Continued fractions built from convex sets and convex functions

In a partially ordered semigroup with the duality (or polarity) transform, it is pos- sible to define a generalisation of continued fractions. General sufficient conditions for convergence of continued fractions are provided. Two particular applications concern the cases of convex sets with the Minkowski addition and the polarity transform and the family of non-negative convex functions with the Legendre–Fenchel and Artstein-Avidan–Milman transforms.

On Two Saigo’s Fractional Integral Operators in the Class of Univalent Functions

2000 Mathematics Subject Classification: Primary 26A33, 30C45; Secondary 33A35

Generic differentiability of convex functions and monotone operators

The aim of this paper is to investigate to what extent the known theory of subdifferentiability and generic differentiability of convex functions defined on open sets can be carried out in the context of convex functions defined on not necessarily open sets. Among the main results obtained I would like to mention a Kenderov type theorem (the subdifferential at a generic point is contained in a sphere), a generic Gâteaux differentiability result in Banach spaces of class S and a generic Fréchet differentiability result in Asplund spaces. At least two methods can be used to prove these results: first, a direct one, and second, a more general one, based on the theory of monotone operators. Since this last theory was previously developed essentially for monotone operators defined on open sets, it was necessary to extend it to the context of monotone operators defined on a larger class of sets, our "quasi open" sets. This is done in Chapter III. As a matter of fact, most of these results have an even more general nature and have roots in the theory of minimal usco maps, as shown in Chapter II.

Abstract Subdifferential Calculus and Semi-Convex Functions

∗ The work is partially supported by NSFR Grant No MM 409/94.

Applications of the Owa-Srivastava Operator to the Class of K-Uniformly Convex Functions

2000 Mathematics Subject Classification: Primary 30C45, 26A33; Secondary 33C15

Subclasses of Starlike Functions of Complex Order Involving Generalized Hypergeometric Functions

MSC2010: 30C45, 33C45

The Space of Differences of Convex Functions on [0, 1]

∗Participant in Workshop in Linear Analysis and Probability, Texas A & M University, College Station, Texas, 2000. Research partially supported by the Edmund Landau Center for Research in Mathematical Analysis and related areas, sponsored by Minerva Foundation (Germany).

The Expanded Human Kallikrein (KLK) gene family : genomic organisation, tissue specific expression and potential functions

The tissue kallikreins are serine proteases encoded by highly conserved multigene families. The rodent kallikrein (KLK) families are particularly large, consisting of 13 26 genes clustered in one chromosomal locus. It has been recently recognised that the human KLK gene family is of a similar size (15 genes) with the identification of another 12 related genes (KLK4-KLK15) within and adjacent to the original human KLK locus (KLK1-3) on chromosome 19q13.4. The structural organisation and size of these new genes is similar to that of other KLK genes except for additional exons encoding 5 or 3 untranslated regions. Moreover, many of these genes have multiple mRNA transcripts, a trait not observed with rodent genes. Unlike all other kallikreins, the KLK4-KLK15 encoded proteases are less related (25–44%) and do not contain a conventional kallikrein loop. Clusters of genes exhibit high prostatic (KLK2-4, KLK15) or pancreatic (KLK6-13) expression, suggesting evolutionary conservation of elements conferring tissue specificity. These genes are also expressed, to varying degrees, in a wider range of tissues suggesting a functional involvement of these newer human kallikrein proteases in a diverse range of physiological processes.

A generative design system based on evolutionary and mathematical functions

Previous work by Professor John Frazer on Evolutionary Architecture provides a basis for the development of a system evolving architectural envelopes in a generic and abstract manner. Recent research by the authors has focused on the implementation of a virtual environment for the automatic generation and exploration of complex forms and architectural envelopes based on solid modelling techniques and the integration of evolutionary algorithms, enhanced computational and mathematical models. Abstract data types are introduced for genotypes in a genetic algorithm order to develop complex models using generative and evolutionary computing techniques. Multi-objective optimisation techniques are employed for defining the fitness function in the evaluation process.

A comparison of safety climate and safety outcomes between construction and resource functions in a large case study organisation

The research described in this paper forms part of an in-depth investigation of safety culture in one of Australia’s largest construction companies. The research builds on a previous qualitative study with organisational safety leaders and further investigates how safety culture is perceived and experienced by organisational members, as well as how this relates to their safety behaviour and related outcomes at work. Participants were 2273 employees of the case study organisation, with 689 from the Construction function and 1584 from the Resources function. The results of several analyses revealed some interesting organisational variance on key measures. Specifically, the Construction function scored significantly higher on all key measures: safety climate, safety motivation, safety compliance, and safety participation. The results are discussed in terms of relevance in an applied research context.

