A method of bisection for discounted Markov decision problems

We describe in this paper how to introduce the concept of bisection into Dynamic Programming of stationary Markovian decision processes with infinite horizon. The combination of these two methods delivers a new class of algorithms. A basic bisection algorithm is given. Its rate of convergence is rather independent of the input data, especially the discount factor or contracting factor. If in any method of successive approximations we have > 0.5, then the bisection method has a faster convergence than the successive approximations. Bisection is especially advantageous if is close to unity. The computation of two inventory control problems with the basic algorithm of bisection is presented. The second example has a discount factor=0.9994. Using Howard's automobile replacement problem the new method is compared with value iteration, policy iteration andPorteus' method of extrapolations. Among them bisection turned out to be the most powerful procedure. The combination withPorteus' method of extrapolation is not as efficient as the bisection method alone. We also investigate how to combine the bisection method with monotone extrapolation when the transition matrices do not have equal row sums.

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Zusammenfassung In dieser Arbeit wird die Idee der Bisektion in die Dynamische Optimierung stationärer Markovscher Entscheidungsprozesse mit unendlichem Planungshorizont eingeführt. Die Verbindung dieser beiden Methoden schafft eine neue Klasse von Algorithmen. Ein Basisalgorithmus, der selbst Ausgangspunkt zahlreicher Verfeinerungen und Spezialisierungen bildet, wird vorgestellt. Seine Konvergenzgeschwindigkeit ist nahezu unabhängig von Input-Daten, speziell dem Diskontfaktor bzw. der Lipschitz-Konstanten. Die Bisektion ist immer dann schneller als die Methode der sukzessiven Approximation, falls>0,5 ist. Deshalb ist das neue Verfahren besonders bei Problemen mit schwacher Kontraktionseigenschaft, d.h. nahe bei eins, geeignet. Der Rechenverlauf des Basisalgorithmus wird anhand zweier Lagerhaltungsmodelle diskutiert von denen das zweite eine Lipschitz-Konstante=0.9994 besitzt. Am Beispiel des Howardschen Autoersatzproblems zeigt sich, daß das Bisektionsverfahren im Vergleich mit der Wertiteration, Politikiteration undPorteus' Extrapolationsverfahren das schnellste Verfahren ist. Die Kombination der Bisektion mit der Extrapolationsmethode ist ungünstiger als die Bisektion allein. Es wird noch untersucht, wie die Bisektion mit der monotonen Extrapolation verbunden werden kann, wenn die Zustands-übergangsmatrizen keine konstanten Zeilensummen besitzen.

     

A comparison of two approaches to the optimal positioning of a new product in an attribute space

This paper is concerned with the optimal positioning of a new product in an attribute space. A deterministic optimization model that relies on the axiom of choice is compared with the model byShocker/Srinivasan [1974] that incorporates a probabilistic measure of choice. Investigating the assumptions and the construction of both models, it is shown that the probability function byShocker/Srinivasan is based on a controversial assumption and incorporates a parameter that has not been given an economic explanation. Furthermore, both models are applied to complex configurations. It is demonstrated that the optimal positions for the new product resulting from the model byShocker/Srinivasan depend heavily on the parameter just mentioned and may run contrary to plausible consequences of the axiom of choice.

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Zusammenfassung Für die optimale Gestaltung neuer Produkte, d.h. ihrer Positionierung in einem Raum von Produkteigenschaften, wird ein Modell angeboten, das auf einer deterministischen Kaufentscheidung beruht, ein anderes, das eine stochastische Kaufentscheidung unterstellt. Es wird gezeigt, daß der zuletzt genannte Modelltyp stark von der Spezifikation eines ökonomisch bisher nicht erklärten Parameters abhängt und z.T. Konsequenzen aufweist, die dem Wahlaxiom zuwider laufen, auf das das erstgenannte Modell aufbaut. Durch einen Vergleich auch komplexer Konfigurationen von Käuferbeurteilungen neuer Produkte wird gezeigt, welche Gestaltungsentscheidungen auf der Grundlage der beiden Modelle zur Optimierung einer Zielfunktion zu treffen sind.

