Approaches to reflective hulls of subcategories

Bibliography: pages 77-81.Reflective subcategories originated as a formal mathematical concept in the 1960's. Perhaps the first abstract definition of reflectivity can be attributed to P. Freyd who, in [Freyd 1960] and [Freyd 1964], gave a definition in terms of reflection arrows. Already in [Isbelll964] the general definition of a reflective subcategory was applied to some concrete situations, and used to formulate one of the first problems concerning reflectivity, namely, whether the intersection of (full, isomorphism-closed) reflective subcategories of the category of uniform spaces is again reflective. This problem, together with analogous questions posed in other contexts (e.g., by H. Herrlich for the category of topological spaces), led to the formulation of the reflective hull problem for subcategories in general, namely, whether a given subcategory is contained in a smallest reflective supercategory. Much of the research concerned with reflectivity and the reflective hull problem considers sufficient conditions for a category such that the reflectivity of (certain) subcategories can be described and the existence of reflective hulls can be guaranteed. These conditions are usually given in terms of (co)completeness and (co)wellpoweredness (see, for example, [Tholen 1987), [Kelly 1987]). A primary objective of this thesis is to provide sufficient and necessary conditions, formulated in subcategory-related terms, for the reflectivity of a given subcategory, and for the characterisation of the existence of reflective hulls. Our approach to finding appropriate descriptions of reflective hulls is essentially a constructive one, in the sense that we attempt to "generate" the reflective hull of a given subcategory (and hence give a concrete description of the hull) by means of certain closure processes applied to the given subcategory. We should also emphasise that our philosophy is not a conservative one in that, apart from applications of our constructions to particular situations, we make as few global assumptions as possible in our considerations. Intuitively, there are several ways in which reflectivity can be viewed as a mathematical concept; the results in this thesis emphasise these points of view. First, reflectivity may be viewed as a completeness property, i.e., as a kind of limit procedure; we study the correspondence between reflective hulls and closures of subcategories under certain types of limits. Reflectivity may also be considered as a cocompleteness property; appropriately we also consider the closure of a given subcategory under certain kinds of colimits and its relation to a possible reflective hull. Both of these constructions are generalisations of natural descriptions of reflection arrows in the special case of partially-ordered classes. Finally, reflectivity can be considered as a (subcategory-related) factorisation property; in this context we consider closures of a subcategory in terms of factorisations relative to the given subcategory, and, related to this, closures under special kinds of colimits relative to the given subcategory. In this thesis we also obtain results concerning the relation between reflectivity and weaker concepts; in particular results concerning intersections of reflective subcategories, and reflective hulls of almost reflective subcategories, are given, and applied to concrete situations, for example, the following problem posed in Rosicky and Tholen 1988: Is the category of complete Boolean algebras an intersection of reflective subcategories of the category of frames

The tectonic development of the Namaqua mobile belt and its foreland in parts of the Northern Cape

The Namaqua Mobile Belt extends from the south-western coast of Southern Africa through northern Namaqualand and adjacent parts of South West Africa to the south-western margin of the Kaapvaal Craton near Prieska. Its Precambrian tectonic development is characterised by several successive periods of deformation and metamorphism, the last of which - the Namaqua tectogenesis - occurred between c. 0,9 and 1,25 Ga B.P. The northern boundary of the mobile belt is the Namaqua front which, at different places along its length, appears as a metamorphic transition, as an oblique-slip fault, and as an interface between areas yielding radiometric ages of 2,5 - 2,9 Ga and 0,9- 1,25 Ga respectively. The foreland of the belt in the area under consideration is formed by the south-western marginal part of the Kaapvaal Craton and by the Kheis tectonic domain; the former comprises granitoids and metamorphites generally older than c.2,5 Ga (the Skalkseput Granite, the Draghoender Granite and the Swartkop sequence), as well as supracrustal cover-rocks ranging in age between c. 2,5 and 1,8 Ga (the Seekoebaard Formation, the Transvaal Supergroup and the Matsap Formation). The area of the latter is underlain by a sequence of metasediments and metavolcanics (the Kheis Group), which has been deformed and metamorphosed prior to the deposition of the Seekoebaard Formation (probably prior to the intrusion of the Draghoender Granite c. 2,9 Ga B.P.)

