@phdthesis{Beinrucker2015,
  author    = {Beinrucker, Andre},
  title     = {Variable selection in high dimensional data analysis with applications},
  school      = {Universit{\"a}t Potsdam},
  pages     = {VII, 107},
  year      = {2015},
  language  = {en}
}
@phdthesis{Bettenbuehl2015,
  author    = {Bettenb{\"u}hl, Mario},
  title     = {Microsaccades},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  isbn      = {978-3-86956-122-6},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72622},
  school      = {Universit{\"a}t Potsdam},
  pages     = {iv, 126},
  year      = {2015},
  abstract  = {The first thing we do upon waking is open our eyes. Rotating them in our eye sockets, we scan our surroundings and collect the information into a picture in our head. Eye movements can be split into saccades and fixational eye movements, which occur when we attempt to fixate our gaze. The latter consists of microsaccades, drift and tremor. Before we even lift our eye lids, eye movements - such as saccades and microsaccades that let the eyes jump from one to another position - have partially been prepared in the brain stem. Saccades and microsaccades are often assumed to be generated by the same mechanisms. But how saccades and microsaccades can be classified according to shape has not yet been reported in a statistical manner. Research has put more effort into the investigations of microsaccades' properties and generation only since the last decade. Consequently, we are only beginning to understand the dynamic processes governing microsaccadic eye movements. Within this thesis, the dynamics governing the generation of microsaccades is assessed and the development of a model for the underlying processes. Eye movement trajectories from different experiments are used, recorded with a video-based eye tracking technique, and a novel method is proposed for the scale-invariant detection of saccades (events of large amplitude) and microsaccades (events of small amplitude). Using a time-frequency approach, the method is examined with different experiments and validated against simulated data. A shape model is suggested that allows for a simple estimation of saccade- and microsaccade related properties. For sequences of microsaccades, in this thesis a time-dynamic Markov model is proposed, with a memory horizon that changes over time and which can best describe sequences of microsaccades.},
  language  = {en}
}
@phdthesis{Trump2015,
  author    = {Trump, Stephanie Sonja},
  title     = {Mathematik in der Physik der Sekundarstufe II!?},
  school      = {Universit{\"a}t Potsdam},
  pages     = {214},
  year      = {2015},
  language  = {de}
}
@phdthesis{Conforti2015,
  author    = {Conforti, Giovanni},
  title     = {Reciprocal classes of continuous time Markov Chains},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-82255},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xvi, 183},
  year      = {2015},
  abstract  = {In this thesis we study reciprocal classes of Markov chains. Given a continuous time Markov chain on a countable state space, acting as reference dynamics, the associated reciprocal class is the set of all probability measures on path space that can be written as a mixture of its bridges. These processes possess a conditional independence property that generalizes the Markov property, and evolved from an idea of Schr{\"o}dinger, who wanted to obtain a probabilistic interpretation of quantum mechanics. Associated to a reciprocal class is a set of reciprocal characteristics, which are space-time functions that determine the reciprocal class. We compute explicitly these characteristics, and divide them into two main families: arc characteristics and cycle characteristics. As a byproduct, we obtain an explicit criterion to check when two different Markov chains share their bridges. Starting from the characteristics we offer two different descriptions of the reciprocal class, including its non-Markov probabilities. The first one is based on a pathwise approach and the second one on short time asymptotic. With the first approach one produces a family of functional equations whose only solutions are precisely the elements of the reciprocal class. These equations are integration by parts on path space associated with derivative operators which perturb the paths by mean of the addition of random loops. Several geometrical tools are employed to construct such formulas. The problem of obtaining sharp characterizations is also considered, showing some interesting connections with discrete geometry. Examples of such formulas are given in the framework of counting processes and random walks on Abelian groups, where the set of loops has a group structure. In addition to this global description, we propose a second approach by looking at the short time behavior of a reciprocal process. In the same way as the Markov property and short time expansions of transition probabilities characterize Markov chains, we show that a reciprocal class is characterized by imposing the reciprocal property and two families of short time expansions for the bridges. Such local approach is suitable to study reciprocal processes on general countable graphs. As application of our characterization, we considered several interesting graphs, such as lattices, planar graphs, the complete graph, and the hypercube. Finally, we obtain some first results about concentration of measure implied by lower bounds on the reciprocal characteristics.},
  language  = {en}
}
@phdthesis{Kaganova2015,
  author    = {Kaganova, Ekaterina},
  title     = {Das Lehrpotential von Schulbuchlehrtexten im Fach Mathematik},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-80705},
  school      = {Universit{\"a}t Potsdam},
  pages     = {287},
  year      = {2015},
