Theory of continuum percolation I. General formalism

The theoretical basis of continuum percolation has changed greatly since its beginning as little more than an analogy with lattice systems. Nevertheless, there is yet no comprehensive theory of this field. A basis for such a theory is provided here with the introduction of the Potts fluid, a system of interacting $s$-state spins which are free to move in the continuum. In the $s \to 1$ limit, the Potts magnetization, susceptibility and correlation functions are directly related to the percolation probability, the mean cluster size and the pair-connectedness, respectively. Through the Hamiltonian formulation of the Potts fluid, the standard methods of statistical mechanics can therefore be used in the continuum percolation problem.Comment: 26 pages, Late

Structural Polymorphism of the Cytoskeleton: A Model of Linker-Assisted Filament Aggregation

The phase behavior of charged rods in the presence of inter-rod linkers is studied theoretically as a model for the equilibrium behavior underlying the organization of actin filaments by linker proteins in the cytoskeleton. The presence of linkers in the solution modifies the effective inter-rod interaction and can lead to inter-filament attraction. Depending on the system's composition and physical properties such as linker binding energies, filaments will either orient perpendicular or parallel to each other, leading to network-like or bundled structures. We show that such a system can have one of three generic phase diagrams, one dominated by bundles, another by networks, and the third containing both bundle and network-like phases. The first two diagrams can be found over a wide range of interaction energies, while the third occurs only for a narrow range. These results provide theoretical understanding of the classification of linker proteins as bundling proteins or crosslinking proteins. In addition, they suggest possible mechanisms by which the cell may control cytoskeletal morphology.Comment: 17 pages, 3 figure

Exact solution of a one-dimensional continuum percolation model

I consider a one dimensional system of particles which interact through a hard core of diameter \si and can connect to each other if they are closer than a distance $d$. The mean cluster size increases as a function of the density $\rho$ until it diverges at some critical density, the percolation threshold. This system can be mapped onto an off-lattice generalization of the Potts model which I have called the Potts fluid, and in this way, the mean cluster size, pair connectedness and percolation probability can be calculated exactly. The mean cluster size is S = 2 \exp[ \rho (d -\si)/(1 - \rho \si)] - 1 and diverges only at the close packing density \rho_{cp} = 1 / \si . This is confirmed by the behavior of the percolation probability. These results should help in judging the effectiveness of approximations or simulation methods before they are applied to higher dimensions.Comment: 21 pages, Late

The Neuroscience Information Framework: A Data and Knowledge Environment for Neuroscience

With support from the Institutes and Centers forming the NIH Blueprint for Neuroscience Research, we have designed and implemented a new initiative for integrating access to and use of Web-based neuroscience resources: the Neuroscience Information Framework. The Framework arises from the expressed need of the neuroscience community for neuroinformatic tools and resources to aid scientific inquiry, builds upon prior development of neuroinformatics by the Human Brain Project and others, and directly derives from the Society for Neuroscience’s Neuroscience Database Gateway. Partnered with the Society, its Neuroinformatics Committee, and volunteer consultant-collaborators, our multi-site consortium has developed: (1) a comprehensive, dynamic, inventory of Web-accessible neuroscience resources, (2) an extended and integrated terminology describing resources and contents, and (3) a framework accepting and aiding concept-based queries. Evolving instantiations of the Framework may be viewed at http://nif.nih.gov, http://neurogateway.org, and other sites as they come on line

Disease Ontology: a backbone for disease semantic integration

The Disease Ontology (DO) database (http://disease-ontology.org) represents a comprehensive knowledge base of 8043 inherited, developmental and acquired human diseases (DO version 3, revision 2510). The DO web browser has been designed for speed, efficiency and robustness through the use of a graph database. Full-text contextual searching functionality using Lucene allows the querying of name, synonym, definition, DOID and cross-reference (xrefs) with complex Boolean search strings. The DO semantically integrates disease and medical vocabularies through extensive cross mapping and integration of MeSH, ICD, NCI's thesaurus, SNOMED CT and OMIM disease-specific terms and identifiers. The DO is utilized for disease annotation by major biomedical databases (e.g. Array Express, NIF, IEDB), as a standard representation of human disease in biomedical ontologies (e.g. IDO, Cell line ontology, NIFSTD ontology, Experimental Factor Ontology, Influenza Ontology), and as an ontological cross mappings resource between DO, MeSH and OMIM (e.g. GeneWiki). The DO project (http://diseaseontology.sf.net) has been incorporated into open source tools (e.g. Gene Answers, FunDO) to connect gene and disease biomedical data through the lens of human disease. The next iteration of the DO web browser will integrate DO's extended relations and logical definition representation along with these biomedical resource cross-mappings

