On the Rademacher maximal function

Tools known as maximal functions are frequently used in harmonic analysis when studying local behaviour of functions. Typically they measure the suprema of local averages of non-negative functions. It is essential that the size (more precisely, the L^p-norm) of the maximal function is comparable to the size of the original function. When dealing with families of operators between Banach spaces we are often forced to replace the uniform bound with the larger R-bound. Hence such a replacement is also needed in the maximal function for functions taking values in spaces of operators. More specifically, the suprema of norms of local averages (i.e. their uniform bound in the operator norm) has to be replaced by their R-bound. This procedure gives us the Rademacher maximal function, which was introduced by Hytönen, McIntosh and Portal in order to prove a certain vector-valued Carleson's embedding theorem. They noticed that the sizes of an operator-valued function and its Rademacher maximal function are comparable for many common range spaces, but not for all. Certain requirements on the type and cotype of the spaces involved are necessary for this comparability, henceforth referred to as the “RMF-property”. It was shown, that other objects and parameters appearing in the definition, such as the domain of functions and the exponent p of the norm, make no difference to this. After a short introduction to randomized norms and geometry in Banach spaces we study the Rademacher maximal function on Euclidean spaces. The requirements on the type and cotype are considered, providing examples of spaces without RMF. L^p-spaces are shown to have RMF not only for p greater or equal to 2 (when it is trivial) but also for 1 < p < 2. A dyadic version of Carleson's embedding theorem is proven for scalar- and operator-valued functions. As the analysis with dyadic cubes can be generalized to filtrations on sigma-finite measure spaces, we consider the Rademacher maximal function in this case as well. It turns out that the RMF-property is independent of the filtration and the underlying measure space and that it is enough to consider very simple ones known as Haar filtrations. Scalar- and operator-valued analogues of Carleson's embedding theorem are also provided. With the RMF-property proven independent of the underlying measure space, we can use probabilistic notions and formulate it for martingales. Following a similar result for UMD-spaces, a weak type inequality is shown to be (necessary and) sufficient for the RMF-property. The RMF-property is also studied using concave functions giving yet another proof of its independence from various parameters.

Cognitive function in schizophrenia: Conflicting findings and future directions

Introduction Schizophrenia is a severe mental disorder with multiple psychopathological domains being affected. Several lines of evidence indicate that cognitive impairment serves as the key component of schizophrenia psychopathology. Although there have been a multitude of cognitive studies in schizophrenia, there are many conflicting results. We reasoned that this could be due to individual differences among the patients (i.e. variation in the severity of positive vs. negative symptoms), different task designs, and/or the administration of different antipsychotics. Methods We thus review existing data concentrating on these dimensions, specifically in relation to dopamine function. We focus on most commonly used cognitive domains: learning, working memory, and attention. Results We found that the type of cognitive domain under investigation, medication state and type, and severity of positive and negative symptoms can explain the conflicting results in the literature. Conclusions This review points to future studies investigating individual differences among schizophrenia patients in order to reveal the exact relationship between cognitive function, clinical features, and antipsychotic treatment.

Excel’s Sumif and Sumifs function

As accountants, we are all familiar with the SUM function, which calculates the sum in a range of numbers. However, there are instances where we might want to sum numbers in a given range based on a specified criteria. In this instance the SUM IF function can achieve this objective.

Ternary function and circuit design using ternary multiplexers

The recent trend towards minimizing the interconnections in large scale integration (LSI) circuits has led to intensive investigation in the development of ternary circuits and the improvement of their design. The ternary multiplexer is a convenient and useful logic module which can be used as a basic building block in the design of a ternary system. This paper discusses a systematic procedure for the simplification and realization of ternary functions using ternary multiplexers as building blocks. Both single level and multilevel multiplexing techniques are considered. The importance of the design procedure is highlighted by considering two specific applications, namely, the development of ternary adder/subtractor and TCD to ternary converter.

The effect of internal audit function quality and internal audit contribution to external audit on audit fees

Corporate governance mandates and listing rules identify internal audit functions (IAF) as a central internal control mechanism. External audits are expected to assess the quality of IAF before placing reliance on its work. We provide evidence on the effect of IAF quality and IAF contribution to external audit on audit fees. Using data from a matched survey of both external and internal audits, we extend prior research which is based mainly on internal audits' assessment and conducted predominantly in highly developed markets. We find a positive relationship between IAF quality and audit fees as well as a reduction in audit fees as a result of external auditors' reliance on IAF. The interaction between IAF quality and IAF contribution to external audit suggests that high quality IAF induces greater external auditor reliance on internal auditors' work and thus result in lower external audit fees.

