On Linear Information Systems

Scott's information systems provide a categorically equivalent, intensional description of Scott domains and continuous functions. Following a well established pattern in denotational semantics, we define a linear version of information systems, providing a model of intuitionistic linear logic (a new-Seely category), with a "set-theoretic" interpretation of exponentials that recovers Scott continuous functions via the co-Kleisli construction. From a domain theoretic point of view, linear information systems are equivalent to prime algebraic Scott domains, which in turn generalize prime algebraic lattices, already known to provide a model of classical linear logic

Experimental investigation of the pre–Darcy regime

The validity of Darcy’s law at very low Reynolds numbers is discussed controversially in literature, as some authors propose a pre–Darcy flow regime below some critical Reynolds number. The scope of this work is to investigate this problem experimentally. Therefore, a packing of glass spheres is perfused by different glycerin–water solutions. A linear behaviour between the flow velocity and the pressure drop through the packed spheres is found in the complete investigated range of Reynolds number Red′, based on the mean-pore diameter d′ and mean-pore velocity v′ with 10−9≤Red′≤10−1. This contradicts the results of different authors like Fand et al. (1987) or Kececioglu and Jiang (1994), postulating a pre–Darcy regime for Red′≤2.8⋅10−6 or Red′≤0.13, respectively

Wind reversals in turbulent Rayleigh-Benard convection

The phenomenon of irregular cessation and subsequent reversal of the large-scale circulation in turbulent Rayleigh-B\'enard convection is theoretically analysed. The force and thermal balance on a single plume detached from the thermal boundary layer yields a set of coupled nonlinear equations, whose dynamics is related to the Lorenz equations. For Prandtl and Rayleigh numbers in the range $10^{-2} \leq \Pr \leq 10^{3}$ and 10^{7} \leq \Ra \leq 10^{12}, the model has the following features: (i) chaotic reversals may be exhibited at Ra $\geq 10^{7}$; (ii) the Reynolds number based on the root mean square velocity scales as \Re_{rms} \sim \Ra^{[0.41 ... 0.47]} (depending on Pr), and as $\Re_{rms} \sim \Pr^{-[0.66 ... 0.76]}$ (depending on Ra); and (iii) the mean reversal frequency follows an effective scaling law \omega / (\nu L^{-2}) \sim \Pr^{-(0.64 \pm 0.01)} \Ra^{0.44 \pm 0.01}. The phase diagram of the model is sketched, and the observed transitions are discussed.Comment: 4 pages, 5 figure

The complete primary structure of the spermadhesin AWN, a zona pellucida-binding protein isolated from boar spermatozoa

AbstractAWN is a boar protein which originates in secretions of the male accessory glands and which becomes sperm surface-associated upon ejaculation. It is one of the components thought to mediate sperm adhesion to the egg's zona pellucida through a carbohydrate-recognition mechanism. AWN may, thus, participate in the initial events of fertilization in the pig. In this report we describe its complete primary structure by combination of protein-chemical and mass spectrometric methods. AWN exists as two isoforms, AWN-1 and AWN-2, which differ in that AWN-2 is N-terminally acetylated. The amino acid sequence of AWN contains 133 amino acid residues and two disulphide bridges between nearest-neighbour cysteine residues. Analysis of the amino acid sequence of the AWN proteins showed significant similarity only to AQN-1 and AQN-3, two other boar spermadhesins

Observed communication semantics for classical processes

Classical Linear Logic (CLL) has long inspired readings of its proofs as communicating processes. Wadler's CP calculus is one of these readings. Wadler gave CP an operational semantics by selecting a subset of the cut-elimination rules of CLL to use as reduction rules. This semantics has an appealing close connection to the logic, but does not resolve the status of the other cut-elimination rules, and does not admit an obvious notion of observational equivalence. We propose a new operational semantics for CP based on the idea of observing communication, and use this semantics to define an intuitively reasonable notion of observational equivalence. To reason about observational equivalence, we use the standard relational denotational semantics of CLL. We show that this denotational semantics is adequate for our operational semantics. This allows us to deduce that, for instance, all the cut-elimination rules of CLL are observational equivalences

