Baby-Step Giant-Step Algorithms for the Symmetric Group

We study discrete logarithms in the setting of group actions. Suppose that $G$ is a group that acts on a set $S$. When $r,s \in S$, a solution $g \in G$ to $r^g = s$ can be thought of as a kind of logarithm. In this paper, we study the case where $G = S_n$, and develop analogs to the Shanks baby-step / giant-step procedure for ordinary discrete logarithms. Specifically, we compute two sets $A, B \subseteq S_n$ such that every permutation of $S_n$ can be written as a product $ab$ of elements $a \in A$ and $b \in B$. Our deterministic procedure is optimal up to constant factors, in the sense that $A$ and $B$ can be computed in optimal asymptotic complexity, and $|A|$ and $|B|$ are a small constant from $\sqrt{n!}$ in size. We also analyze randomized "collision" algorithms for the same problem

Kinetics of the Formation and Dissociation of Actin Filament Branches Mediated by Arp2/3 Complex

AbstractThe actin filament network at the leading edge of motile cells relies on localized branching by Arp2/3 complex from “mother” filaments growing near the plasma membrane. The nucleotide bound to the mother filaments (ATP, ADP and phosphate, or ADP) may influence the branch dynamics. To determine the effect of the nucleotide bound to the subunits of the mother filament on the formation and stability of branches, we compared the time courses of actin polymerization in bulk samples measured using the fluorescence of pyrene actin with observations of single filaments by total internal reflection fluorescence microscopy. Although the branch nucleation rate in bulk samples was nearly the same regardless of the nucleotide on the mother filaments, we observed fewer branches by microscopy on ADP-bound filaments than on ADP-Pi-bound filaments. Observation of branches in the microscope depends on their binding to the slide. Since the probability that a branch binds to the slide is directly related to its lifetime, we used counts of branches to infer their rates of dissociation from mother filaments. We conclude that the nucleotide on the mother filament does not affect the initial branching event but that branches are an order of magnitude more stable on the sides of new ATP- or ADP-Pi filaments than on ADP-actin filaments

Preliminary investigation of pressure influence on multiphase heat transfer report no. ii

Pressure and surface condition in multiphase boiling heat transfe

Molecular Model of the Contractile Ring

We present a model for the actin contractile ring of adherent animal cells. The model suggests that the actin concentration within the ring and consequently the power that the ring exerts both increase during contraction. We demonstrate the crucial role of actin polymerization and depolymerization throughout cytokinesis, and the dominance of viscous dissipation in the dynamics. The physical origin of two phases in cytokinesis dynamics ("biphasic cytokinesis") follows from a limitation on the actin density. The model is consistent with a wide range of measurements of the midzone of dividing animal cells.Comment: PACS numbers: 87.16.Ka, 87.16.Ac http://www.ncbi.nlm.nih.gov/pubmed/16197254 http://www.weizmann.ac.il/complex/tlusty/papers/PhysRevLett2005.pd

Antarctic bedrock topography uncertainty and ice sheet stability

All Rights Reserved. Antarctic bedrock elevation estimates have uncertainties exceeding 1km in certain regions. Bedrock elevation, particularly where the bedrock is below sea level and bordering the ocean, can have a large impact on ice sheet stability. We investigate how present-day bedrock elevation uncertainty affects ice sheet model simulations for a generic past warm period based on the mid-Pliocene, although these uncertainties are also relevant to present-day and future ice sheet stability. We perform an ensemble of simulations with random topographic noise added with various length scales and with amplitudes tuned to the uncertainty of the Bedmap2 data set. Total Antarctic ice sheet retreat in these simulations varies between 12.6 and 17.9m equivalent sea level rise after 3kyrs of warm climate forcing. This study highlights the sensitivity of ice sheet models to existing uncertainties in bedrock elevation and the ongoing need for new data acquisition. Key Points Quantify how Antarctic bed elevation uncertainty affects ice sheet simulations Simulate retreat of the Antarctic ice sheet for a warm Pliocene climate Identify key areas for future improvements to bed elevation data

The scale and persistence of soil moisture anomalies as simulated in a global model

Short term variability of climate is intimately connected with soil moisture variability. Soil moisture provides the storage and subsequent return to the atmosphere, through evaporation and transpiration, of precipitation anomalies over land. Global Circulation Model (GCM) simulations enable consistent identification of correlations and dynamical connections between the hydrologic variables, many of which are incompletely observed. One way to facilitate understanding with these increasingly intricate models is to perform sensitivity studies in which a boundary condition or process is prescribed. In this study we will report on a sensitivity study in which a GCM with a sophisticated land surface representation is used to investigate soil moisture variability in the model climate. The simulations to be used in this study were made at R15 resolution (approximately 4.5 deg latitude x 7.5 deg longitude) with prescribed sea surface temperatures (SST) in the GENESIS model (Thompson and Pollard, 1994), which is coupled to a Land Surface Transfer model (LSX) at 2 deg x 2 deg resolution (Pollard and Thompson, 1994). All the results represented here were taken from the monthly averages of the model results. The LSX model accounts for the physical effects of vegetation with two layers specified at each grid point. Vegetation attributes such as leaf area indices, fractional cover, leaf albedos, etc., were taken from the global dataset in Dorman and Sellers (1989). A six-layer soil model extends from the surface to 4.25 m depth. SST's were prescribed in two ten year experiments using monthly SST values with the daily value being interpolated from the nearest two months. In the first experiment monthly climatological values were used, and in the second, the Atmospheric Model Intercomparison Project (AMIP) observed SST's for the years 1979 through 1988 were used (Gates, 1992). Thus, the former experiment gives a measure of the intrinsic model variability, to be compared with that of the latter experiment, which includes month-to-month variability due to ocean forcing

Random walks - a sequential approach

In this paper sequential monitoring schemes to detect nonparametric drifts are studied for the random walk case. The procedure is based on a kernel smoother. As a by-product we obtain the asymptotics of the Nadaraya-Watson estimator and its as- sociated sequential partial sum process under non-standard sampling. The asymptotic behavior differs substantially from the stationary situation, if there is a unit root (random walk component). To obtain meaningful asymptotic results we consider local nonpara- metric alternatives for the drift component. It turns out that the rate of convergence at which the drift vanishes determines whether the asymptotic properties of the monitoring procedure are determined by a deterministic or random function. Further, we provide a theoretical result about the optimal kernel for a given alternative

Coupling biochemistry and mechanics in cell adhesion: a model for inhomogeneous stress fiber contraction

Biochemistry and mechanics are closely coupled in cell adhesion. At sites of cell-matrix adhesion, mechanical force triggers signaling through the Rho-pathway, which leads to structural reinforcement and increased contractility in the actin cytoskeleton. The resulting force acts back to the sites of adhesion, resulting in a positive feedback loop for mature adhesion. Here we model this biochemical-mechanical feedback loop for the special case when the actin cytoskeleton is organized in stress fibers, which are contractile bundles of actin filaments. Activation of myosin II molecular motors through the Rho-pathway is described by a system of reaction-diffusion equations, which are coupled into a viscoelastic model for a contractile actin bundle. We find strong spatial gradients in the activation of contractility and in the corresponding deformation pattern of the stress fiber, in good agreement with experimental findings.Comment: Revtex, 35 pages, 13 Postscript figures included, in press with New Journal of Physics, Special Issue on The Physics of the Cytoskeleto