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In this paper, an advanced study covering the comparison between two classes of generalized inverses is conducted. Two sets of instances, strictly derived from the recently introduced nonunique S- and σ-inverse, are analyzed, especially in terms of degrees of freedom-oriented interchangeable application in different engineering tasks. Henceforth, the respective collections of right and left inverses can be combined in order to achieve a complex tool for robustification of a plethora of real processes. The great potential of two S- and σ-inverse, in particular in robust control and signal recovery as well as complex optimal tasks, is confirmed in the manuscript and supported by the recently carried out research investigations.

In the field of chemical engineering, mathematical models have been proven to be an indispensable tool for process analysis, process design, and condition monitoring. To gain the most benefit from model-based approaches, the implemented mathematical models have to be based on sound principles, and they need to be calibrated to the process under study with suitable model parameter estimates. Often, the model parameters identified by experimental data, however, pose severe uncertainties leading to incorrect or biased inferences. This applies in particular in the field of pharmaceutical manufacturing, where usually the measurement data are limited in quantity and quality when analyzing novel active pharmaceutical ingredients. Optimally designed experiments, in turn, aim to increase the quality of the gathered data in the most efficient way. Any improvement in data quality results in more precise parameter estimates and more reliable model candidates. The applied methods for parameter sensitivity analyses and design criteria are crucial for the effectiveness of the optimal experimental design. In this work, different design measures based on global parameter sensitivities are critically compared with state-of-the-art concepts that follow simplifying linearization principles. The efficient implementation of the proposed sensitivity measures is explicitly addressed to be applicable to complex chemical engineering problems of practical relevance. As a case study, the homogeneous synthesis of 3,4-dihydro-1H-1-benzazepine-2,5-dione, a scaffold for the preparation of various protein kinase inhibitors, is analyzed followed by a more complex model of biochemical reactions. In both studies, the model-based optimal experimental design benefits from global parameter sensitivities combined with proper design measures.

13 C metabolic flux analysis (MFA) has become an indispensable tool to measure metabolic reaction rates (fluxes) in living organisms, having an increasingly diverse range of applications. Here, the choice of the 13 C labeled tracer composition makes the difference between an information-rich experiment and an experiment with only limited insights. To improve the chances for an informative labeling experiment, optimal experimental design approaches have been devised for 13 C-MFA, all relying on some a priori knowledge about the actual fluxes. If such prior knowledge is unavailable, e.g., for research organisms and producer strains, existing methods are left with a chicken-and-egg problem. In this work, we present a general computational method, termed robustified experimental design (R-ED), to guide the decision making about suitable tracer choices when prior knowledge about the fluxes is lacking. Instead of focusing on one mixture, optimal for specific flux values, we pursue a sampling based approach and introduce a new design criterion, which characterizes the extent to which mixtures are informative in view of all possible flux values. The R-ED workflow enables the exploration of suitable tracer mixtures and provides full flexibility to trade off information and cost metrics. The potential of the R-ED workflow is showcased by applying the approach to the industrially relevant antibiotic producer Streptomyces clavuligerus , where we suggest informative, yet economic labeling strategies.

The search for generation approaches to robust chaos has received considerable attention due to potential applications in cryptography or secure communications. This paper is of interest regarding a 1-D sigmoidal chaotic map, which has never been distinctly investigated. This paper introduces a generic form of the sigmoidal chaotic map with three terms, i.e., xn+1 = ∓AfNL(Bxn) ± Cxn ± D, where A, B, C, and D are real constants. The unification of modified sigmoid and hyperbolic tangent (tanh) functions reveals the existence of a “unified sigmoidal chaotic map” generically fulfilling the three terms, with robust chaos partially appearing in some parameter ranges. A simplified generic form, i.e., xn+1 = ∓fNL(Bxn) ± Cxn, through various S-shaped functions, has recently led to the possibility of linearization using (i) hardtanh and (ii) signum functions. This study finds a linearized sigmoidal chaotic map that potentially offers robust chaos over an entire range of parameters. Chaos dynamics are described in terms of chaotic waveforms, histogram, cobweb plots, fixed point, Jacobian, and a bifurcation structure diagram based on Lyapunov exponents. As a practical example, a true random bit generator using the linearized sigmoidal chaotic map is demonstrated. The resulting output is evaluated using the NIST SP800-22 test suite and TestU01.

