Biomedical subjects

Brian R Hunt

Publications and source records attributed to Brian R Hunt.

16 recordsLinked to original sources

PubMed2006

Characterizing the dynamical importance of network nodes and links.

The largest eigenvalue of the adjacency matrix of networks is a key quantity determining several important dynamical processes on complex networks. Based on this fact, we present a quantitative, objective characterization of the dynamical importance of network nodes and links in terms of their effect on the largest eigenvalue. We show how our characterization of the dynamical importance of nodes can be affected by degree-degree correlations and network community structure. We discuss how our characterization can be used to optimize techniques for controlling certain network dynamical processes and apply our results to real networks.

Journal Article↗

PubMed2006

Emergence of coherence in complex networks of heterogeneous dynamical systems.

We present a general theory for the onset of coherence in collections of heterogeneous maps interacting via a complex connection network. Our method allows the dynamics of the individual uncoupled systems to be either chaotic or periodic, and applies generally to networks for which the number of connections per node is large. We find that the critical coupling strength at which a transition to synchrony takes place depends separately on the dynamics of the individual uncoupled systems and on the largest eigenvalue of the adjacency matrix of the coupling network. Our theory directly generalizes the Kuramoto model of equal strength all-to-all coupled phase oscillators to the case of oscillators with more realistic dynamics coupled via a large heterogeneous network.

Computer Communication Networks↗

PubMed2006

Scale dependence of branching in arterial and bronchial trees.

Although models of branching in arterial and bronchial trees often predict a dependence of bifurcation parameters on the scale of the bifurcating vessels, direct verification of this dependence by comparison with data is uncommon. We compare measurements of bifurcation parameters of airways and arterial trees of different mammals as a function of scale to general features predicted by theoretical models based on minimization of pumping power and network volume. We find that the size dependence is more complex than existing theories based solely on energy and volume minimization explain, and suggest additional factors that may govern the branching at different scales.

Animals↗

PubMed2006

Synchronization in large directed networks of coupled phase oscillators.

We study the emergence of collective synchronization in large directed networks of heterogeneous oscillators by generalizing the classical Kuramoto model of globally coupled phase oscillators to more realistic networks. We extend recent theoretical approximations describing the transition to synchronization in large undirected networks of coupled phase oscillators to the case of directed networks. We also consider the case of networks with mixed positive-negative coupling strengths. We compare our theory with numerical simulations and find good agreement.

Action Potentials↗

PubMed2005

Formation of multifractal population patterns from reproductive growth and local resettlement.

We consider the general character of the spatial distribution of a population that grows through reproduction and subsequent local resettlement of new population members. We present several simple one- and two-dimensional point placement models to illustrate possible generic behavior of these distributions. We show, numerically and analytically, that these models all lead to multifractal spatial distributions of population. Additionally, we make qualitative links between our models and the example of the Earth at Night image, showing the Earth's nighttime man-made light as seen from space. The Earth at Night data suffer from saturation of the sensing photodetectors at high brightness ("clipping"), and we account for how this influences the determined dimension spectrum of the light intensity distribution.

Animals↗

PubMed2005

Convex error growth patterns in a global weather model.

We investigate the error growth, that is, the growth in the distance E between two typical solutions of a weather model. Typically E grows until it reaches a saturation value E(s). We find two distinct broad log-linear regimes, one for E below 2% of E(s) and the other for E above. In each, log (E/E(s)) grows as if satisfying a linear differential equation. When plotting d log(E)/dt vs log(E), the graph is convex. We argue this behavior is quite different from other dynamics problems with saturation values, which yield concave graphs.

Journal Article↗

PubMed2005

Onset of synchronization in large networks of coupled oscillators.

We study the transition from incoherence to coherence in large networks of coupled phase oscillators. We present various approximations that describe the behavior of an appropriately defined order parameter past the transition and generalize recent results for the critical coupling strength. We find that, under appropriate conditions, the coupling strength at which the transition occurs is determined by the largest eigenvalue of the adjacency matrix. We show how, with an additional assumption, a mean-field approximation recently proposed is recovered from our results. We test our theory with numerical simulations and find that it describes the transition when our assumptions are satisfied. We find that our theory describes the transition well in situations in which the mean-field approximation fails. We study the finite-size effects caused by nodes with small degree and find that they cause the critical coupling strength to increase.

Journal Article↗

PubMed2004

Desynchronization waves and localized instabilities in oscillator arrays.

We consider a ring of identical or near-identical coupled periodic oscillators in which the connections have randomly heterogeneous strength. We use the master stability function method to determine the possible patterns at the desynchronization transition that occurs as the coupling strengths are increased. We demonstrate Anderson localization of the modes of instability and show that such localized instability generates waves of desynchronization that spread to the whole array. Similar results should apply to other networks with regular topology and heterogeneous connection strengths.

Journal Article↗

PubMed2004

Reducing storage requirements for biological sequence comparison.

