Opinion Dynamics and Bounded Confidence Models, Analysis and Simulation

When does opinion formation within an interacting group lead to consensus, polarization or fragmentation? The article investigates various models for the dynamics of continuous opinions by analytical methods as well as by computer simulations. Section 2 develops within a unified framework the classical model of consensus formation, the variant of this model due to Friedkin and Johnsen, a time-dependent version and a nonlinear version with bounded confidence of the agents. Section 3 presents for all these models major analytical results. Section 4 gives an extensive exploration of the nonlinear model with bounded confidence by a series of computer simulations. An appendix supplies needed mathematical definitions, tools, and theorems.opinion dynamics, consensus/dissent, bounded confidence, nonlinear dynamical systems.

Truth and Cognitive Division of Labour: First Steps Towards a Computer Aided Social Epistemology

The paper analyzes the chances for the truth to be found and broadly accepted under conditions of cognitive division of labour combined with a social exchange process. Cognitive division of labour means, that only some individuals are active truth seekers, possibly with different capacities. The social exchange process consists in an exchange of opinions between all individuals, whether truth seekers or not. We de- velop a model which is investigated by both, mathematical tools and computer simulations. As an analytical result the Funnel theorem states that under rather weak conditions on the social process a consensus on the truth will be reached if all individuals posses an arbitrarily small inclination for truth seeking. The Leading the pack theorem states that under certain conditions even a single truth seeker may lead all individuals to the truth. Systematic simulations analyze how close and how fast groups can get to the truth depending on the frequency of truth seekers, their capacities as truth seekers, the position of the truth (more to the extreme or more in the centre of an opinion space), and the willingness to take into account the opinions of others when exchanging and updating opinions. A tricky movie visualizes simulations results in a parameter space of higher dimensions.Opinion Dynamics, Consensus/dissent, Bounded Confidence, Truth, Social Epistemology

A mathematical approach to estimate the error during calculating the smoke layer height in industrial facilities

Engineering based calculation procedures in fi re safety science often consist of unknown or uncertain input data which are to be estimated by the engineer using appropriate and plausible assumptions. Thereby, errors in this data are induced in the calculation and thus, impact the number as well as the reliability of the results. In this paper a procedure is presented to directly quantify and consider unknown input properties in the process of calculation using distribution functions and Monte-Carlo Simulations. A sensitivity analysis reveals the properties which have a major impact on the calculation reliability. Furthermore, the results are compared to the numerical models of CFAST and FDS

Quantifying the combustion behavior of polymers by the combustion efficiency with regard to the weighting of fire loads

For assessing fi re loads in industrial buildings it is essential to quantify the burning behavior of materials as accurate as adequate. There for the combustion effi ciency is used. To determine the combustion effi ciency required energies and energy rates can be measured via Cone Calorimeter. Exemplifi ed by two polymers, polyethylene and polymethylmethacrylate, these parameters are determined and analyzed with regard to the calculation of the combustion effi ciency

Die allgemeine Struktur des Monopols. Zur Dynamik des Widerspruchs von Gebrauchswert und Wert

Daß es Monopole gibt, scheint außer Zweifel. Die tägliche Zeitung jedenfalls weiß davon zu berichten, mal direkter mit der quantitativen Auflistung der hundert Größten (,,Inflation und Fusion machen die Großfirmen zu Giganten", Frankfurter Rundschau vom 26. 7. 7 5), mal indirekter durch die Sorge um eine „inhärente Korruption der modernen Demokratie" (so F.A. von Hayek laut Frankfurter Allgemeine Zeitung vom 11.10.75). Dennoch: Unmittelbar gegeben ist dieses Phänomen nicht. Wie wenig unmittelbar gegeben es ist, machen die Probleme deutlich, die sich ergeben, wenn es an eine genauere statistische Erfassung dieses Phänomens geht. In einer empirischen Untersuchung der Stabilität großer Unternehmungen findet sich etwa folgender Satz: ,,From an historical perspective, however, it appears tobe an open question whether big corporation are long-lived or ·whether they tend to be „paper tigers" of glorio4s but relatively short longevity." (1) Grundsätzlich gilt auch hier: ,,Das inhaltliche Problem der Sinnlichkeit ist zugleich ein Formproblem, d.h. es wird vermittels der Sinnlichkeit allein überhaupt kein Gegenstand gegeben." (2

Weiterhin Schwierigkeiten: Entgegnung auf die Bemerkungen von Georgios Stamatis

Der Beitrag von Stamatis bezieht sich zwar auf den Aufsatz „Die allgemeine Struktur des Monopols. Zur Dynamik des Widerspruchs von Gebrauchswert und Wert". (kurz: ASM) in Prokla 24, knüpft jedoch nicht an den dort behandelten Gegenstand, nämlich den Prozeß der Monopolisierung, an. Wenn ich im folgenden kurz auf den Beitrag von Stamatis eingehe, so deshalb, weil in ihm Behauptungen versammelt sind, die eine richtige Kritik am Neoricardianismus behindern.Der Vorbemerkung der Redaktionskonferenz der Prokla in Heft 24 zu ASM läßt sich die Absicht entnehmen, eine marxistische Auseinandersetzung mit dem Werk von P. Sraffa in der BRD zu befördern. Da mit dem Ansatz Sraffas heute auch bestimmte politische Handlungen begründet werden, ist diese Auseinandersetzung auch politisch von Bedeutung. (In Frankreich läuft seit einiger Zeit eine solche Debatte. Für die BRD Siehe etwa den Aufsatz M. Cogoys zum Dilemma der neoricardianischen Theorie.) Ich werde im folgenden erstens anhand von Stamatis Fehlfassung einige Anmerkungen zum „neoricardianischen Ansatz" machen, und sodann zweitens auf die Zerlegbarkeit von Produktionsstrukturen und die dahinterstehende Frage der ungleichen ökonomischen Entwicklung eingehen, einem in ASM behandelten Problem, dem, in reduzierter Gestalt, Stamatis die Hälfte seines Beitrages widmet

Acute lower limb ischemia due to thrombo-embolic arterial occlusions in two previously healthy men with markedly elevated Lp(a)

Lipoprotein (a) (Lp(a)) is a well-documented risk factor for atherosclerotic cardiovascular disease. Its role in acute thrombo-embolic occlusions of peripheral arteries is not known. We describe two cases of multiple, acute, peripheral arterial occlusions in two previously healthy men with markedly elevated Lp(a). Both cases had unsatisfactory results after percutaneous and surgical revascularization procedures. Experience yielded in these two cases suggests that when an unfavorable outcome occurs in a peripheral artery disease patient in the absence of the regular risk factors, Lp(a) should be determined and its role investigated