Sweeping the Space of Admissible Quark Mass Matrices

We propose a new and efficient method of reconstructing quark mass matrices from their eigenvalues and a complete set of mixing observables. By a combination of the principle of NNI (nearest neighbour interaction) bases which are known to cover the general case, and of the polar decomposition theorem that allows to convert arbitrary nonsingular matrices to triangular form, we achieve a parameterization where the remaining freedom is reduced to one complex parameter. While this parameter runs through the domain bounded by a circle with radius R determined by the up-quark masses around the origin in the complex plane one sweeps the space of all mass matrices compatible with the given set of data.Comment: 18 page

Quantum field theory on a discrete space and noncommutative geometry

We analyse in detail the quantization of a simple noncommutative model of spontaneous symmetry breaking in zero dimensions taking into account the noncommutative setting seriously. The connection to the counting argument of Feyman diagrams of the corresponding theory in four dimensions is worked out explicitly. Special emphasis is put on the motivation as well as the presentation of some well-known basic notions of quantum field theory which in the zero-dimensional theory can be studied without being spoiled by technical complications due to the absence of divergencies.Comment: 111 pages, 6 figures, Habilitationsschrif

Leptonic Generation Mixing, Noncommutative Geometry and Solar Neutrino Fluxes

Triangular mass matrices for neutrinos and their charged partners contain full information on neutrino mixing in a most concise form. Although the scheme is general and model independent, triangular matrices are typical for reducible but indecomposable representations of graded Lie algebras which, in turn, are characteristic for the standard model in noncommutative geometry. The mixing matrix responsible for neutrino oscillations is worked out analytically for two and three lepton families. The example of two families fixes the mixing angle to just about what is required by the Mikheyev-Smirnov-Wolfenstein resonance oscillation of solar neutrinos. In the case of three families we classify all physically plausible choices for the neutrino mass matrix and derive interesting bounds on some of the moduli of the mixing matrix.Comment: LaTeX, 12 page

Only Three

It is shown that it is possible to account for all experimental indications for neutrino oscillations with just three flavours. In particular we suggest that the atmospheric neutrino anomaly and the LSND result can be explained by the same mass difference and mixing. Possible implications and future tests of the resulting mass and mixing pattern are given.Comment: 10 pages, 2 Postscript figures (eps

Uncertainty Analysis for Data-Driven Chance-Constrained Optimization

In this contribution our developed framework for data-driven chance-constrained optimization is extended with an uncertainty analysis module. The module quantifies uncertainty in output variables of rigorous simulations. It chooses the most accurate parametric continuous probability distribution model, minimizing deviation between model and data. A constraint is added to favour less complex models with a minimal required quality regarding the fit. The bases of the module are over 100 probability distribution models provided in the Scipy package in Python, a rigorous case-study is conducted selecting the four most relevant models for the application at hand. The applicability and precision of the uncertainty analyser module is investigated for an impact factor calculation in life cycle impact assessment to quantify the uncertainty in the results. Furthermore, the extended framework is verified with data from a first principle process model of a chloralkali plant, demonstrating the increased precision of the uncertainty description of the output variables, resulting in 25% increase in accuracy in the chance-constraint calculation.BMWi, 0350013A, ChemEFlex - Umsetzbarkeitsanalyse zur Lastflexibilisierung elektrochemischer Verfahren in der Industrie; Teilvorhaben: Modellierung der Chlor-Alkali-Elektrolyse sowie anderer Prozesse und deren Bewertung hinsichtlich Wirtschaftlichkeit und möglicher HemmnisseDFG, 414044773, Open Access Publizieren 2019 - 2020 / Technische Universität Berli

Allocation to social positions in class: interactions and relationships in first grade school classes and their consequences

