Optimal entropic uncertainty relation for successive measurements in quantum information theory

We derive an optimal bound on the sum of entropic uncertainties of two or more observables when they are sequentially measured on the same ensemble of systems. This optimal bound is shown to be greater than or equal to the bounds derived in the literature on the sum of entropie uncertainties of two observables which are measured on distinct but identically prepared ensembles of systems. In the case of a two-dimensional Hilbert space, the optimum bound for successive measurements of two-spin components, is seen to be strictly greater than the optimal bound for the case when they are measured on distinct ensembles, except when the spin components are mutually parallel or perpendicular     

Volume of Domains in Symmetric Spaces

The authors derive a formula for the volume of a compact domain in a symmetric space from normal sections through a special submanifold in the symmetric space.This formula generalizes the volume of classical domains as tubes or domains given as motions along the submanifold.Finally,some stereological considerations regarding this formula are provided.     

Precise bounds for the petersen time-varying real parameter uncertainty system stabilized via linear static controllers

Using a class of linear static controllers, we stabilize the Petersen open-loop two-dimensional linear system (Ref. 1), which consists of one time-varying uncertainty in the state matrixA and one timevarying uncertainty in the input matrixB. We show that the worst-case uncertainty strategy for the closed-loop system is a piecewise constant strategy of the angular state with three switches on the half-turn, –/2/2; it is unique with respect to a set of measure zero. Formulas are derived for the worst-case half-turn radius gainr _HT as a function of the parameters of the class of stabilizing linear static controllers. Using the class of scalar-quadratic Lyapunov functions, we show that a necessary and sufficient condition for the closed-loop system to be robustly stable against all time-varying admissible uncertainties is thatr _HT be less than unity. The bound on the time-varying real parameter uncertainties for the closed-loop system to be robustly stable is derived for the class of linear static feedback controllers. We obtain stabilizing linear static controllers such that the bound is as close to infinity as desired. The derived results are compared with numerical results obtained using commerical robust-control software.     

Thermally Induced Measurement Error by a Water-Cooled Enthalpy Probe

Errors in stagnation-pressure measurement, due to a large temperature gradient at the face of a water-cooled enthalpy probe, were experimentally measured and numerically simulated. Two probes were used to measure the stagnation-pressure in a dc plasma jet; a standard water-cooled enthalpy probe and an uncooled ceramic (Thoria) probe. There was a maximum difference of 10% between the two measurements, with the water-cooled probe measuring lower pressures. Numerical simulations of plasma flow around the probe showed that the magnitude of the error depends on the thickness of the thermal boundary layer. The measurement error causes a maximum of 3% error in velocity measurements, using the Bernoulli equation. This error is no worse than other measurement errors associated with water-cooled enthalpy probe meaurements.     

Toxicological screening of human plasma by on‐line SPE‐HPLC‐DAD: identification and quantification of acidic and neutral drugs

A multi‐analyte screening method for the quantification of 50 acidic/neutral drugs in human plasma based on on‐line solid‐phase extraction (SPE)–HPLC with photodiode array detection (DAD) was developed, validated and applied for clinical investigation. Acetone and methanol for protein precipitation, three different SPE materials (two electro‐neutral, one strong anion‐exchange, one weak cation‐exchange) for on‐line extraction, five HPLC‐columns [one C₁₈ (GeminiNX), two phenyl‐hexyl (Gemini C₆‐Phenyl, Kinetex Phenyl‐Hexyl) and two pentafluorophenyl (LunaPFP(2), KinetexPFP)] for analytical separation were tested. For sample pre‐treatment, acetone in the ratio 1:2 (plasma:acetone) showed a better baseline and fewer matrix peaks in the chromatogram than methanol. Only the strong anion‐exchanger SPE cartridge (StrataX‐A, pH 6) allowed the extraction of salicylic acid. Analytical separation was carried out on a Gemini C₆‐Phenyl column (150 × 4.6 mm, 3 µm) using gradient elution with acetonitrile–water 90:10 (v/v) and phosphate buffer (pH 2.3). Linear calibration curves with correlation coefficients r ≥ 0.9950/0.9910 were obtained for 46/four analytes. Additionally, this method allows the quantification of 23 analytes for therapeutic drug monitoring. Limits of quantitation ranged from 0.1 (amobarbital) to 23 mg/L (salicylic acid). Inter‐/intra‐day precisions of quality control samples (low/high) were better than 13% and accuracy (bias) ranged from ?14 to 10%. A computer‐assisted database was created for automated detection of 223 analytes of toxicological interests. Four cases of multi‐drug intoxications are presented. Copyright © 2015 John Wiley & Sons, Ltd.     

Efficient computation of operator‐type response sensitivities for uncertainty quantification and predictive modeling: illustrative application to a spent nuclear fuel dissolver model

