Adelic convex geometry of numbers

Magdeburg, Univ., Fak. für Mathematik, Diss., 2014

Elements of algebraic geometry and the positive theory of partially commutative groups

The first main result of the paper is a criterion for a partially commutative group G to be a domain. It allows us to reduce the study of algebraic sets over G to the study of irreducible algebraic sets, and reduce the elementary theory of G (of a coordinate group over G) to the elementary theories of the direct factors of G (to the elementary theory of coordinate groups of irreducible algebraic sets). Then we establish normal forms for quantifier-free formulas over a non-abelian directly indecomposable partially commutative group H. Analogously to the case of free groups, we introduce the notion of a generalised equation and prove that the positive theory of H has quantifier elimination and that arbitrary first-order formulas lift from H to H * F, where F is a free group of finite rank. As a consequence, the positive theory of an arbitrary partially commutative group is decidable.

Horospheres in hyperbolic geometry

In this paper we investigate the role of horospheres in Integral Geometry and Differential Geometry. In particular we study envelopes of families of horocycles by means of “support maps”. We define invariant “linear combinations” of support maps or curves. Finally we obtain Gauss-Bonnet type formulas and Chern-Lashof type inequalities.

Malaria vaccine development using synthetic peptides as a technical platform.

The review covers the development of synthetic peptides as vaccine candidates for Plasmodium falciparum- and Plasmodium vivax-induced malaria from its beginning up to date and the concomitant progress of solid phase peptide synthesis (SPPS) that enables the production of long peptides in a routine fashion. The review also stresses the development of other complementary tools and actions in order to achieve the long sought goal of an efficacious malaria vaccine.

Continuity of set-valued maps revisited in the light of tame geometry

Continuity of set-valued maps is hereby revisited: after recalling some basic concepts of variational analysis and a short description of the State-of-the-Art, we obtain as by-product two Sard type results concerning local minima of scalar and vector valued functions. Our main result though, is inscribed in the framework of tame geometry, stating that a closed-valued semialgebraic set-valued map is almost everywhere continuous (in both topological and measure-theoretic sense). The result –depending on stratification techniques– holds true in a more general setting of o-minimal (or tame) set-valued maps. Some applications are briefly discussed at the end.

Geometry and physics of knots

KNOTS are usually categorized in terms of topological properties that are invariant under changes in a knot's spatial configuration(1-4). Here we approach knot identification from a different angle, by considering the properties of particular geometrical forms which we define as 'ideal'. For a knot with a given topology and assembled from a tube of uniform diameter, the ideal form is the geometrical configuration having the highest ratio of volume to surface area. Practically, this is equivalent to determining the shortest piece of tube that can be closed to form the knot. Because the notion of an ideal form is independent of absolute spatial scale, the length-to-diameter ratio of a tube providing an ideal representation is constant, irrespective of the tube's actual dimensions. We report the results of computer simulations which show that these ideal representations of knots have surprisingly simple geometrical properties. In particular, there is a simple linear relationship between the length-to-diameter ratio and the crossing number-the number of intersections in a two-dimensional projection of the knot averaged over all directions. We have also found that the average shape of knotted polymeric chains in thermal equilibrium is closely related to the ideal representation of the corresponding knot type. Our observations provide a link between ideal geometrical objects and the behaviour of seemingly disordered systems, and allow the prediction of properties of knotted polymers such as their electrophoretic mobility(5).

Climate Change and Health: A platform for action

This paper provides an introduction to the links between climate change and health and aims to inform policy-makers, politicians and the public of the benefits for health from reducing greenhouse gas (GHG)* emissions from food production, transport, energy, and waste. It also highlights the importance of action by the health sector.It presents a platform for action which demonstrates that creating healthy sustainable places and communities can go hand in hand with reducing the negative impacts of climate change.

MR spectroscopy of the human brain with enhanced signal intensity at ultrashort echo times on a clinical platform at 3T and 7T.

