Coarse topology, enlargeability, and essentialness

Using methods from coarse topology we show that fundamental classes of closed enlargeable manifolds map non-trivially both to the rational homology of their fundamental groups and to the K-theory of the corresponding reduced C*-algebras. Our proofs do not depend on the Baum--Connes conjecture and provide independent confirmation for specific predictions derived from this conjecture.Comment: 21 pages, 2 figures. Revised version. To appear in Ann. Sci. Ecole Norm. Su

An experiment of the impact of a neonicotinoid pesticide on honeybees : the value of a formal analysis of the data

This work received funding from the MASTS pooling initiative (The Marine Alliance for Science and Technology for Scotland) and their support is gratefully acknowledged. MASTS is funded by the Scottish Funding Council (Grant reference HR09011) and contributing institutions.Background: We assess the analysis of the data resulting from a field experiment conducted by Pilling et al. (2013) on the potential effects of thiamethoxam on honey bees. The experiment had low levels of replication, so Pilling et al. concluded that formal statistical analysis would be misleading. This would be true if such an analysis merely comprised tests of statistical significance and if the investigators concluded that lack of significance meant little or no effect. However, an analysis that includes estimation of the size of any effects—with confidence limits—allows one to reach conclusions that are not misleading and that produce useful insights. Main Body: For the data of Pilling et al. we use straightforward statistical analysis to show that the confidence limits are generally so wide that any effects of thiamethoxam could have been large without being statistically significant. Instead of formal analysis, Pilling et al. simply inspected the data and concluded that they provided no evidence of detrimental effects and from this that thiamethoxam poses a “low risk” to bees. Conclusions: Conclusions derived from inspection of the data were not just misleading in this case but are unacceptable in principle, for if data are inadequate for a formal analysis (or only good enough to provide estimates with wide confidence intervals) then they are bound to be inadequate as a basis for reaching any sound conclusions. Given that the data in this case are largely uninformative with respect to the treatment effect, any conclusions reached from such informal approaches can do little more than reflect the prior beliefs of those involved.Publisher PDFPeer reviewe

Internal Energy of the Potts model on the Triangular Lattice with Two- and Three-body Interactions

We calculate the internal energy of the Potts model on the triangular lattice with two- and three-body interactions at the transition point satisfying certain conditions for coupling constants. The method is a duality transformation. Therefore we have to make assumptions on uniqueness of the transition point and that the transition is of second order. These assumptions have been verified to hold by numerical simulations for q=2, 3 and 4, and our results for the internal energy are expected to be exact in these cases.Comment: 9 pages, 4 figure

Lithic artifact assemblage transport and micro-wear modification in a fluvial setting: a radio frequency identification tag experiment

River processes are widely assumed to have impacted the integrity of lithic assemblages when artifacts are found in fluvial sediments, but the specifics of these influences remain largely unknown. We conducted a real-world experiment to determine how the initial stages of fluvial entrainment affected lithic artifact assemblages. We inserted replica artifacts with Radio Frequency Identification (RFID) tags into a gravel-bedded river in Wales (UK) for seven months and related their transport distances to their morphology and the recorded streamflow. Additionally, nine artifacts were recovered at the end of the experiment and analyzed for micro-wear traces. In sum, our results show that in a gravel bedded river with a mean discharge of 5.1 m3s-1, artifact length and width were the main variables influencing artifact transport distances. The experiment also resulted in characteristic micro-wear traces developing on the artifacts over distances of 485 m or less. These results emphasize the multifaceted nature of alluvial site formation processes in a repeatable experiment and highlight new ways to identify the transport of replica Paleolithic material

