Self-avoiding walks and connective constants

The connective constant $\mu(G)$ of a quasi-transitive graph $G$ is the asymptotic growth rate of the number of self-avoiding walks (SAWs) on $G$ from a given starting vertex. We survey several aspects of the relationship between the connective constant and the underlying graph $G$. $\bullet$ We present upper and lower bounds for $\mu$ in terms of the vertex-degree and girth of a transitive graph. $\bullet$ We discuss the question of whether $\mu\ge\phi$ for transitive cubic graphs (where $\phi$ denotes the golden mean), and we introduce the Fisher transformation for SAWs (that is, the replacement of vertices by triangles). $\bullet$ We present strict inequalities for the connective constants $\mu(G)$ of transitive graphs $G$, as $G$ varies. $\bullet$ As a consequence of the last, the connective constant of a Cayley graph of a finitely generated group decreases strictly when a new relator is added, and increases strictly when a non-trivial group element is declared to be a further generator. $\bullet$ We describe so-called graph height functions within an account of "bridges" for quasi-transitive graphs, and indicate that the bridge constant equals the connective constant when the graph has a unimodular graph height function. $\bullet$ A partial answer is given to the question of the locality of connective constants, based around the existence of unimodular graph height functions. $\bullet$ Examples are presented of Cayley graphs of finitely presented groups that possess graph height functions (that are, in addition, harmonic and unimodular), and that do not. $\bullet$ The review closes with a brief account of the "speed" of SAW.Comment: Accepted version. arXiv admin note: substantial text overlap with arXiv:1304.721

Quantitative trait loci conferring grain mineral nutrient concentrations in durum wheat 3 wild emmer wheat RIL population

Mineral nutrient malnutrition, and particularly deficiency in zinc and iron, afflicts over 3 billion people worldwide. Wild emmer wheat, Triticum turgidum ssp. dicoccoides, genepool harbors a rich allelic repertoire for mineral nutrients in the grain. The genetic and physiological basis of grain protein, micronutrients (zinc, iron, copper and manganese) and macronutrients (calcium, magnesium, potassium, phosphorus and sulfur) concentration was studied in tetraploid wheat population of 152 recombinant inbred lines (RILs), derived from a cross between durum wheat (cv. Langdon) and wild emmer (accession G18-16). Wide genetic variation was found among the RILs for all grain minerals, with considerable transgressive effect. A total of 82 QTLs were mapped for 10 minerals with LOD score range of 3.2–16.7. Most QTLs were in favor of the wild allele (50 QTLs). Fourteen pairs of QTLs for the same trait were mapped to seemingly homoeologous positions, reflecting synteny between the A and B genomes. Significant positive correlation was found between grain protein concentration (GPC), Zn, Fe and Cu, which was supported by significant overlap between the respective QTLs, suggesting common physiological and/or genetic factors controlling the concentrations of these mineral nutrients. Few genomic regions (chromosomes 2A, 5A, 6B and 7A) were found to harbor clusters of QTLs for GPC and other nutrients. These identified QTLs may facilitate the use of wild alleles for improving grain nutritional quality of elite wheat cultivars, especially in terms of protein, Zn and Fe

Lattice models and Landau theory for type II incommensurate crystals

Ground state properties and phonon dispersion curves of a classical linear chain model describing a crystal with an incommensurate phase are studied. This model is the DIFFOUR (discrete frustrated phi4) model with an extra fourth-order term added to it. The incommensurability in these models may arise if there is frustration between nearest-neighbor and next-nearest-neighbor interactions. We discuss the effect of the additional term on the phonon branches and phase diagram of the DIFFOUR model. We find some features not present in the DIFFOUR model such as the renormalization of the nearest-neighbor coupling. Furthermore the ratio between the slopes of the soft phonon mode in the ferroelectric and paraelectric phase can take on values different from -2. Temperature dependences of the parameters in the model are different above and below the paraelectric transition, in contrast with the assumptions made in Landau theory. In the continuum limit this model reduces to the Landau free energy expansion for type II incommensurate crystals and it can be seen as the lowest-order generalization of the simplest Lifshitz-point model. Part of the numerical calculations have been done by an adaption of the Effective Potential Method, orginally used for models with nearest-neighbor interaction, to models with also next-nearest-neighbor interactions.Comment: 33 pages, 7 figures, RevTex, submitted to Phys. Rev.

Mothers Matter Too: Benefits of Temperature Oviposition Preferences in Newts

The maternal manipulation hypothesis states that ectothermic females modify thermal conditions during embryonic development to benefit their offspring (anticipatory maternal effect). However, the recent theory suggests that the ultimate currency of an adaptive maternal effect is female fitness that can be maximized also by decreasing mean fitness of individual offspring. We evaluated benefits of temperature oviposition preferences in Alpine newts (Ichthyosaura [formerly Triturus] alpestris) by comparing the thermal sensitivity of maternal and offspring traits across a range of preferred oviposition temperatures (12, 17, and 22°C) and by manipulating the egg-predation risk during oviposition in a laboratory thermal gradient (12–22°C). All traits showed varying responses to oviposition temperatures. Embryonic developmental rates increased with oviposition temperature, whereas hatchling size and swimming capacity showed the opposite pattern. Maternal oviposition and egg-predation rates were highest at the intermediate temperature. In the thermal gradient, females oviposited at the same temperature despite the presence of caged egg-predators, water beetles (Agabus bipustulatus). We conclude that female newts prefer a particular temperature for egg-deposition to maximize their oviposition performance rather than offspring fitness. The evolution of advanced reproductive modes, such as prolonged egg-retention and viviparity, may require, among others, the transition from selfish temperature preferences for ovipositon to the anticipatory maternal effect

Improved Constraints on Sterile Neutrino Mixing from Disappearance Searches in the MINOS, MINOS+, Daya Bay, and Bugey-3 Experiments.

