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Measurability of open orbits in flag supermanifolds
Christopher Graw
Mathematics , 2014,
Abstract: Let $G_\mathbb{R}$ be a Lie group and $G$ its complexification. An open $G_\mathbb{R}$-orbit in a $G$-flag manifold is measurable whenever it carries a $G_\mathbb{R}$-invariant volume element. In this paper the notion of measurability is generalized to the supersymmetric setting and a classification of measurable open orbits in flag supermanifolds is given.
On Flag Domains in the Supersymmetric Setting
Christopher Graw
Mathematics , 2015,
Abstract: Flag domains are open orbits of real forms $G_\mathbb{R}$ of complex reductive Lie supergroups $G$ in $G$-flag supermanifolds $Z = G/P$. This thesis discusses three topics from the theory of these flag domains: 1. Measurability(i.e. existence of $G_\mathbb{R}$-invariant Berezinian densities) 2. Global holomorphic superfunctions 3. Cycle spaces and the Double Fibration Transform A revision of the respective classical results is included in the second chapter. This thesis provides a classification of all measurable flag domains and of the global holomorphic functions on all flag domains. Moreover, the last chapter provides a possible link between the representation theory of real reductive (super) Lie groups and the Bott-Borel-Weyl Theory for complex Lie superalgebras.
The Pathologic Effect of a Novel Neomorphic Fgf9Y162C Allele Is Restricted to Decreased Vision and Retarded Lens Growth
Oliver Puk, Gabriele M?ller, Arie Geerlof, Kathrin Krowiorz, Nafees Ahmad, Sibylle Wagner, Jerzy Adamski, Martin Hrabé de Angelis, Jochen Graw
PLOS ONE , 2011, DOI: 10.1371/journal.pone.0023678
Abstract: Fibroblast growth factor (Fgf) signalling plays a crucial role in many developmental processes. Among the Fgf pathway ligands, Fgf9 (UniProt: P54130) has been demonstrated to participate in maturation of various organs and tissues including skeleton, testes, lung, heart, and eye. Here we establish a novel Fgf9 allele, discovered in a dominant N-ethyl-N-nitrosourea (ENU) screen for eye-size abnormalities using the optical low coherence interferometry technique. The underlying mouse mutant line Aca12 was originally identified because of its significantly reduced lens thickness. Linkage studies located Aca12 to chromosome 14 within a 3.6 Mb spanning interval containing the positional candidate genes Fgf9 (MGI: 104723), Gja3 (MGI: 95714), and Ift88 (MGI: 98715). While no sequence differences were found in Gja3 and Ift88, we identified an A→G missense mutation at cDNA position 770 of the Fgf9 gene leading to an Y162C amino acid exchange. In contrast to previously described Fgf9 mutants, Fgf9Y162C carriers were fully viable and did not reveal reduced body-size, male-to-female sexual reversal or skeletal malformations. The histological analysis of the retina as well as its basic functional characterization by electroretinography (ERG) did not show any abnormality. However, the analysis of head-tracking response of the Fgf9Y162C mutants in a virtual drum indicated a gene-dosage dependent vision loss of almost 50%. The smaller lenses in Fgf9Y162C suggested a role of Fgf9 during lens development. Histological investigations showed that lens growth retardation starts during embryogenesis and continues after birth. Young Fgf9Y162C lenses remained transparent but developed age-related cataracts. Taken together, Fgf9Y162C is a novel neomorphic allele that initiates microphakia and reduced vision without effects on organs and tissues outside the eye. Our data point to a role of Fgf9 signalling in primary and secondary lens fiber cell growth. The results underline the importance of allelic series to fully understand multiple functions of a gene.
