Numerical solution of optimal control problems with constant control delays

We investigate a class of optimal control problems that exhibit constant exogenously given delays in the control in the equation of motion of the differential states. Therefore, we formulate an exemplary optimal control problem with one stock and one control variable and review some analytic properties of an optimal solution. However, analytical considerations are quite limited in case of delayed optimal control problems. In order to overcome these limits, we reformulate the problem and apply direct numerical methods to calculate approximate solutions that give a better understanding of this class of optimization problems. In particular, we present two possibilities to reformulate the delayed optimal control problem into an instantaneous optimal control problem and show how these can be solved numerically with a stateof- the-art direct method by applying Bock’s direct multiple shooting algorithm. We further demonstrate the strength of our approach by two economic examples.

Design and Test of a 0.5 THz Dipole Antenna With Integrated Schottky Diode Detector on a High Dielectric Constant Ceramic Electromagnetic Bandgap Substrate

This paper presents the first analysis of the input impedance and radiation properties of a dipole antenna, placed on top of Fan 's three-dimensional electromagnetic bandgap (EBG) structure, (Applied Physics Letters, 1994) constructed using a high dielectric constant ceramic. The best position of the dipole on the EBG surface is determined following impedance and radiation pattern analyses. Based on this optimum configuration an integrated Schottky heterodyne detector was designed, manufactured and tested from 0.48 to 0.52 THz. The main antenna features were not degraded by the high dielectric constant substrate due to the use of the EBG approach. Measured radiation patterns are in good agreement with the predicted ones.

Der schweizerische Bundesstaat von 1848 bis 1874: Mehrheits- oder Konsensusdemokratie?

Der vorliegende Beitrag geht der Frage nach, ob die schweizerische Demokratie bereits ab der Bundesstaatsgründung im Jahr 1848 eine ausgeprägte Konsensusdemokratie war. Zur Beantwortung dieser Fragestellung bedient sich die Studie des Konzepts von Arend Lijphart (2012) mit der Unterscheidung von Mehrheits- und Konsensusdemokratie. Anhand von Literatur- und Dokumentenanalysen wurden Lijpharts Indikatoren für den schweizerischen Bundesstaat von 1848–1874 codiert. Die Ergebnisse zeigen, dass das politische System der neu gegründeten Schweiz auf Lijpharts Demokratiekarte insbesondere auf der horizontalen Machtteilungsdimension wie erwartet sehr nahe an der Position der USA zu liegen kommt.

Antinociceptive effects of three escalating dexmedetomidine and lignocaine constant rate infusions in conscious horses.

Dexmedetomidine and lignocaine IV are used clinically to provide analgesia in horses. The aims of this study were to investigate the antinociceptive effects, plasma concentrations and sedative effects of 2, 4 and 6 µg/kg/h dexmedetomidine IV, with a bolus of 0.96 µg/kg preceding each continuous rate infusion (CRI), and 20, 40 and 60 µg/kg/min lignocaine IV, with a bolus of 550 µg/kg preceding each CRI, in 10 Swiss Warmblood horses. Electrically elicited nociceptive withdrawal reflexes were evaluated by deltoid muscle electromyography. Nociceptive threshold and tolerance were determined by electromyography and behaviour following single and repeated stimulation. Plasma concentrations of drugs were determined by liquid chromatography and mass spectrometry. Sedation was scored on a visual analogue scale. Dexmedetomidine increased nociceptive threshold to single and repeated stimulation for all CRIs, except at 2 µg/kg/h, where no increase in single stimulation nociceptive threshold was observed. Dexmedetomidine increased nociceptive tolerance to single and repeated stimulation at all CRIs. There was large individual variability in dexmedetomidine plasma concentrations and levels of sedation; the median plasma concentration providing antinociceptive effects to all recorded parameters was 0.15 ng/mL, with a range from <0.02 ng/mL (below the lower limit of quantification) to 0.25 ng/mL. Lignocaine increased nociceptive threshold and tolerance to single and repeated stimulation at CRIs of 40 and 60 µg/kg/min, corresponding to plasma lignocaine concentrations >600 ng/mL. Only nociceptive tolerance to repeated stimulation increased at 20 µg/kg/min lignocaine. Lignocaine at 40 µg/kg/min and dexmedetomidine at 4 µg/kg/h were the lowest CRIs resulting in consistent antinociception. Lignocaine did not induce significant sedation.

