@unpublished{LyTarkhanov2015, author = {Ly, Ibrahim and Tarkhanov, Nikolai Nikolaevich}, title = {A Rad{\´o} theorem for p-harmonic functions}, volume = {4}, number = {3}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-71492}, pages = {10}, year = {2015}, abstract = {Let A be a nonlinear differential operator on an open set X in R^n and S a closed subset of X. Given a class F of functions in X, the set S is said to be removable for F relative to A if any weak solution of A (u) = 0 in the complement of S of class F satisfies this equation weakly in all of X. For the most extensively studied classes F we show conditions on S which guarantee that S is removable for F relative to A.}, language = {en} } @unpublished{LyTarkhanov2015, author = {Ly, Ibrahim and Tarkhanov, Nikolai Nikolaevich}, title = {Asymptotic expansions at nonsymmetric cuspidal points}, volume = {4}, number = {7}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-78199}, pages = {11}, year = {2015}, abstract = {We study asymptotics of solutions to the Dirichlet problem in a domain whose boundary contains a nonsymmetric conical point. We establish a complete asymptotic expansion of solutions near the singular point.}, language = {en} } @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analysis with applications}, school = {Universit{\"a}t Potsdam}, pages = {VII, 107}, year = {2015}, language = {en} } @unpublished{FedosovTarkhanov2015, author = {Fedosov, Boris and Tarkhanov, Nikolai Nikolaevich}, title = {Deformation quantisation and boundary value problems}, volume = {4}, number = {5}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-77150}, pages = {27}, year = {2015}, abstract = {We describe a natural construction of deformation quantisation on a compact symplectic manifold with boundary. On the algebra of quantum observables a trace functional is defined which as usual annihilates the commutators. This gives rise to an index as the trace of the unity element. We formulate the index theorem as a conjecture and examine it by the classical harmonic oscillator.}, language = {en} } @unpublished{ElinShoikhetTarkhanov2015, author = {Elin, Mark and Shoikhet, David and Tarkhanov, Nikolai Nikolaevich}, title = {Analytic semigroups of holomorphic mappings and composition operators}, volume = {4}, number = {6}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-77914}, pages = {30}, year = {2015}, abstract = {In this paper we study the problem of analytic extension in parameter for a semigroup of holomorphic self-mappings of the unit ball in a complex Banach space and its relation to the linear continuous semigroup of composition operators. We also provide a brief review around this topic.}, language = {en} } @incollection{Petsche2015, author = {Petsche, Hans-Joachim}, title = {Einf{\"u}hrung}, series = {Raum und Zahl im Fokus der Wissenschaften : eine multidisziplin{\"a}re Vorlesungsreihe}, booktitle = {Raum und Zahl im Fokus der Wissenschaften : eine multidisziplin{\"a}re Vorlesungsreihe}, publisher = {Trafo}, address = {Berlin}, isbn = {978-3-86464-082-7}, pages = {9 -- 14}, year = {2015}, language = {de} } @article{Petsche2015, author = {Petsche, Hans-Joachim}, title = {Raum und Zahl - philosophische Kontexte}, series = {Raum und Zahl im Fokus der Wissenschaften : eine multidisziplin{\"a}re Vorlesungsreihe}, journal = {Raum und Zahl im Fokus der Wissenschaften : eine multidisziplin{\"a}re Vorlesungsreihe}, publisher = {Trafo}, address = {Berlin}, isbn = {978-3-86464-082-7}, pages = {15 -- 33}, year = {2015}, language = {de} } @article{SixtusFischer2015, author = {Sixtus, Elena and Fischer, Martin H.