Local Anisotropy of Fluids using Minkowski Tensors

Statistics of the free volume available to individual particles have previously been studied for simple and complex fluids, granular matter, amorphous solids, and structural glasses. Minkowski tensors provide a set of shape measures that are based on strong mathematical theorems and easily computed for polygonal and polyhedral bodies such as free volume cells (Voronoi cells). They characterize the local structure beyond the two-point correlation function and are suitable to define indices $0\leq \beta_\nu^{a,b}\leq 1$ of local anisotropy. Here, we analyze the statistics of Minkowski tensors for configurations of simple liquid models, including the ideal gas (Poisson point process), the hard disks and hard spheres ensemble, and the Lennard-Jones fluid. We show that Minkowski tensors provide a robust characterization of local anisotropy, which ranges from $\beta_\nu^{a,b}\approx 0.3$ for vapor phases to $\beta_\nu^{a,b}\to 1$ for ordered solids. We find that for fluids, local anisotropy decreases monotonously with increasing free volume and randomness of particle positions. Furthermore, the local anisotropy indices $\beta_\nu^{a,b}$ are sensitive to structural transitions in these simple fluids, as has been previously shown in granular systems for the transition from loose to jammed bead packs

Gel-Electrophoresis and Diffusion of Ring-Shaped DNA

A model for the motion of ring-shaped DNA in a gel is introduced and studied by numerical simulations and a mean-field approximation. The ring motion is mediated by finger-shaped loops (hernias) that move in an amoeba-like fashion around the gel obstructions. This constitutes an extension of previous reptation tube treatments. It is shown that tension is essential for describing the dynamics in the presence of hernias. It is included in the model as long range interactions over stretched DNA regions. The mobility of ring-shaped DNA is found to saturate much as in the well-studied case of linear DNA. Experiments in polymer gels, however, show that the mobility drops exponentially with the DNA ring size. This is commonly attributed to dangling-ends in the gel that can impale the ring. The predictions of the present model are expected to apply to artificial 2D obstacle arrays (W.D. Volkmuth, R.H. Austin, Nature 358,600 (1992)) which have no dangling-ends. In the zero-field case an exact solution of the model steady-state is obtained, and quantities such as the average ring size are calculated. An approximate treatment of the ring dynamics is given, and the diffusion coefficient is derived. The model is also discussed in the context of spontaneous symmetry breaking in one dimension.Comment: 8 figures, LaTeX, Phys. Rev. E - in pres

Worldwide Relationships in the Fern Genus Pteridium (Bracken) Based on Nuclear Genome Markers

PREMISE: Spore-bearing plants are capable of dispersing very long distances. However, it is not known if gene flow can prevent genetic divergence in widely distributed taxa. Here we address this issue, and examine systematic relationships at a global geographic scale for the fern genus Pteridium. METHODS: We sampled plants from 100 localities worldwide, and generated nucleotide data from four nuclear genes and two plastid regions. We also examined 2801 single nucleotide polymorphisms detected by a restriction site-associated DNA approach. RESULTS: We found evidence for two distinct diploid species and two allotetraploids between them. The “northern” species (Pteridium aquilinum) has distinct groups at the continental scale (Europe, Asia, Africa, and North America). The northern European subspecies pinetorum appears to involve admixture among all of these. A sample from the Hawaiian Islands contained elements of both North American and Asian P. aquilinum. The “southern” species, P. esculentum, shows little genetic differentiation between South American and Australian samples. Components of African genotypes are detected on all continents. CONCLUSIONS: We find evidence of distinct continental-scale genetic differentiation in Pteridium. However, on top of this is a clear signal of recent hybridization. Thus, spore-bearing plants are clearly capable of extensive long-distance gene flow; yet appear to have differentiated genetically at the continental scale. Either gene flow in the past was at a reduced level, or vicariance is possible even in the face of long-distance gene flow

Minkowski Tensors of Anisotropic Spatial Structure

This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors. Minkowski tensors are generalisations of the well-known scalar Minkowski functionals and are explicitly sensitive to anisotropic aspects of morphology, relevant for example for elastic moduli or permeability of microstructured materials. Here we derive explicit linear-time algorithms to compute these tensorial measures for three-dimensional shapes. These apply to representations of any object that can be represented by a triangulation of its bounding surface; their application is illustrated for the polyhedral Voronoi cellular complexes of jammed sphere configurations, and for triangulations of a biopolymer fibre network obtained by confocal microscopy. The article further bridges the substantial notational and conceptual gap between the different but equivalent approaches to scalar or tensorial Minkowski functionals in mathematics and in physics, hence making the mathematical measure theoretic method more readily accessible for future application in the physical sciences

Cell shape analysis of random tessellations based on Minkowski tensors

To which degree are shape indices of individual cells of a tessellation characteristic for the stochastic process that generates them? Within the context of stochastic geometry and the physics of disordered materials, this corresponds to the question of relationships between different stochastic models. In the context of image analysis of synthetic and biological materials, this question is central to the problem of inferring information about formation processes from spatial measurements of resulting random structures. We address this question by a theory-based simulation study of shape indices derived from Minkowski tensors for a variety of tessellation models. We focus on the relationship between two indices: an isoperimetric ratio of the empirical averages of cell volume and area and the cell elongation quantified by eigenvalue ratios of interfacial Minkowski tensors. Simulation data for these quantities, as well as for distributions thereof and for correlations of cell shape and volume, are presented for Voronoi mosaics of the Poisson point process, determinantal and permanental point processes, and Gibbs hard-core and random sequential absorption processes as well as for Laguerre tessellations of polydisperse spheres and STIT- and Poisson hyperplane tessellations. These data are complemented by mechanically stable crystalline sphere and disordered ellipsoid packings and area-minimising foam models. We find that shape indices of individual cells are not sufficient to unambiguously identify the generating process even amongst this limited set of processes. However, we identify significant differences of the shape indices between many of these tessellation models. Given a realization of a tessellation, these shape indices can narrow the choice of possible generating processes, providing a powerful tool which can be further strengthened by density-resolved volume-shape correlations.Comment: Chapter of the forthcoming book "Tensor Valuations and their Applications in Stochastic Geometry and Imaging" in Lecture Notes in Mathematics edited by Markus Kiderlen and Eva B. Vedel Jense

