On the functions counting walks with small steps in the quarter plane

Models of spatially homogeneous walks in the quarter plane ${\bf Z}_+^{2}$ with steps taken from a subset $\mathcal{S}$ of the set of jumps to the eight nearest neighbors are considered. The generating function $(x,y,z)\mapsto Q(x,y;z)$ of the numbers $q(i,j;n)$ of such walks starting at the origin and ending at $(i,j) \in {\bf Z}_+^{2}$ after $n$ steps is studied. For all non-singular models of walks, the functions $x \mapsto Q(x,0;z)$ and $y\mapsto Q(0,y;z)$ are continued as multi-valued functions on ${\bf C}$ having infinitely many meromorphic branches, of which the set of poles is identified. The nature of these functions is derived from this result: namely, for all the 51 walks which admit a certain infinite group of birational transformations of ${\bf C}^2$, the interval $]0,1/|\mathcal{S}|[$ of variation of $z$ splits into two dense subsets such that the functions $x \mapsto Q(x,0;z)$ and $y\mapsto Q(0,y;z)$ are shown to be holonomic for any $z$ from the one of them and non-holonomic for any $z$ from the other. This entails the non-holonomy of $(x,y,z)\mapsto Q(x,y;z)$, and therefore proves a conjecture of Bousquet-M\'elou and Mishna.Comment: 40 pages, 17 figure

Asymptotic Behavior of Inflated Lattice Polygons

We study the inflated phase of two dimensional lattice polygons with fixed perimeter $N$ and variable area, associating a weight $\exp[pA - Jb ]$ to a polygon with area $A$ and $b$ bends. For convex and column-convex polygons, we show that $/A_{max} = 1 - K(J)/\tilde{p}^2 + \mathcal{O}(\rho^{-\tilde{p}})$, where $\tilde{p}=pN \gg 1$, and $\rho<1$. The constant $K(J)$ is found to be the same for both types of polygons. We argue that self-avoiding polygons should exhibit the same asymptotic behavior. For self-avoiding polygons, our predictions are in good agreement with exact enumeration data for J=0 and Monte Carlo simulations for $J \neq 0$. We also study polygons where self-intersections are allowed, verifying numerically that the asymptotic behavior described above continues to hold.Comment: 7 page

La modélisation d'accompagnement : une méthode de recherche participative et adaptative

Ce chapitre vise à présenter la diversité dans la mise en ½uvre d'un processus de modélisation d'accompagnement, mais aussi les points communs qui en émergent. L'objectif est de décrire pour mieux comprendre, sans intention normative. Nous nous appuyons sur l'analyse des cas d'études et des documents listés dans l'introduction. Notre analyse rassemble des cas concrets et des pratiques qui se réclament de la modélisation d'accompagnement et qui seront donc considérés comme tels dans notre analyse. La compatibilité de la diversité observée avec le cadre d'une adhésion aux principes initiaux de la charte sort du cadre de ce chapitre, elle est traitée dans la conclusion générale de l'ouvrage

Fixed-parameter tractability of multicut parameterized by the size of the cutset

Given an undirected graph $G$, a collection $\{(s_1,t_1),..., (s_k,t_k)\}$ of pairs of vertices, and an integer $p$, the Edge Multicut problem ask if there is a set $S$ of at most $p$ edges such that the removal of $S$ disconnects every $s_i$ from the corresponding $t_i$. Vertex Multicut is the analogous problem where $S$ is a set of at most $p$ vertices. Our main result is that both problems can be solved in time $2^{O(p^3)}... n^{O(1)}$, i.e., fixed-parameter tractable parameterized by the size $p$ of the cutset in the solution. By contrast, it is unlikely that an algorithm with running time of the form $f(p)... n^{O(1)}$ exists for the directed version of the problem, as we show it to be W[1]-hard parameterized by the size of the cutset

Asymptotic behaviour of convex and column-convex lattice polygons with fixed area and varying perimeter

We study the inflated phase of two dimensional lattice polygons, both convex and column-convex, with fixed area A and variable perimeter, when a weight \mu^t \exp[- Jb] is associated to a polygon with perimeter t and b bends. The mean perimeter is calculated as a function of the fugacity \mu and the bending rigidity J. In the limit \mu -> 0, the mean perimeter has the asymptotic behaviour \avg{t}/4 \sqrt{A} \simeq 1 - K(J)/(\ln \mu)^2 + O (\mu/ \ln \mu) . The constant K(J) is found to be the same for both types of polygons, suggesting that self-avoiding polygons should also exhibit the same asymptotic behaviour.Comment: 10 pages, 3 figure