     

Über die optimale Beleuchtung einer geraden Straße

The following problem is due toL. Fejes Tóth: For a given sort of lamps letf(x) be the intensity of brightness in each point having distancex from the foot of the lamp. How must infinitely many lamps of this kind be arranged on a both-side infinite rectilinear road, such that the infimum of the intensities of brightness, extended over the whole street, is maximal, subject to the condition that the average number of lamps per kilometer is bounded by a fixed number (“Best distributions”)? The main result of this paper is: Iff is strictly convex, the equidistant distribution is best.     

On the Fourier transformation on spaces of (p,q)-multipliers

LetG denote a locally compact abelian topological group. The aim of the present paper is to prove an “intermediate” result between two well-known results ofL. Hörmander andG. I. Gaudry concerning the structure of the spaces ?_G?μ?t ^p,q (G).     

Eine spezielle Vorgangsdauerverteilung zur Netzplananalyse durch Simulation

Zusammenfassung Es wird eineC genannte Verteilung bereitgestellt, die sich zur Erfassung von Vorgangsdauern bei Netzplanproblemen eignet und durch besondere Wirtschaftlichkeit bei Simulationsmethoden auszeichnet.

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Summary In this paper a distributionC will be presented for the activity duration times in network problems which from the economical point of view is fit for the solution to network problems via Monte Carlo simulation.

     

Zur Entscheidungstheorie bei mehrfacher Zielsetzung

Zusammenfassung Der Begriff eines rationalen Lösunxgsprinzips für Entscheidungsprobleme mit mehrfacher Zielsetzung wird definitorisch eingeführt. Anhand der definierenden Bedingungen werden die neueren Lösungsansätze auf Rationalität untersucht. Zusätzlich wird besonderes Gewicht auf die kritische Untersuchung der den einzelnen Verfahren zugrundeliegenden Informationsannahmen gelegt. Dabei zeigt sich, wie auch aus empirischen Untersuchungen abgeleitet wird, daß es bei der Formulierung von Lösungsansätzen auf eine präzise Darstellung des Lösungsprinzips und der damit im Zusammenhang stehenden Informationsannahme ankommt; erst auf dieser Grundlage kann die entscheidungspraktische Relevanz solcher Verfahren überprüft werden.

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Summary For multiobjective decision problems a notion of a rational solution principle is introduced by definition. The recently suggested solution approaches are tested for rationality under the defining conditions. Additionally, great importance is attached to the critical analysis of the information requirements underlying the different methods. It turns out, as well as it will be derived from empirical investigations, that a precise presentation of the solution principle and of the corresponding information requirements is indispensable formulating such approaches; first on this basis the practical relevance of solution procedures can be examined.

     

Acid–Base Equilibrium and Self-Association in Relation to High Antitumor Activity of Selected Unsymmetrical Bisacridines Established by Extensive Chemometric Analysis

Unsymmetrical bisacridines (UAs) represent a novel class of anticancer agents previously synthesized by our group. Our recent studies have demonstrated their high antitumor potential against multiple cancer cell lines and human tumor xenografts in nude mice. At the cellular level, these compounds affected 3D cancer spheroid growth and their cellular uptake was selectively modulated by quantum dots. UAs were shown to undergo metabolic transformations in vitro and in tumor cells. However, the physicochemical properties of UAs, which could possibly affect their interactions with molecular targets, remain unknown. Therefore, we selected four highly active UAs for the assessment of physicochemical parameters under various pH conditions. We determined the compounds’ pK_a dissociation constants as well as their potential to self-associate. Both parameters were determined by detailed and complex chemometric analysis of UV-Vis spectra supported by nuclear magnetic resonance (NMR) spectroscopy. The obtained results indicate that general molecular properties of UAs in aqueous media, including their protonation state, self-association ratio, and solubility, are strongly pH-dependent, particularly in the physiological pH range of 6 to 8. In conclusion, we describe the detailed physicochemical characteristics of UAs, which might contribute to their selectivity towards tumour cells as opposed to their effect on normal cells.     

