We present a computer-assisted approach to coarse graining the evolutionary dynamics of a system of nonidentical oscillators coupled through a (fixed) network structure. The existence of a spectral gap for the coupling network graph Laplacian suggests that the graph dynamics may quickly become low dimensional. Our first choice of coarse variables consists of the components of the oscillator sta...

Unfortunately, theoretical results from PRAM algorithms do not necessarily match the speedups observed on real parallel machines. In this paper, we present a parallel algorithm that is more practical in that the assumption and cost model used reflect better the reality of commercially available multiprocessors. More precisely, we will use a version of the BSP model [6], referred to as the coars...

Coarse space correction is essential to achieve algorithmic scalability in domain decomposition methods. Our goal here is to build a robust coarse space for Schwarz–type preconditioners for elliptic problems with highly heterogeneous coefficients when the discontinuities are not just across but also along subdomain interfaces, where classical results break down [3, 6, 15, 9]. In previous work, ...

Coarse-grained (CG) force fields have become promising tools for studies of protein behavior, but the balance of speed and accuracy is still a challenge in the research of protein coarse graining methodology. In this work, 20 CG beads have been designed based on the structures of amino acid residues, with which an amino acid can be represented by one or two beads, and a CG solvent model with fi...

We consider two different aspects of FETI-DP domain decomposition methods [8, 23]. In the first part, we describe an adaptive construction of coarse spaces from local eigenvalue problems for the solution of heterogeneous, e.g., multiscale, problems. This strategy of constructing a coarse space is implemented using a deflation approach. In the second part, we introduce new domain decomposition a...

The ribosome is a very large complex that consists of many RNA and protein molecules and plays a central role in protein biosynthesis in all organisms. Extensive interactions between different molecules are critical to ribosomal functional dynamics. In this work, intermolecular interactions in the Escherichia coli 70S ribosome are investigated by coarse-grained (CG) analysis. CG models are defi...

The influence of treefall gaps and coarse woody debris (CWD) on white-footed mouse (Peromyxus 1eucopu.s) abundance was tested experimentally during 1996-1999 in a southern Appalachian hardwood forest. I compared the relative abundance and body size of F! leucopus among unsalvaged gaps that were created by wind disturbance and retained high CWD levels, salvage logged gaps where fallen and damage...

We perform extensive coarse-grained (CG) Langevin dynamics simulations of intrinsically disordered proteins (IDPs), which possess fluctuating conformational statistics between that for excluded volume random walks and collapsed globules. Our CG model includes repulsive steric, attractive hydrophobic, and electrostatic interactions between residues and is calibrated to a large collection of sing...

We discuss a new approach for the construction of the secondlevel Neumann-Neumann coarse space. Our method is based on an inexpensive and parallel analysis of the lower part spectrum of each subdomain stiffness matrix. We show that the method is flexible enough to converge fast on nonstandard decompositions and various types of finite elements used in structural analysis packages.

The objective of this paper is to explain the principles of the design of a coarse space in a simplified way and by pictures. The focus is on ideas rather than on a more historically complete presentation. That can be found, e.g., in [ 28]. Also, space limitation does not allow us even to mention many important methods and papers that should be rightfully included. The coarse space facilitates ...