}, title = {Eine kognitionswissenschaftliche Betrachtung der Konzepte "Raum" und "Zahl"}, series = {Raum und Zahl im Fokus der Wissenschaften : eine multidisziplin{\"a}re Vorlesungsreihe}, journal = {Raum und Zahl im Fokus der Wissenschaften : eine multidisziplin{\"a}re Vorlesungsreihe}, publisher = {Trafo}, address = {Berlin}, isbn = {978-3-86464-082-7}, pages = {35 -- 62}, year = {2015}, language = {de} } @article{Proeve2015, author = {Pr{\"o}ve, Ralf}, title = {Numerische Zeichen und die Repr{\"a}sentation von Sinn}, series = {Raum und Zahl im Fokus der Wissenschaften : eine multidisziplin{\"a}re Vorlesungsreihe}, journal = {Raum und Zahl im Fokus der Wissenschaften : eine multidisziplin{\"a}re Vorlesungsreihe}, publisher = {Trafo}, address = {Berlin}, isbn = {978-3-86464-082-7}, pages = {63 -- 76}, year = {2015}, language = {de} } @article{Heimann2015, author = {Heimann, Heinz-Dieter}, title = {Kreise - Punkte - Linien}, series = {Raum und Zahl im Fokus der Wissenschaften : eine multidisziplin{\"a}re Vorlesungsreihe}, journal = {Raum und Zahl im Fokus der Wissenschaften : eine multidisziplin{\"a}re Vorlesungsreihe}, publisher = {Trafo}, address = {Berlin}, isbn = {978-3-86464-082-7}, pages = {111 -- 127}, year = {2015}, language = {de} } @unpublished{ConfortiRoelly2015, author = {Conforti, Giovanni and Roelly, Sylvie}, title = {Reciprocal class of random walks on an Abelian group}, volume = {4}, number = {1}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72604}, pages = {22}, year = {2015}, abstract = {Processes having the same bridges as a given reference Markov process constitute its reciprocal class. In this paper we study the reciprocal class of a continuous time random walk with values in a countable Abelian group, we compute explicitly its reciprocal characteristics and we present an integral characterization of it. Our main tool is a new iterated version of the celebrated Mecke's formula from the point process theory, which allows us to study, as transformation on the path space, the addition of random loops. Thanks to the lattice structure of the set of loops, we even obtain a sharp characterization. At the end, we discuss several examples to illustrate the richness of reciprocal classes. We observe how their structure depends on the algebraic properties of the underlying group.}, 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} } @unpublished{AlsaedyTarkhanov2015, author = {Alsaedy, Ammar and Tarkhanov, Nikolai Nikolaevich}, title = {Weak boundary values of solutions of Lagrangian problems}, volume = {4}, number = {2}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72617}, pages = {24}, year = {2015}, abstract = {We define weak boundary values of solutions to those nonlinear differential equations which appear as Euler-Lagrange equations of variational problems. As a result we initiate the theory of Lagrangian boundary value problems in spaces of appropriate smoothness. We also analyse if the concept of mapping degree of current importance applies to the study of Lagrangian problems.}, language = {en} } @unpublished{Tarkhanov2015, author = {Tarkhanov, Nikolai Nikolaevich}, title = {A spectral theorem for deformation quantisation}, volume = {4}, number = {4}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-72425}, pages = {8}, year = {2015}, abstract = {We present a construction of the eigenstate at a noncritical level of the Hamiltonian function. Moreover, we evaluate the contributions of Morse critical points to the spectral decomposition.