Mesoscale acid deposition modeling studies

The work performed in support of the EPA/DOE MADS (Mesoscale Acid Deposition) Project included the development of meteorological data bases for the initialization of chemistry models, the testing and implementation of new planetary boundary layer parameterization schemes in the MASS model, the simulation of transport and precipitation for MADS case studies employing the MASS model, and the use of the TASS model in the simulation of cloud statistics and the complex transport of conservative tracers within simulated cumuloform clouds. The work performed in support of the NASA/FAA Wind Shear Program included the use of the TASS model in the simulation of the dynamical processes within convective cloud systems, the analyses of the sensitivity of microburst intensity and general characteristics as a function of the atmospheric environment within which they are formed, comparisons of TASS model microburst simulation results to observed data sets, and the generation of simulated wind shear data bases for use by the aviation meteorological community in the evaluation of flight hazards caused by microbursts

Exact enumeration of Hamiltonian circuits, walks, and chains in two and three dimensions

We present an algorithm for enumerating exactly the number of Hamiltonian chains on regular lattices in low dimensions. By definition, these are sets of k disjoint paths whose union visits each lattice vertex exactly once. The well-known Hamiltonian circuits and walks appear as the special cases k=0 and k=1 respectively. In two dimensions, we enumerate chains on L x L square lattices up to L=12, walks up to L=17, and circuits up to L=20. Some results for three dimensions are also given. Using our data we extract several quantities of physical interest

Conjectures about certain parabolic Kazhdan--Lusztig polynomials

Irreducibility results for parabolic induction of representations of the general linear group over a local non-archimedean field can be formulated in terms of Kazhdan--Lusztig polynomials of type $A$. Spurred by these results and some computer calculations, we conjecture that certain alternating sums of Kazhdan--Lusztig polynomials known as parabolic Kazhdan--Lusztig polynomials satisfy properties analogous to those of the ordinary ones.Comment: final versio

Clinical and biological heterogeneity in children with moderate asthma

To evaluate the relationship between inflammatory markers and severity of asthma in children, the amount of interleukin-8 (IL-8) and granulocyte/macrophage colony-stimulating factor (GM-CSF) released by peripheral blood mononuclear cells, exhaled nitric oxide (FE NO) levels, p65 nuclear factor-kappaB subunit, and phosphorylated IkBalpha expression by peripheral blood mononuclear cells were assessed in six control subjects, 12 steroid-naives subjects with intermittent asthma, and 17 children with moderate asthma. To investigate their predictive value, biomarker levels were correlated with the number of exacerbations during a 18-month follow-up period. We found that GM-CSF release was higher in moderate and intermittent asthmatics than in control subjects, whereas IL-8 release was higher in moderate than in intermittent asthmatics and control subjects. FE NO levels were similar among study groups. In moderate asthmatics, IL-8, GM-CSF, and FE NO significantly correlated with the exacerbation numbers. Moreover, p65 and phosphorylated IkBalpha levels were greater in moderate than in intermittent asthmatics and control subjects. According to GM-CSF, IL-8, and FE NO levels, two distinct subgroups of moderate asthmatics (low and high producers) were identified. High producers experienced more exacerbations than low producers. This study shows ongoing inflammation associated with biological and clinical heterogeneity in moderate asthmatics despite regular treatment and proposes that large prospective studies confirm the importance of biomarkers to assess inflammation and asthma control in children with asthma

Treatment trends in allergic rhinitis and asthma: a British ENT survey

<p>Abstract</p> <p>Background</p> <p>Allergic Rhinitis is a common Ear, Nose and Throat disorder. Asthma and Allergic Rhinitis are diseases with similar underlying mechanism and pathogenesis. The aim of this survey was to highlight current treatment trends for Allergic Rhinitis and Asthma.</p> <p>Method</p> <p>A questionnaire was emailed to all registered consultant members of the British Association of Otorhinolaryngologists - Head and Neck Surgeons regarding the management of patients with Allergic Rhinitis and related disorders.</p> <p>Results</p> <p>Survey response rate was 56%. The results indicate a various approach in the investigation and management of Allergic Rhinitis compatible with recommendations from the Allergic Rhinitis and Its Impact on Asthma guidelines in collaboration with the World Health Organisation.</p> <p>Conclusion</p> <p>A combined management approach for patients with Allergic Rhinitis and concomitant Asthma may reduce medical treatment costs for these conditions and improve symptom control and quality of life.</p