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  • 1
    Publication Date: 2020-08-05
    Description: Das heutige Leben ist durchdrungen von komplexen Technologien. Ohne Kommunikationsnetze, Internet, Mobilfunk, Logistik, Verkehrstechnik, medizinische Apparate, etc. könnte die moderne Gesellschaft nicht funktionieren. Fast alle dieser Technologien haben einen hohen Mathematikanteil. Der "normale Bürger"' weiss davon nichts, der Schulunterricht könnte dem ein wenig abhelfen. Einige mathematische Aspekte dieser Technologien sind einfach und sogar spielerisch intuitiv zugänglich. Solche Anwendungen, die zusätzlich noch der Lebensumwelt der Schüler zugehören, können dazu genutzt werden, die mathematische Modellierung, also die mathematische Herangehensweise an die Lösung praktischer Fragen, anschaulich zu erläutern. Gerade in der diskreten Mathematik können hier, quasi "nebenbei" mathematische Theorien erarbeitet und Teilaspekte (Definitionen, Fragestellungen, einfache Sachverhalte) durch eigenständiges Entdecken der Schüler entwickelt werden. Wir beginnen mit einigen Beispielen.
    Keywords: ddc:510
    Language: German
    Type: reportzib , doc-type:preprint
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  • 2
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    Publication Date: 2020-08-05
    Description: Den kürzesten Weg in einem Graphen zu finden ist ein klassisches Problem der Graphentheorie. Über einen Vortrag zu diesem Thema beim Tag der Mathematik 2007 von R. Borndörfer kam ich in Kontakt mit dem Konrad-Zuse-Zentrum (ZIB), das sich u.a. mit Wegeoptimierung beschäftigt. Ein Forschungsschwerpunkt dort ist im Rahmen eines Projekts zur Chipverifikation das Zählen von Lösungen, das, wie wir sehen werden, eng mit dem Zählen von Wegen zusammenhängt. Anhand von zwei Fragen aus der Graphentheorie soll diese Facharbeit unterschiedliche Lösungsmethoden untersuchen. Wie bestimmt man den kürzesten Weg zwischen zwei Knoten in einem Graphen und wie findet man alle möglichen Wege? Nach einer Einführung in die Graphentheorie und einer Konkretisierung der Probleme wird zunächst für beide eine Lösung mit auf Graphen basierenden Algorithmen vorgestellt. Während der Algorithmus von Dijkstra sehr bekannt ist, habe ich für das Zählen von Wegen einen eigenen Algorithmus auf der Basis der Tiefensuche entwickelt. Im zweiten Teil der Arbeit wird das Konzept der ganzzahligen Programmierung vorgestellt und die Lösungsmöglichkeiten für Wegeprobleme, die sich darüber ergeben. Schließlich wurden die vorgestellten Algorithmen am Beispiel des S- und U-Bahnnetzes von Berlin implementiert und mit Programmen, die die gleichen Fragen über ganzzahlige Programmierung lösen, verglichen.
    Keywords: ddc:510
    Language: German
    Type: reportzib , doc-type:preprint
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  • 3
    Publication Date: 2016-06-09
    Description: This paper is intended to be a first step towards the continuous dependence of dynamical contact problems on the initial data as well as the uniqueness of a solution. Moreover, it provides the basis for a proof of the convergence of popular time integration schemes as the Newmark method. We study a frictionless dynamical contact problem between both linearly elastic and viscoelastic bodies which is formulated via the Signorini contact conditions. For viscoelastic materials fulfilling the Kelvin-Voigt constitutive law, we find a characterization of the class of problems which satisfy a perturbation result in a non-trivial mix of norms in function space. This characterization is given in the form of a stability condition on the contact stresses at the contact boundaries. Furthermore, we present perturbation results for two well-established approximations of the classical Signorini condition: The Signorini condition formulated in velocities and the model of normal compliance, both satisfying even a sharper version of our stability condition.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
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  • 4
    Publication Date: 2020-08-05
    Description: Most data networks nowadays use shortest path protocols to route the traffic. Given administrative routing lengths for the links of the network, all data packets are sent along shortest paths with respect to these lengths from their source to their destination. In this paper, we present an integer programming algorithm for the minimum congestion unsplittable shortest path routing problem, which arises in the operational planning of such networks. Given a capacitated directed graph and a set of communication demands, the goal is to find routing lengths that define a unique shortest path for each demand and minimize the maximum congestion over all links in the resulting routing. We illustrate the general decomposition approach our algorithm is based on, present the integer and linear programming models used to solve the master and the client problem, and discuss the most important implementational aspects. Finally, we report computational results for various benchmark problems, which demonstrate the efficiency of our algorithm.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
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  • 5
    Publication Date: 2020-12-15
    Description: This paper introduces the "line connectivity problem", a generalization of the Steiner tree problem and a special case of the line planning problem. We study its complexity and give an IP formulation in terms of an exponential number of constraints associated with "line cut constraints". These inequalities can be separated in polynomial time. We also generalize the Steiner partition inequalities.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
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  • 6
    Publication Date: 2020-08-05
    Description: Testing is the process of stimulating a system with inputs in order to reveal hidden parts of the system state. In the case of non-deterministic systems, the difficulty arises that an input pattern can generate several possible outcomes. Some of these outcomes allow to distinguish between different hypotheses about the system state, while others do~not. In this paper, we present a novel approach to find, for non-deterministic systems modeled as constraints over variables, tests that allow to distinguish among the hypotheses as good as possible. The idea is to assess the quality of a test by determining the ratio of distinguishing (good) and not distinguishing (bad) outcomes. This measure refines previous notions proposed in the literature on model-based testing and can be computed using model counting techniques. We propose and analyze a greedy-type algorithm to solve this test optimization problem, using existing model counters as a building block. We give preliminary experimental results of our method, and discuss possible improvements.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
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  • 7
    Publication Date: 2021-08-05
    Description: Starting with the description of the Traveling Salesmen Problem formulation as given by van Vyve and Wolsey in the article Approximate extended formulations'', we investigate the effects of small variations onto the performance of contemporary mixed integer programming solvers. We will show that even minor changes in the formulation of the model can result in performance difference of more than a factor of 1000. As the results show it is not obvious which changes will result in performance improvements and which not.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
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  • 8
    Publication Date: 2022-03-14
    Description: Orbitopes can be used to handle symmetries which arise in integer programming formulations with an inherent assignment structure. We investigate the detection of symmetries appearing in this approach. We show that detecting so-called orbitopal symmetries is graph-isomorphism hard in general, but can be performed in linear time if the assignment structure is known.