Relative roles of the different Pax6 domains for pancreatic alpha cell development
Petra Dames, Ramona Puff, Michaela Weise, Klaus G Parhofer, Burkhard G?ke, Magdalena G?tz, Jochen Graw, Jack Favor, Andreas Lechner
BMC Developmental Biology , 2010, DOI: 10.1186/1471-213x-10-39
Abstract: The Pax6Aey18 mutant mouse line, in which the paired domain is inactivated, showed a phenotype similar to that of Pax6-/- knockout mice with a near complete absence of glucagon-positive α-cells (0-4 cells/section; ≤1% of wt), reduced β-cell area (74% of wt) and disorganized islets. The proportion of ghrelin-positive ε-cells was expanded. In Pax6Sey-Neu mutants, which lack the transactivation domain, α-and β-cells where reduced to 25 and 40% of wt, respectively. We also studied two mouse lines with mutations in the homeodomain, Pax64Neu and Pax6132-14Neu. Neighboring amino acids are affected in the two lines and both point mutations abolish DNA binding of the classical P3 homeodomain target sequence. The pancreatic phenotype of the two mutants however was divergent. While Pax64Neu homozygotes showed a reduction of α- and β-cells to 59 and 61%, respectively, pancreatic endocrine development was unaltered in the Pax6132-14Neu mutant strain.We show that inactivation of the Pax6 paired domain leads to a more severe phenotype with regards to the differentiation of pancreatic α-cells than the loss of the transactivation domain. The analysis of two different homeodomain mutants suggests that the binding of Pax6 to P3 homeodomain consensus sequences is not required for α-cell development. It rather seems that the homeodomain has a modulating role in Pax6 function, possibly by facilitating a PH0-like binding confirmation on paired domain target genes like proglucagon. This function is differentially affected by the two homeodomain mutations analyzed in this study.The development of the endocrine pancreas is governed by a cascade of transcription factors [1,2]. The first regulators are Pdx1 and Ptf1a, which initiate pancreatic bud formation from the foregut and ngn3, which separates the endocrine progenitor cells from the exocrine part of the organ. Subsequently, differentiation of the specialized mature endocrine islet cells is dependent upon specific sets of transcription fa
Influence of the Fibroblastic Reticular Network on Cell-Cell Interactions in Lymphoid Organs
Frederik Graw ,Roland R. Regoes
PLOS Computational Biology , 2012, DOI: 10.1371/journal.pcbi.1002436
Abstract: Secondary lymphoid organs (SLO), such as lymph nodes and the spleen, display a complex micro-architecture. In the T cell zone the micro-architecture is provided by a network of fibroblastic reticular cells (FRC) and their filaments. The FRC network is thought to enhance the interaction between immune cells and their cognate antigen. However, the effect of the FRC network on cell interaction cannot be quantified to date because of limitations in immunological methodology. We use computational models to study the influence of different densities of FRC networks on the probability that two cells meet. We developed a 3D cellular automaton model to simulate cell movements and interactions along the FRC network inside lymphatic tissue. We show that the FRC network density has only a small effect on the probability of a cell to come into contact with a static or motile target. However, damage caused by a disruption of the FRC network is greatest at FRC densities corresponding to densities observed in the spleen of na?ve mice. Our analysis suggests that the FRC network as a guiding structure for moving T cells has only a minor effect on the probability to find a corresponding dendritic cell. We propose alternative hypotheses by which the FRC network might influence the functionality of immune responses in a more significant way.
Investigating CTL Mediated Killing with a 3D Cellular Automaton
Frederik Graw ,Roland R. Regoes
PLOS Computational Biology , 2009, DOI: 10.1371/journal.pcbi.1000466
Abstract: Cytotoxic T lymphocytes (CTLs) are important immune effectors against intra-cellular pathogens. These cells search for infected cells and kill them. Recently developed experimental methods in combination with mathematical models allow for the quantification of the efficacy of CTL killing in vivo and, hence, for the estimation of parameters that characterize the effect of CTL killing on the target cell populations. It is not known how these population-level parameters relate to single-cell properties. To address this question, we developed a three-dimensional cellular automaton model of the region of the spleen where CTL killing takes place. The cellular automaton model describes the movement of different cell populations and their interactions. Cell movement patterns in our cellular automaton model agree with observations from two-photon microscopy. We find that, despite the strong spatial nature of the kinetics in our cellular automaton model, the killing of target cells by CTLs can be described by a term which is linear in the target cell frequency and saturates with respect to the CTL levels. Further, we find that the parameters describing CTL killing on the population level are most strongly impacted by the time a CTL needs to kill a target cell. This suggests that the killing of target cells, rather than their localization, is the limiting step in CTL killing dynamics given reasonable frequencies of CTL. Our analysis identifies additional experimental directions which are of particular importance to interpret estimates of killing rates and could advance our quantitative understanding of CTL killing.
Leigh's Disease: The Acute Clinical Course of a Two-Year-Old Child with Subacute Necrotizing Encephalomyelopathy
Bettina Zinka,Andreas Buettner,Matthias Graw
Case Reports in Medicine , 2010, DOI: 10.1155/2010/986302
Abstract: We report the untypical clinical course of a previously healthy two-year-old girl, who died suddenly and unexpectedly after an episode of vomiting. At forensic autopsy no other pathological findings could be diagnosed than multiple reddish, sunken areas in brain stem, mesencephalon, and pons. Histologically they presented as areas of spongiosis of the neuropil with prominent endothelial hyperplasia and vascular proliferation whereas nerve cells were well preserved. On the basis of the characteristic neuropathological findings in combination with the age of the child, we had to take into consideration that the child might have died from subacute necrotizing encephalomyelopathy (Leigh's Disease) despite the untypical, fulminant clinical course.