MOTIVATION: Comparison of nucleic acid and protein sequences is a fundamental tool of modern bioinformatics. A dominant method of such string matching is the 'seed-and-extend' approach, in which occurrences of short subsequences called 'seeds' are used to search for potentially longer matches in a large database of sequences. Each such potential match is then checked to see if it extends beyond the seed. To be effective, the seed-and-extend approach needs to catalogue seeds from virtually every substring in the database of search strings. Projects such as mammalian genome assemblies and large-scale protein matching, however, have such large sequence databases that the resulting list of seeds cannot be stored in RAM on a single computer. This significantly slows the matching process. RESULTS: We present a simple and elegant method in which only a small fraction of seeds, called 'minimizers', needs to be stored. Using minimizers can speed up string-matching computations by a large factor while missing only a small fraction of the matches found using all seeds.

Algorithms↗

PubMed2004

Spatial patterns of desynchronization bursts in networks.

We adapt a previous model and analysis method (the master stability function), extensively used for studying the stability of the synchronous state of networks of identical chaotic oscillators, to the case of oscillators that are similar but not exactly identical. We find that bubbling induced desynchronization bursts occur for some parameter values. These bursts have spatial patterns, which can be predicted from the network connectivity matrix and the unstable periodic orbits embedded in the attractor. We test the analysis of bursts by comparison with numerical experiments. In the case that no bursting occurs, we discuss the deviations from the exactly synchronous state caused by the mismatch between oscillators.

Journal Article↗

PubMed2004

Growing networks with geographical attachment preference: emergence of small worlds.

We introduce a simple mechanism for the evolution of small world networks. Our model is a growing network in which all connections are made locally to geographically nearby sites. Although connections are made purely locally, network growth leads to stretching of old connections and to high clustering. Our results suggest that the abundance of small world networks in geographically constrained systems is a natural consequence of system growth and local interactions.

Journal Article↗

PubMed2004

Localized error bursts in estimating the state of spatiotemporal chaos.

We consider the problem of estimating the current state of an evolving spatiotemporally chaotic system from noisy observations of the system state and a model of the system dynamics. Using a simple scheme for state estimation, we show the possible occurrence of temporally and spatially intermittent large bursts in the estimation error. We discuss the similarity of these bursts with those occurring at the bubbling transition in the synchronization of low dimensional chaotic dynamical systems. We characterize the spatial and temporal behavior of the bursts and investigate how the behavior changes as we vary the number and location of the observations.

Journal Article↗

PubMed2004

A preprocessor for shotgun assembly of large genomes.

The whole-genome shotgun (WGS) assembly technique has been remarkably successful in efforts to determine the sequence of bases that make up a genome. WGS assembly begins with a large collection of short fragments that have been selected at random from a genome. The sequence of bases at each end of the fragment is determined, albeit imprecisely, resulting in a sequence of letters called a "read." Each letter in a read is assigned a quality value, which estimates the probability that a sequencing error occurred in determining that letter. Reads are typically cut off after about 500 letters, where sequencing errors become endemic. We report on a set of procedures that (1) corrects most of the sequencing errors, (2) changes quality values accordingly, and (3) produces a list of "overlaps," i.e., pairs of reads that plausibly come from overlapping parts of the genome. Our procedures, which we call collectively the "UMD Overlapper," can be run iteratively and as a preprocessor for other assemblers. We tested the UMD Overlapper on Celera's Drosophila reads. When we replaced Celera's overlap procedures in the front end of their assembler, it was able to produce a significantly improved genome.

Animals↗

PubMed2003

Anomalous diffusion in infinite horizon billiards.

We consider the long time dependence for the moments of displacement <|r|(q)> of infinite horizon billiards, given a bounded initial distribution of particles. For a variety of billiard models we find <|r|(q)> approximately t(gamma(q)) (up to factors of ln t). The time exponent, gamma(q), is piecewise linear and equal to q/2 for q<2 and q-1 for q>2. We discuss the lack of dependence of this result on the initial distribution of particles and resolve apparent discrepancies between this time dependence and a prior result. The lack of dependence on initial distribution follows from a remarkable scaling result that we obtain for the time evolution of the distribution function of the angle of a particle's velocity vector.

Journal Article↗

PubMed2003

Bifurcation scenarios for bubbling transition.

Dynamical systems with chaos on an invariant submanifold can exhibit a type of behavior called bubbling, whereby a small random or fixed perturbation to the system induces intermittent bursting. The bifurcation to bubbling occurs when a periodic orbit embedded in the chaotic attractor in the invariant manifold becomes unstable to perturbations transverse to the invariant manifold. Generically the periodic orbit can become transversely unstable through a pitchfork, transcritical, period-doubling, or Hopf bifurcation. In this paper a unified treatment of the four types of bubbling bifurcation is presented. Conditions are obtained determining whether the transition to bubbling is soft or hard; that is, whether the maximum burst amplitude varies continuously or discontinuously with variation of the parameter through its critical value. For soft bubbling transitions, the scaling of the maximum burst amplitude with the parameter is derived. For both hard and soft transitions the scaling of the average interburst time with the bifurcation parameter is deduced. Both random (noise) and fixed (mismatch) perturbations are considered. Results of numerical experiments testing our theoretical predictions are presented.

Journal Article↗

PubMed2002

Long time algebraic relaxation in chaotic billiards.

The long-time algebraic relaxation process in spatially periodic billiards with infinite horizon is shown to display a self-similar time-asymptotic form. This form is identical for a class of such billiards, but can be different in an important special case.

Journal Article↗