854 | biostudies-literature

Chromatin domain boundary element search tool for Drosophila.

Project description:Chromatin domain boundary elements prevent inappropriate interaction between distant or closely spaced regulatory elements and restrict enhancers and silencers to correct target promoters. In spite of having such a general role and expected frequent occurrence genome wide, there is no DNA sequence analysis based tool to identify boundary elements. Here, we report chromatin domain Boundary Element Search Tool (cdBEST), to identify boundary elements. cdBEST uses known recognition sequences of boundary interacting proteins and looks for 'motif clusters'. Using cdBEST, we identified boundary sequences across 12 Drosophila species. Of the 4576 boundary sequences identified in Drosophila melanogaster genome, >170 sequences are repetitive in nature and have sequence homology to transposable elements. Analysis of such sequences across 12 Drosophila genomes showed that the occurrence of repetitive sequences in the context of boundaries is a common feature of drosophilids. We use a variety of genome organization criteria and also experimental test on a subset of the cdBEST boundaries in an enhancer-blocking assay and show that 80% of them indeed function as boundaries in vivo. These observations highlight the role of cdBEST in better understanding of chromatin domain boundaries in Drosophila and setting the stage for comparative analysis of boundaries across closely related species.

| S-EPMC3378885 | biostudies-literature

A bipartite boundary element restricts UBE3A imprinting to mature neurons.

Project description:Angelman syndrome (AS) is a severe neurodevelopmental disorder caused by the loss of function from the maternal allele of UBE3A, a gene encoding an E3 ubiquitin ligase. UBE3A is only expressed from the maternally inherited allele in mature human neurons due to tissue-specific genomic imprinting. Imprinted expression of UBE3A is restricted to neurons by expression of UBE3A antisense transcript (UBE3A-ATS) from the paternally inherited allele, which silences the paternal allele of UBE3A in cis However, the mechanism restricting UBE3A-ATS expression and UBE3A imprinting to neurons is not understood. We used CRISPR/Cas9-mediated genome editing to functionally define a bipartite boundary element critical for neuron-specific expression of UBE3A-ATS in humans. Removal of this element led to up-regulation of UBE3A-ATS without repressing paternal UBE3A However, increasing expression of UBE3A-ATS in the absence of the boundary element resulted in full repression of paternal UBE3A, demonstrating that UBE3A imprinting requires both the loss of function from the boundary element as well as the up-regulation of UBE3A-ATS These results suggest that manipulation of the competition between UBE3A-ATS and UBE3A may provide a potential therapeutic approach for AS.

| S-EPMC6369781 | biostudies-literature

Extending Protein Domain Boundary Predictors to Detect Discontinuous Domains.

Project description:A variety of protein domain predictors were developed to predict protein domain boundaries in recent years, but most of them cannot predict discontinuous domains. Considering nearly 40% of multidomain proteins contain one or more discontinuous domains, we have developed DomEx to enable domain boundary predictors to detect discontinuous domains by assembling the continuous domain segments. Discontinuous domains are predicted by matching the sequence profile of concatenated continuous domain segments with the profiles from a single-domain library derived from SCOP and CATH, and Pfam. Then the matches are filtered by similarity to library templates, a symmetric index score and a profile-profile alignment score. DomEx recalled 32.3% discontinuous domains with 86.5% precision when tested on 97 non-homologous protein chains containing 58 continuous and 99 discontinuous domains, in which the predicted domain segments are within ±20 residues of the boundary definitions in CATH 3.5. Compared with our recently developed predictor, ThreaDom, which is the state-of-the-art tool to detect discontinuous-domains, DomEx recalled 26.7% discontinuous domains with 72.7% precision in a benchmark with 29 discontinuous-domain chains, where ThreaDom failed to predict any discontinuous domains. Furthermore, combined with ThreaDom, the method ranked number one among 10 predictors. The source code and datasets are available at https://github.com/xuezhidong/DomEx.

| S-EPMC4621036 | biostudies-literature

OmicsDI is part of the ELIXIR infrastructure

OmicsDI is an Elixir interoperability service. Learn more ›

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