Spinoza

"Spinoza", second edition. Encyclopedia entry for the Springer Encyclopedia of EM Phil and the Sciences, ed. D. Jalobeanu and C. T. Wolfe

Kinetic distance and kinetic maps from molecular dynamics simulation

Characterizing macromolecular kinetics from molecular dynamics (MD) simulations requires a distance metric that can distinguish slowly-interconverting states. Here we build upon diffusion map theory and define a kinetic distance for irreducible Markov processes that quantifies how slowly molecular conformations interconvert. The kinetic distance can be computed given a model that approximates the eigenvalues and eigenvectors (reaction coordinates) of the MD Markov operator. Here we employ the time-lagged independent component analysis (TICA). The TICA components can be scaled to provide a kinetic map in which the Euclidean distance corresponds to the kinetic distance. As a result, the question of how many TICA dimensions should be kept in a dimensionality reduction approach becomes obsolete, and one parameter less needs to be specified in the kinetic model construction. We demonstrate the approach using TICA and Markov state model (MSM) analyses for illustrative models, protein conformation dynamics in bovine pancreatic trypsin inhibitor and protein-inhibitor association in trypsin and benzamidine

Description of \u3ci\u3eScottnema lindsayae\u3c/i\u3e Timm, 1971 (Rhabditida: Cephalobidae) from Taylor Valley, Antarctica and Its Phylogenetic Relationship

The endemic Antarctic nematode Scottnema lindsayae is described from specimens collected in Taylor Valley, McMurdo Dry Valleys, Victoria Land. The recently collected material is compared with the original description and other subsequent descriptions of the species. A more complete scanning electron microscopy (SEM) study of the species is presented. The phylogenetic position of S. lindsayae is inferred using a secondary structure-based alignment of a partial sequence of nuclear Large Subunit (LSU) ribosomal DNA. Phylogenetic trees were inferred using base-paired substitution models implemented in PHASE 2 software and Bayesian inference, and show S. lindsayae as the sister group to Stegelletina taxa

A categorification of Morelli's theorem

We prove a theorem relating torus-equivariant coherent sheaves on toric varieties to polyhedrally-constructible sheaves on a vector space. At the level of K-theory, the theorem recovers Morelli's description of the K-theory of a smooth projective toric variety. Specifically, let $X$ be a proper toric variety of dimension $n$ and let M_\bR = \mathrm{Lie}(T_\bR^\vee)\cong \bR^n be the Lie algebra of the compact dual (real) torus T_\bR^\vee\cong U(1)^n. Then there is a corresponding conical Lagrangian \Lambda \subset T^*M_\bR and an equivalence of triangulated dg categories \Perf_T(X) \cong \Sh_{cc}(M_\bR;\Lambda), where \Perf_T(X) is the triangulated dg category of perfect complexes of torus-equivariant coherent sheaves on $X$ and \Sh_{cc}(M_\bR;\Lambda) is the triangulated dg category of complex of sheaves on M_\bR with compactly supported, constructible cohomology whose singular support lies in $\Lambda$. This equivalence is monoidal---it intertwines the tensor product of coherent sheaves on $X$ with the convolution product of constructible sheaves on M_\bR.Comment: 20 pages. This is a strengthened version of the first half of arXiv:0811.1228v3, with new results; the second half becomes arXiv:0811.1228v

Random Walks on a Fluctuating Lattice: A Renormalization Group Approach Applied in One Dimension

We study the problem of a random walk on a lattice in which bonds connecting nearest neighbor sites open and close randomly in time, a situation often encountered in fluctuating media. We present a simple renormalization group technique to solve for the effective diffusive behavior at long times. For one-dimensional lattices we obtain better quantitative agreement with simulation data than earlier effective medium results. Our technique works in principle in any dimension, although the amount of computation required rises with dimensionality of the lattice.Comment: PostScript file including 2 figures, total 15 pages, 8 other figures obtainable by mail from D.L. Stei

Heat Conduction and Entropy Production in a One-Dimensional Hard-Particle Gas

We present large scale simulations for a one-dimensional chain of hard-point particles with alternating masses. We correct several claims in the recent literature based on much smaller simulations. Both for boundary conditions with two heat baths at different temperatures at both ends and from heat current autocorrelations in equilibrium we find heat conductivities kappa to diverge with the number N of particles. These depended very strongly on the mass ratios, and extrapolation to N -> infty resp. t -> infty is difficult due to very large finite-size and finite-time corrections. Nevertheless, our data seem compatible with a universal power law kappa ~ N^alpha with alpha approx 0.33. This suggests a relation to the Kardar-Parisi-Zhang model. We finally show that the hard-point gas with periodic boundary conditions is not chaotic in the usual sense and discuss why the system, when kept out of equilibrium, leads nevertheless to energy dissipation and entropy production.Comment: 4 pages (incl. 5 figures), RevTe

Variable-free exploration of stochastic models: a gene regulatory network example

Finding coarse-grained, low-dimensional descriptions is an important task in the analysis of complex, stochastic models of gene regulatory networks. This task involves (a) identifying observables that best describe the state of these complex systems and (b) characterizing the dynamics of the observables. In a previous paper [13], we assumed that good observables were known a priori, and presented an equation-free approach to approximate coarse-grained quantities (i.e, effective drift and diffusion coefficients) that characterize the long-time behavior of the observables. Here we use diffusion maps [9] to extract appropriate observables ("reduction coordinates") in an automated fashion; these involve the leading eigenvectors of a weighted Laplacian on a graph constructed from network simulation data. We present lifting and restriction procedures for translating between physical variables and these data-based observables. These procedures allow us to perform equation-free coarse-grained, computations characterizing the long-term dynamics through the design and processing of short bursts of stochastic simulation initialized at appropriate values of the data-based observables.Comment: 26 pages, 9 figure

Genetic Structure of Midwestern \u3ci\u3eAscaris suum\u3c/i\u3e Populations: A Comparison of Isoenzyme and RAPD Markers

Isoenzyme and random amplified polymorphic DNA (RAPD) markers were used to characterize the genetics of geographic variation among population samples of Ascaris suum from midwestern localities. Independent estimates of fixation indices (FST) based on isoenzyme and RAPD markers showed the same general patterns of differentiation and substantial statistical correlation (r=0.70). Of the total estimated gene diversity, 9.4% (isoenzyme) and 9.2% (RAPD) was distributed among infrapopulations. Geographic localities accounted for 7.8% (isoenzyme) and 6.2% (RAPD) of the total gene diversity. Only infrapopulations and localities, which indicates significant population subdivision among A. suum from farms within geographic regions. Departures from random mating were revealed by deficiencies of heterozygotes within infrapopulations and by high positive values of FIS among and between infrapopulations. The average inbreeding (FIS) coefficient among all infrapopulations was 0.22. Thus, the genetic composition of these A. suum infrapopulations, whether from a general geographic region or a single farm, was not consistent with a model of random recruitment from a larger panmictic pool of parasite life cycle stages