Change Actions: Models of Generalised Differentiation

Cai et al. have recently proposed change structures as a semantic framework for incremental computation. We generalise change structures to arbitrary cartesian categories and propose the notion of change action model as a categorical model for (higher-order) generalised differentiation. Change action models naturally arise from many geometric and computational settings, such as (generalised) cartesian differential categories, group models of discrete calculus, and Kleene algebra of regular expressions. We show how to build canonical change action models on arbitrary cartesian categories, reminiscent of the F\`aa di Bruno construction

Towards a unified theory of Sobolev inequalities

We discuss our work on pointwise inequalities for the gradient which are connected with the isoperimetric profile associated to a given geometry. We show how they can be used to unify certain aspects of the theory of Sobolev inequalities. In particular, we discuss our recent papers on fractional order inequalities, Coulhon type inequalities, transference and dimensionless inequalities and our forthcoming work on sharp higher order Sobolev inequalities that can be obtained by iteration.Comment: 39 pages, made some changes to section 1

Proof-Net as Graph, Taylor Expansion as Pullback

We introduce a new graphical representation for multiplicative and exponential linear logic proof-structures, based only on standard labelled oriented graphs and standard notions of graph theory. The inductive structure of boxes is handled by means of a box-tree. Our proof-structures are canonical and allows for an elegant definition of their Taylor expansion by means of pullbacks

Neurotrophins and neurotrophin receptors in pulmonary sarcoidosis - granulomas as a source of expression

<p>Abstract</p> <p>Background</p> <p>Pulmonary sarcoidosis is an inflammatory disease, characterized by an accumulation of CD4⁺lymphocytes and the formation of non-caseating epithelioid cell granulomas in the lungs. The disease either resolves spontaneously or develops into a chronic disease with fibrosis. The neurotrophins nerve growth factor (NGF), brain-derived neurotrophic factor (BDNF) and neurotrophin-3 (NT-3) have been suggested to be important mediators of inflammation and mediate tissue remodelling. In support of this, we have recently reported enhanced NGF levels in the airways of patients with pulmonary sarcoidosis. However, less is known about levels of BDNF and NT-3, and moreover, knowledge in the cellular sources of neurotrophins and the distribution of the corresponding neurotrophin receptors in airway tissue in sarcoidosis is lacking.</p> <p>Methods</p> <p>The concentrations of NGF, BDNF and NT-3 in bronchoalveolar lavage fluid (BALF) of 41 patients with newly diagnosed pulmonary sarcoidosis and 27 healthy controls were determined with ELISA. The localization of neurotrophins and neurotrophin receptors were examined by immunohistochemistry on transbronchial lung biopsies from sarcoidosis patients.</p> <p>Results</p> <p>The sarcoidosis patients showed significantly enhanced NT-3 and NGF levels in BALF, whereas BDNF was undetectable in both patients and controls. NT-3 levels in BALF were found higher in patients with non-Löfgren sarcoidosis as compared to patients with Löfgren's syndrome, and in more advanced disease stage. Epithelioid cells and multinucleated giant cells within the sarcoid granulomas showed marked immunoreactivity for NGF, BDNF and NT-3. Also, immunoreactivity for the neurotrophin receptor TrkA, TrkB and TrkC, was found within the granulomas. In addition, alveolar macrophages showed positive immunoreactivity for NGF, BDNF and NT-3 as well as for TrkA, TrkB and TrkC.</p> <p>Conclusions</p> <p>This study provides evidence of enhanced neurotrophin levels locally within the airways of patients with sarcoidosis. Findings suggest that sarcoid granuloma cells and alveolar macrophages are possible cellular sources of, as well as targets for, neurotrophins in the airways of these patients.</p