Laser-controlled adaptive optic for beam quality enhancement in a multipass thin disk amplifier

We devise a laser-controlled adaptive optical element which operates intracavity under high intensity radiation. This element substitutes a conventional mechanically deformable mirror and is free of critical heat-sensitive components and electronics. The deformation mechanism is based on the projection of a CW control laser onto a specially designed mirror. Mounted to a water-cooled heat sink, the mirror can handle laser radiation beyond 3 MW/cm^2. The properties of the adaptive optical element including the maximum correctable wavefront pitch of 800 nm are discussed. The successful implementation in a multipass thin disk amplifier is presented. An improvement of the beam quality by a factor of three is achieved. We identify measures to enhance the performance of the adaptive optic towards efficient operation in a high-power laser system

Thomas decompositions of parametric nonlinear control systems

This paper presents an algorithmic method to study structural properties of nonlinear control systems in dependence of parameters. The result consists of a description of parameter configurations which cause different control-theoretic behaviour of the system (in terms of observability, flatness, etc.). The constructive symbolic method is based on the differential Thomas decomposition into disjoint simple systems, in particular its elimination properties

A Canonical Model Construction for Iteration-Free PDL with Intersection

We study the axiomatisability of the iteration-free fragment of Propositional Dynamic Logic with Intersection and Tests. The combination of program composition, intersection and tests makes its proof-theory rather difficult. We develop a normal form for formulae which minimises the interaction between these operators, as well as a refined canonical model construction. From these we derive an axiom system and a proof of its strong completeness.Comment: In Proceedings GandALF 2016, arXiv:1609.0364

Structure of Six-Dimensional Microstate Geometries

We investigate the structure of smooth and horizonless microstate geometries in six dimensions, in the spirit of the five-dimensional analysis of Gibbons and Warner [arXiv:1305.0957]. In six dimensions, which is the natural setting for horizonless geometries with the charges of the D1-D5-P black hole, the natural black objects are strings and there are no Chern-Simons terms for the tensor gauge fields. However, we still find that the same reasoning applies: in absence of horizons, there can be no smooth stationary solutions without non-trivial topology. We use topological arguments to describe the Smarr formula in various examples: the uplift of the five-dimensional minimal supergravity microstates to six dimensions, the two-charge D1-D5 microstates, and the non-extremal JMaRT solution. We also discuss D1-D5-P superstrata and confirm that the Smarr formula gives the same result as for the D1-D5 supertubes which are topologically equivalent.Comment: 29 pages, v2: references added, published versio

Fertility transitions along the extensive and intensive margins

This paper examines the fertility transition through a new lens: the extensive margin. Parents with high levels of children might substitute quality for quantity as the constraints on quality relax or those on quantity tighten. However, along the extensive margin, the quantity-quality trade-off cannot operate. At low levels of fertility, we expect quality and quantity to be essential complements. We apply these insights to a large school construction program in the American South during the early 20th century, the Rosenwald Rural Schools Initiative. We find that increased schooling opportunities lead to reductions in fertility among women with high fertility levels, while at the same time inducing higher levels of fertility among women with low levels of fertility. The magnitude of the fertility changes induced in the parent generation is, however, small compared to the changes in fertility induced by the Rosenwald intervention among women that were themselves treated by the intervention. The evidence from the Rosenwald intervention therefore suggests that changes in female opportunity costs induced by increased educational attainment might be among the most important driving forces of the fertility transition.Fertility

Algorithmic Thomas Decomposition of Algebraic and Differential Systems

In this paper, we consider systems of algebraic and non-linear partial differential equations and inequations. We decompose these systems into so-called simple subsystems and thereby partition the set of solutions. For algebraic systems, simplicity means triangularity, square-freeness and non-vanishing initials. Differential simplicity extends algebraic simplicity with involutivity. We build upon the constructive ideas of J. M. Thomas and develop them into a new algorithm for disjoint decomposition. The given paper is a revised version of a previous paper and includes the proofs of correctness and termination of our decomposition algorithm. In addition, we illustrate the algorithm with further instructive examples and describe its Maple implementation together with an experimental comparison to some other triangular decomposition algorithms.Comment: arXiv admin note: substantial text overlap with arXiv:1008.376

