Fork-decompositions of matroids

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On matroids of branch-width three

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Deposition of general ellipsoidal particles

We present a systematic overview of granular deposits composed of ellipsoidal particles with different particle shapes and size polydispersities. We study the density and anisotropy of such deposits as functions of size polydispersity and two shape parameters that fully describe the shape of a general ellipsoid. Our results show that, while shape influences significantly the macroscopic properties of the deposits, polydispersity plays apparently a secondary role. The density attains a maximum for a particular family of non-symmetrical ellipsoids, larger than the density observed for prolate or oblate ellipsoids. As for anisotropy measures, the contact forces show are increasingly preferred along the vertical direction as the shape of the particles deviates for a sphere. The deposits are constructed by means of an efficient molecular dynamics method, where the contact forces are efficiently and accurately computed. The main results are discussed in the light of applications for porous media models and sedimentation processes.Comment: 7 pages, 8 figure

The structure of the 3-separations of 3-connected matroids II

The authors showed in an earlier paper that there is a tree that displays, up to a natural equivalence, all non-trivial 3-separations of a 3-connected matroid. The purpose of this paper is to show that if certain natural conditions are imposed on the tree, then it has a uniqueness property. In particular; suppose that, from every pair of edges that meet at a degree-2 vertex and have their other ends of degree at least three, one edge is contracted. Then the resulting tree is unique

Respiratory symptoms and cross-shift lung function in relation to cotton dust and endotoxin exposure in textile workers in Nepal: a cross-sectional study

Objectives: Inhalation of a cotton-based particulates has previously been associated with respiratory symptoms and impaired lung function. This study investigates the respiratory health of Nepalese textile workers in relation to dust and endotoxin exposure. Methods: A total of 938 individuals from four sectors (garment, carpet, weaving and recycling) of the textile industry in Kathmandu, Nepal completed a health questionnaire and performed spirometry. A subset (n=384) performed cross-shift spirometry. Personal exposure to inhalable dust and airborne endotoxin was measured during a full shift for 114 workers. Results: The overall prevalence of persistent cough, persistent phlegm, wheeze ever, breathlessness ever and chest tightness ever was 8.5%, 12.5%, 3.2%, 6.5% and 12.3%, respectively. Symptoms were most common among recyclers and least common among garment workers. Exposure to inhalable dust significantly predicted persistent cough and chest tightness. Exposure to endotoxin did not have any independent predictive effect. Significant cross-shift reduction in forced expiratory volume in 1 s (FEV1) and forced vital capacity (FVC) were found (p<0.001 for both) being largest for FEV1 in the recyclers (−143 mL), and least in the garment workers (−38 mL; p=0.012). Exposure to inhalable dust predicted a cross-shift reduction in FEV1. Conclusions: This study is the first to investigate the respiratory health of Nepalese cotton workers. The measured association between inhalable dust exposure and reporting of respiratory symptoms and across-shift decrement in FEV1 and FVC indicates that improved dust control measures should be instituted, particularly in the recycling and carpet sectors. The possible role of other biologically active agents of cotton dust beyond endotoxin should be further explored

The structure of the 3-separations of 3-connected matroids

Special Issue Dedicated to Professor W.T. TutteTutte defined a k-separation of a matroid M to be a partition (A,B) of the ground set of M such that ∣A∣,∣B∣ ≥ k and r(A) + r(B) − r(M) < k. If, for all m < n, the matroid M has no m-separations, then M is n-connected. Earlier, Whitney showed that (A,B) is a 1-separation of M if and only if A is a union of 2-connected components of M. When M is 2-connected, Cunningham and Edmonds gave a tree decomposition of M that displays all of its 2-separations. When M is 3-connected, this paper describes a tree decomposition of M that displays, up to a certain natural equivalence, all non-trivial 3-separations of M

Adventures in Invariant Theory

We provide an introduction to enumerating and constructing invariants of group representations via character methods. The problem is contextualised via two case studies arising from our recent work: entanglement measures, for characterising the structure of state spaces for composite quantum systems; and Markov invariants, a robust alternative to parameter-estimation intensive methods of statistical inference in molecular phylogenetics.Comment: 12 pp, includes supplementary discussion of example

Representing Partitions on Trees

In evolutionary biology, biologists often face the problem of constructing a phylogenetic tree on a set X of species from a multiset Π of partitions corresponding to various attributes of these species. One approach that is used to solve this problem is to try instead to associate a tree (or even a network) to the multiset ΣΠ consisting of all those bipartitions {A,X − A} with A a part of some partition in Π. The rational behind this approach is that a phylogenetic tree with leaf set X can be uniquely represented by the set of bipartitions of X induced by its edges. Motivated by these considerations, given a multiset Σ of bipartitions corresponding to a phylogenetic tree on X, in this paper we introduce and study the set P(Σ) consisting of those multisets of partitions Π of X with ΣΠ = Σ. More specifically, we characterize when P(Σ) is non-empty, and also identify some partitions in P(Σ) that are of maximum and minimum size. We also show that it is NP-complete to decide when P(Σ) is non-empty in case Σ is an arbitrary multiset of bipartitions of X. Ultimately, we hope that by gaining a better understanding of the mapping that takes an arbitrary partition system Π to the multiset ΣΠ, we will obtain new insights into the use of median networks and, more generally, split-networks to visualize sets of partitions