Penultimate Approximations in Statistics of Extremes and Reliability of Large Coherent Systems

In reliability theory any coherent system can be represented as either a series-parallel or a parallel-series system. Its lifetime can thus be written as the minimum of maxima or the maximum of minima. For large-scale coherent systems it is sensible to assume that the number of system components goes to infinity. Then, the possible non-degenerate extreme value laws either for maxima or for minima are eligible candidates for the system reliability or at least for the finding of adequate lower and upper bounds for the reliability. The identification of the possible limit laws for the system reliability of homogeneous series-parallel (or parallel-series) systems has already been done under different frameworks. However, it is well-known that in most situations such non-degenerate limit laws are better approximated by an adequate penultimate distribution. Dealing with regular and homogeneous parallel-series systems, we assess both theoretically and through Monte-Carlo simulations the gain in accuracy when a penultimate approximation is used instead of the ultimate one.     

Stochastic Equations and Inclusions with Mean Derivatives and Some Applications

The paper is devoted to a brief introduction into the theory of equations and inclusions with mean derivatives and to investigation of a special type of such inclusions called inclusions of geometric Brownian motion type. The existence of optimal solutions maximizing some cost criteria, is proved.     

Estimation Problems for Periodically Correlated Isotropic Random Fields

Spectral theory of isotropic random fields in Euclidean space developed by M. I. Yadrenko is exploited to find a solution to the problem of optimal linear estimation of the functional

$$ A\zeta ={\sum\limits_{t=0}^{\infty}}\,\,\,{\int_{S_n}} \,\,a(t,x)\zeta (t,x)\,m_n(dx) $$

which depends on unknown values of a periodically correlated (cyclostationary with period T) with respect to time isotropic on the sphere S _n in Euclidean space E ⁿ random field ζ(t, x), t?∈?Z, x?∈?S _n . Estimates are based on observations of the field ζ(t, x)?+?θ(t, x) at points (t, x), t?=???1,???2, ..., x?∈?S _n , where θ(t, x) is an uncorrelated with ζ(t, x) periodically correlated with respect to time isotropic on the sphere S _n random field. Formulas for computing the value of the mean-square error and the spectral characteristic of the optimal linear estimate of the functional Aζ are obtained. The least favourable spectral densities and the minimax (robust) spectral characteristics of the optimal estimates of the functional Aζ are determined for some special classes of spectral densities.

     

Using a cognitive architecture with a physiological substrate to represent effects of a psychological stressor on cognition

Adding a physiological representation to a cognitive architecture offers an attractive approach to modeling the effects of stress on cognition. We introduce ACT-R/Φ, an extended version of the ACT-R cognitive architecture that includes an integrative model of physiology. The extension allows the representation of how physiology and cognition interact. This substrate was used to represent potential effects of a startle response and task-based stress during a mental arithmetic (subtraction) task. We compare predictions from two models loaded into the new hybrid architecture to models previously developed within ACT-R. General behavior differed between models in that the ACT-R/Φ models had dynamic declarative memory noise over the course of the task based on varying epinephrine levels. They attempted more subtractions but were less accurate; this more closely matched human performance than the previous ACT-R models. Using ACT-R/Φ allows a more tractable integration of current physiological and cognitive perspectives on stress. ACT-R/Φ also permits further exploration of the interaction between cognition and physiology, and the emergent effects on behavior caused by the interaction among physiological subsystems. This extension is useful for anyone exploring how the human mind can occur in and be influenced by the physical universe.     

Deformations of Charged Axially Symmetric Initial Data and the Mass–Angular Momentum–Charge Inequality

We show how to reduce the general formulation of the mass–angular momentum–charge inequality, for axisymmetric initial data of the Einstein–Maxwell equations, to the known maximal case whenever a geometrically motivated system of equations admits a solution. It is also shown that the same reduction argument applies to the basic inequality yielding a lower bound for the area of black holes in terms of mass, angular momentum, and charge. This extends previous work by the authors (Cha and Khuri, Ann Henri Poincaré, doi: 10.1007/s00023-014-0332-6, arXiv:1401.3384, 2014), in which the role of charge was omitted. Lastly, we improve upon the hypotheses required for the mass–angular momentum–charge inequality in the maximal case.     

Method development and inter-laboratory comparison about the determination of titanium from titanium dioxide nanoparticles in tissues by inductively coupled plasma mass spectrometry

Nanosized titanium dioxide (TiO₂) is one of the most interesting and valuable nanomaterials for the construction industry but also in health care applications, food, and consumer goods, e.g., cosmetics. Therefore, the properties associated with this material are described in detail. Despite its widespread use, the analytical determination and characterization of nanosized metal oxides is not as straightforward as the comparatively easy-to-detect metallic nanoparticles (e.g., silver or gold). This study presents the method development and the results of the determination of tissue titanium (Ti) levels after treatment of rats with the nanosized TiO₂. Total Ti levels were chosen to evaluate the presence and distribution of TiO₂ nanoparticles. A procedure consisting of incubation with a mixture of nitric acid (HNO₃) and hydrofluoric acid (HF), and heating was developed to digest tissues and TiO₂ nanomaterials in order to determine the total Ti content by inductively coupled plasma mass spectrometry (ICPMS). For the inter-laboratory comparison, altogether four laboratories analyzed the same samples upon digestion using the available ICPMS equipment. A major premise for any toxicokinetic study is the possibility to detect the chemical under investigation in biological samples (tissues). So, the study has to be performed with a dose high enough to allow for subsequent tissue level measurement of the chemical under investigation. On the other hand, dose of the chemical applied should not induce over toxicity in the animal as this may affect its absorption, distribution, metabolism, and excretion. To determine a non-toxic TiO₂ dosage, an acute toxicity study in rats was performed, and the organs obtained were evaluated for the presence of Ti by ICPMS. Despite the differences in methodology and independent of the sample preparation and the ICPMS equipment used, the results obtained for samples with Ti concentrations >4 μg Ti/g tissue agreed well.

