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.

     

An Extensive Assessment of Network Embedding in PPI Network Alignment

Network alignment is a fundamental task in network analysis. In the biological field, where the protein–protein interaction (PPI) is represented as a graph, network alignment allowed the discovery of underlying biological knowledge such as conserved evolutionary pathways and functionally conserved proteins throughout different species. A recent trend in network science concerns network embedding, i.e., the modelling of nodes in a network as a low-dimensional feature vector. In this survey, we present an overview of current PPI network embedding alignment methods, a comparison among them, and a comparison to classical PPI network alignment algorithms. The results of this comparison highlight that: (i) only five network embeddings for network alignment algorithms have been applied in the biological context, whereas the literature presents several classical network alignment algorithms; (ii) there is a need for developing an evaluation framework that may enable a unified comparison between different algorithms; (iii) the majority of the proposed algorithms perform network embedding through matrix factorization-based techniques; (iv) three out of five algorithms leverage external biological resources, while the remaining two are designed for domain agnostic network alignment and tested on PPI networks; (v) two algorithms out of three are stated to perform multi-network alignment, while the remaining perform pairwise network alignment.     

K18- and CAG-hACE2 Transgenic Mouse Models and SARS-CoV-2: Implications for Neurodegeneration Research

COVID-19, caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), is a global pandemic that might lead to very serious consequences. Notably, mental status change, brain confusion, and smell and taste disorders along with neurological complaints have been reported in patients infected with SARS-CoV-2. Furthermore, human brain tissue autopsies from COVID-19 patients show the presence of SARS-CoV-2 neuroinvasion, which correlates with the manifestation of meningitis, encephalitis, leukocyte infiltration, and neuronal damage. The olfactory mucosa has been suggested as a way of entry into the brain. SARS-CoV-2 infection is also known to provoke a hyper-inflammatory reaction with an exponential increase in the production of pro-inflammatory cytokines leading to systemic responses, even in the absence of direct infection of brain cells. Angiotensin-converting enzyme 2 (ACE2), the entry receptor of SARS-CoV-2, has been extensively demonstrated to be present in the periphery, neurons, and glial cells in different brain regions. To dissect the details of neurological complications and develop therapies helping COVID-19 survivors regain pre-infection quality of life, the development of robust clinical models is highly warranted. Several human angiotensin-converting enzyme 2 (hACE2) transgenic mouse models have been developed and used for antiviral drug screening and vaccine development, as well as for better understanding of the molecular pathogenetic mechanisms of SARS-CoV-2 infection. In this review, we summarize recent results from the studies involving two such mouse models, namely K18- and CAG-hACE2 transgenics, to evaluate the direct and indirect impact of SARS-CoV-2 infection on the central nervous system.     

An Experimental Study of a Flux Modulated Solid State Metathesis Reaction

A solid state metathesis (SSM) reaction was investigated with respect to the formation of rare‐earth carbodiimides, the role of the co‐produced salt (LiCl), and the eutectic flux medium (LiCl/KCl). A SSM reaction is characterized by an exothermic reaction in which a salt (often LiCl) is coproduced. When the salt melts, it can serve as a useful medium for the crystallization of a desired product. An improved crystal growth can be observed by using an eutectic flux. However, the composition of an eutectic LiCl/KCl flux is altered when LiCl is produced during the reaction. The thermal effects concerning the endothermic melting of the flux and the exothermic ingnition of the SSM reaction may compensate each other, which is not necessarily a drawback for the reaction to proceed.     

Magnetic Anisotropy of Dichlorobis(η5‐cyclopentadienyl) Complexes of Vanadium,Niobium, and Tantalum

Abstract. The magnetic behavior of the mononuclear nd¹ systems MCp₂Cl₂ (M = V⁴⁺[3d¹], Nb⁴⁺[4d¹], Ta⁴⁺[5d¹], space group P2₁/c, pseudosymmetry of the molecules C_2v) deviates from pure single ion spin magnetism on account of ligand field effect (H_lf), spin‐orbit coupling (H_so), and intermolecular spin‐spin exchange interactions (H_ex). For both VCp₂Cl₂ and NbCp₂Cl₂ excellent adaptations to the measured susceptibility data were obtained (2 K ≤ T ≤ 300 K) on the basis of spectroscopic data (lf, so) and cooperative metal–metal interactions (ex) of antiferromagnetic nature [molecular field model (mf)]. For TaCp₂Cl₂ experimental term structure data are not available. Therefore, Jørgensen's spectroscopical series (g‐factor of the central ion) was applied to extrapolate the data set for TaCp₂Cl₂. H_lf, H_so, and H_ex (antiferromagnetic) increase in the order 3d¹ → 4d¹ → 5d¹ leading, with rising atomic number of the metals, to a distinct enhancement of the magnetic anisotropy. At 4 K the μ_eff components μ_eff,y (oriented perpendicular to the cg–M–cg plane; “cg” = center of gravity of the Cp ring), μ_eff,z (oriented along the twofold pseudoaxis), and μ_eff,x are 1.73, 1.69, 1.68 (V), 1.73, 1.62, 1.59 (Nb), and 1.71, 1.59, 1.49 (Ta). While μ_eff,y is independent of T, both μ_eff,z and μ_eff,x decrease with decreasing T.