Gauge theories induced by bosons in fundamental representation

A lattice theory of scalar bosons in the fundamental representation of the gauge group $SU(N_c)$ and of the global symmetry group $SU(N_f)$ is shown to induce a standard gauge theory only at large $N_f$. The system is in a deconfined phase at strong scalar self-coupling and any finite $N_f$. The requirement of convergence of the effective gauge action imposes a lower limit on the scalar mass.Comment: 11 page

Effects of some ecological factors on Dothichiza populea Sacc. et Br. growth

The aim of the present work was to evaluate the mycelial growth and fruiting vigor of Dothichiza populea Sacc. et Br. under various temperatures, pH values, and light regimes. Effect of temperature on the fungus growth was examined by growing isolates in polythermostat at 5°C to 30°C. The best mycelial growth occurred at 20°C, while at 30°C it was inhibited. Fruiting of the fungus was not observed at 5°C, 25°C, and 30°C. However, the best fruiting of the isolates appeared at 20°C. The influence of different pH of the cultivation medium (3,5-10) on the fungus isolates growth was also evaluated. Optimal pH for the fungus growth ranged between 6 and 8, while formation of reproductive organs occurred at all pH values. The influence of two light regimes (light/dark regime and continuous dark) on the fungus growth was also studied. Obtained results showed that mycelial growth and fruiting of the fungus were considerably better under the light/dark regime

The accuracy of merging approximation in generalized St. Petersburg games

Merging asymptotic expansions of arbitrary length are established for the distribution functions and for the probabilities of suitably centered and normalized cumulative winnings in a full sequence of generalized St. Petersburg games, extending the short expansions due to Cs\"org\H{o}, S., Merging asymptotic expansions in generalized St. Petersburg games, \textit{Acta Sci. Math. (Szeged)} \textbf{73} 297--331, 2007. These expansions are given in terms of suitably chosen members from the classes of subsequential semistable infinitely divisible asymptotic distribution functions and certain derivatives of these functions. The length of the expansion depends upon the tail parameter. Both uniform and nonuniform bounds are presented.Comment: 30 pages long version (to appear in Journal of Theoretical Probability); some corrected typo

A q-deformed nonlinear map

A scheme of q-deformation of nonlinear maps is introduced. As a specific example, a q-deformation procedure related to the Tsallis q-exponential function is applied to the logistic map. Compared to the canonical logistic map, the resulting family of q-logistic maps is shown to have a wider spectrum of interesting behaviours, including the co-existence of attractors -- a phenomenon rare in one dimensional maps.Comment: 17 pages, 19 figure

A homeostatic function of CXCR2 signalling in articular cartilage

Funding This work was funded by Arthritis Research UK (grants 17859, 17971, 19654), INNOCHEM EU FP6 (grant LSHB-CT-2005-51867), MRC (MR/K013076/1) and the William Harvey Research FoundationPeer reviewedPublisher PD

Solution of gauge theories induced by fundamental representation scalars

Gauge theories induced by scalars in the fundamental representation of the $U(N_c)_{gauge}\times U(N_f)_{global}$ group are investigated in the large $N_c$ and $N_f$ limit. A master field is defined from bilinears of the scalar field following an Eguchi-Kawai type reduction of spacetime. The density function for the master field satisfies an integral equation that can be solved exactly in two dimensions (D=2) and in a convergent series of approximations at $D>2$. While at D=2 the system is in the same phase at all $\epsilon=N_c/N_f$, it undergoes a phase transition at a critical value, $\epsilon_c(D)$, for $D>2$.Comment: 12 pages, LaTe

