Non-negativity preserving numerical algorithms for stochastic differential equations

Construction of splitting-step methods and properties of related non-negativity and boundary preserving numerical algorithms for solving stochastic differential equations (SDEs) of Ito-type are discussed. We present convergence proofs for a newly designed splitting-step algorithm and simulation studies for numerous numerical examples ranging from stochastic dynamics occurring in asset pricing theory in mathematical finance (SDEs of CIR and CEV models) to measure-valued diffusion and superBrownian motion (SPDEs) as met in biology and physics.Comment: 23 pages, 7 figures. Figures 6.2 and 6.3 in low resolution due to upload size restrictions. Original resolution at http://gisc.uc3m.es/~moro/profesional.htm

Ceteris Paribus Laws

Laws of nature take center stage in philosophy of science. Laws are usually believed to stand in a tight conceptual relation to many important key concepts such as causation, explanation, confirmation, determinism, counterfactuals etc. Traditionally, philosophers of science have focused on physical laws, which were taken to be at least true, universal statements that support counterfactual claims. But, although this claim about laws might be true with respect to physics, laws in the special sciences (such as biology, psychology, economics etc.) appear to have—maybe not surprisingly—different features than the laws of physics. Special science laws—for instance, the economic law “Under the condition of perfect competition, an increase of demand of a commodity leads to an increase of price, given that the quantity of the supplied commodity remains constant” and, in biology, Mendel's Laws—are usually taken to “have exceptions”, to be “non-universal” or “to be ceteris paribus laws”. How and whether the laws of physics and the laws of the special sciences differ is one of the crucial questions motivating the debate on ceteris paribus laws. Another major, controversial question concerns the determination of the precise meaning of “ceteris paribus”. Philosophers have attempted to explicate the meaning of ceteris paribus clauses in different ways. The question of meaning is connected to the problem of empirical content, i.e., the question whether ceteris paribus laws have non-trivial and empirically testable content. Since many philosophers have argued that ceteris paribus laws lack empirically testable content, this problem constitutes a major challenge to a theory of ceteris paribus laws

The Role of Settlement Structures Within the Concept of Sustainability - The Arnum West Case Study

Today catch phrases like too much energy consumption, energy shortage and declining energy supplies can be heard throughout the “western†world. Given that oil and natural gas are non-renewable resources, it is inevitable that at some point there will be a peak first in worldwide oil and later in natural gas production. In times of limited energy resources, decision makers and planners should draw their attention to long lasting structures – such as settlements – and make them sustainable. Historic cities, which we perceive as “niceâ€, “quaint†and “worth livingâ€, emerged from the satisfaction of different human needs in the scale of self-regulating internal body energy consumption. Some examples of grown cities are Toledo, ES; Siena, IT; Hallein, AT and Nurnberg (centre), DE. With the advent of external energy usage at the end of the 19th century, the scale of settlements exploded, leading to the now evident urban sprawl. The separation of functions envisioned in the “Charter of Athens†led to low density housing subdivisions, shopping- and recreational centres, office parks, civic institutions and endemic car usage in between. As a result, area-wide provision of public transport often becomes infeasible, forcing city planners to build large highway networks and parking infrastructure. The evident problem is the excessive level of motorized transport and its adverse effects, which to this extent can no longer reasonably be sustained. Current attempts to solve this issue are under way, but they do not use the right level of impact. One way to resolve the problem in the long run is to change the way settlements are organised. Arnum is located in the southern periphery of Hannover, Germany. In the course of a proposed extension of the city railway from Hannover to Arnum, an architectural contest was undertaken for Arnum West. Our paper will be a follow up and a complement to our contribution to that competition. We will identify sustainable settlement structures and their main indicators. After analysing a variety of different instruments, we will highlight effective tools to make settlements sustainable – such as integration of functions, preference of pedestrians, cyclists and public transport or parking space management – and show ways how they can be implemented in the context of the Arnum West case study. Furthermore, we will demonstrate the impacts of different settlement structures on the environment using three scenarios: business as usual, business as usual with the impact of the sustainable Arnum West case study as part of the existing settlement – a state of transition so to speak – and a fictitious sustainable settlement as a whole. We want to show ways how to change the settlement structure, because it forms the basis for human behaviour. On a long-term basis, it is imperative to change the behaviour towards a sustainable way of living.

