A Probabilistic Approach to Robust Optimal Experiment Design with Chance Constraints

Accurate estimation of parameters is paramount in developing high-fidelity models for complex dynamical systems. Model-based optimal experiment design (OED) approaches enable systematic design of dynamic experiments to generate input-output data sets with high information content for parameter estimation. Standard OED approaches however face two challenges: (i) experiment design under incomplete system information due to unknown true parameters, which usually requires many iterations of OED; (ii) incapability of systematically accounting for the inherent uncertainties of complex systems, which can lead to diminished effectiveness of the designed optimal excitation signal as well as violation of system constraints. This paper presents a robust OED approach for nonlinear systems with arbitrarily-shaped time-invariant probabilistic uncertainties. Polynomial chaos is used for efficient uncertainty propagation. The distinct feature of the robust OED approach is the inclusion of chance constraints to ensure constraint satisfaction in a stochastic setting. The presented approach is demonstrated by optimal experimental design for the JAK-STAT5 signaling pathway that regulates various cellular processes in a biological cell.Comment: Submitted to ADCHEM 201

Stochastic Nonlinear Model Predictive Control with Efficient Sample Approximation of Chance Constraints

This paper presents a stochastic model predictive control approach for nonlinear systems subject to time-invariant probabilistic uncertainties in model parameters and initial conditions. The stochastic optimal control problem entails a cost function in terms of expected values and higher moments of the states, and chance constraints that ensure probabilistic constraint satisfaction. The generalized polynomial chaos framework is used to propagate the time-invariant stochastic uncertainties through the nonlinear system dynamics, and to efficiently sample from the probability densities of the states to approximate the satisfaction probability of the chance constraints. To increase computational efficiency by avoiding excessive sampling, a statistical analysis is proposed to systematically determine a-priori the least conservative constraint tightening required at a given sample size to guarantee a desired feasibility probability of the sample-approximated chance constraint optimization problem. In addition, a method is presented for sample-based approximation of the analytic gradients of the chance constraints, which increases the optimization efficiency significantly. The proposed stochastic nonlinear model predictive control approach is applicable to a broad class of nonlinear systems with the sufficient condition that each term is analytic with respect to the states, and separable with respect to the inputs, states and parameters. The closed-loop performance of the proposed approach is evaluated using the Williams-Otto reactor with seven states, and ten uncertain parameters and initial conditions. The results demonstrate the efficiency of the approach for real-time stochastic model predictive control and its capability to systematically account for probabilistic uncertainties in contrast to a nonlinear model predictive control approaches.Comment: Submitted to Journal of Process Contro

Stability for Receding-horizon Stochastic Model Predictive Control

A stochastic model predictive control (SMPC) approach is presented for discrete-time linear systems with arbitrary time-invariant probabilistic uncertainties and additive Gaussian process noise. Closed-loop stability of the SMPC approach is established by appropriate selection of the cost function. Polynomial chaos is used for uncertainty propagation through system dynamics. The performance of the SMPC approach is demonstrated using the Van de Vusse reactions.Comment: American Control Conference (ACC) 201

Tax competition in Europe - Europe in competition with other world regions?

Corporate tax levels have fallen substantially in Europe during the last decades. A broad literature has identified tax competition as one reason for this decline in corporate tax levels. However, none of these studies explicitly asks the question whether tax competition within regions is different from tax competition across regions, e.g. due to global regionalism of foreign direct investments. This is a crucial question to answer in order to discuss the desirability of tax harmonization in a distinct region, for example, within the European Union. Therefore, the study aims to give hints on the question whether the decline in corporate tax levels in Europe is mainly driven by tax competition between EU member states or by pressure from other world regions. The results of this study, which makes use of tax reaction functions, indicate that there is evidence for tax competition within Europe, whereas there is no robust evidence that European countries compete with countries from other world regions

Field Conference 1984 of the INQUA Subcommission on Shorelines of Northwestern Europe

Die Veranstaltung umfaßte eine Exkursion entlang einer geologischen Traverse vom Wesermündungs- und Jadebusengebiet über den Unterelberaum, die schleswig-holsteinische und dänische Westküste bis Skagen. Dabei wurden die paläogeographischen Veränderungen der Küstenlinien, die Sedimentabfolgen und zeitliche Einstufung der morphogenetischen Prozesse des Weichsel-Spätglazials und Holozän untersucht. Ein Symposium in Klim, Dänemark, befaßte sich mit gleichen Themen aus dem gesamten Nord- und Ostseebereich.researc

Measuring correlations of cold atom systems using multiple quantum probes

We present a non-destructive method to probe a complex quantum system using multiple impurity atoms as quantum probes. Our protocol provides access to different equilibrium properties of the system by changing its coupling to the probes. In particular, we show that measurements with two probes reveal the system's non-local two-point density correlations, for probe-system contact interactions. We illustrate our findings with analytic and numerical calculations for the Bose-Hubbard model in the weakly and strongly-interacting regimes, under conditions relevant to ongoing experiments in cold atom systems.Comment: 11 pages, 6 figures. v2: enhanced discussion in light of other correlation measurement methods available; matches published versio

The Effects of Aerobic and Muscular Endurance Based Resistance Exercises on the Cardiorespiratory System in College Age Females

The purpose of this study was to evaluate the cardiorespiratory response in college age females, between the ages of 19 and 24, before and after participating in a six week moderate-vigorous aerobic exercise program compared to a six week moderate-vigorous aerobic exercise program combined with a muscular endurance based resistance training program. Specifically, which mode of exercise has the most significant effect on cardiorespiratory fitness? Methods: Twelve sedentary college age females between the ages of 19 to 24 years, with a mean age of 20.9 years, participated in the study. Eligible participants were randomly assigned to one of three groups: an aerobic exercise only group (n=5), a combination of aerobic exercise and muscular endurance based resistance training group (n=3), and a control group (n=4). Subjects in the aerobic exercise only group participated in a six week program of moderate-vigorous aerobic exercise at 60-75% of their measured target heart rate reserve for a total of 50 minutes, three days per week. Subjects in the combination exercise group participated in a six week program of aerobic exercise at 60-75% of their measured target heart rate reserve for 30 minutes, in addition to a muscular endurance based resistance training program, three days per week. Subjects in the control group were asked to refrain from exercise during the six week period. Anthropometric measurements and cardiorespiratory fitness were assessed pre- and post-training period. Cardiorespiratory fitness was assessed through graded exercise testing (Bruce protocol) and continuous pulmonary gas exchange and indirect calorimetry. Results: A mixed ANOVA analysis (p\u3c0.05) showed no significant difference between maximal VO2 measurements in regard to time and group (p=0.50). A paired samples t-test further showed no significant difference between the pre- and post-training measurements in maximal VO2 (p=0.162). A second mixed ANOVA analysis (p\u3c0.05) showed no significant difference between measured HRmax in regard to time and the experimental group (p=0.113). A paired samples t-test further showed no significant difference between the pre- and post-training measurements in maximal heart rate (p=0.892). Conclusion: In sedentary females, between the ages of 19 and 24, six weeks of moderate-vigorous aerobic exercise plus muscular endurance resistance training elicited no significant difference from six weeks of moderate-vigorous aerobic exercise alone, in regard to the effects on cardiorespiratory fitness. The findings of this study were not in agreement with the suggestion that combination training has a greater impact on the components of cardiorespiratory endurance than aerobic exercise alone. However, the suggestion that no significant change would occur over an extended period of time within sedentary females who had no alteration in physical activity level was supported. Furthermore, in order to elicit a change in cardiorespiratory fitness, physical activity level must be positively altered