}, language = {en} } @book{VanLeeuwenChengReich2015, author = {Van Leeuwen, Peter Jan and Cheng, Yuan and Reich, Sebastian}, title = {Nonlinear data assimilation}, series = {Frontiers in applied dynamical systems: reviews and tutorials ; 2}, journal = {Frontiers in applied dynamical systems: reviews and tutorials ; 2}, publisher = {Springer}, address = {Cham}, isbn = {978-3-319-18346-6}, doi = {10.1007/978-3-319-18347-3}, pages = {xii, 118}, year = {2015}, abstract = {This book contains two review articles on nonlinear data assimilation that deal with closely related topics but were written and can be read independently. Both contributions focus on so-called particle filters. The first contribution by Jan van Leeuwen focuses on the potential of proposal densities. It discusses the issues with present-day particle filters and explorers new ideas for proposal densities to solve them, converging to particle filters that work well in systems of any dimension, closing the contribution with a high-dimensional example. The second contribution by Cheng and Reich discusses a unified framework for ensemble-transform particle filters. This allows one to bridge successful ensemble Kalman filters with fully nonlinear particle filters, and allows a proper introduction of localization in particle filters, which has been lacking up to now.}, language = {en} } @article{ConfortiPraRoelly2015, author = {Conforti, Giovanni and Pra, Paolo Dai and Roelly, Sylvie}, title = {Reciprocal Class of Jump Processes}, series = {Journal of theoretical probability}, volume = {30}, journal = {Journal of theoretical probability}, publisher = {Springer}, address = {New York}, issn = {0894-9840}, doi = {10.1007/s10959-015-0655-3}, pages = {551 -- 580}, year = {2015}, abstract = {Processes having the same bridges as a given reference Markov process constitute its reciprocal class. In this paper we study the reciprocal class of compound Poisson processes whose jumps belong to a finite set . We propose a characterization of the reciprocal class as the unique set of probability measures on which a family of time and space transformations induces the same density, expressed in terms of the reciprocal invariants. The geometry of plays a crucial role in the design of the transformations, and we use tools from discrete geometry to obtain an optimal characterization. We deduce explicit conditions for two Markov jump processes to belong to the same class. Finally, we provide a natural interpretation of the invariants as short-time asymptotics for the probability that the reference process makes a cycle around its current state.}, language = {en} } @article{Steup2015, author = {Steup, Martin}, title = {Raum und Zahl in der Pflanzenphysiologie}, series = {Raum und Zahl}, journal = {Raum und Zahl}, publisher = {Trafo}, address = {Berlin}, isbn = {978-3-86464-082-7}, pages = {77 -- 109}, year = {2015}, language = {de} } @incollection{KiyLuckeSass2015, author = {Kiy, Alexander and Lucke, Ulrike and Sass, K.}, title = {Gewusst was: Mit einer E-Learning-Toolbox die pers{\"o}nliche virtuelle Umgebung gestalten}, series = {DeLFI 2015 - die 13. E-Learning Fachtagung Informatik der Gesellschaft f{\"u}r Informatik e.V. : 1.-4. September 2015 M{\"u}nchen, Deutschland}, booktitle = {DeLFI 2015 - die 13. E-Learning Fachtagung Informatik der Gesellschaft f{\"u}r Informatik e.V. : 1.-4. September 2015 M{\"u}nchen, Deutschland}, number = {247}, editor = {Pongratz, Hans J. and Keil, R.}, publisher = {Gesellschaft f{\"u}r Informatik e.V.