Theoretical analysis of the evolution of immune memory
Frederik Graw, Carsten Magnus, Roland R Regoes
BMC Evolutionary Biology , 2010, DOI: 10.1186/1471-2148-10-380
Abstract: In this study, we examine how memory traits evolve as a response to different pathogen environments using an individual-based model. We find that even without a cost related to the maintenance of a memory pool, the positive effect of bigger memory pool sizes saturates. The optimal diversity of a limited memory pool is determined by the probability of re-infection, rather than by the prevalence of a pathogen in the environment, or the frequency of exposure.Relating immune memory traits to the pathogen environment of the hosts, our population biological framework sheds light on the evolutionary determinants of immune memory.During their whole life individuals are exposed to many different pathogens, which can cause diseases and sometimes death. Each new pathogen poses a new challenge for the immune system and its different agents. However, vertebrates have evolved immunological memory - a strategy based on remembering previously encountered pathogens that protects against re-infection. This phenomenon was already recognized by the ancient Greeks: The historian Thucydides noted during an outbreak of plague in Athens that those who recovered from the disease were never attacked twice [1]. The establishment of memory is perhaps "the most important consequence of the adaptive immune system" [2]. Immunological memory is divided into cell and antibody mediated branches. The main players of these branches are T and B cells, respectively. Memory cell populations are maintained for many years sometimes leading to life-long immunity [3-5]. Vaccination stimulates the production of immune cells and is one of the most important interventions of disease management and public health.Many studies have investigated the molecular and mechanistic aspects of how immunological memory is generated and maintained [6-11]. However, beyond the proximal explanations of this phenomenon there is an increasing interest in the evolutionary conditions that favor immunological memory (broadly underst
Correction: Theoretical analysis of the evolution of immune memory
Frederik Graw, Carsten Magnus, Roland R Regoes
BMC Evolutionary Biology , 2011, DOI: 10.1186/1471-2148-11-54
Abstract: We regret any inconvenience that the incorrect Figure in the original article might have caused.
Numerická simulace v biomechanice – forenzní p íklad Numerical simulation in biomechanics – a forensic example
Ji?í Adamec,Matthias Graw,Norbert Praxl
Acta Universitatis Palackianae Olomucensis : Gymnica , 2006,
Abstract: P íspěvek prezentuje vybrany p íklad forenzní aplikace biomechanickych metod zahrnujících numerickou simulaci s pou itím model lidského těla. Postup biomechanické rekonstrukce je demonstrován na konkrétním p ípadu smrtelného pádu z vy ky. Základem biomechanické rekonstrukce jsou stopy na místě nálezu těla spolu se zraněními zji těnymi p i provedné soudní pitvě. Kone nym cílem biomechanické analyzy je jednozna né a bezesporné p i azení ve kerych zji těnych stop a objasnění celé události z mechanického hlediska. Některá zranění zji těná v tomto konkrétním p ípadě byla pro pád z vy ky typická, ást nálezu ale nebylo mo no prima vista za adit. Policejní vy et ování na místě nálezu také p ineslo některá fakta, která nebylo mo no uspokojivě vysvětlit. Numerická simulace s pou itím model lidského těla p inesla údaje umo ňující vysvětlení mnoha do té doby nejasnych aspekt p ípadu. Tato metoda poskytuje objektivní a kvantitativní informace umo nující daleko p esněj í analyzu studovaného jevu nebo události – kinematické i dynamické parametry lidského těla a jeho interakce s okolními strukturami. Dokonce je mo né zji ovat i síly p sobící uvnit organismu a díky tomu p esněji predikovat trauma. V echny d le ité neznámé parametry (po áte ní podmínky numerické simulace, jako pozice těla a jeho jednotlivych segment , jeho orientace v prostoru, po áte ní rychlost atp.) lze parametrizovat a obsáhnout tak v echny mo né konstelace. Dal í velmi d le itou p edností této metody je propracovaná a efektivní vizualizace vysledk vypo t , která usnadňujě pochopení studovanych událostí a jev i bez d kladnych biomechanickych znalostí. Největ í omezení pou ití model lidského těla p edstavuje v sou asné době nemo nost simulovat aktivní pohyby; modely svych chováním odpovídají zcela pasivnímu lidskému tělu. The paper presents an example of a forensic application of biomechanical methods including numerical simulation with human body models. By means of a case study of an unwitnessed lethal fall the course of the biomechanical forensic reconstruction is demonstrated. The traces available at the place of finding and the injuries of the victim are the facts that the analysis is based on. The ultimate expected result of the biomechanical analysis is the assignment of all available traces and the explanation of the event. The injuries observed in the described case were partly typical fall injuries, but there were also some injuries that could not be prima vista assigned. The police investigation at the place of finding also brought to light some facts that could not be satisfactoril
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