Development and characterization of a small electromembrane extraction probe coupled with mass spectrometry for real-time and online monitoring of in vitro drug metabolism

A small and very simple electromembrane extraction probe (EME-probe) was developed and coupled directly to electrospray ionization mass spectrometry (ESI-MS), and this system was used to monitor in real time in vitro metabolism by rat liver microsomes of drug substances from a small reaction (incubation) chamber (37 °C). The drug-related substances were continuously extracted from the 1.0 mL metabolic reaction mixture and into the EME-probe by an electrical potential of 2.5 V. The extraction probe consisted of a 1-mm long and 350-μm ID thin supported liquid membrane (SLM) of 2-nitrophenyl octyl ether. The drugs and formed metabolites where extracted through the SLM and directly into a 3 μL min^?1 flow of 60 mM HCOOH inside the probe serving as the acceptor solution. The acceptor solution was directed into the ESI-MS-system, and the MS continuously monitored the drug-related substances extracted by the EME-probe. The extraction efficiency of the EME-probe was dependant on the applied electrical potential and the length of the SLM, and these parameters as well as the volume of the reaction chamber were set to the values mentioned above to avoid serious depletion from the reaction chamber (soft extraction). Soft extraction was mandatory in order not to affect the reaction kinetics by sample composition changes induced by the EME-probe. The EME-probe/MS-system was used to establish kinetic profiles for the in vitro metabolism of promethazine, amitriptyline and imipramine as model substances.     

Online dynamic pH junction–sweeping for the determination of benzoic and sorbic acids in food products by capillary electrophoresis

A simple, low-cost, and efficient online focusing method that combines a dynamic pH junction and sweeping by capillary electrophoresis with polymer solutions was developed and optimized for the simultaneous determination of benzoic acid (BA) and sorbic acid (SA). A sample solution consisting of 2.5 mM phosphate at pH 3.0 and a buffer solution containing 15 mM tetraborate (pH 9.2), 40 mM sodium dodecyl sulfate, and 0.100 % (w/v) poly(ethylene oxide) were utilized to realize dynamic pH junction–sweeping for BA and SA. Under the optimized conditions, the entire analysis process was completed in 7 min, and a 900-fold sensitivity enhancement was achieved with limits of detection (S/N?=?3) as low as 8.2 and 6.1 nM for BA and SA, respectively. The linear ranges were between 20 nM and 20 μM for BA and 20 nM and 10 μM for SA, with correlation coefficients greater than 0.992. The recoveries of the proposed method ranged from 90 to 113 %. These satisfactory results indicate that this method has the potential to be an effective analytical tool for the rapid screening of BA and SA in different food products.

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Figure An online focusing strategy combining dynamic pH junction and sweeping for sensitive determination of benzoic and sorbic acid in food products using capillary electrophoresis wit polymer solutions

     

Kinetics of bioconjugate nanoparticle label binding in a sandwich-type immunoassay

Nanoparticle labels have enhanced the performance of diagnostic, screening, and other measurement applications and hold further promise for more sensitive, precise, and cost-effective assay technologies. Nevertheless, a clear view of the biomolecular interactions on the molecular level is missing. Controlling the ratio of molecular recognition over undesired nonspecific adhesion is the key to improve biosensing with nanoparticles. To improve this ratio with an aim to disallow nonspecific binding, a more detailed perspective into the kinetic differences between the cases is needed. We present the application of two novel methods to determine complex binding kinetics of bioconjugate nanoparticles, interferometry, and force spectroscopy. Force spectroscopy is an atomic force microscopy technique and optical interferometry is a direct method to monitor reaction kinetics in second-hour timescale, both having steadily increasing importance in nanomedicine. The combination is perfectly suited for this purpose, due to the high sensitivity to detect binding events and the ability to investigate biological samples under physiological conditions. We have attached a single biofunctionalized nanoparticle to the outer tip apex and studied the binding behavior of the nanoparticle in a sandwich-type immunoassay using dynamic force spectroscopy in millisecond timescale. Utilization of the two novel methods allowed characterization of binding kinetics in a time range spanning from 50 ms to 4 h. These experiments allowed detection and demonstration of differences between specific and nonspecific binding. Most importantly, nonspecific binding of a nanoparticle was reduced at contact times below 100 ms with the solid-phase surface.

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Figure A single biofunctionalized nanoparticle was attached to the outer tip apex and the binding behavior of the nanoparticle in a sandwich-type immunoassay, A) without analyte, B) with analyte and C) saturating analyte concentration, was recorded using dynamic force spectroscopy in millisecond timescale. The setting allowed measurement of the association speed of nonspecific binding.