The pharmacokinetics of dexmedetomidine administered as a constant rate infusion in horses.

Dexmedetomidine, the most selective α2 -adrenoceptor agonist in clinical use, is increasingly being used in both conscious and anaesthetized horses; however, the pharmacokinetics and sedative effects of this drug administered alone as an infusion are not previously described in horses. Seven horses received an infusion of 8 μg dexmedetomidine/kg/h for 150 min, venous blood samples were collected, and dexmedetomidine concentrations were assayed using liquid chromatography-mass spectrometry (LC/MS) and analyzed using noncompartmental pharmacokinetic analysis. Sedation was scored as the distance from the lower lip of the horse to the ground measured in centimetre. The harmonic mean (SD) plasma elimination half-life (Lambda z half-life) for dexmedetomidine was 20.9 (5.1) min, clearance (Cl) was 0.3 (0.20) L/min/kg, and volume of distribution at steady-state (Vdss ) was 13.7 (7.9) L/kg. There was a considerable individual variation in the concentration of dexmedetomidine vs. time profile. The level of sedation covaried with the plasma concentration of dexmedetomidine. This implies that for clinical use of dexmedetomidine constant rate infusion in conscious horses, infusion rates can be easily adjusted to effect, and this is preferable to an infusion at a predetermined value.

Ignacy Koschembahr-Łyskowski: profesor Uniwersytetu Fryburskiego (1895-1900)

Ignacy Koschembahr-Łyskowski: a professor at the University of Fribourg (1895-1900) Ignacy Koschembahr-Łyskowski (1864-1945) was a Polish legal scholar researching into Roman and Private laws; one of the drafters of Polish unified Private Law in the Interwar era. After having obtained his PhD in Berlin in 1888 and postdoctoral degree in Breslau in 1894, he moved to Fribourg (Switzerland), where he stayed 5 years (1895-1900) as a professor for Roman law. Koschembahr-Łyskowski wrote there his fundamental works on the methodology of Roman law (1898) and its usefulness for modernity, as well as about the codification of Swiss Private Law (1899), demonstrating the usefulness of the Roman law experience for modern legislation. An overview of his works shows a surprising topicality of his ideas. The survey concentrates on his teaching in Fribourg as well as his writings, and is based on many newly discovered documents from the local archives, that have never been published before.

Accurate rotational constant and bond lengths of hexafluorobenzene by femtosecond rotational Raman coherence spectroscopy and ab initio calculations

The gas-phase rotational motion of hexafluorobenzene has been measured in real time using femtosecond (fs) time-resolved rotational Raman coherence spectroscopy (RR-RCS) at T = 100 and 295 K. This four-wave mixing method allows to probe the rotation of non-polar gas-phase molecules with fs time resolution over times up to ∼5 ns. The ground state rotational constant of hexafluorobenzene is determined as B 0 = 1029.740(28) MHz (2σ uncertainty) from RR-RCS transients measured in a pulsed seeded supersonic jet, where essentially only the v = 0 state is populated. Using this B 0 value, RR-RCS measurements in a room temperature gas cell give the rotational constants B v of the five lowest-lying thermally populated vibrationally excited states ν7/8, ν9, ν11/12, ν13, and ν14/15. Their B v constants differ from B 0 by between −1.02 MHz and +2.23 MHz. Combining the B 0 with the results of all-electron coupled-cluster CCSD(T) calculations of Demaison et al. [Mol. Phys.111, 1539 (2013)] and of our own allow to determine the C-C and C-F semi-experimental equilibrium bond lengths r e(C-C) = 1.3866(3) Å and r e(C-F) = 1.3244(4) Å. These agree with the CCSD(T)/wCVQZ r e bond lengths calculated by Demaison et al. within ±0.0005 Å. We also calculate the semi-experimental thermally averaged bond lengths r g(C-C)=1.3907(3) Å and r g(C-F)=1.3250(4) Å. These are at least ten times more accurate than two sets of experimental gas-phase electron diffraction r g bond lengths measured in the 1960s.