Harnessing the Creative Potential of Consumers: Money, Participation and Creativity in Idea Crowdsourcing

Given the growing importance of innovation and consumer engagement, many firms are strongly interested in finding ways to encourage their consumers to generate creative new product ideas for them in their crowdsourcing initiatives. To that end, managers often use monetary rewards – one of the most commonly used managerial tools to stimulate desired behaviors. A critical question in this respect is whether the use of monetary rewards is effective in stimulating creativity and, if so, how large those rewards should be. This study aims to answer these questions. The results of an experiment suggest that introducing monetary rewards does not contribute to the number of new product ideas generated by a single consumer or the novelty of his/her ideas, and when the reward is relatively small it can even be harmful. Monetary rewards, however, are effective in encouraging widespread participation in crowdsourcing initiatives and improving the appropriateness of the new product ideas. As a whole, these findings take us a step further toward better understanding the motivational mechanisms of consumer creativity in new product ideation

Antiinflammatory Therapy with Canakinumab for Atherosclerotic Disease

Background: Experimental and clinical data suggest that reducing inflammation without affecting lipid levels may reduce the risk of cardiovascular disease. Yet, the inflammatory hypothesis of atherothrombosis has remained unproved. Methods: We conducted a randomized, double-blind trial of canakinumab, a therapeutic monoclonal antibody targeting interleukin-1β, involving 10,061 patients with previous myocardial infarction and a high-sensitivity C-reactive protein level of 2 mg or more per liter. The trial compared three doses of canakinumab (50 mg, 150 mg, and 300 mg, administered subcutaneously every 3 months) with placebo. The primary efficacy end point was nonfatal myocardial infarction, nonfatal stroke, or cardiovascular death. RESULTS: At 48 months, the median reduction from baseline in the high-sensitivity C-reactive protein level was 26 percentage points greater in the group that received the 50-mg dose of canakinumab, 37 percentage points greater in the 150-mg group, and 41 percentage points greater in the 300-mg group than in the placebo group. Canakinumab did not reduce lipid levels from baseline. At a median follow-up of 3.7 years, the incidence rate for the primary end point was 4.50 events per 100 person-years in the placebo group, 4.11 events per 100 person-years in the 50-mg group, 3.86 events per 100 person-years in the 150-mg group, and 3.90 events per 100 person-years in the 300-mg group. The hazard ratios as compared with placebo were as follows: in the 50-mg group, 0.93 (95% confidence interval [CI], 0.80 to 1.07; P = 0.30); in the 150-mg group, 0.85 (95% CI, 0.74 to 0.98; P = 0.021); and in the 300-mg group, 0.86 (95% CI, 0.75 to 0.99; P = 0.031). The 150-mg dose, but not the other doses, met the prespecified multiplicity-adjusted threshold for statistical significance for the primary end point and the secondary end point that additionally included hospitalization for unstable angina that led to urgent revascularization (hazard ratio vs. placebo, 0.83; 95% CI, 0.73 to 0.95; P = 0.005). Canakinumab was associated with a higher incidence of fatal infection than was placebo. There was no significant difference in all-cause mortality (hazard ratio for all canakinumab doses vs. placebo, 0.94; 95% CI, 0.83 to 1.06; P = 0.31). Conclusions: Antiinflammatory therapy targeting the interleukin-1β innate immunity pathway with canakinumab at a dose of 150 mg every 3 months led to a significantly lower rate of recurrent cardiovascular events than placebo, independent of lipid-level lowering. (Funded by Novartis; CANTOS ClinicalTrials.gov number, NCT01327846.

Molecular Systematics of the Deep-Sea Hydrothermal Vent Endemic Brachyuran Family Bythograeidae: A Comparison of Three Bayesian Species Tree Methods

Brachyuran crabs of the family Bythograeidae are endemic to deep-sea hydrothermal vents and represent one of the most successful groups of macroinvertebrates that have colonized this extreme environment. Occurring worldwide, the family includes six genera (Allograea, Austinograea, Bythograea, Cyanagraea, Gandalfus, and Segonzacia) and fourteen formally described species. To investigate their evolutionary relationships, we conducted Maximum Likelihood and Bayesian molecular phylogenetic analyses, based on DNA sequences from fragments of three mitochondrial genes (16S rDNA, Cytochrome oxidase I, and Cytochrome b) and three nuclear genes (28S rDNA, the sodium–potassium ATPase a-subunit ‘NaK’, and Histone H3A). We employed traditional concatenated (i.e., supermatrix) phylogenetic methods, as well as three recently developed Bayesian multilocus methods aimed at inferring species trees from potentially discordant gene trees. We found strong support for two main clades within Bythograeidae: one comprising the members of the genus Bythograea; and the other comprising the remaining genera. Relationships within each of these two clades were partially resolved. We compare our results with an earlier hypothesis on the phylogenetic relationships among bythograeid genera based on morphology. We also discuss the biogeography of the family in the light of our results. Our species tree analyses reveal differences in how each of the three methods weighs conflicting phylogenetic signal from different gene partitions and how limits on the number of outgroup taxa may affect the results