    Keywords: ddc:510
    Language: English
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  • 9
    Publication Date: 2019-01-29
    Description: Regional hyperthermia is a cancer therapy aiming at heating tumors using phased array applicators. This article provides an overview over current mathematical challenges of delivering individually optimal treatments. The focus is on therapy planning and identification of technical as well as physiological quantities from MR thermometry measurements.
    Keywords: ddc:510
    Language: English
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  • 10
    Publication Date: 2019-05-10
    Description: Reasons for the failure of adaptive methods to deliver improved efficiency when integrating monodomain models for myocardiac excitation are discussed. Two closely related techniques for reducing the computational complexity of linearly implicit integrators, deliberate sparsing and splitting, are investigated with respect to their impact on computing time and accuracy.
    Keywords: ddc:510
    Language: English
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  • 11
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    Publication Date: 2020-08-05
    Description: We investigate the computation of periodic timetables for public transport by mixed integer programming. After introducing the problem, we describe two mathematical models for periodic timetabling, the PERIODIC EVENT SCHEDULING PROBLEM (PESP) and the QUADRATIC SEMI-ASSIGNMENT PROBLEM. Specifically, we give an overview of existing integer programming (IP) formulations for both models. An important contribution of our work are new IP formulations for the PESP based on time discretization. We provide an analytical comparison of these formulations and describe different techniques that allow a more efficient solution by mixed integer programming. In a preliminary computational study, on the basis of standard IP solvers, we compare different formulations for computing periodic timetables. Our results justify a further investigation of the time discretization approach. Typically the timetable is optimized for the current traffic situation. The main difficulty with this approach is that after introducing the new timetable the passengers’ travel behavior may differ from that assumed for the computation. Motivated by this problem, we examine an iterative timetabling procedure that is a combination of timetable computation and passenger routing. We discuss the algorithmic issues of the passenger routing and study properties of the computed timetables. Finally, we confirm our theoretical results on the basis of an own implementation.
    Description: Wir untersuchen die Berechnung von Taktfahrplänen für den öffentlichen Verkehr mit gemischt-ganzzahliger Programmierung (MIP). Im Anschluss an die Problembeschreibung, stellen wir zwei mathematische Modellierungen vor, das PERIODIC EVENT SCHEDULING PROBLEM (PESP) und das QUADRATIC SEMI-ASSIGNMENT PROBLEM. Wichtiger Bestandteil ist ein Überblick über existierende ganzzahlige Formulierungen beider Modelle. Wir entwickeln neue ganzzahlige Formulierungen für das PESP auf der Basis von Zeitdiskretisierung. Diese werden analytisch miteinander verglichen und wir beschreiben verschiedene Techniken, die eine effizientere Lösung der Formulierungen mit gemischt-ganzzahliger Programmierung ermöglichen. In einer ersten Rechenstudie, unter Verwendung gängiger MIP-Löser, vergleichen wir verschiedene ganzzahlige Formulierungen zur Berechnung von Taktfahrplänen. Unsere Ergebnisse rechtfertigen eine weitere Untersuchung des Zeitdiskretisierungsansatzes. In der Regel werden Fahrpläne mit Bezug auf die gegenwärtige Verkehrssituation optimiert. Dies birgt jedoch folgendes Problem. Wenn der neue Fahrplan eingeführt wird, ist es möglich, dass die Passagiere ein anderes Fahrverhalten zu Tage legen, als für die Berechnung des Fahrplans angenommen wurde. Vor diesem Hintergrund behandeln wir ein iteratives Verfahren zur Berechnung von Taktfahrplänen. Dieses ist eine Kombination aus Fahrplanberechnung und Passagierrouting. Neben den algorithmischen Details des Passagierroutings untersuchen wir Eigenschaften der berechneten Fahrpläne. Abschließend bestätigen wir unsere theoretischen Ergebnisse auf Grundlage einer eigenen Implementierung des Verfahrens.
    Keywords: ddc:510
    Language: English
    Type: masterthesis , doc-type:masterThesis
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  • 12
    Publication Date: 2020-08-05
    Description: This paper describes several experiments to explore the options for solving a class of mixed integer nonlinear programming problems that stem from a real-world mine production planning project. The only type of nonlinear constraints in these problems are bilinear equalities involving continuous variables, which enforce the ratios between elements in mixed material streams. A branch-and-bound algorithm to handle the integer variables has been tried in another project. However, this branch-and-bound algorithm is not effective for handling the nonlinear constraints. Therefore state-of-the-art nonlinear solvers are utilized to solve the resulting nonlinear subproblems in this work. The experiments were carried out using the NEOS server for optimization. After finding that current nonlinear programming solvers seem to lack suitable preprocessing capabilities, we preprocess the instances beforehand and use an heuristic approach to solve the nonlinear subproblems. In the appendix, we explain how to add a polynomial constraint handler that uses IPOPT as embedded nonlinear programming solver for the constraint programming framework SCIP. This is one of the crucial steps for implementing our algorithm in SCIP. We briefly described our approach and give an idea of the work involved.
