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

Interpretations of Presburger Arithmetic in Itself

Presburger arithmetic PrA is the true theory of natural numbers with addition. We study interpretations of PrA in itself. We prove that all one-dimensional self-interpretations are definably isomorphic to the identity self-interpretation. In order to prove the results we show that all linear orders that are interpretable in (N,+) are scattered orders with the finite Hausdorff rank and that the ranks are bounded in terms of the dimension of the respective interpretations. From our result about self-interpretations of PrA it follows that PrA isn't one-dimensionally interpretable in any of its finite subtheories. We note that the latter was conjectured by A. Visser.Comment: Published in proceedings of LFCS 201

A note on Makeev's conjectures

A counterexample is given for the Knaster-like conjecture of Makeev for functions on $S^2$. Some particular cases of another conjecture of Makeev, on inscribing a quadrangle into a smooth simple closed curve, are solved positively

Tackling the Tibetan Plateau in a down suit: Insights into thermoregulation by bar-headed geese during migration

This is the final version. Available from Company of Biologists via the DOI in this recordData accessibility: Following the manuscript being accepted data will be uploaded to a public repository such as Dryad.Birds migrating through extreme environments can experience a range of challenges while matching the demands of flight, including highly variable ambient temperatures, humidity and oxygen levels. However, there has been limited research into avian thermoregulation during migration in extreme environments. This study aimed to investigate the effect of flight performance and high-altitude on body temperature (Tb) of free flying bar-headed geese (Anser indicus), a species that completes a high-altitude trans-Himalayan migration through very cold, hypoxic environments. We measured abdominal Tb, along with altitude (via changes in barometric pressure), heart rate and body acceleration of bar-headed geese during their migration across the Tibetan Plateau. Bar-headed geese vary the circadian rhythm of Tb in response to migration, with peak daily Tb during daytime hours outside of migration but early in the morning or overnight during migration, reflecting changes in body acceleration. However, during flights changes in Tb were not consistent with changes in flight performance (as measured by heart rate or rate of ascent) or altitude. Overall, our results suggest that bar-headed geese are able to thermoregulate during high-altitude migration, maintaining Tb within a relatively narrow range despite appreciable variation in flight intensity and environmental conditions.Biotechnology and Biological Sciences Research Council (BBSRC)Natural Sciences and Engineering Research Council of Canada (NSERC)Max Planck Institute for OrnithologyUS Geological SurveyWestern Ecological and Patuxent Wildlife Research Centers, Avian Influenza Programm

A customized monocyte cDNA microarray for diagnosis of rheumatoid arthritis and prognosis of anti-TNF-α therapy

Background In rheumatoid arthritis (RA) macrophages (Mf) play a pivotal role. They become highly activated in synovitis and at the cartilage–pannus junction. Furthermore, therapeutic neutralization of molecules produced by activated Mf lead to clinical improvement in RA, and circulating monocytes (MO) of the peripheral blood in patients with RA spontaneously express proinflammatory genes (IL-1β, IL-6, TNF). Methods A custom RA-MO cDNA microarray was generated using differentially expressed genes obtained from gene subtraction and from comparative whole genome wide U133A analysis in normal donors, active and anti-TNF-α created RA patients. Genes were selected using MAS 5.0, multtest and PAM. The custom microarray consists of 313 genes including guide dots, and positive (housekeeping genes and spike controls) and negative controls for image and statistical analysis. Each probe was spotted in 16 replicates. Results The RA-MO chipset-II was validated using the following: non-stimulated and LPS, PMA, Vit.D3+LPS, PMA+LPS stimulated U937 cells; nonstimulated and LPS stimulated healthy donor MO; MO from normal donors (n = 3) and RA patients before and during anti-TNF-α treatment (n = 5 each); and synovial tissue from normal individuals (n = 2) and RA patients (n = 2). Not only LPS/PMA regulated genes but also RA specific and anti-TNF-α regulated genes were validated. In addition, we could clarify whether these genes are differentially transcribed only in MO or whether they can also be found in RA tissue Mf. Our data indicate a high degree of reproducibility that is sufficient for diagnostic applications and therapy monitoring. Conclusion The RA-MO chipset-II microarray is competitive and flexible for enlargement of the number of genes. The current gene selection will contribute to validating the role of monocytes in disease activity, to therapeutic interventions, and may improve the knowledge on the regulation of pathways in activated monocytes in chronic inflammation