Questions to Artificial Nature: A Philosophical Study of Interdisciplinary Models and their Functions in Scientific Practice

This thesis presents an interdisciplinary analysis of how models and simulations function in the production of scientific knowledge. The work is informed by three scholarly traditions: studies on models and simulations in philosophy of science, so-called micro-sociological laboratory studies within science and technology studies, and cultural-historical activity theory. Methodologically, I adopt a naturalist epistemology and combine philosophical analysis with a qualitative, empirical case study of infectious-disease modelling. This study has a dual perspective throughout the analysis: it specifies the modelling practices and examines the models as objects of research. The research questions addressed in this study are: 1) How are models constructed and what functions do they have in the production of scientific knowledge? 2) What is interdisciplinarity in model construction? 3) How do models become a general research tool and why is this process problematic? The core argument is that the mediating models as investigative instruments (cf. Morgan and Morrison 1999) take questions as a starting point, and hence their construction is intentionally guided. This argument applies the interrogative model of inquiry (e.g., Sintonen 2005; Hintikka 1981), which conceives of all knowledge acquisition as process of seeking answers to questions. The first question addresses simulation models as Artificial Nature, which is manipulated in order to answer questions that initiated the model building. This account develops further the "epistemology of simulation" (cf. Winsberg 2003) by showing the interrelatedness of researchers and their objects in the process of modelling. The second question clarifies why interdisciplinary research collaboration is demanding and difficult to maintain. The nature of the impediments to disciplinary interaction are examined by introducing the idea of object-oriented interdisciplinarity, which provides an analytical framework to study the changes in the degree of interdisciplinarity, the tools and research practices developed to support the collaboration, and the mode of collaboration in relation to the historically mutable object of research. As my interest is in the models as interdisciplinary objects, the third research problem seeks to answer my question of how we might characterise these objects, what is typical for them, and what kind of changes happen in the process of modelling. Here I examine the tension between specified, question-oriented models and more general models, and suggest that the specified models form a group of their own. I call these Tailor-made models, in opposition to the process of building a simulation platform that aims at generalisability and utility for health-policy. This tension also underlines the challenge of applying research results (or methods and tools) to discuss and solve problems in decision-making processes.

Androgen receptor-dependent and independent functions of ARIP4

Androgen receptor (AR) is necessary for normal male phenotype development and essential for spermatogenesis. AR is a classical steroid receptor mediating actions of male sex steroids testosterone and 5-alpha-dihydrotestosterone. Numerous coregulators interact with the receptor and regulate AR activity on target genes. This study deals with the characterization of androgen receptor-interacting protein 4 (ARIP4). ARIP4 binds DNA, interacts with AR in vitro and in cultured yeast and mammalian cells, and modulates AR-dependent transactivation. ARIP4 is an active DNA-dependent ATPase, and this enzymatic activity is essential for the ability of ARIP4 to modulate AR function. On the basis of sequence homology in its ATPase domain, ARIP4 belongs to the SNF2 family of proteins involved in chromatin remodeling, DNA repair, and homologous recombination. Similar to its closest homologs ATRX and Rad54, ARIP4 does not seem to be a classical chromatin remodeling protein in that it does not appear to form large protein complexes in vivo or remodel mononucleosomes in vitro. However, ARIP4 is able to generate superhelical torsion on linear DNA fragments. ARIP4 is covalently modified by SUMO-1, and mutation of six potential SUMO attachment sites abolishes the ability of ARIP4 to bind DNA, hydrolyze ATP, and activate AR function. ARIP4 expression starts in early embryonic development. In mouse embryo ARIP4 is present mainly in the neural tube and limb buds. In adult mouse tissues ARIP4 expression is virtually ubiquitous. In mouse testis ARIP4 is expressed in the nuclei of Sertoli cells in a stage-dependent manner. ARIP4 is also present in the nuclei of Leydig cells, spermatogonia, pachytene and diplotene spermatocytes. Testicular expression pattern of ARIP4 does not differ significantly in wild-type, FSHRKO, and LuRKO mice. In the testis of hpg mice, ARIP4 is found mainly in interstitial cells and has very low, if any, expression in Sertoli and germ cells. Heterozygous Arip4+/ mice are fertile and appear normal; however, they are haploinsufficient with regard to androgen action in Sertoli cells. In contrast, Arip4 / embryos are not viable. They have significantly reduced body size at E9.5 and die by E11.5. Compared to wild-type littermates, Arip4 / embryos possess a higher percentage of apoptotic cells at E9.5 and E10.5. Fibroblasts derived from Arip4 / embryos cease growing after 2-3 passages and exhibit a significantly increased apoptosis and decreased proliferation rate than cells from wild-type embryos. Our findings demonstrate that ARIP4 plays an essential role in mouse embryonic development. In addition, testicular expression and AR coregulatory activity of ARIP4 suggest a role of ARIP4-AR interaction in the somatic cells of the testis.