}, address = {Bonn}, isbn = {978-3-88579-641-1}, issn = {1617-5468}, publisher = {Universit{\"a}t Potsdam}, pages = {43 -- 55}, year = {2015}, language = {de} } @incollection{Guenther2015, author = {G{\"u}nther, Oliver}, title = {Zum Geleit}, series = {Raum und Zahl im Fokus der Wissenschaften : eine multidisziplin{\"a}re Vorlesungsreihe}, booktitle = {Raum und Zahl im Fokus der Wissenschaften : eine multidisziplin{\"a}re Vorlesungsreihe}, publisher = {Trafo}, address = {Berlin}, isbn = {978-3-86464-082-7}, pages = {7 -- 8}, year = {2015}, language = {de} } @book{GuentherPetscheFischeretal.2015, author = {G{\"u}nther, Oliver and Petsche, Hans-Joachim and Fischer, Martin H. and Franz, Norbert P. and Steup, Martin and Sixtus, Elena and Heimann, Heinz-Dieter and Pr{\"o}ve, Ralf}, title = {Raum und Zahl im Fokus der Wissenschaften}, series = {Studieren ++ : Konzepte, Perspektiven, Kompetenzen ; 1}, journal = {Studieren ++ : Konzepte, Perspektiven, Kompetenzen ; 1}, editor = {Petsche, Hans-Joachim}, publisher = {Trafo}, address = {Berlin}, isbn = {978-3-86464-082-7}, pages = {168}, year = {2015}, abstract = {Die nun begonnene Reihe „studieren++" resultiert aus einer von der Universit{\"a}t Potsdam angebotenen Vorlesungsreihe. Das Besondere an dieser Vorlesungsreihe ist der multidisziplin{\"a}re Anspruch und die konsequent umgesetzte Zusammenarbeit {\"u}ber Disziplingrenzen hinweg. Die nicht nur {\"u}ber Instituts-, sondern {\"u}ber Fakult{\"a}tsgrenzen praktizierte Interdisziplinarit{\"a}t erlaubt die Betrachtung eines Problems oder Sachverhalts aus unterschiedlichen Blickwinkeln. Wissenschaftliche Fragestellungen sind komplex und nicht immer auf eine Disziplin beschr{\"a}nkt. Sie in ihrer G{\"a}nze erfassen und nachhaltige L{\"o}sungsstrategien oder Konzepte entwickeln zu k{\"o}nnen gelingt oft nur durch eine multidisziplin{\"a}re Kooperation. Eine Lehrveranstaltung wie die vorliegende ist nicht nur f{\"u}r die Studierenden einer Universit{\"a}t eine hervorragende M{\"o}glichkeit, um {\"u}ber die Grenzen der eigenen Disziplin hinaus zu blicken und die Zusammenarbeit mit Wissenschaftlerinnen und Wissenschaftlern aus anderen Bereichen zu pflegen. So lernt man, sich in andere Sichtweisen hineinzuversetzen und sich zwischen den Disziplinen zu bewegen - eine Kompetenz, die in der hochkomplexen Arbeitswelt von heute von hohem Nutzen ist. Der vorliegende erste Band der Reihe hat „Raum und Zahl" zum Thema und ist aus einer Ringvorlesung aus dem Wintersemester 2013/2014 entstanden. Drei der f{\"u}nf Fakult{\"a}ten, insgesamt neun Institute der Universit{\"a}t Potsdam, haben sich an der Vorlesung beteiligt und sich dieses spannenden Themas angenommen. Als jemand, der sich jahrelang wissenschaftlich mit algorithmischer Geometrie sowie mit raumbezogenen Datenbanken und Navigationssystemen besch{\"a}ftigt hat, kann ich nur bekr{\"a}ftigen, dass die Bez{\"u}ge zwischen Raum und Zahl, zwischen R{\"a}umen und Zahlen, noch viel st{\"a}rker im {\"o}ffentlichen Bewusstsein verankert geh{\"o}ren. R{\"a}ume auch quantitativ zu erfassen und zu verstehen ist eine Kulturtechnik, die an Wichtigkeit eher noch zunimmt, vor allem vor dem Hintergrund, dass wir genetisch nicht allzu gut auf derartige Herausforderungen vorbereitet sind. Denn viele unserer einschl{\"a}gigen Gene entstammen noch aus der Zeit der Savanne, einer Zeit, zu der das Raumkonzept sich fast ausschließlich auf die unmittelbare r{\"a}umliche Umgebung bezog und Zahlen jenseits von 10 nur wenig Relevanz f{\"u}r das eigene {\"U}berleben hatten. Als Pr{\"a}sident der Universit{\"a}t Potsdam freut es mich ganz besonders, dass sich die hier vertretenen Wissenschaftler bereit erkl{\"a}rt haben, ihre {\"U}berlegungen mit den Studierenden und ihren Kolleginnen und Kollegen zu teilen. Herrn Kollegen Hans-Joachim Petsche m{\"o}chte ich f{\"u}r sein Engagement danken und ihm zu dieser gelungenen Reihe gratulieren. Der Geist der Wissenschaft, der nicht nur einsam im B{\"u}ro oder Labor gelebt wird, sondern gerade an einer Universit{\"a}t auch aktiv nach außen getragen werden sollte, wird hier in besonderer Weise sichtbar. Ich w{\"u}nsche Ihnen viel Freude bei der Lekt{\"u}re des Bandes und freue mich auf weitere Ver{\"o}ffentlichungen in dieser Reihe.}, subject = {Raum}, language = {de} }