Pencil-Beam Surveys for Trans-Neptunian Objects: Limits on Distant Populations

Two populations of minor bodies in the outer Solar System remain particularly elusive: Scattered Disk objects and Sedna-like objects. These populations are important dynamical tracers, and understanding the details of their spatial- and size-distributions will enhance our understanding of the formation and on-going evolution of the Solar System. By using newly-derived limits on the maximum heliocentric distances that recent pencil-beam surveys for Trans-Neptunian Objects were sensitive to, we determine new upper limits on the total numbers of distant SDOs and Sedna-like objects. While generally consistent with populations estimated from wide-area surveys, we show that for magnitude-distribution slopes of {\alpha} > 0.7-1.0, these pencil-beam surveys provide stronger upper limits than current estimates in literature.Comment: Submitted to Icaru

Time-keeping and decision-making in living cells: Part I

To survive and reproduce, a cell must process information from its environment and its own internal state and respond accordingly, in terms of metabolic activity, gene expression, movement, growth, division and differentiation. These signal–response decisions are made by complex networks of interacting genes and proteins, which function as biochemical switches and clocks, and other recognizable information-processing circuitry. This theme issue of Interface Focus (in two parts) brings together articles on time-keeping and decision-making in living cells—work that uses precise mathematical modelling of underlying molecular regulatory networks to understand important features of cell physiology. Part I focuses on time-keeping: mechanisms and dynamics of biological oscillators and modes of synchronization and entrainment of oscillators, with special attention to circadian clocks

Time-keeping and decision-making in living cells: Part II

SCOPUS: re.jinfo:eu-repo/semantics/publishe

Phase Dynamics of Nearly Stationary Patterns in Activator-Inhibitor Systems

The slow dynamics of nearly stationary patterns in a FitzHugh-Nagumo model are studied using a phase dynamics approach. A Cross-Newell phase equation describing slow and weak modulations of periodic stationary solutions is derived. The derivation applies to the bistable, excitable, and the Turing unstable regimes. In the bistable case stability thresholds are obtained for the Eckhaus and the zigzag instabilities and for the transition to traveling waves. Neutral stability curves demonstrate the destabilization of stationary planar patterns at low wavenumbers to zigzag and traveling modes. Numerical solutions of the model system support the theoretical findings

Synchronization and Coarsening (without SOC) in a Forest-Fire Model

We study the long-time dynamics of a forest-fire model with deterministic tree growth and instantaneous burning of entire forests by stochastic lightning strikes. Asymptotically the system organizes into a coarsening self-similar mosaic of synchronized patches within which trees regrow and burn simultaneously. We show that the average patch length grows linearly with time as t-->oo. The number density of patches of length L, N(L,t), scales as ^{-2}M(L/), and within a mean-field rate equation description we find that this scaling function decays as e^{-1/x} for x-->0, and as e^{-x} for x-->oo. In one dimension, we develop an event-driven cluster algorithm to study the asymptotic behavior of large systems. Our numerical results are consistent with mean-field predictions for patch coarsening.Comment: 5 pages, 4 figures, 2-column revtex format. To be submitted to PR

A mathematical framework for critical transitions: normal forms, variance and applications

Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find early-warning signs. We show that it is possible to classify critical transitions by using bifurcation theory and normal forms in the singular limit. Based on this elementary classification, we analyze stochastic fluctuations and calculate scaling laws of the variance of stochastic sample paths near critical transitions for fast subsystem bifurcations up to codimension two. The theory is applied to several models: the Stommel-Cessi box model for the thermohaline circulation from geoscience, an epidemic-spreading model on an adaptive network, an activator-inhibitor switch from systems biology, a predator-prey system from ecology and to the Euler buckling problem from classical mechanics. For the Stommel-Cessi model we compare different detrending techniques to calculate early-warning signs. In the epidemics model we show that link densities could be better variables for prediction than population densities. The activator-inhibitor switch demonstrates effects in three time-scale systems and points out that excitable cells and molecular units have information for subthreshold prediction. In the predator-prey model explosive population growth near a codimension two bifurcation is investigated and we show that early-warnings from normal forms can be misleading in this context. In the biomechanical model we demonstrate that early-warning signs for buckling depend crucially on the control strategy near the instability which illustrates the effect of multiplicative noise.Comment: minor corrections to previous versio

The Physarum polycephalum Genome Reveals Extensive Use of Prokaryotic Two-Component and Metazoan-Type Tyrosine Kinase Signaling

Physarum polycephalum is a well-studied microbial eukaryote with unique experimental attributes relative to other experimental model organisms. It has a sophisticated life cycle with several distinct stages including amoebal, flagellated, and plasmodial cells. It is unusual in switching between open and closed mitosis according to specific life-cycle stages. Here we present the analysis of the genome of this enigmatic and important model organism and compare it with closely related species. The genome is littered with simple and complex repeats and the coding regions are frequently interrupted by introns with a mean size of 100 bases. Complemented with extensive transcriptome data, we define approximately 31,000 gene loci, providing unexpected insights into earlyeukaryoteevolution.Wedescribeextensiveuseofhistidinekinase-basedtwo-componentsystemsandtyrosinekinasesignaling, the presence of bacterial and plant type photoreceptors (phytochromes, cryptochrome, and phototropin) and of plant-type pentatricopeptide repeat proteins, as well as metabolic pathways, and a cell cycle control system typically found in more complex eukaryotes. Our analysis characterizes P. polycephalum as a prototypical eukaryote with features attributed to the last common ancestor of Amorphea, that is, the Amoebozoa and Opisthokonts. Specifically, the presence of tyrosine kinases inAcanthamoeba and Physarum as representatives of two distantly related subdivisions ofAmoebozoa argues against the later emergence of tyrosine kinase signaling in the opisthokont lineage and also against the acquisition by horizontal gene transfe

Cosmological Applications of Gravitational Lensing

The last decade has seen an enormous increase of activity in the field of gravitational lensing, mainly driven by improvements of observational capabilities. I will review the basics of gravitational lens theory, just enough to understand the rest of this contribution, and will then concentrate on several of the main applications in cosmology. Cluster lensing, and weak lensing, will constitute the main part of this review.Comment: 26 pages, including 2 figures (a third figure can be obtained from the author by request) gziped and uuencoded postscript file; to be published in Proceedings of the Laredo Advanced Summer School, Sept. 9