Weighted Tree-Numbers of Matroid Complexes

International audienceWe give a new formula for the weighted high-dimensional tree-numbers of matroid complexes. This formula is derived from our result that the spectra of the weighted combinatorial Laplacians of matroid complexes consist of polynomials in the weights. In the formula, Crapo’s $\beta$-invariant appears as the key factor relating weighted combinatorial Laplacians and weighted tree-numbers for matroid complexes.Nous présentons une nouvelle formule pour les nombres d’arbres pondérés de grande dimension des matroïdes complexes. Cette formule est dérivée du résultat que le spectre des Laplaciens combinatoires pondérés des matrides complexes sont des polynômes à plusieurs variables. Dans la formule, le $\beta$;-invariant de Crapo apparaît comme étant le facteur clé reliant les Laplaciens combinatoires pondérés et les nombres d’arbres pondérés des matroïdes complexes

Optimisation of pipeline route in the presence of obstacles based on a least cost path algorithm and laplacian smoothing

Subsea pipeline route design is a crucial task for the offshore oil and gas industry, and the route selected can significantly affect the success or failure of an offshore project. Thus, it is essential to design pipeline routes to be eco-friendly, economical and safe. Obstacle avoidance is one of the main problems that affect pipeline route selection. In this study, we propose a technique for designing an automatic obstacle avoidance. The Laplacian smoothing algorithm was used to make automatically generated pipeline routes fairer. The algorithms were fast and the method was shown to be effective and easy to use in a simple set of case studies

Twisted Levi Sequences and Explicit Styles on Sp(4)

Let G be a connected reductive group over a field F. A twisted Levi subgroup G0 of G is a reductive subgroup such that G' [circle times]F F[over-bar] is a Levi subgroup of G' [circle times]F F[over-bar]. Twisted Levi subgroups have been an important tool in studying the structure theory of representations of p-adic groups. For example, supercuspidal representations are built out of certain representations of twisted Levi subgroups ([20]), and Hecke algebra isomorphisms are established with Hecke algebras on twisted Levi subgroups, which suggests an inductive structure of representations (see [9] for example).National Science Foundation (U.S.). Focused Research Grou

Application of morphing technique with mesh-merging in rapid hull form generation

ABSTRACTMorphing is a geometric interpolation technique that is often used by the animation industry to transform one form into another seemingly seamlessly. It does this by producing a large number of ‘intermediate’ forms between the two ‘extreme’ or ‘parent’ forms. It has already been shown that morphing technique can be a powerful tool for form design and as such can be a useful addition to the armoury of product designers. Morphing procedure itself is simple and consists of straightforward linear interpolation. However, establishing the correspondence between vertices of the parent models is one of the most difficult and important tasks during a morphing process. This paper discusses the mesh-merging method employed for this process as against the already established mesh-regularising method. It has been found that the merging method minimises the need for manual manipulation, allowing automation to a large extent

Mechanical Behaviors of Wire-woven Metals Composed of Two Different Thickness of Wires

AbstractWire-weaving is virtually only a practical method to fabricate multi-layered truss type cellular metals, except for stacking multiple single layered structures. To date, the wire-woven metals have been fabricated of wires of a uniform thickness. In this work, variations of wire-woven metals fabricated of two different thickness wires in out-of-plane and in-plane directions are introduced. The mechanical properties subjected to compressive or shear loading are investigated

Noninvasive Diagnostic and Prognostic Assessment Tools for Liver Fibrosis and Cirrhosis in Patients with Chronic Liver Disease

Liver fibrosis, that is, excessive accumulation of extracellular matrix protein, occurs and is the wound‐healing response and common final pathway of various chronic liver diseases. Advanced hepatic fibrosis caused by chronic liver inflammation eventually progresses to cirrhosis, and prognosis and management of chronic liver diseases depend on the fibrotic severities. Therefore, the early and precise evaluation of severity and status of liver fibrosis provides useful information for diagnosis as well as treatment planning and treatment efficacy and prognosis. Although invasive liver biopsy is the gold standard to assess the nature and severity of hepatic fibrosis, it has several recognized limitations including sampling error and inter‐observer variability in interpretation and staging. Furthermore, the dynamic process of fibrosis resulting from progression and regression is difficult to capture with biopsy alone. Therefore, alternative, simple, reliable, and noninvasive direct and indirect serum markers able to predict the presence of significant fibrosis or cirrhosis in patients with chronic liver disease with considerable accuracy were needed. The hepatology experts are actively researching noninvasive methods of fibrosis quantification. The aims of this chapter were to review the nature and limitations of the several noninvasive methods for the assessment of presence and severity of liver fibrosis in patients with chronic liver disease

A weighted cellular matrix-tree theorem, with applications to complete colorful and cubical complexes

We present a version of the weighted cellular matrix-tree theorem that is suitable for calculating explicit generating functions for spanning trees of highly structured families of simplicial and cell complexes. We apply the result to give weighted generalizations of the tree enumeration formulas of Adin for complete colorful complexes, and of Duval, Klivans and Martin for skeleta of hypercubes. We investigate the latter further via a logarithmic generating function for weighted tree enumeration, and derive another tree-counting formula using the unsigned Euler characteristics of skeleta of a hypercube and the Crapo $\beta$-invariant of uniform matroids.Comment: 22 pages, 2 figures. Sections 6 and 7 of previous version simplified and condensed. Final version to appear in J. Combin. Theory Ser.