Latent TGF-beta Binding Proteins : Adhesive functions and matrix association of LTBP-2 and potential functions of LTBP-1 and LTBP-3 in mesothelioma

Latent transforming growth factor-beta (TGF-beta) binding proteins (LTBPs) -1, -3 and -4 are ECM components whose major function is to augment the secretion and matrix targeting of TGF-beta, a multipotent cytokine. LTBP-2 does not bind small latent TGF-beta but has suggested functions as a structural protein in ECM microfibrils. In the current work we focused on analyzing possible adhesive functions of LTBP-2 as well as on characterizing the kinetics and regulation of LTBP-2 secretion and ECM deposition. We also explored the role of TGF-beta binding LTBPs in endothelial cells activated to mimic angiogenesis as well as in malignant mesothelioma. We found that, unlike most adherent cells, several melanoma cell lines efficiently adhered to purified recombinant LTBP-2. Further characterization revealed that the adhesion was mediated by alpha3beta1 and alpha6beta1 integrins. Heparin also inhibited the melanoma cell adhesion suggesting a role for heparan sulphate proteoglycans. LTBP-2 was also identified as a haptotactic substrate for melanoma cell migration. We used cultured human embryonic lung fibroblasts to analyze the temporal and spatial association of LTBP-2 into ECM. By We found that LTBP-2 was efficiently assembled to the ECM only in confluent cultures following the deposition of fibronectin (FN) and fibrillin-1. In early, subconfluent cultures it remained primarily in soluble form after secretion. LTBP-2 colocalized transiently with FN and fibrillin-1. Silencing of fibrillin-1 expression by lentiviral shRNAs profoundly disrupted the deposition of LTBP-2 indicating that the ECM association of LTBP-2 depends on a pre-formed fibrillin-1 network. Considering the established role of TGF-beta as a regulator of angiogenesis we induced morphological activation of endothelial cells by phorbol 12-myristate 13-acetate (PMA) and followed the fate of LTBP-1 in the endothelial ECM. This resulted in profound proteolytic processing of LTBP-1 and release of latent TGF-beta complexes from the ECM. The processing was coupled with increased activation of MT-MMPs and specific upregulation of MT1-MMP. The major role of MT1-MMP in the proteolysis of LTBP-1 was confirmed by suppressing the expression with lentivirally induced short-hairpin RNAs as well as by various metalloproteinases inhibitors. TGF-beta can promote tumorigenesis of malignant mesothelioma (MM), which is an aggressive tumor of the pleura with poor prognosis. TGF-beta activity was analyzed in a panel of MM tumors by immunohistochemical staining of phosphorylated Smad-2 (P-Smad2). The tumor cells were strongly positive for P-Smad2 whereas LTBP-1 immunoreactivity was abundant in the stroma, and there was a negative correlation between LTBP-1 and P-Smad2 staining. In addition, the high P-Smad2 immunoreactivity correlated with shorter survival of patients. mRNA analysis revealed that TGF-beta1 was the most highly expressed isoform in both normal human pleura and MM tissue. LTBP-1 and LTBP-3 were both abundantly expressed. LTBP-1 was the predominant isoform in established MM cell lines whereas the expression of LTBP-3 was high in control cells. Suppression of LTBP-3 expression by siRNAs resulted in increased TGF-beta activity in MM cell lines accompanied by decreased proliferation. Our results suggest that decreased expression of LTBP-3 in MM could alter the targeting of TGF-beta to the ECM and lead to its increased activation. The current work emphasizes the coordinated process of the assembly and appropriate targeting of LTBPs with distinct adhesive or cytokine harboring properties into the ECM. The hierarchical assembly may have implications in the modulation of signaling events during morphogenesis and tissue remodeling.