Searches for electron antineutrino, muon neutrino, and muon antineutrino disappearance driven by sterile neutrino mixing have been carried out by the Daya Bay and MINOS+ collaborations. This Letter presents the combined results of these searches, along with exclusion results from the Bugey-3 reactor experiment, framed in a minimally extended four-neutrino scenario. Significantly improved constraints on the θ_{μe} mixing angle are derived that constitute the most constraining limits to date over five orders of magnitude in the mass-squared splitting Δm_{41}^{2}, excluding the 90% C.L. sterile-neutrino parameter space allowed by the LSND and MiniBooNE observations at 90% CL_{s} for Δm_{41}^{2}<13  eV^{2}. Furthermore, the LSND and MiniBooNE 99% C.L. allowed regions are excluded at 99% CL_{s} for Δm_{41}^{2}<1.6 eV^{2}

RNA Interference in Schistosoma mansoni Schistosomula: Selectivity, Sensitivity and Operation for Larger-Scale Screening

RNA interference (RNAi) is a technique to selectively suppress mRNA of individual genes and, consequently, their cognate proteins. RNAi using double-stranded (ds) RNA has been used to interrogate the function of mainly single genes in the flatworm, Schistosoma mansoni, one of a number of schistosome species causing schistosomiasis. In consideration of large-scale screens to identify candidate drug targets, we examined the selectivity and sensitivity (the degree of suppression) of RNAi for 11 genes produced in different tissues of the parasite: the gut, tegument (surface) and otherwise. We used the schistosomulum stage prepared from infective cercariae larvae which are accessible in large numbers and adaptable to automated screening platforms. We found that RNAi suppresses transcripts selectively, however, the sensitivity of suppression varies (40%–>75%). No obvious changes in the parasite occurred post-RNAi, including after targeting the mRNA of genes that had been computationally predicted to be essential for survival. Additionally, we defined operational parameters to facilitate large-scale RNAi, including choice of culture medium, transfection strategy to deliver dsRNA, dose- and time-dependency, and dosing limits. Finally, using fluorescent probes, we show that the developing gut allows rapid entrance of dsRNA into the parasite to initiate RNAi

Estimating the Fractal Dimension, K_2-entropy, and the Predictability of the Atmosphere

The series of mean daily temperature of air recorded over a period of 215 years is used for analysing the dimensionality and the predictability of the atmospheric system. The total number of data points of the series is 78527. Other 37 versions of the original series are generated, including ``seasonally adjusted'' data, a smoothed series, series without annual course, etc. Modified methods of Grassberger and Procaccia are applied. A procedure for selection of the ``meaningful'' scaling region is proposed. Several scaling regions are revealed in the ln C(r) versus ln r diagram. The first one in the range of larger ln r has a gradual slope and the second one in the range of intermediate ln r has a fast slope. Other two regions are settled in the range of small ln r. The results lead us to claim that the series arises from the activity of at least two subsystems. The first subsystem is low-dimensional (d_f=1.6) and it possesses the potential predictability of several weeks. We suggest that this subsystem is connected with seasonal variability of weather. The second subsystem is high-dimensional (d_f>17) and its error-doubling time is about 4-7 days. It is found that the predictability differs in dependence on season. The predictability time for summer, winter and the entire year (T_2 approx. 4.7 days) is longer than for transition-seasons (T_2 approx. 4.0 days for spring, T_2 approx. 3.6 days for autumn). The role of random noise and the number of data points are discussed. It is shown that a 15-year-long daily temperature series is not sufficient for reliable estimations based on Grassberger and Procaccia algorithms.Comment: 27 pages (LaTex version 2.09) and 15 figures as .ps files, e-mail: [email protected]

Phylogeography of the Microcoleus vaginatus (Cyanobacteria) from Three Continents – A Spatial and Temporal Characterization

It has long been assumed that cyanobacteria have, as with other free-living microorganisms, a ubiquitous occurrence. Neither the geographical dispersal barriers nor allopatric speciation has been taken into account. We endeavoured to examine the spatial and temporal patterns of global distribution within populations of the cyanobacterium Microcoleus vaginatus, originated from three continents, and to evaluate the role of dispersal barriers in the evolution of free-living cyanobacteria. Complex phylogeographical approach was applied to assess the dispersal and evolutionary patterns in the cyanobacterium Microcoleus vaginatus (Oscillatoriales). We compared the 16S rRNA and 16S-23S ITS sequences of strains which had originated from three continents (North America, Europe, and Asia). The spatial distribution was investigated using a phylogenetic tree, network, as well as principal coordinate analysis (PCoA). A temporal characterization was inferred using molecular clocks, calibrated from fossil DNA. Data analysis revealed broad genetic diversity within M. vaginatus. Based on the phylogenetic tree, network, and PCoA analysis, the strains isolated in Europe were spatially separated from those which originated from Asia and North America. A chronogram showed a temporal limitation of dispersal barriers on the continental scale. Dispersal barriers and allopatric speciation had an important role in the evolution of M. vaginatus. However, these dispersal barriers did not have a permanent character; therefore, the genetic flow among populations on a continental scale was only temporarily present. Furthermore, M. vaginatus is a recently evolved species, which has been going through substantial evolutionary changes