"Using the approach of qualitative social network research, this article focuses on two ‘systems of social inequality’ on the basis of which learning is organized: one is the institutional and organizational framework structuring the encounters between teachers and students, the other is a system of social inequality incorporated at the level of emotions and affections. Both systems seem to be virtually inevitable and, due to the tacit nature of their workings in class interactions, escape attempts at deliberate control. The article demonstrates how the web of social relationships in the early grades acts to reinforce both systems of social inequality and how they mutually affect one another in the class setting. Two first grade classes were studied for this purpose using mixed methods. The findings clearly support these conclusions: in both classes under study, a configuration of relationships consisting of a range of distinct (student) positions has emerged, and all parties involved have a similar perception of this social configuration. These social positions, each of which offer different opportunities for learning, are reflected both in interactions (as evidenced by video analysis) and the students’ stories (as evidenced in interviews). Such stabilization processes determine student careers early on and render the class setting 'porous' as a space of learning." [author's abstract

Differential Algebras in Non-Commutative Geometry

We discuss the differential algebras used in Connes' approach to Yang-Mills theories with spontaneous symmetry breaking. These differential algebras generated by algebras of the form functions $\otimes$ matrix are shown to be skew tensorproducts of differential forms with a specific matrix algebra. For that we derive a general formula for differential algebras based on tensor products of algebras. The result is used to characterize differential algebras which appear in models with one symmetry breaking scale.Comment: 21 page

Gravity, Non-Commutative Geometry and the Wodzicki Residue

We derive an action for gravity in the framework of non-commutative geometry by using the Wodzicki residue. We prove that for a Dirac operator $D$ on an $n$ dimensional compact Riemannian manifold with $n\geq 4$, $n$ even, the Wodzicki residue Res$(D^{-n+2})$ is the integral of the second coefficient of the heat kernel expansion of $D^{2}$. We use this result to derive a gravity action for commutative geometry which is the usual Einstein Hilbert action and we also apply our results to a non-commutative extension which, is given by the tensor product of the algebra of smooth functions on a manifold and a finite dimensional matrix algebra. In this case we obtain gravity with a cosmological constant.Comment: 17p., MZ-TH/93-3

Non-renormalization theorems of Supersymmetric QED in the Wess-Zumino gauge

The non-renormalization theorem of chiral vertices and the generalized non-renormalization theorem of the photon self energy are derived in SQED on the basis of algebraic renormalization. For this purpose the gauge coupling is extended to an external superfield. This extension already provides detailed insight into the divergence structure. Moreover, using the local supercoupling together with an additional external vector multiplet that couples to the axial current, the model becomes complete in the sense of multiplicative renormalization, with two important implications. First, a Slavnov--Taylor identity describing supersymmetry, gauge symmetry, and axial symmetry including the axial anomaly can be established to all orders. Second, from this Slavnov-Taylor identity we can infer a Callan-Symanzik equation expressing all aspects of the non-renormalization theorems. In particular, the gauge $\beta$-function appears explicitely in the closed form.Comment: Latex, 47 page

Zum Design(begriff) der Netzwerkgesellschaft: Design als zentrales Element der Identitätsformation in Netzwerken

Der Verfasser setzt sich zunächst mit Dirk Baeckers Begriff der 'next society' auseinander, der damit entgegen der Mainstream-Soziologie Design-Elemente zur Anwendung bringt. Vor diesem Hintergrund wird das eigene rationale Designkonzept vorgestellt, das einen Designbegriff auf Basis einer zunächst vorgenommenen Konzentration auf Designphänomene im engeren Sinn gewinnt, also auf Gestaltungsprozesse von Designern. Besonderes Augenmerk wird dabei darauf gelegt, dass dieser Designbegriff auch als eine gangbare Alternative zum Übersetzungsbegriff der Akteur-Netzwerk-Theorie fungiert. Design trägt nicht nur zur Identitätsbildung von Akteuren bei, sondern auch zur Konstituierung ganzer Milieus und Kulturen. Insofern vermittelt der Designbegriff zwischen sozialen Mikro- und Makrophänomenen. Abschließend wird ein ausgeweitetes Designkonzept vorgeschlagen, das alle gestalterischen Aspekte der Identitätsformation erfassen soll, die sich in sozialen Netzwerken beobachten lassen. Den Transmissionsriemen dafür stellt eine aktuelle Debatte einer Ausweitung des Betätigungsfeldes der Designer dar, die bereits weit über die Designprofession hinaus wirkt, die Debatte über 'design thinking'. Design thinking kann als die Grammatik viel versprechender Kontrollprojekte in der 'next society' aufgefasst werden. (ICE2