Numerical simulation of a linear stochastic oscillator with additive noise

The ability of numerical methods to reproduce long-time features of a linear stochastic oscillator is examined. It is shown that certain, widely-used, methods fail to capture the correct second moment growth rate, whereas a customized extension of the partitioned Euler method behaves well in this respect. It is also shown that the partitioned Euler method inherits an infinite-oscillation property. A weaker oscillation result is proved for a wide class of numerical methods

Bayesianische Bestätigung des Irrationalen? Zum Problem der genuinen Bestätigung

Der herkömmliche bayesianische Bestätigungsbegriff hat das Problem, dass ihm zufolge auch pseudowissenschaftliche Erklärungshypothesen bestätigt werden. Ein Beispiel ist der rationalisierte Kreationismus, demzufolge die aktuelle Welt so ist wie sie ist, weil Gott sie so geschaffen hat. Solche Pseudoerklärungen zeichnen sich dadurch aus, dass durch sie beliebige Erfahrungen ex-post, also im nachhinein, erklärbar sind. Intuitiv betrachtet sind sie erst gar nicht bestätigungsfähig. Alternative Bestätigungsbegriffe, welche diese Intuition einzufangen versuchen, sind das novel prediction (NP) und das use novelty (UN) Kriterium der Bestätigung. Gegen beide Kriterien gibt es schwerwiegende Einwände. In diesem Vortrag entwickle ich das Kriterium der genuinen Bestätigung, welches das Problem der Pseudoerklärungen rein probabilistisch löst und noch weitere Vorzüge gegenüber den bisher vorgeschlagenen Bestätigungsbe-griffen besitzt

Beliefs about Teaching and Learning in the Digital Age

Obwohl gut ausgebaute personelle und technische Rahmenbedingungen an deutschen Hochschulen einen flächendeckenden Einsatz digitaler Lehr-Lern-Technologien in den letzten Jahren immer weiter vereinfacht haben, ist nur eine geringe und fachspezifisch recht unterschiedlich gestaltete Einbindung dieser Technologien in die Lehre zu beobachten. Die Erforschung von Beliefs (dt. Überzeugungen) von Hochschullehrenden stellt eine Möglichkeit dar, so die Annahme des Beitrags, Zusammenhänge zwischen den subjektiven Sichtweisen der Lehrenden auf Lehr-Lern-Prozesse und der Einbindung digitaler Lehr-Lern-Technologien abseits objektiver Rahmenbedingungen zu identifizieren. Im folgenden Beitrag wird ein Forschungsdesign vorgestellt, das sich mit der Frage befasst, welche individuellen Überzeugungen Lehrende ihrem Lehrhandeln zugrunde legen und welche Bedeutung sie digitalen Lehr-Lern-Technologien für einen gelingenden Lehr-Lern-Prozess zuweisen. Dargestellt werden ausserdem Überlegungen, welchen Einfluss lehrbezogene und mediale Sozialisationen auf die Überzeugungen zum Einsatz von digitalen Technologien in der Lehre besitzen könnten. Abschliessend werden qualitative und quantitative Forschungsmethoden dargelegt, die für eine Erhebung der Zusammenhänge angedacht sind. Das Forschungsdesign wird in einem Promotionsvorhaben an der Hochschule Osnabrück mit der Untersuchungsgruppe der Professor/-innen umgesetzt.Although digital technology is becoming more and more common in university life due to a good infrastructural development, we can observe a rare use of digital technologies by teachers in higher education. Also the usage of technology differs widely from one discipline to another. The concept of beliefs provides an explanatory potential to take a closer look at possible links between teachers' personal views on teaching and learning and the usage of digital technologies in higher education. This paper presents an approach to examine the teachers' beliefs on the concept of good teaching, and their beliefs about the ability of digital technology to improve their teaching successfully. A planned study ought to collect the underlying teachers' beliefs about teaching, learning, and digital technology. First considerations are represented concerning the collection and analysis of qualitative and quantitative data. The study will take part in a case study at the University of Applied Sciences Osnabrück

Interactive Causes: Revising the Markov Condition

This paper suggests a revision of the theory of causal nets (TCN). In Section 1 we introduce an axiomatization of TCN based on a realistic understanding. It is shown that the causal Markov condition entails three independent principles. In Section 2 we analyze inde-terministic decay as the major counterexample to one of these principles: screening-off by common causes (SCC). We call (SCC)-violating common causes interactive causes. In Sec-tion 3 we develop a revised version of TCN, called TCN*, which accounts for interactive causes. It is shown that there are interactive causal models that admit of no faithful non-interactive reconstruction

Letter, Carl Schurz to Riggs, March 27, 1900

This handwritten letter, dated March 27, 1900, is written from Carl Schurz to Riggs. The letter is an accpetance to an invitation.https://scholarsjunction.msstate.edu/fvw-manuscripts-schurz/1052/thumbnail.jp

Letter, Carl Schurz to Sinclair, February 9, Year Unknown

This handwritten letter, dated February 9, is written from Carl Schurz to Mr. Sinclair. The letter offers to write an article.https://scholarsjunction.msstate.edu/fvw-manuscripts-schurz/1058/thumbnail.jp