    Keywords: ddc:510
    Language: English
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  • 13
    Publication Date: 2020-08-05
    Description: Dieser kurze Aufsatz zur Algorithmengeschichte ist Eberhard Knobloch, meinem Lieblings-Mathematikhistoriker, zum 65. Geburtstag gewidmet. Eberhard Knobloch hat immer, wenn ich ihm eine historische Frage zur Mathematik stellte, eine Antwort gewusst – fast immer auch sofort. Erst als ich mich selbst ein wenig und dazu amateurhaft mit Mathematikgeschichte beschäftigte, wurde mir bewusst, wie schwierig dieses „Geschäft“ ist. Man muss nicht nur mehrere (alte) Sprachen beherrschen, sondern auch die wissenschaftliche Bedeutung von Begriffen und Symbolen in früheren Zeiten kennen. Man muss zusätzlich herausfinden, was zur Zeit der Entstehung der Texte „allgemeines Wissen“ war, insbesondere, was seinerzeit gültige Beweisideen und -schritte waren, und daher damals keiner präzisen Definition oder Einführung bedurfte. Es gibt aber noch eine Steigerung des historischen Schwierigkeitsgrades: Algorithmengeschichte. Dies möchte ich in diesem Artikel kurz darlegen in der Hoffnung, dass sich Wissenschaftshistoriker dieses Themas noch intensiver annehmen, als sie das bisher tun. Der Grund ist, dass heute Algorithmen viele Bereiche unserer Alltagswelt steuern und unser tägliches Leben oft von funktionierenden Algorithmen abhängt. Daher wäre eine bessere Kenntnis der Algorithmengeschichte von großem Interesse.
    Keywords: ddc:510
    Language: German
    Type: reportzib , doc-type:preprint
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  • 14
    Publication Date: 2016-06-09
    Description: We consider first order optimality conditions for state constrained optimal control problems. In particular we study the case where the state equation has not enough regularity to admit existence of a Slater point in function space. We overcome this difficulty by a special transformation. Under a density condition we show existence of Lagrange multipliers, which have a representation via measures and additional regularity properties.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
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  • 15
    Publication Date: 2016-06-09
    Description: The enormous time lag between fast atomic motion and complex pro- tein folding events makes it almost impossible to compute molecular dy- namics on a high resolution. A common way to tackle this problem is to model the system dynamics as a Markov process. Yet for large molec- ular systems the resulting Markov chains can hardly be handled due to the curse of dimensionality. Coarse graining methods can be used to re- duce the dimension of a Markov chain, but it is still unclear how far the coarse grained Markov chain resembles the original system. In order to answer this question, two different coarse-graining methods were analysed and compared: a classical set-based reduction method and an alternative subspace-based approach, which is based on membership vectors instead of sets. On the basis of a small toy system, it could be shown, that in con- trast to the subset-based approach, the subspace-based reduction method preserves the Markov property as well as the essential dynamics of the original system.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
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  • 16
    Publication Date: 2021-02-19
    Description: Line planning is an important step in the strategic planning process of a public transportation system. In this paper, we discuss an optimization model for this problem in order to minimize operation costs while guaranteeing a certain level of quality of service, in terms of available transport capacity. We analyze the problem for path and tree network topologies as well as several categories of line operation that are important for the Quito Trolebus system. It turns out that, from a computational complexity worst case point of view, the problem is hard in all but the most simple variants. In practice, however, instances based on real data from the Trolebus System in Quito can be solved quite well, and significant optimization potentials can be demonstrated.
    Keywords: ddc:510
    Language: English
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  • 17
    Publication Date: 2020-08-05
    Description: It is well known that competitive analysis yields too pessimistic results when applied to the paging problem and it also cannot make a distinction between many paging strategies. Many deterministic paging algorithms achieve the same competitive ratio, ranging from inefficient strategies as flush-when-full to the good performing least-recently-used (LRU). In this paper, we study this fundamental online problem from the viewpoint of stochastic dominance. We show that when sequences are drawn from distributions modelling locality of reference, LRU is stochastically better than any other online paging algorithm.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
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  • 18
    Publication Date: 2020-12-15
    Description: Die Angebotsplanung im öffentlichen Nahverkehr umfasst die Aufgaben der Netz-, Linien-,Fahr- und Preisplanung. Wir stellen zwei mathematische Optimierungsmodelle zur Linien- und Preisplanung vor. Wir zeigen anhand von Berechnungen für die Verkehrsbetriebe in Potsdam(ViP), dass sich damit komplexe Zusammenhänge quantitativ analysieren lassen. Auf diese Weise untersuchen wir die Auswirkungen von Freiheitsgraden auf die Konstruktion von Linien und die Wahl von Reisewegen der Passagiere, Abhängigkeiten zwischen Kosten und Reisezeiten sowie den Einfluss verschiedener Preissysteme auf Nachfrage und Kostendeckung.
    Keywords: ddc:510
    Language: German
    Type: reportzib , doc-type:preprint
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  • 19
    Publication Date: 2022-03-14
    Description: This article introduces constraint integer programming (CIP), which is a novel way to combine constraint programming (CP) and mixed integer programming (MIP) methodologies. CIP is a generalization of MIP that supports the notion of general constraints as in CP. This approach is supported by the CIP framework SCIP, which also integrates techniques from SAT solving. SCIP is available in source code and free for non-commercial use. We demonstrate the usefulness of CIP on two tasks. First, we apply the constraint integer programming approach to pure mixed integer programs. Computational experiments show that SCIP is almost competitive to current state-of-the-art commercial MIP solvers. Second, we employ the CIP framework to solve chip design verification problems, which involve some highly non-linear constraint types that are very hard to handle by pure MIP solvers. The CIP approach is very effective here: it can apply the full sophisticated MIP machinery to the linear part of the problem, while dealing with the non-linear constraints by employing constraint programming techniques.
