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

Forelimb muscle and joint actions in Archosauria: insights from Crocodylus johnstoni (Pseudosuchia) and Mussaurus patagonicus (Sauropodomorpha)

Many of the major locomotor transitions during the evolution of Archosauria, the lineage including crocodiles and birds as well as extinct Dinosauria, were shifts from quadrupedalism to bipedalism (and vice versa). Those occurred within a continuum between more sprawling and erect modes of locomotion and involved drastic changes of limb anatomy and function in several lineages, including sauropodomorph dinosaurs. We present biomechanical computer models of two locomotor extremes within Archosauria in an analysis of joint ranges of motion and the moment arms of the major forelimb muscles in order to quantify biomechanical differences between more sprawling, pseudosuchian (represented the crocodile Crocodylus johnstoni) and more erect, dinosaurian (represented by the sauropodomorph Mussaurus patagonicus) modes of forelimb function. We compare these two locomotor extremes in terms of the reconstructed musculoskeletal anatomy, ranges of motion of the forelimb joints and the moment arm patterns of muscles across those ranges of joint motion. We reconstructed the three-dimensional paths of 30 muscles acting around the shoulder, elbow and wrist joints. We explicitly evaluate how forelimb joint mobility and muscle actions may have changed with postural and anatomical alterations from basal archosaurs to early sauropodomorphs. We thus evaluate in which ways forelimb posture was correlated with muscle leverage, and how such differences fit into a broader evolutionary context (i.e. transition from sprawling quadrupedalism to erect bipedalism and then shifting to graviportal quadrupedalism). Our analysis reveals major differences of muscle actions between the more sprawling and erect models at the shoulder joint. These differences are related not only to the articular surfaces but also to the orientation of the scapula, in which extension/flexion movements in Crocodylus (e.g. protraction of the humerus) correspond to elevation/depression in Mussaurus. Muscle action is highly influenced by limb posture, more so than morphology. Habitual quadrupedalism in Mussaurus is not supported by our analysis of joint range of motion, which indicates that glenohumeral protraction was severely restricted. Additionally, some active pronation of the manus may have been possible in Mussaurus, allowing semi-pronation by a rearranging of the whole antebrachium (not the radius against the ulna, as previously thought) via long-axis rotation at the elbow joint. However, the muscles acting around this joint to actively pronate it may have been too weak to drive or maintain such orientations as opposed to a neutral position in between pronation and supination. Regardless, the origin of quadrupedalism in Sauropoda is not only linked to manus pronation but also to multiple shifts of forelimb morphology, allowing greater flexion movements of the glenohumeral joint and a more columnar forelimb posture

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

Amorphous Phase in Palladium—Silicon Alloys

By rapid cooling from the melt, an amorphous phase has been obtained in palladium—silicon alloys containing 15 to 23 at.% Si. This phase is stable at room temperature and crystallization cannot be detected after one month at 250°C. With rates of heating greater than 20°C/min, rapid crystallization takes place at 400°C, with a heat release of approximately 1000 cal/mole. The electrical resistivity of an alloy containing 17 at.% Si at room temperature is 2.6 times that of the equilibrium alloy. The resistivity decreases linearly with decreasing temperature and is about 95% of the room-temperature value at 2°K. Various factors involved in the retention of amorphous phases in rapidly quenched liquid alloys are discussed

Metastable Solid Solutions in the Gallium Antimonide-Germanium Pseudobinary System

Abstract unavailable

Metastable Electron Compound in Ag-Ge Alloys

Abstract unavailable

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