Theory of continuum percolation III. Low density expansion

We use a previously introduced mapping between the continuum percolation model and the Potts fluid (a system of interacting s-states spins which are free to move in the continuum) to derive the low density expansion of the pair connectedness and the mean cluster size. We prove that given an adequate identification of functions, the result is equivalent to the density expansion derived from a completely different point of view by Coniglio et al. [J. Phys A 10, 1123 (1977)] to describe physical clustering in a gas. We then apply our expansion to a system of hypercubes with a hard core interaction. The calculated critical density is within approximately 5% of the results of simulations, and is thus much more precise than previous theoretical results which were based on integral equations. We suggest that this is because integral equations smooth out overly the partition function (i.e., they describe predominantly its analytical part), while our method targets instead the part which describes the phase transition (i.e., the singular part).Comment: 42 pages, Revtex, includes 5 EncapsulatedPostscript figures, submitted to Phys Rev

Transitions in the Horizontal Transport of Vertically Vibrated Granular Layers

Motivated by recent advances in the investigation of fluctuation-driven ratchets and flows in excited granular media, we have carried out experimental and simulational studies to explore the horizontal transport of granular particles in a vertically vibrated system whose base has a sawtooth-shaped profile. The resulting material flow exhibits novel collective behavior, both as a function of the number of layers of particles and the driving frequency; in particular, under certain conditions, increasing the layer thickness leads to a reversal of the current, while the onset of transport as a function of frequency occurs gradually in a manner reminiscent of a phase transition. Our experimental findings are interpreted here with the help of extensive, event driven Molecular Dynamics simulations. In addition to reproducing the experimental results, the simulations revealed that the current may be reversed as a function of the driving frequency as well. We also give details about the simulations so that similar numerical studies can be carried out in a more straightforward manner in the future.Comment: 12 pages, 18 figure

Generalized model for dynamic percolation

We study the dynamics of a carrier, which performs a biased motion under the influence of an external field E, in an environment which is modeled by dynamic percolation and created by hard-core particles. The particles move randomly on a simple cubic lattice, constrained by hard-core exclusion, and they spontaneously annihilate and re-appear at some prescribed rates. Using decoupling of the third-order correlation functions into the product of the pairwise carrier-particle correlations we determine the density profiles of the "environment" particles, as seen from the stationary moving carrier, and calculate its terminal velocity, V_c, as the function of the applied field and other system parameters. We find that for sufficiently small driving forces the force exerted on the carrier by the "environment" particles shows a viscous-like behavior. An analog Stokes formula for such dynamic percolative environments and the corresponding friction coefficient are derived. We show that the density profile of the environment particles is strongly inhomogeneous: In front of the stationary moving carrier the density is higher than the average density, $\rho_s$, and approaches the average value as an exponential function of the distance from the carrier. Past the carrier the local density is lower than $\rho_s$ and the relaxation towards $\rho_s$ may proceed differently depending on whether the particles number is or is not explicitly conserved.Comment: Latex, 32 pages, 4 ps-figures, submitted to PR

A hybrid human and machine resource curation pipeline for the Neuroscience Information Framework

The breadth of information resources available to researchers on the Internet continues to expand, particularly in light of recently implemented data-sharing policies required by funding agencies. However, the nature of dense, multifaceted neuroscience data and the design of contemporary search engine systems makes efficient, reliable and relevant discovery of such information a significant challenge. This challenge is specifically pertinent for online databases, whose dynamic content is ‘hidden’ from search engines. The Neuroscience Information Framework (NIF; http://www.neuinfo.org) was funded by the NIH Blueprint for Neuroscience Research to address the problem of finding and utilizing neuroscience-relevant resources such as software tools, data sets, experimental animals and antibodies across the Internet. From the outset, NIF sought to provide an accounting of available resources, whereas developing technical solutions to finding, accessing and utilizing them. The curators therefore, are tasked with identifying and registering resources, examining data, writing configuration files to index and display data and keeping the contents current. In the initial phases of the project, all aspects of the registration and curation processes were manual. However, as the number of resources grew, manual curation became impractical. This report describes our experiences and successes with developing automated resource discovery and semiautomated type characterization with text-mining scripts that facilitate curation team efforts to discover, integrate and display new content. We also describe the DISCO framework, a suite of automated web services that significantly reduce manual curation efforts to periodically check for resource updates. Lastly, we discuss DOMEO, a semi-automated annotation tool that improves the discovery and curation of resources that are not necessarily website-based (i.e. reagents, software tools). Although the ultimate goal of automation was to reduce the workload of the curators, it has resulted in valuable analytic by-products that address accessibility, use and citation of resources that can now be shared with resource owners and the larger scientific community