    Keywords: ddc:510
    Language: English
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  • 20
    Publication Date: 2016-06-09
    Description: An extended mathematical framework for barrier methods for state constrained optimal control compared to [Schiela, ZIB-Report 07-07] is considered. This allows to apply the results derived there to more general classes of optimal control problems, in particular to boundary control and finite dimensional control.
    Keywords: ddc:510
    Language: English
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  • 21
    Publication Date: 2021-08-05
    Description: In the recent years there has been tremendous progress in the development of algorithms to find optimal solutions for integer programs. In many applications it is, however, desirable (or even necessary) to generate all feasible solutions. Examples arise in the areas of hardware and software verification and discrete geometry. In this paper, we investigate how to extend branch-and-cut integer programming frameworks to support the generation of all solutions. We propose a method to detect so-called unrestricted subtrees, which allows us to prune the integer program search tree and to collect several solutions simultaneously. We present computational results of this branch-and-count paradigm which show the potential of the unrestricted subtree detection.
    Keywords: ddc:510
    Language: English
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  • 22
    Publication Date: 2020-08-05
    Description: Edmonds showed that the so-called rank inequalities and the nonnegativity constraints provide a complete linear description of the matroid polytope. By essentially adding Grötschel's cardinality forcing inequalities, we obtain a complete linear description of the cardinality constrained matroid polytope which is the convex hull of the incidence vectors of those independent sets that have a feasible cardinality. Moreover, we show how the separation problem for the cardinality forcing inequalities can be reduced to that for the rank inequalities. We also give necessary and sufficient conditions for a cardinality forcing inequality to be facet defining.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
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  • 23
    Publication Date: 2020-08-05
    Description: The paper describes a method for solution of very large overdetermined algebraic polynomial systems on an example that appears from a classification of all integrable 3-dimensional scalar discrete quasilinear equations $Q_3=0$ on an elementary cubic cell of the lattice ${\mathbb Z}^3$. The overdetermined polynomial algebraic system that has to be solved is far too large to be formulated. A probing' technique which replaces independent variables by random integers or zero allows to formulate subsets of this system. An automatic alteration of equation formulating steps and equation solving steps leads to an iteration process that solves the computational problem.
    Keywords: ddc:510
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  • 24
    Publication Date: 2020-08-05
    Description: An algorithmic method using conservation law multipliers is introduced that yields necessary and sufficient conditions to find invertible mappings of a given nonlinear PDE to some linear PDE and to construct such a mapping when it exists. Previous methods yielded such conditions from admitted point or contact symmetries of the nonlinear PDE. Through examples, these two linearization approaches are contrasted.
    Keywords: ddc:510
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  • 25
    Publication Date: 2021-02-26
    Description: We classify all integrable 3-dimensional scalar discrete affine linear equations $Q_3=0$ on an elementary cubic cell of the lattice ${\mathbb Z}^3$. An equation $Q_3=0$ %of such form is called integrable if it may be consistently imposed on all $3$-dimensional elementary faces of the lattice ${\mathbb Z}^4$. Under the natural requirement of invariance of the equation under the action of the complete group of symmetries of the cube we prove that the only ontrivial(non-linearizable) integrable equation from this class is the well-known dBKP-system.
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  • 26
    Publication Date: 2020-12-11
    Description: The article describes the online mathematics test {\tt http://lie.math.brocku.ca/mathtest}, its typical applications and experiences gathered.
    Keywords: ddc:510
    Language: English
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  • 27
    Publication Date: 2020-08-05
    Description: We introduce (TTPlib), a data library for train timetabling problems that can be accessed at http://ttplib.zib.de. In version 1.0, the library contains data related to 50 scenarios. Most instances result from the combination of macroscopic railway networks and several train request sets for the German long distance area containing Hannover, Kassel and Fulda, short denoted by Ha-Ka-Fu. In this paper, we introduce the data concepts of TTPlib, describe the scenarios included in the library and provide a free visualization tool TraVis.
    Keywords: ddc:510
    Language: English
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  • 28
    Publication Date: 2020-08-05
    Description: The purpose of this paper is twofold. An immediate practical use of the presented algorithm is its applicability to the parametric solution of underdetermined linear ordinary differential equations (ODEs) with coefficients that are arbitrary analytic functions in the independent variable. A second conceptual aim is to present an algorithm that is in some sense dual to the fundamental Euclids algorithm, and thus an alternative to the special case of a Gr\"{o}bner basis algorithm as it is used for solving linear ODE-systems. In the paper Euclids algorithm and the new dual version' are compared and their complementary strengths are analysed on the task of solving underdetermined ODEs. An implementation of the described algorithm is interactively accessible at http://lie.math.brocku.ca/crack/uode.
    Keywords: ddc:510
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  • 29
    Publication Date: 2020-08-05
    Description: This paper proposes a new method for probabilistic analysis of online algorithms that is based on the notion of stochastic dominance. We develop the method for the Online Bin Coloring problem introduced by Krumke et al. Using methods for the stochastic comparison of Markov chains we establish the strong result that the performance of the online algorithm GreedyFit is stochastically dominated by the performance of the algorithm OneBin for any number of items processed. This result gives a more realistic picture than competitive analysis and explains the behavior observed in simulations.