Generalised Umbral Moonshine

Umbral moonshine describes an unexpected relation between 23 finite groups arising from lattice symmetries and special mock modular forms. It includes the Mathieu moonshine as a special case and can itself be viewed as an example of the more general moonshine phenomenon which connects finite groups and distinguished modular objects. In this paper we introduce the notion of generalised umbral moonshine, which includes the generalised Mathieu moonshine [Gaberdiel M.R., Persson D., Ronellenfitsch H., Volpato R., Commun. Number Theory Phys. 7 (2013), 145-223] as a special case, and provide supporting data for it. A central role is played by the deformed Drinfel'd (or quantum) double of each umbral finite group $G$, specified by a cohomology class in $H^3(G,U(1))$. We conjecture that in each of the 23 cases there exists a rule to assign an infinite-dimensional module for the deformed Drinfel'd double of the umbral finite group underlying the mock modular forms of umbral moonshine and generalised umbral moonshine. We also discuss the possible origin of the generalised umbral moonshine

On the Expressive Power of Hybrid Branching-Time Logics

Hybrid branching-time logics are a powerful extension of branching-time logics like CTL, CTL^* or even the modal mu-calculus through the addition of binders, jumps and variable tests. Their expressiveness is not restricted by bisimulation-invariance anymore. Hence, they do not retain the tree model property, and the finite model property is equally lost. Their satisfiability problems are typically undecidable, their model checking problems (on finite models) are decidable with complexities ranging from polynomial to non-elementary time. In this paper we study the expressive power of such hybrid branching-time logics beyond some earlier results about their invariance under hybrid bisimulations. In particular, we aim to extend the hierarchy of non-hybrid branching-time logics CTL, CTL^+, CTL^* and the modal mu-calculus to their hybrid extensions. We show that most separation results can be transferred to the hybrid world, even though the required techniques become a bit more involved. We also present some collapse results for restricted classes of models that are especially worth investigating, namely linear, tree-shaped and finite models

Expression, localization, and kinetic characterization of the phospholipid biosynthesis enzyme CTP: phosphocholine cytidylyltransferase from the protozoan parasite Leishmania major

The eukaryotic parasite Leishmania is the causative agent of the disease leishmaniasis. L. major is the most common of 21 species that causes visceral leishmaniasis in humans, and 30 that cause the same disease in other mammals. Visceral leishmaniasis causes fever, weight loss, and over a short amount of time, multiple organ failure, and has a 100% mortality rate within 2 years. This makes it the second largest parasitic killer in the world behind malaria. Over 90% of the worldâ??s cases of visceral leishmaniasis have been reported in underdeveloped countries of India, Bangladesh, Nepal, Sudan, Ethiopia and Brazil, with 500,000 new cases being diagnosed worldwide each year. Nonetheless, the most popular drugs of choice for leishmaniasis treatment remain toxic, expensive, or subject to refractory infections. Phospholipids used to construct biological membranes account for approximately 70% of total cellular lipid in Leishmania, and of that 30-40% is phosphatidylcholine (PC). PC is formed via the Kennedy pathway in Leishmania, as well as in many higher eukaryotes, including mammals. The enzyme CTP: phosphocholine cytidylyltransferase (CCT) catalyzes the addition of cytidine triphosphate (CTP) to phosphocholine yielding CDP-choline, a second, critical, rate limiting step in the formation of PC by the Kennedy pathway that has been shown to be reversibly membrane associated. Amino acid sequence analysis of CCT shows a high level of homology in the CCT catalytic region but a lack of the known C-terminal membrane-binding region in L. infantum and L. major. Thus, the nuclear localization signal, along with the classical C-terminal membrane binding domain is absent in these organisms and has been recently unknown whether CCT localizes to the nucleus, endoplasmic reticulum, or cytoplasm. In investigation of the enzyme, the gene for L. major CCT has been tagged with a red fluorescent protein gene (mCherry) and successfully cloned into non-pathogenic Leishmania tarentolae. Confocal microscopy has revealed that L. major CCT is primarily cytoplasmic, while most likely also able to reversibly associate with internal membranes such as the endoplasmic reticulum and plasma membrane. In addition, a truncated mutant of L. major CCT containing the catalytic domain has been expressed in Escherichia coli and purified. In vitro assay of the enzyme yielded a maximal velocity (Vmax) of approximately 350 nmol/min/mg and substrate constant (Km) values of 3 mM and 0.2 mM respectively for the substrates phosphocholine and CTP. The Mg2+ ion was used as a cofactor in the reaction, but the enzyme was also able to achieve maximal activity using Mn2+, Co2+, Ni2+, and possibly Fe2+. This summarizes investigation of CCT as a possible therapeutic target for more efficacious treatment of leishmaniasis