Semi-Classical Mechanics in Phase Space: A Study of Wigner's Function

We explore the semi-classical structure of the Wigner functions ($\Psi $(q, p)) representing bound energy eigenstates $|\psi \rangle $ for systems with f degrees of freedom. If the classical motion is integrable, the classical limit of $\Psi $ is a delta function on the f-dimensional torus to which classical trajectories corresponding to ($|\psi \rangle $) are confined in the 2f-dimensional phase space. In the semi-classical limit of ($\Psi $ ($\hslash $) small but not zero) the delta function softens to a peak of order ($\hslash ^{-\frac{2}{3}f}$) and the torus develops fringes of a characteristic 'Airy' form. Away from the torus, $\Psi $ can have semi-classical singularities that are not delta functions; these are discussed (in full detail when f = 1) using Thom's theory of catastrophes. Brief consideration is given to problems raised when ($\Psi $) is calculated in a representation based on operators derived from angle coordinates and their conjugate momenta. When the classical motion is non-integrable, the phase space is not filled with tori and existing semi-classical methods fail. We conjecture that (a) For a given value of non-integrability parameter ($\epsilon $), the system passes through three semi-classical regimes as ($\hslash $) diminishes. (b) For states ($|\psi \rangle $) associated with regions in phase space filled with irregular trajectories, ($\Psi $) will be a random function confined near that region of the 'energy shell' explored by these trajectories (this region has more than f dimensions). (c) For ($\epsilon \neq $0, $\hslash $) blurs the infinitely fine classical path structure, in contrast to the integrable case ($\epsilon $ = 0, where $\hslash $ )imposes oscillatory quantum detail on a smooth classical path structure.

Characterization of the molecular components and function of BARE-1, Hin-Mu and Mu transposition machineries

Transposable elements, transposons, are discrete DNA segments that are able to move or copy themselves from one locus to another within or between their host genome(s) without a requirement for DNA homology. They are abundant residents in virtually all the genomes studied, for instance, the genomic portion of TEs is approximately 3% in Saccharomyces cerevisiae, 45% in humans, and apparently more than 70% in some plant genomes such as maize and barley. Transposons plays essential role in genome evolution, in lateral transfer of antibiotic resistance genes among bacteria and in life cycle of certain viruses such as HIV-1 and bacteriophage Mu. Despite the diversity of transposable elements they all use a fundamentally similar mechanism called transpositional DNA recombination (transposition) for the movement within and between the genomes of their host organisms. The DNA breakage and joining reactions that underlie their transposition are chemically similar in virtually all known transposition systems. The similarity of the reactions is also reflected in the structure and function of the catalyzing enzymes, transposases and integrases. The transposition reactions take place within the context of a transposition machinery, which can be particularly complex, as in the case of the VLP (virus like particle) machinery of retroelements, which in vivo contains RNA or cDNA and a number of element encoded structural and catalytic proteins. Yet, the minimal core machinery required for transposition comprises a multimer of transposase or integrase proteins and their binding sites at the element DNA ends only. Although the chemistry of DNA transposition is fairly well characterized, the components and function of the transposition machinery have been investigated in detail for only a small group of elements. This work focuses on the identification, characterization, and functional studies of the molecular components of the transposition machineries of BARE-1, Hin-Mu and Mu. For BARE-1 and Hin-Mu transpositional activity has not been shown previously, whereas bacteriophage Mu is a general model of transposition. For BARE-1, which is a retroelement of barley (Hordeum vulgare), the protein and DNA components of the functional VLP machinery were identified from cell extracts. In the case of Hin-Mu, which is a Mu-like prophage in Haemophilus influenzae Rd genome, the components of the core machinery (transposase and its binding sites) were characterized and their functionality was studied by using an in vitro methodology developed for Mu. The function of Mu core machinery was studied for its ability to use various DNA substrates: Hin-Mu end specific DNA substrates and Mu end specific hairpin substrates. The hairpin processing reaction by MuA was characterized in detail. New information was gained of all three machineries. The components or their activity required for functional BARE-1 VLP machinery and retrotransposon life cycle were present in vivo and VLP-like structures could be detected. The Hin-Mu core machinery components were identified and shown to be functional. The components of the Mu and Hin-Mu core machineries were partially interchangeable, reflecting both evolutionary conservation and flexibility within the core machineries. The Mu core machinery displayed surprising flexibility in substrate usage, as it was able to utilize Hin-Mu end specific DNA substrates and to process Mu end DNA hairpin substrates. This flexibility may be evolutionarily and mechanistically important.