    Keywords: ddc:510
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  • 30
    Publication Date: 2020-12-15
    Description: The optimization of fare systems in public transit allows to pursue objectives such as the maximization of demand, revenue, profit, or social welfare. We propose a non-linear optimization approach to fare planning that is based on a detailed discrete choice model of user behavior. The approach allows to analyze different fare structures, optimization objectives, and operational scenarios involving, e.g., subsidies. We use the resulting models to compute optimized fare systems for the city of Potsdam, Germany.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
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  • 31
    Publication Date: 2022-03-14
    Description: Pseudo-Boolean problems generalize SAT problems by allowing linear constraints and a linear objective function. Different solvers, mainly having their roots in the SAT domain, have been proposed and compared,for instance, in Pseudo-Boolean evaluations. One can also formulate Pseudo-Boolean models as integer programming models. That is,Pseudo-Boolean problems lie on the border between the SAT domain and the integer programming field. In this paper, we approach Pseudo-Boolean problems from the integer programming side. We introduce the framework SCIP that implements constraint integer programming techniques. It integrates methods from constraint programming, integer programming, and SAT-solving: the solution of linear programming relaxations, propagation of linear as well as nonlinear constraints, and conflict analysis. We argue that this approach is suitable for Pseudo-Boolean instances containing general linear constraints, while it is less efficient for pure SAT problems. We present extensive computational experiments on the test set used for the Pseudo-Boolean evaluation 2007. We show that our approach is very efficient for optimization instances and competitive for feasibility problems. For the nonlinear parts, we also investigate the influence of linear programming relaxations and propagation methods on the performance. It turns out that both techniques are helpful for obtaining an efficient solution method.
    Keywords: ddc:510
    Language: English
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  • 32
    Publication Date: 2020-08-05
    Description: Millionen von Menschen werden allein in Deutschland täglich von Bussen, Bahnen und Flugzeugen transportiert. Der öffentliche Personenverkehr (ÖV) ist von großer Bedeutung für die Lebensqualität einzelner aber auch für die Leistungsfähigkeit ganzer Regionen. Qualität und Effizienz von ÖV-Systemen hängen ab von politischen Rahmenbedingungen (staatlich geplant, wettbewerblich organisiert) und der Eignung der Infrastruktur (Schienensysteme, Flughafenstandorte), vom vorhandenen Verkehrsangebot (Fahr- und Flugplan), von der Verwendung angemessener Technologien (Informations-, Kontroll- und Buchungssysteme) und dem bestmöglichen Einsatz der Betriebsmittel (Energie, Fahrzeuge und Personal). Die hierbei auftretenden Entscheidungs-, Planungs- und Optimierungsprobleme sind z.T. gigantisch und "schreien" aufgrund ihrer hohen Komplexität nach Unterstützung durch Mathematik. Dieser Artikel skizziert den Stand und die Bedeutung des Einsatzes von Mathematik bei der Planung und Durchführung von öffentlichem Personenverkehr, beschreibt die bestehenden Herausforderungen und regt zukunftsweisende Maßnahmen an.
    Keywords: ddc:510
    Language: German
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  • 33
    Publication Date: 2019-05-10
    Description: Pulse thermography of concrete structures is used in civil engineering for detecting voids, honeycombing and delamination. The physical situation is readily modeled by Fourier's law. Despite the simplicity of the PDE structure, quantitatively realistic numerical 3D simulation faces two major obstacles. First, the short heating pulse induces a thin boundary layer at the heated surface which encapsulates all information and therefore has to be resolved faithfully. Even with adaptive mesh refinement techniques, obtaining useful accuracies requires an unsatisfactorily fine discretization. Second, bulk material parameters and boundary conditions are barely known exactly. We address both issues by a semi-analytic reformulation of the heat transport problem and by parameter identification. Numerical results are compared with measurements of test specimens.
    Keywords: ddc:510
    Language: English
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  • 34
    Publication Date: 2016-06-09
    Description: In this paper we are concerned with the application of interior point methods in function space to gradient constrained optimal control problems, governed by partial differential equations. We will derive existence of solutions together with first order optimality conditions. Afterwards we show continuity of the central path, together with convergence rates depending on the interior point parameter.
    Keywords: ddc:510
    Language: English
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  • 35
    Publication Date: 2016-06-09
    Description: We consider an interior point method in function space for PDE constrained optimal control problems with state constraints. Our emphasis is on the construction and analysis of an algorithm that integrates a Newton path-following method with adaptive grid refinement. This is done in the framework of inexact Newton methods in function space, where the discretization error of each Newton step is controlled by adaptive grid refinement in the innermost loop. This allows to perform most of the required Newton steps on coarse grids, such that the overall computational time is dominated by the last few steps. For this purpose we propose an a-posteriori error estimator for a problem suited norm.
    Keywords: ddc:510
    Language: English
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  • 36
    Publication Date: 2020-08-05
    Description: Ticket pricing in public transport usually takes a welfare or mnemonics maximization point of view. These approaches do not consider fairness in the sense that users of a shared infrastructure should pay for the costs that they generate. We propose an ansatz to determine fair ticket prices that combines concepts from cooperative game theory and integer programming. An application to pricing railway tickets for the intercity network of the Netherlands demonstrates that, in this sense, prices that are much fairer than standard ones can be computed in this way.
    Keywords: ddc:510
    Language: English
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  • 37
    Publication Date: 2014-02-26
    Description: We present a second order sharp interface finite volume method for the solution of the three-dimensional poisson equation with variable coefficients on Cartesian grids. In particular, we focus on interface problems with discontinuities in the coefficient, the source term, the solution, and the fluxes across the interface. The method uses standard piecewiese trilinear finite elements for normal cells and a double piecewise trilinear ansatz for the solution on cells intersected by the interface resulting always in a compact 27-point stencil. Singularities associated with vanishing partial volumes of intersected grid cells are removed by a two-term asymptotic approach. In contrast to the 2D method presented by two of the authors in [M.~Oevermann, R.~Klein: A Cartesian grid finite volume method for elliptic equations with variable coefficients and embedded interfaces, J.~Comp.~Phys.~219 (2006)] we use a minimization technique to determine the unknown coefficients of the double trilinear ansatz. This simplifies the treatment of the different cut-cell types and avoids additional special operations for degenerated interface topologies. The resulting set of linear equations has been solved with a BiCGSTAB solver preconditioned with an algebraic multigrid. In various testcases -- including large coefficient ratios and non-smooth interfaces -- the method achieves second order of accuracy in the L_inf and L_2 norm.
