An improved algorithm for computing topological entropy

A new algorithm is presented for computing the topological entropy of a unimodal map of the interval. The accuracy of the algorithm is discussed and some graphs of the topological entropy which are obtained using the algorithm are displayed.     

On the Role of Physics in the Growth and Pattern Formation of Multi-Cellular Systems: What can we Learn from Individual-Cell Based Models?

We demonstrate that many collective phenomena in multi-cellular systems can be explained by models in which cells, despite their complexity, are represented as simple particles which are parameterized mainly by their physical properties. We mainly focus on two examples that nevertheless span a wide range of biological sub-disciplines: Unstructured cell populations growing in cell culture and growing cell layers in early animal development. While cultured unstructured cell populations would apriori been classified as particularly suited for a biophysical approach since the degree to which they are committed to a genetic program is expected to be modest, early animal development would be expected to mark the other extreme—here the degree of determinism according to a genetic program would be expected to be very high. We consider a number of phenomena such as the growth kinetics and spatial structure formation of monolayers and multicellular spheroids, the effect of the presence of another cell type surrounding the growing cell population, the effect of mutations and the critical surface dynamics of monolayers. Different from unstructured cell populations, cells in early development and at tissue interfaces usually form highly organized structures. An example are tissue layers. Under certain circumstances such layers are observed to fold. We show that folding pattern again can largely be explained by physical mechanisms either by a buckling instability or active cell shape changes. The paper combines new and published material and aims at an overview of a wide range of physical aspects in unstructured populations and growing tissue layers.     

Simple synthesis of endo-2-bromo-5-thiabicyclo[2.1.1]hexane

A brief synthesis of endo-2-bromo-5-thiabicyclo [2.1.1]hexane ( 9 ) has been developed involving conversion of 3-cyclopentenol ( 6 ) to 3-thioacetoxycyclopentene ( 7 ), bromination of this giving trans-1,2-dibromo-4-thioacetoxycyclopentane ( 8 ), and treatment of the latter with base. Compound 9 is oxidized to its S-oxide 10 and S, S-dioxide 11 . Comparative ¹³C and ¹H NMR data are given for 9–11 .     

Computing the topological entropy of maps of the interval with three monotone pieces

An algorithm is presented for computing the topological entropy of a piecewise monotone map of the interval having three monotone pieces. The accuracy of the algorithm is discussed and some graphs of the topological entropy obtained using the algorithm are displayed. Some of the ideas behind the algorithm have application to piecewise monotone functions with more than three monotone pieces.     

André-Quillen cohomology and rational homotopy of function spaces

We develop a simple theory of André-Quillen cohomology for commutative differential graded algebras over a field of characteristic zero. We then relate it to the homotopy groups of function spaces and spaces of homotopy self-equivalences of rational nilpotent CW-complexes. This puts certain results of Sullivan in a more conceptual framework.     

Precision Penning trap mass measurements of rare isotopes produced by projectile fragmentation

The low-energy beam and ion trap facility LEBIT at NSCL/MSU is at present the only facility where precision experiments are performed with stopped rare isotope beams produced by fast-beam fragmentation. LEBIT combines high-pressure-gas stopping with advanced ion manipulation techniques to provide brilliant low-energy beams. So far these beams have mainly been used for mass measurements on short-lived rare isotopes with a 9.4T Penning trap mass spectrometer. Recent examples include ^70m Br , located at the proton dripline, ³²Si and the iron isotopes ^63-65Fe . While the measurement of ³²Si helps to solve a long-standing dispute over the validity of the isobaric multiplet mass equation (IMME) for the A = 32 , T = 2 multiplet, the mass measurements of ^65m,g Fe marked the first time a nuclear isomeric state has been discovered by Penning trap mass spectrometry.