Recently, the spin-echo full-intensity acquired localized (SPECIAL) spectroscopy technique was proposed to unite the advantages of short TEs on the order of milliseconds (ms) with full sensitivity and applied to in vivo rat brain. In the present study, SPECIAL was adapted and optimized for use on a clinical platform at 3T and 7T by combining interleaved water suppression (WS) and outer volume saturation (OVS), optimized sequence timing, and improved shimming using FASTMAP. High-quality single voxel spectra of human brain were acquired at TEs below or equal to 6 ms on a clinical 3T and 7T system for six volunteers. Narrow linewidths (6.6 +/- 0.6 Hz at 3T and 12.1 +/- 1.0 Hz at 7T for water) and the high signal-to-noise ratio (SNR) of the artifact-free spectra enabled the quantification of a neurochemical profile consisting of 18 metabolites with Cramér-Rao lower bounds (CRLBs) below 20% at both field strengths. The enhanced sensitivity and increased spectral resolution at 7T compared to 3T allowed a two-fold reduction in scan time, an increased precision of quantification for 12 metabolites, and the additional quantification of lactate with CRLB below 20%. Improved sensitivity at 7T was also demonstrated by a 1.7-fold increase in average SNR (= peak height/root mean square [RMS]-of-noise) per unit-time.

Lassa virus entry in antigen presenting cells and evaluation of a novel nanoparticle vaccine platform against arena viruses

Arenaviruses are a large and diverse family of viruses that merit significant attention as causative agents of severe hemorrhagic fevers in humans. Lassa virus (LASV) in Africa and the South American hemorrhagic fever viruses Junin (JUNV), Machupo (MACV), and Guanarito (GTOV) have emerged as important human pathogens and represent serious public health problems in their respective endemic areas. A hallmark of fatal arenaviruses hemorrhagic fevers is a marked immunosuppression of the infected patients. Antigen presenting cells (APCs) such as macrophages and in particular dendritic cells (DCs) are early and preferred targets of arenaviruses infection. Instead of being recognized and presented as foreign antigens by DCs, arenaviruses subvert the normal mechanisms of pathogen recognition, invade DCs and establish a productive infection. Viral replication perturbs the DCs' ability to present antigens and to activate T and B cells, contributing to the marked virus-induced immunosuppression observed in fatal disease. Considering their crucial role in the development of an anti-viral immune response, the mechanisms by which arenaviruses, and in particular LASV, invade DCs are of particular interest. The C-type lectin DC-specific Intercellular adhesion molecule-3-grabbing nonintegrin (DC-SIGN) was recently identified as a potential entry receptor for LASV. The first project of my thesis focused therefore on the investigation of the role of DC-SIGN in LASV entry into primary human DCs. My data revealed that DC-SIGN serves as an attachment factor for LASV on human DCs and can facilitate capture of free virus and subsequent cell entry. However, in contrast to other emerging viruses, of the phlebovirus family, I found that DC-SIGN does likely not function as an authentic entry receptor for LASV. Moreover, I was able to show that LASV enters DCs via an unusually slow pathway that depends on actin, but is independent of clathrin and dynamin. Considering the lack of effective treatments and the limited public health infrastructure in endemic regions, the development of protective vaccines against arenaviruses is an urgent need. To address this issue, the second project of my thesis aimed at the development of a novel recombinant arenavirus vaccine based on a nanoparticle (NPs) platform and its evaluation in a small animal model. During the first phase of the project I designed, produced, and characterized suitable vaccine antigens. In the second phase of the project, I generated antigen-conjugated NPs, developed vaccine formulations, and tested the NPs for their ability to elicit anti-viral T cell responses as well as anti-viral antibodies. I demonstrated that the NPs platform is able to activate both cellular and humoral branches of the adaptive anti-viral immunity, providing proof-of-principle. In sum, my first project will allow, in a long term perspective, a better understanding of the viral pathogenesis and contribute to the development of novel antiviral strategies. The second project will expectidly offer a new treatment option against arenaviruses.