    Keywords: ddc:510
    Language: English
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  • 38
    Publication Date: 2020-08-05
    Description: Given a combinatorial optimization problem and a subset $N$ of natural numbers, we obtain a cardinality constrained version of this problem by permitting only those feasible solutions whose cardinalities are elements of $N$. In this paper we briefly touch on questions that addresses common grounds and differences of the complexity of a combinatorial optimization problem and its cardinality constrained version. Afterwards we focus on polytopes associated with cardinality constrained combinatorial optimization problems. Given an integer programming formulation for a combinatorial optimization problem, by essentially adding Grötschel's cardinality forcing inequalities, we obtain an integer programming formulation for its cardinality restricted version. Since the cardinality forcing inequalities in their original form are mostly not facet defining for the associated polyhedra, we discuss possibilities to strengthen them.
    Keywords: ddc:510
    Language: English
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  • 39
    Publication Date: 2020-08-05
    Description: This survey concerns optimization problems arising in the design of survivable communication networks. It turns out that such problems can be modeled in a natural way as non-compact linear programming formulations based on multicommodity flow network models. These non-compact formulations involve an exponential number of path flow variables, and therefore require column generation to be solved to optimality. We consider several path-based survivability mechanisms and present results, both known and new, on the complexity of the corresponding column generation problems (called the pricing problems). We discuss results for the case of the single link (or node) failures scenarios, and extend the considerations to multiple link failures. Further, we classify the design problems corresponding to different survivability mechanisms according to the structure of their pricing problem. Finally, we show that almost all encountered pricing problems are hard to solve for scenarios admitting multiple failures.
    Keywords: ddc:510
    Language: English
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  • 40
    Publication Date: 2021-02-19
    Description: We introduce an optimization model for the line planning problem in a public transportation system that aims at minimizing operational costs while ensuring a given level of quality of service in terms of available transport capacity. We discuss the computational complexity of the model for tree network topologies and line structures that arise in a real-world application at the Trolebus Integrated System in Quito. Computational results for this system are reported.
    Keywords: ddc:510
    Language: English
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  • 41
    Publication Date: 2021-02-19
    Description: Line planning is an important step in the strategic planning process of a public transportation system. In this paper, we discuss an optimization model for this problem in order to minimize operation costs while guaranteeing a certain level of quality of service, in terms of available transport capacity. We analyze the problem for path and tree network topologies as well as several categories of line operation that are important for the Quito Trolebus system. It turns out that, from a computational complexity worst case point of view, the problem is hard in all but the most simple variants. In practice, however, instances based on real data from the Trolebus System in Quito can be solved quite well, and significant optimization potentials can be demonstrated.
    Keywords: ddc:510
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  • 42
    Electronic Resource
    Electronic Resource
    Springer
    Experimental brain research 3 (1967), S. 117-134 
    ISSN: 1432-1106
    Keywords: Supraspinal effects ; Extrapyramidal pathways ; Spinal activity ; Cat
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary Effects of stimulation of the sensorimotor cortex on activity of the lumbosacral cord were studied in pyramidotomized cats. The following actions initiated by corticofugal volleys were found: 1. postsynaptic effects on motoneurones, mainly excitatory in flexor motoneurones and inhibitory or excitatory in extensor motoneurones, 2. facilitation of spinal reflexes to motoneurones at an interneuronal level, 3. depolarization of presynaptic terminals of group Ib and cutaneous fibres. The latencies of the earliest cortical effects on motoneurones as indicated by modification of monosynaptic reflexes or PSPs were 9–12 msec. Experiments with lesions of different spinal tracts suggest that the effects on motoneurones are mediated mainly by pathways in the ventral part of the lateral funiculus (probably reticulospinal), the facilitation of reflex transmission by pathways in the dorsal part of the lateral funiculus (probably rubrospinal) and primary afferent depolarization by both the former and the latter pathways. The strongest cortical effects were evoked by stimulation of an area around the postcruciate dimple.
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  • 43
    Electronic Resource
    Electronic Resource
    Springer
    Experimental brain research 3 (1967), S. 372-381 
    ISSN: 1432-1106
    Keywords: Red nucleus ; Inferior olive ; Muscle spindles ; Cat
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary In cats anesthetized with halothane the influence of central stimulation upon the dynamic sensitivity of muscle spindles in the flexor digitorum longus muscle was studied. One mesencephalic and one medullary region were found which caused an increase in dynamic spindle sensitivity when stimulated electrically. Histological identification of stimulating points showed these regions to be the caudal pole of the red nucleus and the inferior olivary nucleus respectively. Lesions in the olive decreased rubral effects on the spindles, indicating that the red nucleus and the olive are parts of the same system descending to dynamic fusimotor neurones. Further evidence for this point are given in a following paper (APPELBERG 1967).
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  • 44
    Electronic Resource
    Electronic Resource
    Springer
    Experimental brain research 3 (1967), S. 382-390 
    ISSN: 1432-1106
    Keywords: Red nucleus ; Inferior olive ; Cerebellum ; Muscle spindles ; Cat
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary In the preceding paper (Appelberg and Molander 1967) the caudal part of the red nucleus and parts of the inferior olivary nucleus were shown to cause increased dynamic sensitivity of muscle spindles when stimulated repetitively. The results to be presented will show that single shock electrical stimulation in the caudal part of the red nucleus evoked a field potential in the inferior olivary nucleus. This response seemed to be monosynaptically evoked and was observed only in parts of the olive where repetitive stimulation caused increased dynamic sensitivity of muscle spindles. Stimulation in the red nucleus as well as single shock stimulation in the actual part of the inferior olive also caused a potential in the vermis of the posterior cerebellar lobe. In conditioning — test experiments with the two stimuli the conditioning shock was seen to cause alternating periods of decreased and increased responsiveness in the pathway concerned. The same type of interaction was seen between two responses caused by double shock stimulation in the red nucleus. It is concluded that information from the caudal part of the red nucleus reaches dynamic fusimotor neurones in the spinal cord via a relay in the inferior olivary nucleus; an additional relay in the pathway is also predicted. The cerebellum seems to receive information about ongoing activity in the pathway but mesencephalic stimulation was seen to cause spindle effects also in decerebellated animals.