Feasible Dose Reduction in Routine Chest Computed Tomography Maintaining Constant Image Quality Using the Last Three Scanner Generations: From Filtered Back Projection to Sinogram-affirmed Iterative Reconstruction and Impact of the Novel Fully Integrated Detector Design Minimizing Electronic Noise

OBJECTIVE The aim of the present study was to evaluate a dose reduction in contrast-enhanced chest computed tomography (CT) by comparing the three latest generations of Siemens CT scanners used in clinical practice. We analyzed the amount of radiation used with filtered back projection (FBP) and an iterative reconstruction (IR) algorithm to yield the same image quality. Furthermore, the influence on the radiation dose of the most recent integrated circuit detector (ICD; Stellar detector, Siemens Healthcare, Erlangen, Germany) was investigated. MATERIALS AND METHODS 136 Patients were included. Scan parameters were set to a thorax routine: SOMATOM Sensation 64 (FBP), SOMATOM Definition Flash (IR), and SOMATOM Definition Edge (ICD and IR). Tube current was set constantly to the reference level of 100 mA automated tube current modulation using reference milliamperes. Care kV was used on the Flash and Edge scanner, while tube potential was individually selected between 100 and 140 kVp by the medical technologists at the SOMATOM Sensation. Quality assessment was performed on soft-tissue kernel reconstruction. Dose was represented by the dose length product. RESULTS Dose-length product (DLP) with FBP for the average chest CT was 308 mGy*cm ± 99.6. In contrast, the DLP for the chest CT with IR algorithm was 196.8 mGy*cm ± 68.8 (P = 0.0001). Further decline in dose can be noted with IR and the ICD: DLP: 166.4 mGy*cm ± 54.5 (P = 0.033). The dose reduction compared to FBP was 36.1% with IR and 45.6% with IR/ICD. Signal-to-noise ratio (SNR) was favorable in the aorta, bone, and soft tissue for IR/ICD in combination compared to FBP (the P values ranged from 0.003 to 0.048). Overall contrast-to-noise ratio (CNR) improved with declining DLP. CONCLUSION The most recent technical developments, namely IR in combination with integrated circuit detectors, can significantly lower radiation dose in chest CT examinations.

Elucidating the Functional Relationship Between Working Memory Capacity and Psychometric Intelligence: A Fixed-Links Modeling Approach for Experimental Repeated-Measures Designs

Numerous studies reported a strong link between working memory capacity (WMC) and fluid intelligence (Gf), although views differ in respect to how close these two constructs are related to each other. In the present study, we used a WMC task with five levels of task demands to assess the relationship between WMC and Gf by means of a new methodological approach referred to as fixed-links modeling. Fixed-links models belong to the family of confirmatory factor analysis (CFA) and are of particular interest for experimental, repeated-measures designs. With this technique, processes systematically varying across task conditions can be disentangled from processes unaffected by the experimental manipulation. Proceeding from the assumption that experimental manipulation in a WMC task leads to increasing demands on WMC, the processes systematically varying across task conditions can be assumed to be WMC-specific. Processes not varying across task conditions, on the other hand, are probably independent of WMC. Fixed-links models allow for representing these two kinds of processes by two independent latent variables. In contrast to traditional CFA where a common latent variable is derived from the different task conditions, fixed-links models facilitate a more precise or purified representation of the WMC-related processes of interest. By using fixed-links modeling to analyze data of 200 participants, we identified a non-experimental latent variable, representing processes that remained constant irrespective of the WMC task conditions, and an experimental latent variable which reflected processes that varied as a function of experimental manipulation. This latter variable represents the increasing demands on WMC and, hence, was considered a purified measure of WMC controlled for the constant processes. Fixed-links modeling showed that both the purified measure of WMC (β = .48) as well as the constant processes involved in the task (β = .45) were related to Gf. Taken together, these two latent variables explained the same portion of variance of Gf as a single latent variable obtained by traditional CFA (β = .65) indicating that traditional CFA causes an overestimation of the effective relationship between WMC and Gf. Thus, fixed-links modeling provides a feasible method for a more valid investigation of the functional relationship between specific constructs.