An Algebra of Pieces of Space -- Hermann Grassmann to Gian Carlo Rota

We sketch the outlines of Gian Carlo Rota's interaction with the ideas that Hermann Grassmann developed in his Ausdehnungslehre of 1844 and 1862, as adapted and explained by Giuseppe Peano in 1888. This leads us past what Rota variously called 'Grassmann-Cayley algebra', or 'Peano spaces', to the Whitney algebra of a matroid, and finally to a resolution of the question "What, really, was Grassmann's regressive product?". This final question is the subject of ongoing joint work with Andrea Brini, Francesco Regonati, and William Schmitt. The present paper was presented at the conference "The Digital Footprint of Gian-Carlo Rota: Marbles, Boxes and Philosophy" in Milano on 17 Feb 2009. It will appear in proceedings of that conference, to be published by Springer Verlag.Comment: 28 page

The effect of aging and cardiorespiratory fitness on the lung diffusing capacity response to exercise in healthy humans

Aging is associated with deterioration in the structure and function of the pulmonary circulation. We characterized the lung diffusing capacity for carbon monoxide (DLCO), alveolar-capillary membrane conductance (Dm(CO)), and pulmonary-capillary blood volume (V(C)) response to discontinuous incremental exercise at 25, 50, 75, and 90% of peak work (Wpeak) in four groups: 1) Young [27 ± 3 y, maximal oxygen consumption (V̇O₂max) 110 ± 18% age-predicted]; 2) Young Highly-Fit (27 ± 3 y, V̇O₂max 147 ± 8% age-predicted); 3) Old (69 ± 5 y, V̇O₂max 116 ± 13% age-predicted); and 4) Old Highly-Fit (65 ± 5 y, V̇O₂max 162 ± 18% age-predicted). At rest and at 90% Wpeak, DLCO, Dm(CO), and VC were decreased with age. At 90% Wpeak, DLCO, Dm(CO) and VC were greater in Old Highly-Fit vs. Old adults. The slope of the DLCO-cardiac output (Q̇) relationship from rest to end-exercise at 90% Wpeak was not different between Young, Young Highly-Fit, Old and Old Highly-Fit (1.35 vs. 1.44 vs. 1.10 vs. 1.35 mlCO·mmHg⁻¹·Lblood⁻¹, P = 0.388), with no evidence of a plateau in this relationship during exercise; this was also true for Dm(CO)-Q̇ and V(C)-Q̇. V̇O2max was positively correlated with: 1) DLCO, Dm(CO), and V(C) at rest; 2) the rest to end-exercise change in DLCO, Dm(CO), and V(C). In conclusion, these data suggest that despite the age-associated deterioration in the structure and function of the pulmonary circulation, expansion of the pulmonary capillary network does not become limited during exercise in healthy individuals regardless of age or cardiorespiratory fitness level

The orbit rigidity matrix of a symmetric framework

A number of recent papers have studied when symmetry causes frameworks on a graph to become infinitesimally flexible, or stressed, and when it has no impact. A number of other recent papers have studied special classes of frameworks on generically rigid graphs which are finite mechanisms. Here we introduce a new tool, the orbit matrix, which connects these two areas and provides a matrix representation for fully symmetric infinitesimal flexes, and fully symmetric stresses of symmetric frameworks. The orbit matrix is a true analog of the standard rigidity matrix for general frameworks, and its analysis gives important insights into questions about the flexibility and rigidity of classes of symmetric frameworks, in all dimensions. With this narrower focus on fully symmetric infinitesimal motions, comes the power to predict symmetry-preserving finite mechanisms - giving a simplified analysis which covers a wide range of the known mechanisms, and generalizes the classes of known mechanisms. This initial exploration of the properties of the orbit matrix also opens up a number of new questions and possible extensions of the previous results, including transfer of symmetry based results from Euclidean space to spherical, hyperbolic, and some other metrics with shared symmetry groups and underlying projective geometry.Comment: 41 pages, 12 figure

Topological Graph Polynomials in Colored Group Field Theory

In this paper we analyze the open Feynman graphs of the Colored Group Field Theory introduced in [arXiv:0907.2582]. We define the boundary graph \cG_{\partial} of an open graph \cG and prove it is a cellular complex. Using this structure we generalize the topological (Bollobas-Riordan) Tutte polynomials associated to (ribbon) graphs to topological polynomials adapted to Colored Group Field Theory graphs in arbitrary dimension

The Way of Love: Practicing an Irigarayan Ethic

Merwe, W.L. [Promotor]van der Olthuis, J.H. [Promotor]Halsema, J.M. [Copromotor

Smoking in asthma is associated with elevated levels of corticosteroid resistant sputum cytokines—an exploratory study

