On statistical acceleration convergence of double sequences

In this article the notion of statistical acceleration convergence of double sequences in Pringsheim's sense has been introduced. We prove the decompostion theorems for  statistical acceleration convergence of double sequences and some theorems related to that concept have been established using the four dimensional matrix transformations. We provided some examples, where the results of acceleration convergence fails to hold for the statistical cases

Multi-Dimensional Sigma-Functions

In 1997 the present authors published a review (Ref. BEL97 in the present manuscript) that recapitulated and developed classical theory of Abelian functions realized in terms of multi-dimensional sigma-functions. This approach originated by K.Weierstrass and F.Klein was aimed to extend to higher genera Weierstrass theory of elliptic functions based on the Weierstrass $\sigma$-functions. Our development was motivated by the recent achievements of mathematical physics and theory of integrable systems that were based of the results of classical theory of multi-dimensional theta functions. Both theta and sigma-functions are integer and quasi-periodic functions, but worth to remark the fundamental difference between them. While theta-function are defined in the terms of the Riemann period matrix, the sigma-function can be constructed by coefficients of polynomial defining the curve. Note that the relation between periods and coefficients of polynomials defining the curve is transcendental. Since the publication of our 1997-review a lot of new results in this area appeared (see below the list of Recent References), that promoted us to submit this draft to ArXiv without waiting publication a well-prepared book. We complemented the review by the list of articles that were published after 1997 year to develop the theory of $\sigma$-functions presented here. Although the main body of this review is devoted to hyperelliptic functions the method can be extended to an arbitrary algebraic curve and new material that we added in the cases when the opposite is not stated does not suppose hyperellipticity of the curve considered.Comment: 267 pages, 4 figure

Sums, numbers and infinity:Collections in Bolzano's mathematics and philosophy

This dissertation is a collection of essays almost exclusively focussing on Bernard Bolzano's theory of collections, and its connections to his conception of mathematics. The first significant contribution of this work is that it develops a novel approach for comparing and appraising Bolzano’s collections against the alternatives offered by set theory and mereology. This approach consists in focusing not on the metaphysical comparison but on the role Bolzano's collections play in his mathematics vis à vis the role the sets of set theory (ZFC) play for modern-day mathematics. The second important contribution of this dissertation is a novel interpretation of the interaction between Bolzano's theory of concepts on the one hand, and his way of comparing the size of infinite collections of natural numbers on the other. This culminates in a completely new interpretation of Bolzano's famous Paradoxes of the Infinite as a work that is not an anticipation of Cantorian set theory, but an attempt at deploying philosophical insights on the infinite to develop a sound treatment of infinite series, both converging and diverging ones

Marine Viruses 2016

The research effort, publication rate and scientific community within the field of marine viruses have been growing rapidly over the past decade and viruses are now known to play key roles in microbial population dynamics, diversity and evolution as well as biogeochemical cycling. The compilation of papers included in the current Special Issue highlights the exploration of eukaryotic and prokaryotic viruses, from discovery to complex interplays between virus and host and virus–host interactions with ecologically relevant environmental variables. The discovery of novel viruses and new mechanisms underlying virus distribution and diversity exemplify the fascinating world of marine viruses. The oceans greatly shape Earth’s climate, hold 1.37 billion km3 of seawater, produce half of the oxygen in the atmosphere, and are integral to all known life. In a time where life in the oceans is under increasing threat (global warming, pollution, economic use) it is pressing to understand how viruses affect host population dynamics, biodiversity, biogeochemical cycling and ecosystem efficiency

LOV domain signaling: A study of LOV-LOV interactions

Die vorliegende Arbeit befasst sich mit der Signalentstehung und –weiterleitung in LOV (light-, oxygen- or voltage-sensitive) Domänen. Durch die Absorption von blauem oder nahem UV-Licht bilden diese Blaulichtphotorezeptoren ein Flavin-Cysteinyl-Addukt, welches den Signalzustand des Proteins darstellt. Durch die Adduktbildung werden dynamische und strukturelle Änderungen in der LOV Domäne initiiert wodurch die physiologische Funktion des Proteins reguliert wird. Im Rahmen dieser Arbeit wurde einerseits die Photochemie des Flavinmononukleotid (FMN) Chromophors anhand einer modifizierten LOV1 Domäne aus C. reinhardtii (CrLOV1) und des Fluoreszenzreporters iLOV spektroskopisch untersucht. Im Fall von CrLOV1 wurde der Elektronendonor Tyrosin in unmittelbarer Nachbarschaft zum FMN in das Proteingerüst eingebaut. In dieser Mutante lässt sich anstelle der natürlichen Adduktbildung ein Elektronentransfer vom eingebauten Tyrosin auf das FMN nachweisen, obwohl das reaktive Cystein vorhanden ist. Die Abschaltung des natürlichen Reaktionspfads in CrLOV1 durch eine einzige Punktmutation trägt auch zum weiteren Verständnis des Adduktbildungsmechanismus im Wildtyp-System bei. In der als Fluoreszenzreporter optimierten, künstlichen LOV Domäne iLOV wurden ebenfalls Elektronentransferreaktionen untersucht. In diesem Fall wurde jedoch Asparaginsäure als Protondonor in das Proteingerüst eingebaut. Als Elektronendonoren agieren die natürlich vorhandenen Aminosäuren Tryptophan und Tyrosin. Der Mechanismus des Elektronentransfers konnte mittels zeitaufgelöster Absorptionsspektroskopie aufgeklärt werden. Der zweite Teil der vorliegenden Arbeit befasst sich mit intermolekularen Wechselwirkungen zwischen LOV Domänen. Die Änderungen des oligomeren Zustands von LOV Domänen stehen in Zusammenhang mit ihrer biologischen Funktion. Zum besseren Verständnis dieser wurden die Systeme CrLOV1 und die LOV Domäne aus R. sphaeroides mittels Größenausschlusschromatographie und Förster Resonanzenergietransfer (FRET) hinsichtlich ihres Assoziations- und Dissoziationsverhaltens untersucht. Zu diesem Zwecke wurden die LOV Domänen mit den Fluoreszenzfarbstoffen Cy3 und Cy5 markiert. Im Fall der LOV Domäne aus R. sphaeroides konnten somit die Änderungen des oligomeren Zustands nach Aktivierung mit blauem Licht und im Dunkelzustand detailliert untersucht werden. Im Gegensatz dazu zeigte CrLOV1 keine intermolekularen Wechselwirkungen. Diese Ergebnisse sind wichtig für das weitere Verständnis der Funktion von LOV Domänen