Mucin histochemistry of tracheal goblet cells after oral administration of ambroxol. Acta vet Brno 2001; 70

Abstract Vajner L., V. Konrádová, J. Uhlík, J. Zocová: Mucin Histochemistry of Tracheal Goblet Cells after Oral Administration of Ambroxol. Acta Vet. Brno 2001, 70: 9-13. Previous studies on the effect of various mucolytic drugs on the tracheal epithelium ultrastructure revealed ambroxol as the most harmful one. To complete these studies, we decided to evaluate the effect of ambroxol on the glycoconjugate content in the secretion of tracheal goblet cells. Using the methods of both conventional and lectin histochemistry, the percentage of tracheal goblet cells containing various glycoconjugates was evaluated. Twenty minutes after oral administration of 7.5 mg of ambroxol, goblet cells containing neutral glycoconjugates disappeared from the rabbit tracheal epithelium. Among goblet cells containing acidic glycoconjugates, the percentage of sialylated glycoconjugate-containing ones slightly decreased compared with control healthy rabbits. Oral administration of ambroxol only slightly affected the composition of glycoconjugates contained in goblet cells of the tracheal epithelium in rabbits. Tracheal goblet cells, conventional and lectin histochemistry, mucolytic drug ambroxol, rabbit Ambroxol, the most frequently used mucolytic agent in clinical practice, affects both ciliated and secretory cells in the respiratory system. It stimulates ciliary activity as well as incorporation of precursors into phospholipids in granular pneumocytes causing thus a decrement of mucus adhesion to the hypophase. According to pharmacological studies, it facilitates incorporation of hydrolytic enzymes into lysosomes of the airways' secretory cells. Activation of these acidic mucopolysaccharide-degrading enzymes leads to a decrease of the sputum viscosity (·míd and Holcát 1994). In our previous studies, reactions of the rabbit tracheal epithelium to oral administration of a single therapeutic dose of 6 various mucolytic drugs were compared. The adverse effect of ambroxol was the most pronounced (Konrádová et al. 1985ab; To complete the study, changes of the glycoconjugate content of the tracheal goblet cells were studied under the same experimental conditions using both conventional and lectin histochemistry

Why measuring individual innovativeness is so difficult: a critical review of standard methods and new ideas to measure innovativeness

Innovative people are desperately wanted in nowadays world, wherefore tools to measure individual innovativeness are needed. This work reviews the commonly used metrics to gauge innovativeness, such as the Individual Innovativeness Scale (IIS). Hereby, it demonstrates via a survey that often a simple self-evaluation question contains the same information as conventional psychological surveys. As an alternative, another survey investigates whether bibliographical information can predict innovativeness. Finally, a new type of experiments to measure innovativeness is proposed, enabled by recent progress in neuroscience, that will not rely on classical self-report questions but on empirical data on the candidate’s brain activity in response to external stimuli

Scalable quantum photonic devices emitting indistinguishable photons in the telecom C-band

Epitaxial semiconductor quantum dots (QDs) are a promising resource for quantum light generation and the realization of non-linear quantum photonic elements operating at the single-photon level. Their random spatial distribution resulting from their self-organized nature, however, restrains the fabrication yield of quantum devices with the desired functionality. As a solution, the QDs can be imaged and localized, enabling deterministic device fabrication. Due to the significant electronic noise of camera sensors operating in the telecommunication C-band, $1530-1560~\mathrm{nm}$, this technique remained challenging. In this work, we report on the imaging of QDs epitaxially grown on InP with emission wavelengths in the telecom C-band demonstrating a localization accuracy of $80~\mathrm{nm}$. This is enabled by the hybrid integration of QDs in a planar sample geometry with a bottom metallic reflector to enhance the out-of-plane emission. To exemplify our approach, we successfully fabricate circular Bragg grating cavities around single pre-selected QDs with an overall cavity placement uncertainty of $90~\mathrm{nm}$. QD-cavity coupling is demonstrated by a Purcell enhancement up to $\sim5$ with an estimated photon extraction efficiency of $(16.6\pm2.7)\%$ into a numerical aperture of $0.4$. We demonstrate triggered single-photon emission with $g^{(2)}(0)=(3.2\pm0.6)\times10^{-3}$ and record-high photon indistinguishability associated with two-photon interference visibilities of $V = (19.3\pm2.6)\%$ and $V_{\mathrm{PS}} = 99.8^{+0.2}_{-2.6}\%$ without and with temporal postselection, respectively. While the performance of our devices readily enables proof-of-principle experiments in quantum information, further improvements in the yield and coherence may enable the realization of non-linear devices at the single photon level and advanced quantum networks at the telecom wavelength.Comment: 9 pages, 4 figures, Supplemental Material: 20 pages, 18 figure

Involvement of mast cells in monocrotaline-induced pulmonary hypertension in rats