An ecological approach to problems of Dark Energy, Dark Matter, MOND and Neutrinos

Modern astronomical data on galaxy and cosmological scales have revealed powerfully the existence of certain dark sectors of fundamental physics, i.e., existence of particles and fields outside the standard models and inaccessible by current experiments. Various approaches are taken to modify/extend the standard models. Generic theories introduce multiple de-coupled fields A, B, C, each responsible for the effects of DM (cold supersymmetric particles), DE (Dark Energy) effect, and MG (Modified Gravity) effect respectively. Some theories use adopt vanilla combinations like AB, BC, or CA, and assume A, B, C belong to decoupled sectors of physics. MOND-like MG and Cold DM are often taken as opposite frameworks, e.g. in the debate around the Bullet Cluster. Here we argue that these ad hoc divisions of sectors miss important clues from the data. The data actually suggest that the physics of all dark sectors is likely linked together by a self-interacting oscillating field, which governs a chameleon-like dark fluid, appearing as DM, DE and MG in different settings. It is timely to consider an interdisciplinary approach across all semantic boundaries of dark sectors, treating the dark stress as one identity, hence accounts for several "coincidences" naturally.Comment: 12p, Proceedings to the 6-th Int. Conf. of Gravitation and Cosmology. Neutrino section expande

Intraspecfic variation in cold-temperature metabolic phenotypes of Arabidopsis lyrata ssp petraea

Atmospheric temperature is a key factor in determining the distribution of a plant species. Alongside this, plant populations growing at the margin of their range may exhibit traits that indicate genetic differentiation and adaptation to their local abiotic environment. We investigated whether geographically separated marginal populations of Arabidopsis lyrata ssp. petraea have distinct metabolic phenotypes associated with exposure to cold temperatures. Seeds of A. petraea were obtained from populations along a latitudinal gradient, namely Wales, Sweden and Iceland and grown in a controlled cabinet environment. Mannose, glucose, fructose, sucrose and raffinose concentrations were different between cold treatments and populations, especially in the Welsh population, but polyhydric alcohol concentrations were not. The free amino acid compositions were population specific, with fold differences in most amino acids, especially in the Icelandic populations, with gross changes in amino acids, particularly those associated with glutamine metabolism. Metabolic fingerprints and profiles were obtained. Principal component analysis (PCA) of metabolite fingerprints revealed metabolic characteristic phenotypes for each population and temperature. It is suggested that amino acids and carbohydrates were responsible for discriminating populations within the PCA. Metabolite fingerprinting and profiling has proved to be sufficiently sensitive to identify metabolic differences between plant populations at different atmospheric temperatures. These findings show that there is significant natural variation in cold metabolism among populations of A. l. petraea which may signify plant adaptation to local climates

On the Application of a Monolithic Array for Detecting Intensity-Correlated Photons Emitted by Different Source Types

It is not widely appreciated that many subtleties are involved in the accurate measurement of intensity-correlated photons; even for the original experiments of Hanbury Brown and Twiss (HBT). Using a monolithic 4x4 array of single-photon avalanche diodes (SPADs), together with an off-chip algorithm for processing streaming data, we investigate the difficulties of measuring second-order photon correlations g2 in a wide variety of light fields that exhibit dramatically different correlation statistics: a multimode He-Ne laser, an incoherent intensity-modulated lamp-light source and a thermal light source. Our off-chip algorithm treats multiple photon-arrivals at pixel-array pairs, in any observation interval, with photon fluxes limited by detector saturation, in such a way that a correctly normalized g2 function is guaranteed. The impact of detector background correlations between SPAD pixels and afterpulsing effects on second-order coherence measurements is discussed. These results demonstrate that our monolithic SPAD array enables access to effects that are otherwise impossible to measure with stand-alone detectors.Comment: 17 pages, 6 figure