The Mind-Body Problem in the Origin of Logical Empiricism: Herbert Feigl and Psychophysical Parallelism

In the 19th century, "Psychophysical Parallelism" was the most popular solution of the mind-body problem among physiologists, psychologists and philosophers. (This is not to be mixed up with Leibnizian and other cases of "Cartesian" parallelism.) The fate of this non-Cartesian view, as founded by Gustav Theodor Fechner, is reviewed. It is shown that Feigl's "identity theory" eventually goes back to Alois Riehl who promoted a hybrid version of psychophysical parallelism and Kantian mind-body theory which was taken up by Feigl's teacher Moritz Schlick.

Parallel algorithms for simulating continuous time Markov chains

We have previously shown that the mathematical technique of uniformization can serve as the basis of synchronization for the parallel simulation of continuous-time Markov chains. This paper reviews the basic method and compares five different methods based on uniformization, evaluating their strengths and weaknesses as a function of problem characteristics. The methods vary in their use of optimism, logical aggregation, communication management, and adaptivity. Performance evaluation is conducted on the Intel Touchstone Delta multiprocessor, using up to 256 processors

Student-Authored Word Problems and Their Impact on High School Mathematics Students’ Engagement

Student-Authored Word Problems and Their Impact on High School Mathematics Students’ Engagement Jake Heidelberger May, 2012 Abstract The focus of this action research was the impact of writing their own word problems on student engagement and attitudes toward word problems. I focused on two sections of Advanced Algebra 2, mostly junior year students, during the linear functions as mathematical models unit of study. Data were collected from preliminary and concluding surveys, daily exit slips, and student interviews. After reviewing the traditional approach to solving word problems, I asked my students to use the problems we worked through as a guide and to write their own word problem and its solution key. As a result of this action research project, student confidence increased and more students saw the connections between mathematics and the real world. Breaking down the barriers and obstacles that prevent students from succeeding is at the very core of education, and the creative elements inherent within student-authored word problems certainly seem to have benefited my students. Based on my results, I fully intend to explore this teaching method further in my future teaching career, and to share it with my colleagues. Advisor: Dr. Kenneth E. Vo

Peter Weiss: Meine Ortschaft

„Meine Ortschaft” - ein Possessivpronomen, ein nicht näher bezeichneter Punkt auf der Landkarte: „Ortschaft”, lesen wir im Universal-Duden, sei auch ein Synonym für „Gemeinde”. In der Tat, um eine sehr spezielle „Gemeinde” an einem sehr speziellen Ort geht es hier, um Auschwitz nämlich, oder präziser, um das, was zwanzig Jahre nach seiner Befreiung von dieser Todesfabrik übriggeblieben ist

The Gelfand-Kirillov dimension of rank 2 Nichols algebras of diagonal type

Most interests in the theory of Nichols algebras emerged from the the theory of pointed Hopf algebras. For their classification it is an essential step to classify finite (Gelfand-Kirillov-) dimensional Nichols-algebras under some finiteness conditions. Nichols algebras have been discussed iby various authors. Especially, those of diagonal type which yielded interesting applications, for example as the positive part of quantized enveloping algebra of a simple finite-dimensional Lie algebras g. Finite-dimensional Nichols algebras of diagonal type have been classified in a series of papers. One important step for this has been the introduction of the root-system and the associated Weyl groupoid.In this context the following implications were observed: (1) If a Nichols algebra is of finite dimension, then the corresponding Weyl grouppoid is finite. (2) If the Weyl grouppoid of a Nichols algebra is finite, the Gelfand-Kirillov dimension of a Nichols algebra is finite. For (1) the converse is true under some circumstances. The converse of (2) has been conjectured to be true. Recently, the topic of finite Gelfand-Kirillov dimensional Nichols algebras has received increased attention. In particular rank 2 Nichols algebras of diagonal type with finite Gelfand-Kirillov dimension over a field of characteristic zero have been classified and were used to also classify finite Gelfand-Kirillov-dimensional Nichols algebras over abelian groups. The goal of this work is to extend this result to any characteristic. Note that there are more braidings yielding a finite root system in positive characteristic, especially there are examples with simple roots a yielding X(a,a) = 1 where X denotes the corresponding bicharacter. Roots of this kind imply infinite Gelfand-Kirillov dimension in characteristic zero. Hence new tools have to be developed generalizing the results for characteristic zero in addition

Heavy p-type carbon doping of MOCVD GaAsP using CBrCl₃

CBrCl₃ is shown to be a useful precursor for heavy p-type carbon doping of GaAsxP1−x grown via metalorganic chemical vapor deposition (MOCVD) across a range of compositions. Structural and electrical properties of the GaAsP films were measured for various processing conditions. Use of CBrCl3 decreased the growth rate of GaAsP by up to 32% and decreases x by up to 0.025. The dependence of these effects on precursor inputs is investigated, allowing C-doped GaAsP films to be grown with good thickness and compositional control. Hole concentrations of greater than 2×10¹⁹ cm−3 were measured for values of x from 0.76 to 0.90.National Science Foundation (U.S.) (Award 0939514)National Research Foundation of SingaporeNational Science Foundation (U.S.) (Award DMR-14-19807

Fast and reliable MCMC for cosmological parameter estimation

Markov Chain Monte Carlo (MCMC) techniques are now widely used for cosmological parameter estimation. Chains are generated to sample the posterior probability distribution obtained following the Bayesian approach. An important issue is how to optimize the efficiency of such sampling and how to diagnose whether a finite-length chain has adequately sampled the underlying posterior probability distribution. We show how the power spectrum of a single such finite chain may be used as a convergence diagnostic by means of a fitting function, and discuss strategies for optimizing the distribution for the proposed steps. The methods developed are applied to current CMB and LSS data interpreted using both a pure adiabatic cosmological model and a mixed adiabatic/isocurvature cosmological model including possible correlations between modes. For the latter application, because of the increased dimensionality and the presence of degeneracies, the need for tuning MCMC methods for maximum efficiency becomes particularly acute.Comment: 12 pages, 17 figures. Submitted to MNRA