  abstract  = {Das Schulbuch ist ein etablierter und bedeutender Bestandteil des Mathematikunterrichts. Lehrer nutzen es, um ihren Unterricht vorzubereiten und/oder zu gestalten; Sch{\"u}ler, um in selbigem zu lernen und zu bestehen, vielleicht sogar aus eigenem Interesse; Eltern, um sich dar{\"u}ber zu informieren, was ihr Kind eigentlich k{\"o}nnen soll und wie sie ihm gegebenenfalls helfen k{\"o}nnen. Dar{\"u}ber hinaus ist das Schulbuch ein markantes gesellschaftliches Produkt, dessen Zweck es ist, das Unterrichtsgeschehen zu steuern und zu beeinflussen. Damit ist es auch ein Anzeiger daf{\"u}r, was und wie im Mathematikunterricht gelehrt werden sollte und wird. Die Lehrtexte als zentrale Bestandteile von Schulb{\"u}chern verweisen in diesem Zusammenhang insbesondere auf die Phasen der Einf{\"u}hrung neuen Lernstoffs. Daraus legitimiert sich {\"u}bergreifend die Fragestellung, was und wie (gut) Mathematikschulbuchlehrtexte lehren bzw. was und wie (gut) adressierte Sch{\"u}ler aus ihnen (selbstst{\"a}ndig) lernen, d.h. Wissen erwerben k{\"o}nnen. Angesichts der komplexen und vielf{\"a}ltigen Bedeutung von Schulbuchlehrtexten verwundert es, dass die mathematikdidaktische Forschung bislang wenig Interesse an ihnen zeigt: Es fehlen sowohl eine theoretische Konzeption der Gr{\"o}ße ‚Lehrpotential eines schulmathematischen Lehrtextes' als auch ein analytisches Verfahren, um das anhand eines Mathematikschulbuchlehrtextes Verstehbare und Lernbare zu ermitteln. Mit der vorliegenden Arbeit wird sowohl in theoretisch-methodologischer als auch in empirischer Hinsicht der Versuch unternommen, diesen Defiziten zu begegnen. Dabei wird das ‚Lehrpotential eines Mathematikschulbuchlehrtextes' auf der Grundlage der kognitionspsychologischen Schematheorie und unter Einbeziehung textlinguistischer Ans{\"a}tze als eine textimmanente und analytisch zug{\"a}ngliche Gr{\"o}ße konzipiert. Anschließend wird das Lehrpotential von f{\"u}nf Lehrtexten ausgew{\"a}hlter aktueller Schulb{\"u}cher der Jahrgangsstufen 6 und 7 zu den Inhaltsbereichen ‚Br{\"u}che' und ‚lineare Funktionen' analysiert. Es zeigt sich, dass die untersuchten Lehrtexte aus deutschen Schulb{\"u}chern f{\"u}r Sch{\"u}ler sehr schwer verst{\"a}ndlich sind, d.h. es ist kompliziert, einigen Teiltexten im Rahmen des Gesamttextes einen Sinn abzugewinnen. Die Lehrtexte sind insbesondere dann kaum sinnhaft lesbar, wenn ein Sch{\"u}ler versucht, die mitgeteilten Sachverhalte zu verstehen, d.h. Antworten auf die Fragen zu erhalten, warum ein mathematischer Sachverhalt gerade so und nicht anders ist, wozu ein neuer Sachverhalt/Begriff gebraucht wird, wie das Neue mit bereits Bekanntem zusammenh{\"a}ngt usw. Deutlich zug{\"a}nglicher und sinnhafter erscheinen die Mathematikschulbuchlehrtexte hingegen unter der Annahme, dass ihre zentrale Botschaft in der Mitteilung besteht, welche Aufgabenstellungen in der jeweiligen Lehreinheit vorkommen und wie man sie bearbeitet. Demnach k{\"o}nnen Sch{\"u}ler anhand dieser Lehrtexte im Wesentlichen lernen, wie sie mit mathematischen Zeichen, die f{\"u}r sie kaum etwas bezeichnen, umgehen sollen. Die hier vorgelegten Analyseergebnisse gewinnen in einem soziologischen Kontext an Tragweite und Brisanz. So l{\"a}sst sich aus ihnen u.a. die These ableiten, dass die analysierten Lehrtexte keine ‚ungl{\"u}cklichen' Einzelf{\"a}lle sind, sondern dass die ‚Aufgabenorientierung in einem mathematischen Gewand' ein Charakteristikum typischer (deutscher) Mathematikschulbuchlehrtexte und - noch grunds{\"a}tzlicher - einen Wesenszug typischer schulmathematischer Kommunikation darstellt.},
  language  = {de}
}
@phdthesis{AlSaedy2015,
  author    = {Al-Saedy, Ammar Jaffar Muhesin},
  title     = {Normally solvable lagrangian boundary value problems},
  school      = {Universit{\"a}t Potsdam},
  pages     = {110},
  year      = {2015},
  language  = {en}
}
@phdthesis{Wallenta2015,
  author    = {Wallenta, Daniel},
  title     = {Sequences of compact curvature},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-87489},
  school      = {Universit{\"a}t Potsdam},
  pages     = {viii, 73},
  year      = {2015},
  abstract  = {By perturbing the differential of a (cochain-)complex by "small" operators, one obtains what is referred to as quasicomplexes, i.e. a sequence whose curvature is not equal to zero in general. In this situation the cohomology is no longer defined. Note that it depends on the structure of the underlying spaces whether or not an operator is "small." This leads to a magical mix of perturbation and regularisation theory. In the general setting of Hilbert spaces compact operators are "small." In order to develop this theory, many elements of diverse mathematical disciplines, such as functional analysis, differential geometry, partial differential equation, homological algebra and topology have to be combined. All essential basics are summarised in the first chapter of this thesis. This contains classical elements of index theory, such as Fredholm operators, elliptic pseudodifferential operators and characteristic classes. Moreover we study the de Rham complex and introduce Sobolev spaces of arbitrary order as well as the concept of operator ideals. In the second chapter, the abstract theory of (Fredholm) quasicomplexes of Hilbert spaces will be developed. From the very beginning we will consider quasicomplexes with curvature in an ideal class. We introduce the Euler characteristic, the cone of a quasiendomorphism and the Lefschetz number. In particular, we generalise Euler's identity, which will allow us to develop the Lefschetz theory on nonseparable Hilbert spaces. Finally, in the third chapter the abstract theory will be applied to elliptic quasicomplexes with pseudodifferential operators of arbitrary order. We will show that the Atiyah-Singer index formula holds true for those objects and, as an example, we will compute the Euler characteristic of the connection quasicomplex. In addition to this we introduce geometric quasiendomorphisms and prove a generalisation of the Lefschetz fixed point theorem of Atiyah and Bott.},
  language  = {en}
}