On convexity of solutions of ordinary differential equations

We prove a result on the convex dependence of solutions of ordinary differential equations on an ordered finite-dimensional real vector space with respect to the initial data.Comment: 10 page

Realizability and uniqueness in graphs

AbstractConsider a finite graph G(V,E). Let us associate to G a finite list P(G) of invariants. To any P the following two natural problems arise: (R) Realizability. Given P, when is P=P(G) for some graph G?, (U) Uniqueness. Suppose P(G)=P(H) for graphs G and H. When does this imply G ≅ H? The best studied questions in this context are the degree realization problem for (R) and the reconstruction conjecture for (U). We discuss the problems (R) and (U) for the degree sequence and the size sequence of induced subgraphs for undirected and directed graphs, concentrating on the complexity of the corresponding decision problems and their connection to a natural search problem on graphs

Expression of mRNA for phospholipase A(2), cyclooxygenases, and lipoxygenases in cultured human umbilical vascular endothelial and smooth muscle cells and in biopsies from umbilical arteries and veins

Arachidonic acid (AA) is released by phospholipase A(2) (PLA(2)) and then converted into vasoactive and inflammatory eicosanoids by cyclooxygenases (COX) and lipoxygenases (LOX). These eicosanoids are important paracrine regulators of vascular permeability, blood flow, local pro- and anticoagulant activity and they play a major role in the local inflammatory response. We have investigated the presence of mRNAs for PLA(2) and for isoforms of COX and LOX in both human endothelial cells (EC) and in human smooth muscle cells (SMC) in culture and in vascular biopsies of human umbilical veins (HUVB) and arteries (HUAB) by using the reversed transcription-polymerase chain reaction (RT-PCR) technique. Results show detectable levels of PLA(2) type IV (cPLA(2)) in cultured EC and SMC and in vascular wall biopsies from HUAB and HUVB. The cultured EC and SMC demonstrate higher levels of both COX-1 and COX-2 with PCR analyses than do vascular wall biopsies from HUAB and HUVB. This indicates a difference in the native expression of COX-1 and COX-2 in cultures of EC and SMC compared to that in biopsies from intact vessel walls. The EC and SMC in culture do not express mRNA for 5-LOX, that was, however, expressed in the vascular wall biopsies. This speaks in favour of a constitutive, i.e, in vivo expression of 5-LOX in SMC in the vascular wall of both umbilical vein and arteries. Thus results from in vitro studies of constitutive COX and LOX expression in EC and vascular SMC in culture cannot simply be extrapolated to represent in vivo conditions

Exponential moments of affine processes

We investigate the maximal domain of the moment generating function of affine processes in the sense of Duffie, Filipovi\'{c} and Schachermayer [Ann. Appl. Probab. 13 (2003) 984-1053], and we show the validity of the affine transform formula that connects exponential moments with the solution of a generalized Riccati differential equation. Our result extends and unifies those preceding it (e.g., Glasserman and Kim [Math. Finance 20 (2010) 1-33], Filipovi\'{c} and Mayerhofer [Radon Ser. Comput. Appl. Math. 8 (2009) 1-40] and Kallsen and Muhle-Karbe [Stochastic Process Appl. 120 (2010) 163-181]) in that it allows processes with very general jump behavior, applies to any convex state space and provides both sufficient and necessary conditions for finiteness of exponential moments.Comment: Published in at http://dx.doi.org/10.1214/14-AAP1009 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Randomness Relative to Cantor Expansions

Imagine a sequence in which the first letter comes from a binary alphabet, the second letter can be chosen on an alphabet with 10 elements, the third letter can be chosen on an alphabet with 3 elements and so on. When such a sequence can be called random? In this paper we offer a solution to the above question using the approach to randomness proposed by Algorithmic Information Theory.Comment: several small change

A discrete element model for cohesive soil

Soil can roughly be classified into cohesionless, cohesive, and cemented soil. In this contribution, a discrete element model for the simulation of cohesive soil is presented. It is based on a model for cohesionless material with spherical particles, normal repulsive and frictional contacts, as well as rolling resistance with an elastic limit to compensate the excessive particle rolling. The cohesive behavior is modeled by an additional attractive normal force between particles. The model is not derived from the microscopic origin of cohesion, such as liquid bridges or electrostatic forces. Instead, it is set up in analogy to the macroscopic shear failure characteristics of cohesive soil. It is observed in video inspections of a bulldozer blade operating in cohesive soil that after the cutting takes place the soil recovers more of its initial cohesion in areas of high compression. In areas away from the blade, the material behaves more like cohesionless soil, forming an angle of response. This behavior is reproduced by introducing a memory effect in the simulation. By that, the amount of cohesion is limited by the pressure that the contacting particles have experienced during the simulation. The discrete element model is shown to be scale invariant in the quasi-static regime, i.e. if all length scales of the model are scaled by a constant factor, the results remain unaffected by the scaling. The model is applied to a bulldozer blade pushing cohesive soil. The contact parameters are calibrated by simulated triaxial compression tests. A comparison between simulation and measurement shows good qualitative agreement

A discrete element model for cohesive soil

Soil can roughly be classified into cohesionless, cohesive, and cemented soil. In this contribution, a discrete element model for the simulation of cohesive soil is presented. It is based on a model for cohesionless material with spherical particles, normal repulsive and frictional contacts, as well as rolling resistance with an elastic limit to compensate the excessive particle rolling. The cohesive behavior is modeled by an additional attractive normal force between particles. The model is not derived from the microscopic origin of cohesion, such as liquid bridges or electrostatic forces. Instead, it is set up in analogy to the macroscopic shear failure characteristics of cohesive soil. It is observed in video inspections of a bulldozer blade operating in cohesive soil that after the cutting takes place the soil recovers more of its initial cohesion in areas of high compression. In areas away from the blade, the material behaves more like cohesionless soil, forming an angle of response. This behavior is reproduced by introducing a memory effect in the simulation. By that, the amount of cohesion is limited by the pressure that the contacting particles have experienced during the simulation. The discrete element model is shown to be scale invariant in the quasi-static regime, i.e. if all length scales of the model are scaled by a constant factor, the results remain unaffected by the scaling. The model is applied to a bulldozer blade pushing cohesive soil. The contact parameters are calibrated by simulated triaxial compression tests. A comparison between simulation and measurement shows good qualitative agreement

An atomic hydrogen beam to test ASACUSA's apparatus for antihydrogen spectroscopy

The ASACUSA collaboration aims to measure the ground state hyperfine splitting (GS-HFS) of antihydrogen, the antimatter pendant to atomic hydrogen. Comparisons of the corresponding transitions in those two systems will provide sensitive tests of the CPT symmetry, the combination of the three discrete symmetries charge conjugation, parity, and time reversal. For offline tests of the GS-HFS spectroscopy apparatus we constructed a source of cold polarised atomic hydrogen. In these proceedings we report the successful observation of the hyperfine structure transitions of atomic hydrogen with our apparatus in the earth's magnetic field.Comment: 8 pages, 4 figures, proceedings for conference EXA 2014 (Exotic Atoms - Vienna