Kinetics of Phase Separation in Thin Films: Simulations for the Diffusive Case

We study the diffusion-driven kinetics of phase separation of a symmetric binary mixture (AB), confined in a thin-film geometry between two parallel walls. We consider cases where (a) both walls preferentially attract the same component (A), and (b) one wall attracts A and the other wall attracts B (with the same strength). We focus on the interplay of phase separation and wetting at the walls, which is referred to as {\it surface-directed spinodal decomposition} (SDSD). The formation of SDSD waves at the two surfaces, with wave-vectors oriented perpendicular to them, often results in a metastable layered state (also referred to as ``stratified morphology''). This state is reminiscent of the situation where the thin film is still in the one-phase region but the surfaces are completely wet, and hence coated with thick wetting layers. This metastable state decays by spinodal fluctuations and crosses over to an asymptotic growth regime characterized by the lateral coarsening of pancake-like domains. These pancakes may or may not be coated by precursors of wetting layers. We use Langevin simulations to study this crossover and the growth kinetics in the asymptotic coarsening regime.Comment: 39 pages, 19 figures, submitted to Phys.Rev.

Hodge Theory on Metric Spaces

Hodge theory is a beautiful synthesis of geometry, topology, and analysis, which has been developed in the setting of Riemannian manifolds. On the other hand, spaces of images, which are important in the mathematical foundations of vision and pattern recognition, do not fit this framework. This motivates us to develop a version of Hodge theory on metric spaces with a probability measure. We believe that this constitutes a step towards understanding the geometry of vision. The appendix by Anthony Baker provides a separable, compact metric space with infinite dimensional \alpha-scale homology.Comment: appendix by Anthony W. Baker, 48 pages, AMS-LaTeX. v2: final version, to appear in Foundations of Computational Mathematics. Minor changes and addition

Low-dimensional Bose gases

We present an improved many-body T-matrix theory for partially Bose-Einstein condensed atomic gases by treating the phase fluctuations exactly. The resulting mean-field theory is valid in arbitrary dimensions and able to describe the low-temperature crossover between three, two and one-dimensional Bose gases. When applied to a degenerate two-dimensional atomic hydrogen gas, we obtain a reduction of the three-body recombination rate which compares favorably with experiment. Supplementing the mean-field theory with a renormalization-group approach to treat the critical fluctuations, we also incorporate into the theory the Kosterlitz-Thouless transition that occurs in a homogeneous Bose gas in two dimensions. In particular, we calculate the critical conditions for the Kosterlitz-Thouless phase transition as a function of the microscopic parameters of the theory. The proposed theory is further applied to a trapped one-dimensional Bose gas, where we find good agreement with exact numerical results obtained by solving a nonlinear Langevin field equation.Comment: 14 pages, 13 figures, revte

Collective modes of a quasi two-dimensional Bose condensate in large gas parameter regime

We have theoretically studied the collective modes of a quasi two-dimensional (Q2D) Bose condensate in the large gas parameter regime by using a formalism which treats the interaction energy beyond the mean-field approximation. In the calculation we use the perturbative expansion for the interaction energy by incorporating the Lee, Huang and Yang (LHY) correction term. The results show that incorporation of this higher order term leads to detectable modifications in the mode frequencies.Comment: 10 pages, 2 figure

Structure and Instability of High-Density Equations for Traffic Flow

Similar to the treatment of dense gases, fluid-dynamic equations for the dynamics of congested vehicular traffic are derived from Enskog-like kinetic equations. These contain additional terms due to the anisotropic vehicle interactions. The calculations are carried out up to Navier-Stokes order. A linear instability analysis indicates an additional kind of instability compared to previous macroscopic traffic models. The relevance for describing granular flows is outlined.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.htm

Grain Dynamics in a Two-dimensional Granular Flow

We have used particle tracking methods to study the dynamics of individual balls comprising a granular flow in a small-angle two-dimensional funnel. We statistically analyze many ball trajectories to examine the mechanisms of shock propagation. In particular, we study the creation of, and interactions between, shock waves. We also investigate the role of granular temperature and draw parallels to traffic flow dynamics.Comment: 17 pages, 24 figures. To appear in Phys.Rev.E. High res./color figures etc. on http://www.nbi.dk/CATS/Granular/GrainDyn.htm