Biomedical subjects

James P Sethna

Publications and source records attributed to James P Sethna.

7 recordsLinked to original sources

PubMed2006

Sloppy-model universality class and the Vandermonde matrix.

In a variety of contexts, physicists study complex, nonlinear models with many unknown or tunable parameters to explain experimental data. We explain why such systems so often are sloppy: the system behavior depends only on a few "stiff" combinations of the parameters and is unchanged as other "sloppy" parameter combinations vary by orders of magnitude. We observe that the eigenvalue spectra for the sensitivity of sloppy models have a striking, characteristic form with a density of logarithms of eigenvalues which is roughly constant over a large range. We suggest that the common features of sloppy models indicate that they may belong to a common universality class. In particular, we motivate focusing on a Vandermonde ensemble of multiparameter nonlinear models and show in one limit that they exhibit the universal features of sloppy models.

Algorithms↗

PubMed2006

Mesoscale theory of grains and cells: crystal plasticity and coarsening.

Crystals with spatial variations in their axes naturally evolve into cells or grains separated by sharp walls. At high temperatures, polycrystalline grains form from the melt and coarsen with time: the dislocations can both climb and glide. At low temperatures under shear the dislocations (which allow only glide) form into cell structures. We present here a mesoscale theory of dislocation motion. It provides a quantitative description of deformation and rotation, grounded in a microscopic order parameter field exhibiting the topologically conserved quantities. The topological current of the Nye dislocation density tensor is derived from a microscopic theory of glide driven by Peach-Koehler forces between dislocations using a simple closure approximation. The resulting theory is shown to form sharp dislocation walls in finite time, both with and without dislocation climb.

Journal Article↗

PubMed2004

Bayesian ensemble approach to error estimation of interatomic potentials.

Using a Bayesian approach a general method is developed to assess error bars on predictions made by models fitted to data. The error bars are estimated from fluctuations in ensembles of models sampling the model-parameter space with a probability density set by the minimum cost. The method is applied to the development of interatomic potentials for molybdenum using various potential forms and databases based on atomic forces. The calculated error bars on elastic constants, gamma-surface energies, structural energies, and dislocation properties are shown to provide realistic estimates of the actual errors for the potentials.

Bayes Theorem↗

PubMed2004

Mean-field approaches to the totally asymmetric exclusion process with quenched disorder and large particles.

The process of protein synthesis in biological systems resembles a one-dimensional driven lattice gas in which the particles (ribosomes) have spatial extent, covering more than one lattice site. Realistic, nonuniform gene sequences lead to quenched disorder in the particle hopping rates. We study the totally asymmetric exclusion process with large particles and quenched disorder via several mean-field approaches and compare the mean-field results with Monte Carlo simulations. Mean-field equations obtained from the literature are found to be reasonably effective in describing this system. A numerical technique is developed for computing the particle current rapidly. The mean-field approach is extended to include two-point correlations between adjacent sites. The two-point results are found to match Monte Carlo simulations more closely.

Biophysics↗

PubMed2003

Statistical mechanical approaches to models with many poorly known parameters.

Models of biochemical regulation in prokaryotes and eukaryotes, typically consisting of a set of first-order nonlinear ordinary differential equations, have become increasingly popular of late. These systems have large numbers of poorly known parameters, simplified dynamics, and uncertain connectivity: three key features of a class of problems we call sloppy models, which are shared by many other high-dimensional multiparameter nonlinear models. We use a statistical ensemble method to study the behavior of these models, in order to extract as much useful predictive information as possible from a sloppy model, given the available data used to constrain it. We discuss numerical challenges that emerge in using the ensemble method for a large system. We characterize features of sloppy model parameter fluctuations by various spectral decompositions and find indeed that five parameters can be used to fit an elephant. We also find that model entropy is as important to the problem of model choice as model energy is to parameter choice.

Algorithms↗

PubMed2002

Coulomb blockade and the Kondo effect in single-atom transistors.

Using molecules as electronic components is a powerful new direction in the science and technology of nanometre-scale systems. Experiments to date have examined a multitude of molecules conducting in parallel, or, in some cases, transport through single molecules. The latter includes molecules probed in a two-terminal geometry using mechanically controlled break junctions or scanning probes as well as three-terminal single-molecule transistors made from carbon nanotubes, C(60) molecules, and conjugated molecules diluted in a less-conducting molecular layer. The ultimate limit would be a device where electrons hop on to, and off from, a single atom between two contacts. Here we describe transistors incorporating a transition-metal complex designed so that electron transport occurs through well-defined charge states of a single atom. We examine two related molecules containing a Co ion bonded to polypyridyl ligands, attached to insulating tethers of different lengths. Changing the length of the insulating tether alters the coupling of the ion to the electrodes, enabling the fabrication of devices that exhibit either single-electron phenomena, such as Coulomb blockade, or the Kondo effect.

Journal Article↗

PubMed2002

Universal pulse shape scaling function and exponents: critical test for avalanche models applied to Barkhausen noise.

In order to test if the universal aspects of Barkhausen noise in magnetic materials can be predicted from recent variants of the nonequilibrium zero-temperature Random Field Ising Model, we perform a quantitative study of the universal scaling function derived from the Barkhausen pulse shape in simulations and experiment. Through data collapses and scaling relations we determine the critical exponents tau and 1/sigma nu z in both simulation and experiment. Although we find agreement in the critical exponents, we find differences between theoretical and experimental pulse shape scaling functions as well as between different experiments.

Journal Article↗