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  • 45
    ISSN: 1432-1106
    Keywords: Monosynaptic reflex ; Presynaptic inhibition ; Extensor nerve ; Spinal cord ; Cat
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary 1. Electrical stimulation of extensor nerves of the ankle has been used to investigate the presynaptic inhibition in a synergic monosynaptic reflex arc. 2. Depression of monosynaptic reflex response as well as increase in excitability of Ia afferent terminals in the MG (medial gastrocnemius) reflex arc is found following the conditioning stimulation of LGS (lateral gastrocnemius-soleus) nerve at Group I strength. 3. Excitability increase of the Ia terminals of the LGS nerve is also found following the conditioning stimulation of either a group of fibres of the same nerve or the MG nerve. 4. Conditioning by Group I afferent volleys from either the LGS or the PBST (posterior biceps-semitendinosus) muscles produces comparable changes in excitability of the Ia terminals from MG muscle. 5. The hypothesis is advanced that the depression of the monosynaptic reflex discharge during repetitive stimulation is mainly caused by the depolarization of the Ia afferent terminals, i.e. by presynaptic inhibition.
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  • 46
    Electronic Resource
    Electronic Resource
    Springer
    Diabetologia 3 (1967), S. 249-265 
    ISSN: 1432-0428
    Keywords: Spontaneous Diabetes ; Dog ; Cat ; Diabetes in dogs and cats ; Pancreas ; Islets of Langerhans ; B cells ; Insulitis ; Hyalin ; Capillaries ; Kidney ; Retina ; Microaneurysms ; Pituitary
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Description / Table of Contents: Résumé Les auteurs présentent une étude histopathologique de 30 chiens et de 5 chats spontanément diabétiques. — Les îlots de Langerhans et les cellules B étaient fortement diminués en nombre chez la grande majorité des chiens. Les cellules B étaient souvent dégranulées et hydropiques. Chez les chiens dont le diabète avait évolué pendant longtemps, les îlots étaient très rares et les cellules B absentes. — Chez les 5 chats spontanément diabétiques par contre, les îlots et les cellules B étaient nombreuses. Les cellules B étaient dégranulées et hydropiques chez 4 chats. Chez 1 des chats, les cellules B paraissaient normales. De nombreux îlots présentaient des dépôts de substance hyaline dans le stroma. Chez un chat, il existait une infiltration lymphocytaire très dense dans un îlot. — Ni chez les chiens, ni chez les chats, il n'a été vu de lésions glomérulaires identiques à celles de glomérulosclérose diabétique humaine. Les lésions les plus fréquentes consistaient en un épaississement des axes membraneux des touffes glomérulaires et une hypertrophie de la paroi des artérioles afférentes.— Dans les rétines des chiens diabétiques il existait une acellularité focale ou généralisée de la paroi des capillaires. Un petit nombre de microanévrysmes ont été trouvés chez 3 chiens diabétiques. L'incidence plus faible des lésions de rétinopathie vasculaire, comparativement aux diabétiques humains, s'explique probablement par la durée de vie plus courte du chien et du chat. Il est possible aussi que les capillaires rétiniens de ces animaux soient moins susceptibles de développer des lésions dégénératives. — Un degré marqué de stéatose hépatique a été observé chez beaucoup de chiens et de chats. Les surrénales étaient souvent hypertrophiées et contenaient des adénomes, mais ces lésions ne paraissent pas différentes de celles que l'on peut trouver chez des chiens et des chats non diabétiques de même âge. L'hypophyse a été prélevée chez 7 chiens. Dans 2 cas, elle contenait un adénome. Une étude cytologique plus complète des hypophyses sera publiée ultérieurement.
    Abstract: Zusammenfassung Die Autoren berichten über die Ergebnisse von Untersuchungen an 30 spontan-diabetischen Hunden und 5 spontan-diabetischen Katzen. Bei der großen Mehrzahl der diabetischen Hunde war die Zahl der Langerhansschen Inseln und der B-Zellen stark herabgesetzt. Die B-Zellen waren oft degranuliert und hydropisch. Bei Hunden mit schon lang anhaltender Krankheit waren die Inseln nur noch vereinzelt und B-Zellen überhaupt nicht mehr nachweisbar. — Im Gegensatz zu diesen Ergebnissen fanden sich bei allen 5 Katzen zahlreiche Inseln und B-Zellen. Bei 4 dieser Katzen jedoch waren die B-Zellen, wie bei den Hunden, degranuliert und hydropisch entartet. Bei einer Katze war das Aussehen der B-Zellen normal. Im Stroma der Inseln von 2 Katzen konnten starke Hyalinablagerungen nachgewiesen werden. In einem Falle zeigten die Inseln eine starke lymphocytäre Infiltration. — Weder bei den Hunden noch bei den Katzen waren typische Läsionen der Glomeruli, wie sie bei der Glomerulosklerose des menschlichen Diabetes auftreten, nachweisbar. Die häufigsten Veränderungen bestanden aus einer mehr oder weniger ausgeprägten Verdickung des mesangialen Teils der Kapillaren der Glomeruli und aus einer Hypertrophie der Wand der zuführenden Arteriolen. Bei einigen Hunden und Katzen bestanden auf chronische Pyelonephritis zurückführende Narben. — In der Retina der diabetischen Hunde waren zellenlose und funktionslose Kapillaren vorhanden, und degenerierte Pericyten (“ghostcells”) waren häufiger als bei normalen Hunden. In drei Hunden wurden einige Mikroaneurismen beobachtet. Daß diese für die Retinopathie des Diabetes typischen Läsionen beim Hund verhältnismäßig selten auftreten könnte mit der kürzeren Lebensdauer der Krankheit bei diesen Tieren zusammenhängen. Es ist jedoch nicht ausgeschlossen, daß die Retina von Hunden und Katzen weniger zu degenerativen Veränderungen neigt. — In der Leber vieler Hunde und Katzen wurde eine schwere Steatose beobachtet. In vier Hunden zeigte sich beginnende Lebercirrhose. In diabetischen Hunden und Katzen waren die Nebennieren oft hypertrophisch und enthielten Adenome, die allerdings auch bei nichtdiabetischen alternden Hunden beobachtet wurden. In 2 von 7 Hypophysen diabetischer Hunde fanden sich Adenome, über deren cytologische Untersuchung in einer späteren Veröffentlichung berichtet wird.
