24 research outputs found
Parameterizations of sub-attractors in hyperbolic balance laws
This article investigates the properties of the global attractor of hyperbolic balance laws on the circle, given by : u_t+f(u)_x=g(u). The new tool of sub-attractors is introduced. They contain all solutions on the global attractor up to a given number of zeros. The article proves finite dimensionality of all sub-attractors, provides a full parameterization of all sub-attractors and derives a system of ODEs for the embedding parameters that describes the full PDE dynamics on the sub-attractor
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Slow motion of quasi-stationary multi-pulse solutions by semistrong interaction in reaction-diffusion systems
In this paper, we study a class of singularly perturbed
reaction-diffusion systems, which exhibit under certain conditions slowly
varying multi-pulse solutions. This class contains among others the
Gray-Scott and several versions of the Gierer-Meinhardt model. We first use a
classical singular perturbation approach for the stationary problem and
determine in this way a manifold of quasi-stationary -pulse solutions.
Then, in the context of the time-dependent problem, we derive an equation for
the leading order approximation of the slow motion along this manifold. We
apply this technique to study 1-pulse and 2-pulse solutions for classical and
modified Gierer-Meinhardt system. In particular, we are able to treat
different types of boundary conditions, calculate folds of the slow manifold,
leading to slow-fast motion, and to identify symmetry breaking singularities
in the manifold of 2-pulse solutions
Slow motion of quasi-stationary multi-pulse solutions by semistrong interaction in reaction-diffusion systems
In this paper, we study a class of singularly perturbed reaction-diffusion systems, which exhibit under certain conditions slowly varying multi-pulse solutions. This class contains among others the Gray-Scott and several versions of the Gierer-Meinhardt model. We first use a classical singular perturbation approach for the stationary problem and determine in this way a manifold of quasi-stationary -pulse solutions. Then, in the context of the time-dependent problem, we derive an equation for the leading order approximation of the slow motion along this manifold. We apply this technique to study 1-pulse and 2-pulse solutions for classical and modified Gierer-Meinhardt system. In particular, we are able to treat different types of boundary conditions, calculate folds of the slow manifold, leading to slow-fast motion, and to identify symmetry breaking singularities in the manifold of 2-pulse solutions
Gender identity and expression in focus: The report of the United Nations Independent Expert on sexual orientation and gender identity, by Victor Madrigal-Borloz.: Published by the United Nations on 12/07/2018 United Nations official document number: A/73/152
In his recent report, the United Nations Independent Expert on protection against violence and discrimination based on sexual orientation and gender identity, Victor Madrigal-Borloz, examines the “process of abandoning the classification of certain forms of gender as a pathology” – “depathologization”—and elaborates on the “full scope of the duty of the State to respect and promote respect of gender recognition as a component of identity” (p. 2). The report also discusses active measures to respect gender identity and concludes with a list of recommendations. While other United Nations special procedures and agencies have addressed and condemned violence and discrimination on the grounds of gender identity and expression, this report provides a deeper analysis on its root causes. It is the first special procedures report that exclusively addresses human rights with regard to gender identity and expression, and must be considered a mile-stone in the development and enunciation of international human rights law in this regard
Genome-Wide Screen for Mycobacterium tuberculosis Genes That Regulate Host Immunity
In spite of its highly immunogenic properties, Mycobacterium tuberculosis (Mtb) establishes persistent infection in otherwise healthy individuals, making it one of the most widespread and deadly human pathogens. Mtb's prolonged survival may reflect production of microbial factors that prevent even more vigorous immunity (quantitative effect) or that divert the immune response to a non-sterilizing mode (qualitative effect). Disruption of Mtb genes has produced a list of several dozen candidate immunomodulatory factors. Here we used robotic fluorescence microscopy to screen 10,100 loss-of-function transposon mutants of Mtb for their impact on the expression of promoter-reporter constructs for 12 host immune response genes in a mouse macrophage cell line. The screen identified 364 candidate immunoregulatory genes. To illustrate the utility of the candidate list, we confirmed the impact of 35 Mtb mutant strains on expression of endogenous immune response genes in primary macrophages. Detailed analysis focused on a strain of Mtb in which a transposon disrupts Rv0431, a gene encoding a conserved protein of unknown function. This mutant elicited much more macrophage TNFα, IL-12p40 and IL-6 in vitro than wild type Mtb, and was attenuated in the mouse. The mutant list provides a platform for exploring the immunobiology of tuberculosis, for example, by combining immunoregulatory mutations in a candidate vaccine strain