<p>Background: Current cigarette smoking is associated with reduced acute responses to corticosteroids and worse clinical outcomes in stable chronic asthma. The mechanism by which current smoking promotes this altered behavior is currently unclear. Whilst cytokines can induce corticosteroid insensitivity in-vitro, how current and former smoking affects airway cytokine concentrations and their responses to oral corticosteroids in stable chronic asthma is unclear.</p> <p>Objectives: To examine blood and sputum cytokine concentrations in never, ex and current smokers with asthma before and after oral corticosteroids.</p> <p>Methods: Exploratory study utilizing two weeks of oral dexamethasone (equivalent to 40 mg/day prednisolone) in 22 current, 21 never and 10 ex-smokers with asthma. Induced sputum supernatant and plasma was obtained before and after oral dexamethasone. 25 cytokines were measured by multiplex microbead system (Invitrogen, UK) on a Luminex platform.</p> <p>Results: Smokers with asthma had elevated sputum cytokine interleukin (IL) -6, -7, and -12 concentrations compared to never smokers with asthma. Few sputum cytokine concentrations changed in response to dexamethasone IL-17 and IFNα increased in smokers, CCL4 increased in never smokers and CCL5 and CXCL10 reduced in ex-smokers with asthma. Ex-smokers with asthma appeared to have evidence of an ongoing corticosteroid resistant elevation of cytokines despite smoking cessation. Several plasma cytokines were lower in smokers wi</p> <p>Conclusion: Cigarette smoking in asthma is associated with a corticosteroid insensitive increase in multiple airway cytokines. Distinct airway cytokine profiles are present in current smokers and never smokers with asthma and could provide an explanatory mechanism for the altered clinical behavior observed in smokers with asthma.</p&gt

Distribution of Capillary Transit Times in Isolated Lungs of Oxygen-Tolerant Rats

Rats pre-exposed to 85% O2 for 5–7 days tolerate the otherwise lethal effects of 100% O2. The objective was to evaluate the effect of rat exposure to 85% O2 for 7 days on lung capillary mean transit time (t¯c) and distribution of capillary transit times (h c(t)). This information is important for subsequent evaluation of the effect of this hyperoxia model on the redox metabolic functions of the pulmonary capillary endothelium. The venous concentration vs. time outflow curves of fluorescein isothiocyanate labeled dextran (FITC-dex), an intravascular indicator, and coenzyme Q1 hydroquinone (CoQ1H2), a compound which rapidly equilibrates between blood and tissue on passage through the pulmonary circulation, were measured following their bolus injection into the pulmonary artery of isolated perfused lungs from rats exposed to room air (normoxic) or 85% O2 for 7 days (hyperoxic). The moments (mean transit time and variance) of the measured FITC-dex and CoQ1H2 outflow curves were determined for each lung, and were then used in a mathematical model [Audi et al. J. Appl. Physiol. 77: 332–351, 1994] to estimate t¯c and the relative dispersion (RDc) of h c(t). Data analysis reveals that exposure to hyperoxia decreases lung t¯c by 42% and increases RDc, a measure h c(t) heterogeneity, by 40%

Small grid embeddings of 3-polytopes

We introduce an algorithm that embeds a given 3-connected planar graph as a convex 3-polytope with integer coordinates. The size of the coordinates is bounded by $O(2^{7.55n})=O(188^{n})$. If the graph contains a triangle we can bound the integer coordinates by $O(2^{4.82n})$. If the graph contains a quadrilateral we can bound the integer coordinates by $O(2^{5.46n})$. The crucial part of the algorithm is to find a convex plane embedding whose edges can be weighted such that the sum of the weighted edges, seen as vectors, cancel at every point. It is well known that this can be guaranteed for the interior vertices by applying a technique of Tutte. We show how to extend Tutte's ideas to construct a plane embedding where the weighted vector sums cancel also on the vertices of the boundary face

Extracellular Matrix Aggregates from Differentiating Embryoid Bodies as a Scaffold to Support ESC Proliferation and Differentiation

Embryonic stem cells (ESCs) have emerged as potential cell sources for tissue engineering and regeneration owing to its virtually unlimited replicative capacity and the potential to differentiate into a variety of cell types. Current differentiation strategies primarily involve various growth factor/inducer/repressor concoctions with less emphasis on the substrate. Developing biomaterials to promote stem cell proliferation and differentiation could aid in the realization of this goal. Extracellular matrix (ECM) components are important physiological regulators, and can provide cues to direct ESC expansion and differentiation. ECM undergoes constant remodeling with surrounding cells to accommodate specific developmental event. In this study, using ESC derived aggregates called embryoid bodies (EB) as a model, we characterized the biological nature of ECM in EB after exposure to different treatments: spontaneously differentiated and retinoic acid treated (denoted as SPT and RA, respectively). Next, we extracted this treatment-specific ECM by detergent decellularization methods (Triton X-100, DOC and SDS are compared). The resulting EB ECM scaffolds were seeded with undifferentiated ESCs using a novel cell seeding strategy, and the behavior of ESCs was studied. Our results showed that the optimized protocol efficiently removes cells while retaining crucial ECM and biochemical components. Decellularized ECM from SPT EB gave rise to a more favorable microenvironment for promoting ESC attachment, proliferation, and early differentiation, compared to native EB and decellularized ECM from RA EB. These findings suggest that various treatment conditions allow the formulation of unique ESC-ECM derived scaffolds to enhance ESC bioactivities, including proliferation and differentiation for tissue regeneration applications. © 2013 Goh et al