Structure-Function Studies of GDNF Family Ligand-RET signalling

Glial cell line-derived neurotrophic factor (GDNF) and its family members neurturin (NRTN), artemin (ARTN) and persephin (PSPN) are growth factors, which are involved in the development, differentiation and maintenance of many neuron types. In addition, they function outside of the nervous system, e.g. in the development of kidney, testis and liver. GDNF family ligand (GFL) signalling happens through a tetrameric receptor complex, which includes two glycosylphosphatidylinositol (GPI)-anchored GDNF family receptor (GFRα) molecules and two RET (rearranged during transfection) receptor tyrosine kinases. Each of the ligands binds preferentially one of the four GFRα receptors: GDNF binds to GFRα1, NRTN to GFRα2, ARTN to GFRα3 and PSPN to GFRα4. The signal is then delivered by RET, which cannot bind the GFLs on its own, but can bind the GFL-GFRα complex. Under normal cellular conditions, RET is only phosphorylated on the cell surface after ligand binding. At least the GDNF-GFRα1 complex is believed to recruit RET to lipid rafts, where downstream signalling occurs. In general, GFRαs consist of three cysteine-rich domains, but all GFRα4s except for chicken GFRα4 lack domain 1 (D1). We characterised the biochemical and cell biological properties of mouse PSPN receptor GFRα4 and showed that it has a significantly weaker capacity than GFRα1 to recruit RET to the lipid rafts. In spite of that, it can phosphorylate RET in the presence of PSPN and contribute to neuronal differentiation and survival. Therefore, the recruitment of RET to the lipid rafts does not seem to be crucial for the biological activity of all GFRα receptors. Secondly, we demonstrated that GFRα1 D1 stabilises the GDNF-GFRα1 complex and thus affects the phosphorylation of RET and contributes to the biological activity. This may be important in physiological conditions, where the concentration of the ligand or the soluble GFRα1 receptor is low. Our results also suggest a role for D1 in heparin binding and, consequently, in the biodistribution of released GFRα1 or in the formation of the GFL-GFRα-RET complex. We also presented the crystallographic structure of GDNF in the complex with GFRα1 domains 2 and 3. The structure differs from the previously published ARTN-GFRα3 structure in three significant ways. The biochemical data verify the structure and reveal residues participating in the interactions between GFRα1 and GDNF, and preliminarily also between GFRα1 and RET and heparin. Finally, we showed that, the precursor of the oncogenic MEN 2B (multiple endocrine neoplasia type 2) form of RET gets phosphorylated already during its synthesis in the endoplasmic reticulum (ER). We also demonstrated that it associates with Src homology 2 domain-containing protein (SHC) and growth factor receptor-bound protein (GRB2) in the ER, and has the capacity to activate several downstream signalling molecules.

Relation between Chandrasekhar's X-function and the eigenvalues of integral operators with difference kernels

Abstract is not available.

