7,190 research outputs found
Tracing the bounds on Bell-type inequalities
Bell-type inequalities and violations thereof reveal the fundamental
differences between standard probability theory and its quantum counterpart. In
the course of previous investigations ultimate bounds on quantum mechanical
violations have been found. For example, Tsirelson's bound constitutes a global
upper limit for quantum violations of the Clauser-Horne-Shimony-Holt (CHSH) and
the Clauser-Horne (CH) inequalities. Here we investigate a method for
calculating the precise quantum bounds on arbitrary Bell-type inequalities by
solving the eigenvalue problem for the operator associated with each Bell-type
inequality. Thereby, we use the min-max principle to calculate the norm of
these self-adjoint operators from the maximal eigenvalue yielding the upper
bound for a particular set of measurement parameters. The eigenvectors
corresponding to the maximal eigenvalues provide the quantum state for which a
Bell-type inequality is maximally violated.Comment: presented at: Foundations of Probability and Physics-3, Vaexjoe
University, Sweden, June 7-12, 200
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
The dynamics of hourly electricity prices
The dynamics of hourly electricity prices in day-ahead markets is an important element of competitive power markets that were only established in the last decade. In electricity markets, the market microstructure does not allow for continuous trading, since operators require advance notice in order to verify that the schedule is feasible and lies within transmission constraints. Instead agents have to submit their bids and offers for delivery of electricity for all hours of the next day before a specified market closing time. We suggest the use of dynamic semiparametric factor models (DSFM) for the behavior of hourly electricity prices. We find that a model with three factors is able to explain already a high proportion of the variation in hourly electricity prices. Our analysis also provides insights into the characteristics of the market, in particular with respect to the driving factors of hourly prices and their dynamic behavior through time.Power Markets, Dynamic Semiparametric Factor Models, Day-ahead Electricity Prices
Does Benford's law hold in economic research and forecasting?
First and higher order digits in data sets of natural and socio-economic processes often follow a distribution called Benford's law. This phenomenon has been used in many business and scientific applications, especially in fraud detection for financial data. In this paper, we analyse whether Benford's law holds in economic research and forecasting. First, we examine the distribution of leading digits of regression coefficients and standard errors in research papers, published in Empirica and Applied Economics Letters. Second, we analyse forecasts of GDP growth and CPI inflation in Germany, published in Consensus Forecasts. There are two main findings: The relative frequencies of the first and second digits in economic research are broadly consistent with Benford's law. In sharp contrast, the second digits of Consensus Forecasts exhibit a massive excess of zeros and fives, raising doubts on their information content. --Benford's Law,fraud detection,regression coefficients and standard errors,growth and inflation forecasts
Orbital frequencies in the carbonate sedimentary record: distorted by diagenesis?
The most important archive of Earth’s climate change through geologic history is the sedimentary rock record. Rhythmic sedimentary alternations are usually interpreted as a consequence of periodic variations in the orbital parameters of the Earth. This interpretation enables the application of cyclostratigraphy as a very precise chronometer, when based on the assumption that orbital frequencies are faithfully recorded in the sedimentary archive. However, there are numerous uncertainties with the application of this concept. Particularly in carbonates, sediment properties such as mineralogical composition and fossil associations are severely altered during post-depositional alteration (diagenesis). We here point out that the assumption of a 1:1 recording of orbital signals in many cases is questionable for carbonate rhythmites. We use computer simulations to show the effect of diagenetic overprint on records of orbital signals in the carbonate record. Such orbital signals may be distorted in terms of frequency, amplitude, and phase by diagenetic processes, and cycles not present in the insolation record may emerge. This questions the routine use of carbonate rhythmites for chronostratigraphic datin
A Large Along-Track Baseline Approach for Ground Moving Target Indication Using TanDEM-X
In the paper a new method for ground moving target indication (GMTI) using two satellites (i.e. the TerraSAR-X and the TanDEM-X satellite) together is presented. The along-track baseline between the satellites is chosen to be in the order of several kilometres, so that each satellite observes the same moving vehicles at different times in the order of one to several seconds. The proposed method allows the estimation of the ground velocity of the moving targets as well as the estimation of the broadside positions without the need of complex bistatic processing techniques
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