This work honors the 75th birthday of Professor Ionel Michael Navon by presenting original results highlighting the computational efficiency of the adjoint sensitivity analysis methodology for function‐valued operator responses by means of an illustrative paradigm dissolver model. The dissolver model analyzed in this work has been selected because of its applicability to material separations and its potential role in diversion activities associated with proliferation and international safeguards. This dissolver model comprises eight active compartments in which the 16 time‐dependent nonlinear differential equations modeling the physical and chemical processes comprise 619 scalar and time‐dependent model parameters, related to the model's equation of state and inflow conditions. The most important response for the dissolver model is the time‐dependent nitric acid in the compartment furthest away from the inlet, where measurements are available at 307 time instances over the transient's duration of 10.5 h. The sensitivities to all model parameters of the acid concentrations at each of these instances in time are computed efficiently by applying the adjoint sensitivity analysis methodology for operator‐valued responses. The uncertainties in the model parameters are propagated using the above‐mentioned sensitivities to compute the uncertainties in the computed responses. A predictive modeling formalism is subsequently used to combine the computational results with the experimental information measured in the compartment furthest from the inlet and then predict optimal values and uncertainties throughout the dissolver. This predictive modeling methodology uses the maximum entropy principle to construct an optimal approximation of the unknown a priori distribution for the a priori known mean values and uncertainties characterizing the model parameters and the computed and experimentally measured model responses. This approximate a priori distribution is subsequently combined using Bayes' theorem with the “likelihood” provided by the multi‐physics computational models. Finally, the posterior distribution is evaluated using the saddle‐point method to obtain analytical expressions for the optimally predicted values for the parameters and responses of both multi‐physics models, along with corresponding reduced uncertainties. This work shows that even though the experimental data pertains solely to the compartment furthest from the inlet (where the data were measured), the predictive modeling procedure used herein actually improves the predictions and reduces the predicted uncertainties for the entire dissolver, including the compartment furthest from the measurements, because this predictive modeling methodology combines and transmits information simultaneously over the entire phase‐space, comprising all time steps and spatial locations. Copyright © 2016 John Wiley & Sons, Ltd.     

A novel microwave assisted reverse micelle fabrication route for Th (IV)‐MOFs as highly efficient adsorbent nanostructures with controllable structural properties to CO and CH4 adsorption: Design,and a systematic study

Reducing gas contaminants by affordable and effective adsorbents is a major challenge in the 21^st century. In the present study, thorium metal organic framework (Th‐MOF) nanostructures are introduced as highly efficient adsorbents. These compounds were manufactured via a novel route resulting from the development of microwave assisted reverse micelle (MARM) and ultrasound assisted reverse micelle (UARM) methods. The products were characterized utilizing XRD, SEM, TGA/DSC, BET, and FT‐IR analyses. Based on the results, the samples synthesized by MARM had uniform size distribution, high thermal stability, and significant surface area. Calculations using DFT/B3LYP indicated that the compounds have a tendency to the polymeric form, which could theoretically confirm the formation of Th‐MOF. Results of analysis of variance (ANOVA) showed that synthesis parameters played a critical role in the manufacturing of products with distinctive properties. Response surface methodology (RSM) predicted the possibility of creating Th‐MOF adsorbents with the surface area of 2579 m²/g, which was a considerable value in comparison with the properties of other adsorbents. Adsorption studies showed that, in the optimum conditions, the Th‐MOF products had high adsorption capacity for CO and CH₄. It is believed that the synthesis protocol developed in the present study and the systematic studies conducted on the samples which lead to products with ideal adsorption properties.     

Development and assessment of an intrusive polynomial chaos expansion-based continuous adjoint method for shape optimization under uncertainties

This article contributes to the development of methods for shape optimization under uncertainties, associated with the flow conditions, based on intrusive Polynomial Chaos Expansion (iPCE) and continuous adjoint. The iPCE to the Navier–Stokes equations for laminar flows of incompressible fluids is developed to compute statistical moments of the Quantity of Interest which are, then, compared with those obtained through the Monte Carlo method. The optimization is carried out using a continuous adjoint-enabled, gradient-based loop. Two different formulations for the continuous adjoint to the iPCE PDEs are derived, programmed, and verified. Intrusive PCE methods for the computation of the statistical moments require mathematical development, derivation of a new system of governing equations and their numerical solution. The development is presented for a chaos order of two and two uncertain variables and can be used as a guide to those willing to extend this development to a different set of uncertain variables or chaos order. The developed method and software, programmed in OpenFOAM, is applied to two optimization problems pertaining to the flow around isolated airfoils with uncertain farfield conditions.     

Interval methods as a simulation tool for the dynamics of biological wastewater treatment processes with parameter uncertainties

This paper presents sophisticated interval algorithms for the simulation of discrete-time dynamical systems with bounded uncertainties of both initial conditions and system parameters. Since naive implementations of interval algorithms might lead to guaranteed enclosures of all system states which are too conservative to be practically useful, we present algorithmic extensions of classical approaches which are applicable to the simulation of non-cooperative systems with time-varying uncertain parameters. Overestimation arising in the interval evaluation of dynamical system models due to the wrapping effect is reduced by an exact pseudo-linear transformation of nonlinear state equations and by new heuristics for the subdivision of interval enclosures which especially prefer splitting of unstable intervals. To highlight the typical procedure for parameterization of interval-based simulation routines and to demonstrate their efficiency, a nonlinear model of biological wastewater treatment processes is discussed. For this application, we consider the maximum specific growth rate of substrate consuming bacteria as a time-varying uncertain parameter. Only worst-case bounds are assumed to be available for the range of this parameter while no information is provided about its actual variation rate.     

Robust sampled‐data H∞ control for mechanical systems

This article addresses the issue of robust sampled‐data control for a class of uncertain mechanical systems with input delays and linear fractional uncertainties which appear in all the mass, damping, and stiffness matrices. Then, a novel Lyapunov–Krasovskii functional is constructed to obtain sufficient conditions under which the uncertain mechanical system is robustly, asymptotically stable with disturbance attenuation level about its equilibrium point for all admissible uncertainties. More precisely, Schur complement and Jenson's integral inequality are utilized to substantially simplify the derivation of the main results. In particular, a set of sampled‐data controller is designed in terms of the solution of certain linear matrix inequalities that can be solved effectively using available MATLAB software. Finally, a numerical example with simulation result is provided to show the effectiveness and less conservativeness of the proposed sampled‐data control scheme. © 2014 Wiley Periodicals, Inc. Complexity 20: 19–29, 2015