Counting matroids in minor-closed classes

A flat cover is a collection of flats identifying the non-bases of a matroid. We introduce the notion of cover complexity, the minimal size of such a flat cover, as a measure for the complexity of a matroid, and present bounds on the number of matroids on $n$ elements whose cover complexity is bounded. We apply cover complexity to show that the class of matroids without an $N$-minor is asymptotically small in case $N$ is one of the sparse paving matroids $U_{2,k}$, $U_{3,6}$, $P_6$, $Q_6$, or $R_6$, thus confirming a few special cases of a conjecture due to Mayhew, Newman, Welsh, and Whittle. On the other hand, we show a lower bound on the number of matroids without $M(K_4)$-minor which asymptoticaly matches the best known lower bound on the number of all matroids, due to Knuth.Comment: 13 pages, 3 figure

On the number of matroids

We consider the problem of determining $m_n$, the number of matroids on $n$ elements. The best known lower bound on $m_n$ is due to Knuth (1974) who showed that $\log \log m_n$ is at least $n-3/2\log n-1$. On the other hand, Piff (1973) showed that $\log\log m_n\leq n-\log n+\log\log n +O(1)$, and it has been conjectured since that the right answer is perhaps closer to Knuth's bound. We show that this is indeed the case, and prove an upper bound on $\log\log m_n$ that is within an additive $1+o(1)$ term of Knuth's lower bound. Our proof is based on using some structural properties of non-bases in a matroid together with some properties of independent sets in the Johnson graph to give a compressed representation of matroids.Comment: Final version, 17 page

An entropy argument for counting matroids

We show how a direct application of Shearers' Lemma gives an almost optimum bound on the number of matroids on $n$ elements.Comment: Short note, 4 page

Evaluation of coagulation activation after Rhinovirus infection in patients with asthma and healthy control subjects: an observational study

Background Asthma exacerbations are frequently triggered by rhinovirus infections. Both asthma and respiratory tract infection can activate haemostasis. Therefore we hypothesized that experimental rhinovirus-16 infection and asthmatic airway inflammation act in synergy on the haemostatic balance. Methods 28 patients (14 patients with mild allergic asthma and 14 healthy non-allergic controls) were infected with low-dose rhinovirus type 16. Venous plasma and bronchoalveolar lavage fluid (BAL fluid) were obtained before and 6 days after infection to evaluate markers of coagulation activation, thrombin-antithrombin complexes, von Willebrand factor, plasmin-antiplasmin complexes, plasminogen activator inhibitor type-1, endogenous thrombin potential and tissue factor-exposing microparticles by fibrin generation test, in plasma and/or BAL fluid. Data were analysed by nonparametric tests (Wilcoxon, Mann Whitney and Spearman correlation). Results 13 patients with mild asthma (6 females, 19-29 y) and 11 healthy controls (10 females, 19-31 y) had a documented Rhinovirus-16 infection. Rhinovirus-16 challenge resulted in a shortening of the fibrin generation test in BAL fluid of asthma patients (t = -1: 706 s vs. t = 6: 498 s; p = 0.02), but not of controls (t = -1: 693 s vs. t = 6: 636 s; p = 0.65). The fold change in tissue factor-exposing microparticles in BAL fluid inversely correlated with the fold changes in eosinophil cationic protein and myeloperoxidase in BAL fluid after virus infection (r = -0.517 and -0.528 resp., both p = 0.01). Rhinovirus-16 challenge led to increased plasminogen activator inhibitor type-1 levels in plasma in patients with asthma (26.0 ng/mL vs. 11.5 ng/mL in healthy controls, p = 0.04). Rhinovirus-16 load in BAL showed a linear correlation with the fold change in endogenous thrombin potential, plasmin-antiplasmin complexes and plasminogen activator inhibitor type-1. Conclusions Experimental rhinovirus infection induces procoagulant changes in the airways of patients with asthma through increased activity of tissue factor-exposing microparticles. These microparticle-associated procoagulant changes are associated with both neutrophilic and eosinophilic inflammation. Systemic activation of haemostasis increases with Rhinoviral load

Cardiac foetal reprogramming:a tool to exploit novel treatment targets for the failing heart

As the heart matures during embryogenesis from its foetal stages, several structural and functional modifications take place to form the adult heart. This process of maturation is in large part due to an increased volume and work load of the heart to maintain proper circulation throughout the growing body. In recent years, it has been observed that these changes are reversed to some extent as a result of cardiac disease. The process by which this occurs has been characterized as cardiac foetal reprogramming and is defined as the suppression of adult and re-activation of a foetal genes profile in the diseased myocardium. The reasons as to why this process occurs in the diseased myocardium are unknown; however, it has been suggested to be an adaptive process to counteract deleterious events taking place during cardiac remodelling. Although still in its infancy, several studies have demonstrated that targeting foetal reprogramming in heart failure can lead to substantial improvement in cardiac functionality. This is highlighted by a recent study which found that by modulating the expression of 5-oxoprolinase (OPLAH, a novel cardiac foetal gene), cardiac function can be significantly improved in mice exposed to cardiac injury. Additionally, the utilization of angiotensin receptor neprilysin inhibitors (ARNI) has demonstrated clear benefits, providing important clinical proof that drugs that increase natriuretic peptide levels (part of the foetal gene programme) indeed improve heart failure outcomes. In this review, we will highlight the most important aspects of cardiac foetal reprogramming and will discuss whether this process is a cause or consequence of heart failure. Based on this, we will also explain how a deeper understanding of this process may result in the development of novel therapeutic strategies in heart failure

Integrable and superintegrable systems associated with multi-sums of products

We construct and study certain Liouville integrable, superintegrable, and non-commutative integrable systems, which are associated with multi-sums of products.Comment: 26 pages, submitted to Proceedings of the royal society

A distributed topology information system for optical networks based on the semantic web

The research networking community has embraced novel network architectures to provide e-Science applications with dedicated connections instead of shared links. IP and optical services converge in these new infrastructures to form hybrid networks. Lightpaths are the services offered to clients in the optical portion of the network. They are chosen because they guarantee the appropriate QoS in terms of bandwidth and latency. NDL-the Network Description Language-is a data model offering users and providers of lightpaths with a common ontology to describe topology information of hybrid optical networks. The strength of NDL is that it supports a wide range of applications, including pathfinding, visualisation and asset management, via the definition of a common data model to exchange network descriptions. Since NDL is based on the Semantic Web techniques, it is straightforward to relate NDL with application-specific ontologies. In this paper we present the current status of the NDL schemas and its use in several applications

Transition between Two Oscillation Modes

A model for the symmetric coupling of two self-oscillators is presented. The nonlinearities cause the system to vibrate in two modes of different symmetries. The transition between these two regimes of oscillation can occur by two different scenarios. This might model the release of vortices behind circular cylinders with a possible transition from a symmetric to an antisymmetric Benard-von Karman vortex street.Comment: 12 pages, 0 figure