Ultra High Frequency (UHF) quotes and trades are examined in high resolution and data patterns that do not correspond to plausible market activity as in Brownlees and Gallo (Comput Stat Data Anal 51(4):2232–2245, 2006) are identified. Noise patterns other than microstructure noise are isolated and diagnostic methods are evaluated accordingly. A flexible paradigm of data handling that synthesizes statistical technique and limit order book modelling is presented, extending Barndorff-Nielsen et al. (Econom J 12(3):C1–C32, 2009), which operationalises the use of expanded filtration in empirical microstructure research. Empirical evidence from the NASDAQ 100 is presented, comprehensively demonstrating that removal of non-microstructure noise from the limit order book adds significant robustness to estimation across techniques and levels of market depth.

This book introduces a comprehensive methodology for adaptive control design of parabolic partial differential equations with unknown functional parameters, including reaction-convection-diffusion systems ubiquitous in chemical, thermal, biomedical, aerospace, and energy systems. Andrey Smyshlyaev and Miroslav Krstic develop explicit feedback laws that do not require real-time solution of Riccati or other algebraic operator-valued equations. The book emphasizes stabilization by boundary control and using boundary sensing for unstable PDE systems with an infinite relative degree. The book also presents a rich collection of methods for system identification of PDEs, methods that employ Lyapunov, passivity, observer-based, swapping-based, gradient, and least-squares tools and parameterizations, among others. Including a wealth of stimulating ideas and providing the mathematical and control-systems background needed to follow the designs and proofs, the book will be of great use to students and researchers in mathematics, engineering, and physics. It also makes a valuable supplemental text for graduate courses on distributed parameter systems and adaptive control.

Unconstrained convex quadratic optimization problems subject to parameter perturbations are considered. A robustification approach is proposed and analyzed which reduces the sensitivity of the optimal function value with respect to the parameter. Since reducing the sensitivity and maintaining a small objective value are competing goals, strategies for balancing these two objectives are discussed. Numerical examples illustrate the approach.

One of the approaches to compare forecasting methods is to test whether the risk from a benchmark prediction is smaller than the others. The test can be embedded into a general problem of testing inequality constraints using a one-sided sup functional. Hansen showed that such tests suffer from asymptotic bias. This article generalizes this observation, and proposes a hybrid method to robustify the power properties by coupling a one-sided sup test with a complementary test. The method can also be applied to testing stochastic dominance or moment inequalities. Simulation studies demonstrate that the new test performs well relative to the existing methods. For illustration, the new test was applied to analyze the forecastability of stock returns using technical indicators employed by White.

This article deals with estimation of the regression function and its derivatives using local polynomial fitting. An important question is: How to determine the order of the polynomial to be fitted in a particular fixed neighborhood? This depends on the local curvature of the unknown curve. A higher order fit leads to a possible bias reduction, but results in an increase of variability. A precise evaluation of this increase is presented, and from this it is also clear that it is preferable to choose the order of fit adaptively. In this article we provide, for a given bandwidth, such a data-driven variable order selection procedure. The basic idea is to obtain a good estimate of the mean squared error at each location point and to use this estimate as a criterion for the order selection. The performance of the proposed selection procedure is illustrated via simulated examples. It turns out that the adaptive order fit is more robust against bandwidth variation; even if the bandwidth varies by a factor of 3, the resulting estimates are qualitatively indistinguishable. Hence the issue of choosing the bandwidth becomes less important and a crude bandwidth selector might suffice. We propose such a simple rule for selecting the bandwidth, and demonstrate its performance for the adaptive order fit via some simulated examples.