Optimal General Matchings

Given a graph $G=(V,E)$ and for each vertex $v \in V$ a subset $B(v)$ of the set $\{0,1,\ldots, d_G(v)\}$, where $d_G(v)$ denotes the degree of vertex $v$ in the graph $G$, a $B$-factor of $G$ is any set $F \subseteq E$ such that $d_F(v) \in B(v)$ for each vertex $v$, where $d_F(v)$ denotes the number of edges of $F$ incident to $v$. The general factor problem asks the existence of a $B$-factor in a given graph. A set $B(v)$ is said to have a {\em gap of length} $p$ if there exists a natural number $k \in B(v)$ such that $k+1, \ldots, k+p \notin B(v)$ and $k+p+1 \in B(v)$. Without any restrictions the general factor problem is NP-complete. However, if no set $B(v)$ contains a gap of length greater than $1$, then the problem can be solved in polynomial time and Cornuejols \cite{Cor} presented an algorithm for finding a $B$-factor, if it exists. In this paper we consider a weighted version of the general factor problem, in which each edge has a nonnegative weight and we are interested in finding a $B$-factor of maximum (or minimum) weight. In particular, this version comprises the minimum/maximum cardinality variant of the general factor problem, where we want to find a $B$-factor having a minimum/maximum number of edges. We present an algorithm for the maximum/minimum weight $B$-factor for the case when no set $B(v)$ contains a gap of length greater than $1$. This also yields the first polynomial time algorithm for the maximum/minimum cardinality $B$-factor for this case

How does a cadaver model work for testing ultrasound diagnostic capability for rheumatic-like tendon damage?

To establish whether a cadaver model can serve as an effective surrogate for the detection of tendon damage characteristic of rheumatoid arthritis (RA). In addition, we evaluated intraobserver and interobserver agreement in the grading of RA-like tendon tears shown by US, as well as the concordance between the US findings and the surgically induced lesions in the cadaver model. RA-like tendon damage was surgically induced in the tibialis anterior tendon (TAT) and tibialis posterior tendon (TPT) of ten ankle/foot fresh-frozen cadaveric specimens. Of the 20 tendons examined, six were randomly assigned a surgically induced partial tear; six a complete tear; and eight left undamaged. Three rheumatologists, experts in musculoskeletal US, assessed from 1 to 5 the quality of US imaging of the cadaveric models on a Likert scale. Tendons were then categorized as having either no damage, (0); partial tear, (1); or complete tear (2). All 20 tendons were blindly and independently evaluated twice, over two rounds, by each of the three observers. Overall, technical performance was satisfactory for all items in the two rounds (all values over 2.9 in a Likert scale 1-5). Intraobserver and interobserver agreement for US grading of tendon damage was good (mean κ values 0.62 and 0.71, respectively), with greater reliability found in the TAT than the TPT. Concordance between US findings and experimental tendon lesions was acceptable (70-100 %), again greater for the TAT than for the TPT. A cadaver model with surgically created tendon damage can be useful in evaluating US metric properties of RA tendon lesions

Stronger diversity effects with increased environmental stress : a study of multitrophic interactions between oak, powdery mildew and ladybirds

Recent research has suggested that increasing neighbourhood tree species diversity may mitigate the impact of pests or pathogens by supporting the activities of their natural enemies and/or reducing the density of available hosts. In this study, we attempted to assess these mechanisms in a multitrophic study system of young oak (Quercus), oak powdery mildew (PM, caused by Erysiphe spp.) and a mycophagous ladybird (Psyllobora vigintiduo-punctata). We assessed ladybird mycophagy on oak PM in function of different neighbourhood tree species compositions. We also evaluated whether these species interactions were modulated by environmental conditions as suggested by the Stress Gradient Hypothesis. We adopted a complementary approach of a field experiment where we monitored oak saplings subjected to a reduced rainfall gradient in a young planted forest consisting of different tree species mixtures, as well as a lab experiment where we independently evaluated the effect of different watering treatments on PM infections and ladybird mycophagy. In the field experiment, we found effects of neighbourhood tree species richness on ladybird mycophagy becoming more positive as the target trees received less water. This effect was only found as weather conditions grew drier. In the lab experiment, we found a preference of ladybirds to graze on infected leaves from trees that received less water. We discuss potential mechanisms that might explain this preference, such as emissions of volatile leaf chemicals. Our results are in line with the expectations of the Natural Enemies Hypothesis and support the hypothesis that biodiversity effects become stronger with increased environmental stress