Massive X-ray screening reveals two allosteric drug binding sites of SARS-CoV-2 main protease
The coronavirus disease (COVID-19) caused by SARS-CoV-2 is creating tremendous health problems and economical challenges for mankind. To date, no effective drug is available to directly treat the disease and prevent virus spreading. In a search for a drug against COVID-19, we have performed a massive X-ray crystallographic screen of repurposing drug libraries containing 5953 individual compounds against the SARS-CoV-2 main protease (Mpro), which is a potent drug target as it is essential for the virus replication. In contrast to commonly applied X-ray fragment screening experiments with molecules of low complexity, our screen tested already approved drugs and drugs in clinical trials. From the three-dimensional protein structures, we identified 37 compounds binding to Mpro. In subsequent cell-based viral reduction assays, one peptidomimetic and five non-peptidic compounds showed antiviral activity at non-toxic concentrations. Interestingly, two compounds bind outside the active site to the native dimer interface in close proximity to the S1 binding pocket. Another compound binds in a cleft between the catalytic and dimerization domain of Mpro. Neither binding site is related to the enzymatic active site and both represent attractive targets for drug development against SARS-CoV-2. This X-ray screening approach thus has the potential to help deliver an approved drug on an accelerated time-scale for this and future pandemics
X-ray screening identifies active site and allosteric inhibitors of SARS-CoV-2 main protease
The coronavirus disease (COVID-19) caused by SARS-CoV-2 is creating tremendous human suffering. To date, no effective drug is available to directly treat the disease. In a search for a drug against COVID-19, we have performed a high-throughput X-ray crystallographic screen of two repurposing drug libraries against the SARS-CoV-2 main protease (M^(pro)), which is essential for viral replication. In contrast to commonly applied X-ray fragment screening experiments with molecules of low complexity, our screen tested already approved drugs and drugs in clinical trials. From the three-dimensional protein structures, we identified 37 compounds that bind to M^(pro). In subsequent cell-based viral reduction assays, one peptidomimetic and six non-peptidic compounds showed antiviral activity at non-toxic concentrations. We identified two allosteric binding sites representing attractive targets for drug development against SARS-CoV-2
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Cascades of heteroclinic connections in hyperbolic balance laws
The Dissertation investigates the relation between global attractors of hyperbolic balance laws and viscous balance laws on the circle. Hence it is thematically located at the crossroads of hyperbolic and parabolic partial differential equations with one-dimensional space variable and periodic boundary conditions given by: (H): u_t + [f(u)]_x = g(u) and (P): u_t + [f(u)]_x = e u_xx + g(u). The results of the work can be split into two areas: The description of the global attractor of equation (H) and the persistence of solutions on the global attractor of (P) when e vanishes. The key idea of the work is the introduction of finite dimensional sub-attractors. This tool allows to overcome several difficulties in the description of the global attractor of equation (H) and closes one of the last remaining gaps in its complete description: Theorem 2.6.1 yields a complete parameterization of all finite dimensional sub-attractors in the hyperbolic setting. The second main result corrects a result on the persistence of heteroclinic connections by Fan and Hale [FH95] for the case e-->0 (Connection Lemma 3.2.8). The Cascading Theorem 3.2.9 then yields convergence of heteroclinic connections to a cascade of heteroclinics in case of non-persistence. In addition to the introduction and conclusions, the work consists of three chapters: Chapter 2 gives a self contained overview about what is known for global attractors for both equations and concludes with the result on the parameterizations of the sub-attractors of the hyperbolic equation (H). Chapter 3 is exclusively concerned with the question of persistence. The two main results on persistence (the Connection Lemma and the Cascading Theorem) are stated and proved. Chapter 4 concludes with geometrical investigations of persisting and non-persisting heteroclinic connections for e-->0 for some low dimensional sub-attractor cases. Not all results are rigorous in this chapter