EORTC Radiation Oncology Group quality assurance platform: establishment of a digital central review facility.

OBJECTIVE: Quality assurance (QA) in clinical trials is essential to ensure treatment is safely and effectively delivered. As QA requirements have increased in complexity in parallel with evolution of radiation therapy (RT) delivery, a need to facilitate digital data exchange emerged. Our objective is to present the platform developed for the integration and standardization of QART activities across all EORTC trials involving RT. METHODS: The following essential requirements were identified: secure and easy access without on-site software installation; integration within the existing EORTC clinical remote data capture system; and the ability to both customize the platform to specific studies and adapt to future needs. After retrospective testing within several clinical trials, the platform was introduced in phases to participating sites and QART study reviewers. RESULTS: The resulting QA platform, integrating RT analysis software installed at EORTC Headquarters, permits timely, secure, and fully digital central DICOM-RT based data review. Participating sites submit data through a standard secure upload webpage. Supplemental information is submitted in parallel through web-based forms. An internal quality check by the QART office verifies data consistency, formatting, and anonymization. QART reviewers have remote access through a terminal server. Reviewers evaluate submissions for protocol compliance through an online evaluation matrix. Comments are collected by the coordinating centre and institutions are informed of the results. CONCLUSIONS: This web-based central review platform facilitates rapid, extensive, and prospective QART review. This reduces the risk that trial outcomes are compromised through inadequate radiotherapy and facilitates correlation of results with clinical outcomes.

Wing geometry as a tool for studying the Lutzomyia longipalpis (Diptera: Psychodidae) complex

Toro Toro (T) and Yungas (Y) have been described as genetically well differentiated populations of the Lutzomyia longipalpis (Lutz & Neiva, 1912) complex in Bolivia. Here we use geometric morphometrics to compare samples from these populations and new populations (Bolivia and Nicaragua), representing distant geographical origins, qualitative morphological variation ("one-spot" or "two-spots" phenotypes), ecologically distinct traits (peridomestic and silvatic populations), and possibly different epidemiological roles (transmitting or nor transmitting Leishmania chagasi). The Nicaragua (N) (Somotillo) sample was "one-spot" phenotype and a possible peridomestic vector. The Bolivian sample of the Y was also "one-spot" phenotype and a demonstrated peridomestic vector of visceral leishmaniasis (VL). The three remaining samples were silvatic, "two-spots" phenotypes. Two of them (Uyuni and T) were collected in the highlands of Bolivian where VL never has been reported. The last one (Robore, R) came from the lowlands of Bolivia, where human cases of VL are sporadically reported. The decomposition of metric variation into size and shape by geometric morphometric techniques suggests the existence of two groups (N/Y/R, and U/T). Several arguments indicate that such subdivision of Lu. longipalpis could correspond to different evolutionary units.

Geometry and physics of catenanes applied to the study of DNA replication.

The concept of ideal geometric configurations was recently applied to the classification and characterization of various knots. Different knots in their ideal form (i.e., the one requiring the shortest length of a constant-diameter tube to form a given knot) were shown to have an overall compactness proportional to the time-averaged compactness of thermally agitated knotted polymers forming corresponding knots. This was useful for predicting the relative speed of electrophoretic migration of different DNA knots. Here we characterize the ideal geometric configurations of catenanes (called links by mathematicians), i.e., closed curves in space that are topologically linked to each other. We demonstrate that the ideal configurations of different catenanes show interrelations very similar to those observed in the ideal configurations of knots. By analyzing literature data on electrophoretic separations of the torus-type of DNA catenanes with increasing complexity, we observed that their electrophoretic migration is roughly proportional to the overall compactness of ideal representations of the corresponding catenanes. This correlation does not apply, however, to electrophoretic migration of certain replication intermediates, believed up to now to represent the simplest torus-type catenanes. We propose, therefore, that freshly replicated circular DNA molecules, in addition to forming regular catenanes, may also form hemicatenanes.