Background: Mast cells (MCs) are implicated in inflammation and tissue remodeling. Accumulation of lung MCs is described in pulmonary hypertension (PH); however, whether MC degranulation and c-kit, a tyrosine kinase receptor critically involved in MC biology, contribute to the pathogenesis and progression of PH has not been fully explored.Methods: Pulmonary MCs of idiopathic pulmonary arterial hypertension (IPAH) patients and monocrotaline-injected rats (MCT-rats) were examined by histochemistry and morphometry. Effects of the specific c-kit inhibitor PLX and MC stabilizer cromolyn sodium salt (CSS) were investigated in MCT-rats both by the preventive and therapeutic approaches. Hemodynamic and right ventricular hypertrophy measurements, pulmonary vascular morphometry and analysis of pulmonary MC localization/counts/activation were performed in animal model studies.Results: There was a prevalence of pulmonary MCs in IPAH patients and MCT-rats as compared to the donors and healthy rats, respectively. Notably, the perivascular MCs were increased and a majority of them were degranulated in lungs of IPAH patients and MCT-rats (p < 0.05 versus donor and control, respectively). In MCT-rats, the pharmacological inhibitions of MC degranulation and c-kit with CSS and PLX, respectively by a preventive approach (treatment from day 1 to 21 of MCT-injection) significantly attenuated right ventricular systolic pressure (RVSP) and right ventricular hypertrophy (RVH). Moreover, vascular remodeling, as evident from the significantly decreased muscularization and medial wall thickness of distal pulmonary vessels, was improved. However, treatments with CSS and PLX by a therapeutic approach (from day 21 to 35 of MCT-injection) neither improved hemodynamics and RVH nor vascular remodeling.Conclusions: The accumulation and activation of perivascular MCs in the lungs are the histopathological features present in clinical (IPAH patients) and experimental (MCT-rats) PH. Moreover, the accumulation and activation of MCs in the lungs contribute to the development of PH in MCT-rats. Our findings reveal an important pathophysiological insight into the role of MCs in the pathogenesis of PH in MCT- rats

A Wyler-type approach to categorical topology

Bibliography: pages 74-77.Chapter 0 contains a summary of well-known terminology which will subsequently be used in the thesis. In Chapter 1 we begin by describing how topological categories may be viewed as categories of models corresponding to theories into the category of complete lattices. This leads naturally to the study of categories of T-models corresponding to theories into categories other than the category of complete lattices. It is shown, for example, that a concrete category corresponds to a poset-valued theory just in the case that it is (co)fibration complete. This shows that a concrete category is of the form Mod(T) only for poset-valued theories T. We make some technical observations regarding the correspondence between transformations and concrete functors. In particular, the fact that natural transformations between theories are in a bijective correspondence to finality preserving concrete functors between their respective categories of models will be of importance in Chapter 2. A theoretic interpretation is given of those categories which are (co)reflective modifications of certain concrete categories. Chapter 2 deals with the theoretic interpretation of certain topological completions of concrete categories. These are described in abstract theoretic terms using the correspondence between transformations and concrete functors. We also consider how concrete categories are embedded into (co)fibration complete categories. These "weak" completions have the nice property that they are always legitimate. For an arbitrary concrete category, the relationship between its topological completions and the various order-theoretic completions of its fibres is rather weak. However, if one assumes some additional structure properties, such as (co)fibration completeness, then the concepts of a categorical completion and an order-theoretic completion are more closely related, as shown by the result that for certain kinds of cofibrations, taking the universal order-theoretic completion of each fibre even yields the universal final topological completion. Chapter 3 is entirely concerned with the main goal of this thesis. We study so-called "convenient" topological categories, i.e., topological categories with additional structure. The purpose is to characterise each such type of category as a category of T-models for some theory T which satisfies a special "preservation" property with respect to pullbacks. The cartesian closed topological categories are characterised as those categories of T-models where the associated theory T sends a pointwise pullback of any regular sink into product covering family of diagrams. The concretely cartesian closed topological categories are characterised as those for which the associated theory T sends the pointwise pullback of an arbitrary sink into a product covering family. We also characterise the concretely cartesian closed categories by means of a certain natural transformation, given by the product of two structures. Perhaps the most satisfactory result of this Chapter is the characterisation of the universally topological categories. The theories corresponding to these categories may be described in two ways : firstly, they are shown to be frame-valued, send pullbacks into covering diagrams, and send morphisms into downset-preserving, cover-reflecting maps; secondly, they are shown to send the pointwise pullback of any sink into an order-covering diagram. Similarly, the concrete quasitopoi may be characterised by those theories which send the pullback of any regular sink into an order-covering family of diagrams. Finally, we consider hereditary topological categories. These are characterised as categories of T-models for which the theory T preserves terminal objects and sends the pointwise pullback of an arbitrary sink along an embedding into a weakly covering diagram family. In this context, a notion of strong heredity is introduced and characterised by a frame-valued theory sending pullbacks along monomorphisms into order-covering diagrams