USAEME-GC/MS Method for Easy and Sensitive Determination of Nine Bisphenol Analogues in Water and Wastewater

A new, simple and sensitive method for isolating nine compounds from the bisphenol group (analogues: A, B, C, E, F, G, Cl₂, Z, AP) based on one-step liquid–liquid microextraction with in situ acylation followed by gas chromatography-mass spectrometry was developed and validated using influent and effluent wastewaters. The chemometric approach based on the Taguchi method was used to optimize the main conditions of simultaneous extraction and derivatization. The recoveries of the proposed procedure ranged from 85 to 122%, and the repeatability expressed by the coefficient of variation did not exceed 8%. The method’s limits of detection were in the range of 0.4–64 ng/L, and the method’s limits of quantification ranged from 1.3 to 194 ng/L. The developed method was used to determine the presence of the tested compounds in wastewater from a municipal wastewater treatment plant located in northeastern Poland. From this sample, eight analytes were detected. Concentrations of bisphenol A of 400 ng/L in influent and 100 ng/L in effluent were recorded, whereas other bisphenols reached 67 and 50 ng/L for influent and effluent, respectively. The removal efficiency of bisphenol analogues in the tested wastewater treatment plant ranged from 7 to approximately 88%.     

Propolis Contra Pharmacological Interventions in Bees

In addition to wax, propolis is a mixture of resins, terpenes, and etheric and aromatic oils. This composition supports its very strong biochemical activity that affects bee health. Bee colonies are externally exposed to the activity of other different pharmacologically active substances and toxic agents used in beekeeping procedures, veterinary interventions, and the environment. Even if free form common diseases, they may suffer from parasites or toxins. In any such case the abundance and variety of honeyflow, besides proper therapy, is crucial for the maintenance of bee health. Propolis itself cannot be considered as food but can be considered as micro-nutrients for bees. This is due to the fact that some of its compounds may penetrate different bee products, and this way be consumed by bees and their larvae, while stored in the hive. This perspective shows propolis as natural agent reducing the toxicity of pyrethroid acaricides, stimulating production of detoxification enzymes, enhancing the action of antibiotics, and increasing expression of genes that encode proteins responsible for detoxication. The aim of this review is to summarize current data on the possible impact on veterinary public health of the introduction into propolis of residues of pharmacological agents approved in the EU for use in the treatment of bee colonies and their environment.     

Epilobium angustifolium L. as a Potential Herbal Component of Topical Products for Skin Care and Treatment—A Review

Epilobium angustifolium L. (EA) has been used as a topical agent since ancient times. There has been an increasing interest in applying EA as a raw material used topically in recent years. However, in the literature, there are not many reports on the comprehensive application of this plant to skin care and treatment. EA contains many valuable secondary metabolites, which determine antioxidant, anti-inflammatory, anti-aging, and antiproliferative activity effects. One of the most important active compounds found in EA is oenothein B (OeB), which increases the level of ROS and protects cells from oxidative damage. OeB also influences wound healing and reduces inflammation by strongly inhibiting hyaluronidase enzymes and inhibiting COX-1 and COX-2 cyclooxygenases. Other compounds that play a key role in the context of application to the skin are flavonoids, which inhibit collagenase and hyaluronidase enzymes, showing anti-aging and anti-inflammatory properties. While terpenes in EA play an important role in fighting bacterial skin infections, causing, among other things cell membrane, permeability increase as well as the modification of the lipid profiles and the alteration of the adhesion of the pathogen to the animal cells. The available scientific information on the biological potential of natural compounds can be the basis for the wider use of EA in skin care and treatment. The aim of the article is to review the existing literature on the dermocosmetic use of E. angustifolium.