λ-Rearrangements Characterization of Pringsheim Limit Points

Sufficient conditions are given to assure that a four-dimensional matrix A will have the property that any double sequence x with finite P-limit point has- a λ-rearrangement z such that each finite P-limit point of x is a P-limit point of Az

Structural parameters and dynamics of lyotropic liquid crystalline phases in hydrated monolinolein

To date, the stability of inverse bicontinuous cubic phases and the mechanism of lamellar to cubic transitions are poorly understood due to limited experimental resolution and reproducibility. Systematic experimental data is imperative for reasonable testing and verification of established theoretical models in this area. This thesis focuses on two aspects of lyotropic phase behaviour; the equilibrium behaviour of lyotropic liquid crystalline phases and the transitions between the equilibrium states. When monolinolein (ML) is mixed with water it forms a variety of inverse lyotropic phases, for example the lamellar, inverse bicontinuous phases (QII G and QII D) and the inverse hexagonal phase (HII) which makes this lipid an ideal candidate for study of these phases. The monolinolein equilibrium phase behaviour has been characterised as a function of pressure, temperature and hydration using SAXS (small angle X-ray scattering) and the data used to verify the existence of the pivotal surface in the QII G phase. Knowing the location of the pivotal surface allows one to calculate the total energy of these structures. The second part of this thesis discusses the kinetics of the lamellar to QII G transition in monolinolein under limited hydration conditions using the pressure jump time resolved X-ray diffraction technique. Lamellar to inverse bicontinuous cubic phase transitions are relevant to fundamental cellular processes such as membrane fusion and fission due to structural similarities of the mechanisms. The sequence of structural changes observed from kinetic experiments are discussed in relation to the Stalk Mechanism and the data analysed using a quantitative model

Lipid-specific IgM antibodies in multiple sclerosis and viral immunity

Multiple sclerosis (MS) is an inflammatory demyelinating disease of the central nervous system (CNS) and the leading cause of disability in young adults. Over the last 20 years, a plethora of drugs have been approved for the treatment of MS, many of which target the immune response to reduce CNS inflammation. Although effective, many of these therapies have been associated with an increased risk of developing progressive multifocal leukoencephalopathy (PML), a fatal infection of the CNS by the John Cunningham virus. As a result, these effective therapeutics are used with caution pending the establishment of reliable risk stratification tools. A recent association between intrathecal lipid-reactive IgM synthesis and reduced incidence of PML in natalizumab-treated MS prompted our investigation into the antiviral properties of lipid-reactive IgM antibodies. Using murine heterogenous CNS cultures, we investigated the antiviral properties of both human and mouse IgMs. Initial investigations focused on the sulfatide-reactive IgM O4, a major target of the IgM response in MS patients. Using microarray analysis, RT-qPCR, and fluorescence in situ hybridisation, alongside genetic knock-out cultures and a range of pharmacological inhibitors, it was deduced that O4 could stimulate microglia to upregulate interferon beta (IFN-β) in a cGAS-STING-dependent manner, triggering global interferon stimulated gene (ISG) expression in major cell-types of the CNS. This interferon (IFN) response limited the replication of two genetically unrelated viruses, with final experiments focused on developing an in vivo model to investigate these antiviral IgMs. The data presented in this thesis provide a plausible explanation for the association between intrathecal IgM synthesis and reduced incidence of PML in natalizumab-treated MS patients. This research will aid risk stratification of MS patients, allowing safe access to effective therapeutics. Further understanding of the mechanism of this antibody-mediated response could lead to the development of an antiviral therapy for use as a co-treatment in MS or as a broad-spectrum therapeutic for the treatment of viral encephalitis