Causes and consequences of variation in nestling immune function

Defence against pathogens is a vital need of all living organisms that has led to the evolution of complex immune mechanisms. However, although immunocompetence the ability to resist pathogens and control infection has in recent decades become a focus for research in evolutionary ecology, the variation in immune function observed in natural populations is relatively little understood. This thesis examines sources of this variation (environmental, genetic and maternal effects) during the nestling stage and its fitness consequences in wild populations of passerines: the blue tit (Cyanistes caeruleus) and the collared flycatcher (Ficedula albicollis). A developing organism may face a dilemma as to whether to allocate limited resources to growth or to immune defences. The optimal level of investment in immunity is shaped inherently by specific requirements of the environment. If the probability of contracting infection is low, maintaining high growth rates even at the expense of immune function may be advantageous for nestlings, as body mass is usually a good predictor of post-fledging survival. In experiments with blue tits and haematophagous hen fleas (Ceratophyllus gallinae) using two methods, methionine supplementation (to manipulate nestlings resource allocation to cellular immune function) and food supplementation (to increase resource availability), I confirmed that there is a trade-off between growth and immunity and that the abundance of ectoparasites is an environmental factor affecting allocation of resources to immune function. A cross-fostering experiment also revealed that environmental heterogeneity in terms of abundance of ectoparasites may contribute to maintaining additive genetic variation in immunity and other traits. Animal model analysis of extensive data collected from the population of collared flycatchers on Gotland (Sweden) allowed examination of the narrow-sense heritability of PHA-response the most commonly used index of cellular immunocompetence in avian studies. PHA-response is not heritable in this population, but is subject to a non-heritable origin (presumably maternal) effect. However, experimental manipulation of yolk androgen levels indicates that the mechanism of the maternal effect in PHA-response is not in ovo deposition of androgens. The relationship between PHA-response and recruitment was studied for over 1300 collared flycatcher nestlings. Multivariate selection analysis shows that it is body mass, not PHA-response, that is under direct selection. PHA-response appears to be related to recruitment because of its positive relationship with body mass. These results imply that either PHA-response fails to capture the immune mechanisms that are relevant for defence against pathogens encountered by fledglings or that the selection pressure from parasites is not as strong as commonly assumed.

Use of protein A gene fusions for the analysis of structure-function relationship of the transactivator protein C of bacteriophage Mu

A sensitive dimerization assay for DNA binding proteins has been developed using gene fusion technology. For this purpose, we have engineered a gene fusion using protein A gene of Staphylococcus aureus and C gene, the late gene transactivator of bacteriophage Mu. The C gene was fused to the 3' end of the gene for protein A to generate an A- C fusion. The overexpressed fusion protein was purified in a single step using immunoglobulin affinity chromatography. Purified fusion protein exhibits DNA binding activity as demonstrated by electrophoretic mobility shift assays. When the fusion protein A-C was mixed with C and analyzed for DNA binding, in addition to C and A-C specific complexes, a single intermediate complex comprising of a heterodimer of C and A-C fusion proteins was observed. Further, the protein A moiety in the fusion protein A-C does not contribute to DNA binding as demonstrated by proteolytic cleavage and circular dichroism (CD) analysis. The assay has also been applied to analyze the DNA binding domain of C protein by generating fusions between protein A and N- and C-terminal deletion mutants of C. The results indicate a role for the region towards the carboxy terminal of the protein in DNA binding. The general applicability of this method is discussed.

Genetic studies of the PRP17 gene of Saccharomyces cerevisiae: a domain essential for function maps to a nonconserved region of the protein

The PRP17 gene product is required for the second step of pre-mRNA splicing reactions. The C-terminal half of this protein bears four repeat units with homology to the beta transducin repeat. Missense mutations in three temperature-sensitive prp17 mutants map to a region in the N-terminal half of the protein. We have generated, in vitro, 11 missense alleles at the beta transducin repeat units and find that only one affects function in vivo. A phenotypically silent missense allele at the fourth repeat unit enhances the slow-growing phenotype conferred by an allele at the third repeat, suggesting an interaction between these domains. Although many missense mutations in highly conserved amino acids lack phenotypic effects, deletion analysis suggests an essential role for these units. Only mutations in the N-terminal nonconserved domain of PRP17 are synthetically lethal in combination with mutations in PRP16 and PRP18, two other gene products required for the second splicing reaction. A mutually allele-specific interaction between Prp17 and snr7, with mutations in U5 snRNA, was observed. We therefore suggest that the functional region of Prp17p that interacts with Prp18p, Prp16p, and U5 snRNA is the N terminal region of the protein.