Parametrizations of sub-attractors in hyperbolic balance laws
This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.We investigate the properties of the global attractor of hyperbolic balance laws on the circle, given by ut + f(u)x = g(u). The new tool of sub-attractors is introduced. They contain all solutions on the global attractor up to a given number of zeros. The paper proves finite dimensionality of all sub-attractors, provides a full parametrization of all sub-attractors and derives a system of ordinary differential equations for the embedding parameters that describe the full partial differential equation dynamics on the sub-attractor.Peer Reviewe
Kaskaden heterokliner Verbindungen in hyperbolischen Gleichgewichtssätzen
The Dissertation investigates the relation between global attractors of
hyperbolic balance laws and viscous balance laws on the circle. Hence it is
thematically located at the crossroads of hyperbolic and parabolic partial
differential equations with one-dimensional space variable and periodic
boundary conditions given by: u_t + [f(u)]_x = g(u) (H) and u_t + [f(u)]_x =
eu_xx + g(u). (P) The results of the work can be split into two areas: The
description of the global attractor of equation (H) and the persistence of
solutions on the global attractor of (P) when e vanishes. The key idea of the
work is the introduction of finite dimensional sub-attractors. This tool
allows to overcome several difficulties in the description of the global
attractor of equation (H) and closes one of the last remaining gaps in its
complete description: Theorem 2.6.1 yields a complete parameterization of all
finite dimensional sub-attractors in the hyperbolic setting. The second main
result corrects a result on the persistence of heteroclinic connections by Fan
and Hale [FH95] for the case e-->0 (Connection Lemma 3.2.8). The Cascading
Theorem 3.2.9 then yields convergence of heteroclinic connections to a cascade
of heteroclinics in case of non-persistence. In addition to the introduction
and conclusions, the work consists of three chapters: Chapter 2 gives a self
contained overview about what is known for global attractors for both
equations and concludes with the result on the parameterizations of the sub-
attractors of the hyperbolic equation (H). Chapter 3 is exclusively concerned
with the question of persistence. The two main results on persistence (the
Connection Lemma and the Cascading Theorem) are stated and proved. Chapter 4
concludes with geometrical investigations of persisting and non-persisting
heteroclinic connections for e-->0 for some low dimensional sub-attractor
cases. Not all results are rigorous in this chapter.Die vorgelegte Arbeit beschäftigt sich mit der Frage des Verhältnisses
globaler Attraktoren von hyperbolischen Gleichgewichtssätzen auf der einen und
den viskosen Gleichgewichtssätzen auf der anderen Seite. Sie liegt also am
Schnittpunkt der Theorie der hyperbolischen und parabolischen partiellen
Differenzialgleichungen mit eindimensionaler Ortsvariable und periodischen
Randwerten, die gegeben sind durch: u_t + [f(u)]_x = g(u) (H) beziehungsweise
u_t + [f(u)]_x = eu_xx + g(u). (P) Die Hauptresultate der Arbeit gliedern sich
in zwei Teilbereiche: Durch das neu eingefĂĽhrte Konzept endlich dimensionaler
Sub-Attraktoren gelingt es einige Schwierigkeiten bei der Beschreibung des
globalen Attraktors von (H) zu ĂĽberwinden und eine der letzten LĂĽcken zu
dessen vollständiger Beschreibung zu schliessen. Theorem 2.6.1 liefert eine
vollständige Parameterisierung aller endlich dimensionaler Sub-Attraktoren im
hyperbolischen Setting. Das zweite Haupresultat liegt im Bereich der
Persistenz von Lösungen beim Übergang von e-->0. Hier gelingt es ein Resultat
ĂĽber die Persistenz von heteroklinen Verbindungen der parabolischen Gleichung
von Fan und Hale [FH95] zu widerlegen (Connection Lemma 3.2.8) und in Theorem
3.2.1 zu korrigieren. Das Cascading Theorem 3.2.9 liefert dann im Falle der
nicht-Persistenz die Konvergenz des heteroklinen Orbits der parabolischen
Gleichung gegen eine Kaskade heterokliner Verbindungen der hyperbolischen
Gleichung. Die Arbeit gliedert sich neben Einleitung und Diskussion in drei
Teile: In Kapitel 2 werden die bereits bestehenden Resultate ĂĽber globale
Attraktoren beider Gleichungen zur VerfĂĽgung gestellt. Als Abschluss wird
Theorem 2.6.1 formuliert und bewiesen. Kapitel 3 beschäftigt sich
ausschlieĂźlich mit dem Problem der Persistenz von heterokinen Verbindungen und
dem Beweis der beiden diesbezĂĽglichen Hauptresultate. Kapitel 4 schlieĂźlich
rundet die Arbeit ab mit einer Betrachtung der geometrischen Eigenschaften der
niedrig dimensionalen sub-Attraktoren der hyperbolischen Gleichung und einer
Ăśbertragung dieser Eigenschaften auf die sub-Attraktoren der parabolischen
Gleichung. Nicht alle Resultate in diesem Kapitel sind rigeros