From actin monomers to bundles: The roles of twinfilin and α-actinin in Drosophila melanogaster development

The actin cytoskeleton is essential for a large variety of cell biological processes. Actin exists in either a monomeric or a filamentous form, and it is very important for many cellular functions that the local balance between these two actin populations is properly regulated. A large number of proteins participate in the regulation of actin dynamics in the cell, and twinfilin, one of the proteins examined in this thesis, belongs to this category. The second level of regulation involves proteins that crosslink or bundle actin filaments, thereby providing the cell with a certain shape. α-Actinin, the second protein studied, mainly acts as an actin crosslinking protein. Both proteins are conserved in organisms ranging from yeast to mammals. In this thesis, the roles of twinfilin and α-actinin in development were examined using Drosophila melanogaster as a model organism. Twinfilin is an actin monomer binding protein that is structurally related to cofilin. In vitro, twinfilin reduces actin polymerisation by sequestering actin monomers. The Drosophila twinfilin (twf) gene was identified and found to encode a protein functionally similar to yeast and mammalian twinfilins. A strong hypomorphic twf mutation was identified, and flies homozygous for this allele were viable and fertile. The adult twf mutant flies displayed reduced viability, a rough eye phenotype and severely malformed bristles. The shape of the adult bristle is determined by the actin bundles that are regularly spaced around the perimeter of the developing pupal bristles. Examination of the twf pupal bristles revealed an increased level of filamentous actin, which in turn resulted in splitting and displacement of the actin bundles. The bristle defect was rescued by twf overexpression in developing bristles. The Twinfilin protein was localised at sites of actin filament assembly, where it was required to limit actin polymerisation. A genetic interaction between twinfilin and twinstar (the gene encoding Cofilin) was detected, consistent with the model predicting that both proteins act to limit the amount of filamentous actin. α-Actinin has been implicated in several diverse cell biological processes. In Drosophila, the only function for α-actinin yet known is in the organisation of the muscle sarcomere. Muscle and non-muscle cells utilise different α-actinin isoforms, which in Drosophila are produced by alternative splicing of a single gene. In this work, novel α-actinin deletion alleles, including ActnΔ233, were generated, which specifically disrupted the transcript encoding the non-muscle α-actinin isoform. Nevertheless, ActnΔ233 homozygous mutant flies were viable and fertile with no obvious defects. By comparing α-actinin protein distribution in wild type and ActnΔ233 mutant animals, it could be concluded that non-muscle α-actinin is the only isoform expressed in young embryos, in the embryonic central nervous system and in various actin-rich structures of the ovarian germline cells. In the ActnΔ233 mutant, α-actinin was detected not only in muscle tissue, but also in embryonic epidermal cells and in certain follicle cell populations in the ovaries. The population of α-actinin protein present in non-muscle cells of the ActnΔ233 mutant is referred to as FC-α-actinin (Follicle Cell). The follicular epithelium in the Drosophila ovary is a well characterised model system for studies on patterning and morphogenesis. Therefore, α-actinin expression, regulation and function in this tissue were further analysed. Examination of the α-actinin localisation pattern revealed that the basal actin fibres of the main body follicle cells underwent an organised remodelling during the final stages of oogenesis. This involved the assembly of a transient adhesion site in the posterior of the cell, in which α-actinin and Enabled (Ena) accumulated. Follicle cells genetically manipulated to lack all α-actinin isoforms failed to remodel their cytoskeleton and translocate Ena to the posterior of the cell, while the actin fibres as such were not affected. Neither was epithelial morphogenesis disrupted. The reorganisation of the basal actin cytoskeleton was also disturbed following ectopic expression of Decapentaplegic (Dpp) or as a result of a heat shock. At late oogenesis, the main body follicle cells express both non-muscle α-actinin and FC-α-actinin, while the dorsal anterior follicle cells express only non-muscle α-actinin. The dorsal anterior cells are patterned by the Dpp and Epidermal growth factor receptor (EGFR) signalling pathways, and they will ultimately secrete the dorsal appendages of the egg. Experiments involving ectopic activation of EGFR and Dpp signalling showed that FC-α-actinin is negatively regulated by combined EGFR and Dpp signalling. Ubiquitous overexpression of the adult muscle-specific α-actinin isoform induced the formation of aberrant actin bundles in migrating follicle cells that did not normally express FC-α-actinin, provided that the EGFR signalling pathway was activated in the cells. Taken together, this work contributes new data to our knowledge of α-actinin function and regulation in Drosophila. The cytoskeletal remodelling shown to depend on α-actinin function provides the first evidence that α-actinin has a role in the organisation of the cytoskeleton in a non-muscle tissue. Furthermore, the cytoskeletal remodelling constitutes a previously undescribed morphogenetic event, which may provide us with a model system for in vivo studies on adhesion dynamics in Drosophila.