    Notes: Summary A histological study of 30 spontaneously diabetic dogs and 5 spontaneously diabetic cats is presented. — The islets of Langerhans and the B cells were strongly reduced in number in a large majority of the diabetic dogs. The B cells were often degranulated and hydropic. In cases of longer duration, the islets were scarce and B cells could no longer be found. — In contrast to the findings in diabetic dogs, all five cats showed numerous islets and B cells. However in 4 cats, the B cells showed complete degranulation and hydropic changes, as in the dogs. In one cat, the B cells had a normal appearance. Extensive hyalin deposits were found in the stroma of the islets in 2 cats. In one cat, an islet showed a dense lymphocytic infiltration. — No lesions identical to human diabetic glomerulosclerosis were found in any of the dogs or cats. The changes most frequently observed were a variable degree of thickening of the mesangial stalk of the glomerular capillaries, and an hypertrophy of the wall of the afferent arteriole. Scars resulting from chronic pyelonephritis, were found in a few dogs and cats. — Acellular, non-functional capillaries, with degeneration of pericytes (“ghost-cells”) were found in larger numbers in the retinas of the diabetic dogs than in non-diabetic control dogs. A very few microaneurysms could be found in 3 dogs. The lower incidence of the most typical lesions of diabetic retinopathy in dogs, as compared with the human diabetic, is probably related to the shorter duration of the disease in these animals. However, a lower susceptibility of the retina of dogs and cats to develop degenerative changes cannot be excluded. — A severe steatosis was observed in the liver of many dogs and cats. In 4 dogs, the liver showed early cirrhosis. In diabetic dogs and cats, the adrenal cortex often showed hypertrophy and contained adenomas; however, these changes have also been reported in non-diabetic aging dogs. An adenoma was found in 2 of the 7 pituitaries obtained from diabetic dogs; the cytological aspect of these adenomas and of the pituitaries will be reported in a later publication.
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  • 47
    Electronic Resource
    Electronic Resource
    Springer
    Experimental brain research 3 (1967), S. 95-110 
    ISSN: 1432-1106
    Keywords: Mossy fibre pathways ; Cerebellum ; Cat
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary 1. Field potentials in the vermal cerebellar cortex generated by a mossy fibre volley along reticulo-, cuneo- and spino-cerebellar tracts were recorded with microelectrodes and analysed by the same procedures as was done for the mossy fibre responses in the cortex by juxta-fastigial (J.F.) and trans-folial (T.F.) stimulations in the previous paper (Eccles, Sasaki and Strata 1967a). li 3. All these results corroborate the analyses and the interpretations of the field potentials in the cerebellar cortex produced by T.F.- and J.F.-evoked mossy fibre volleys in the previous paper. 4. There have not been found electrophysiologically significant differences, as Szentágothai (1964) has suggested, between the modes of mossy fibre terminations of the reticulo-cerebellar and the spino-cerebellar systems.
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  • 48
    Electronic Resource
    Electronic Resource
    Springer
    Experimental brain research 3 (1967), S. 353-367 
    ISSN: 1432-1106
    Keywords: Tectum opticum ; Movement detecting neurons ; Directional sensitive neurons ; Cat
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Description / Table of Contents: Zusammenfassung Es wurden 80 Einheiten des Tectum opticum der Katze abgeleitet und ihre Reaktionen auf stationäre und bewegte optische Reize geprüft. Neben den Neuronen, die in ihrer Reaktionsweise retinalen Einheiten vergleichbar waren, fanden sich überwiegend (89%) Neurone, die auf bewegte optische Reize reagierten. Unter den letzteren zeigte die Mehrheit (70%) richtungsspezifisches Verhalten. Bei einigen Neuronen war in einem beschränkten Bereich von 1–7.5∘/sec die Reaktion gesetzmäßig abhängig von der Winkelgeschwindigkeit des Bewegungsreizes (Potenzfunktion mit dem Exponenten 0.67). Die rezeptiven Felder waren meist rund mit einem durchschnittlichen Durchmesser von 8.1∘ (3–22∘). 68% der Einheiten reagierten nicht auf diffusen Lichtreiz. Die Reaktionen auf nicht bewegte Punktlichtreize waren rasch adaptierend und inkonstant in ihrer Art und Stärke. In kurzen Abständen mehrfach wiederholte Bewegungsreize bewirkten bei einem Teil der Bewegungsneurone rasche Adaptation. Zwei kurz aufeinander folgende Punktlichtreize ergaben eine Reaktion, die niedriger als die Summe der Erregungen der jeweils einzeln gegebenen Lichtreize war, wenn die zeitliche Folge der beiden Reize der Vorzugsrichtung des Neurons entgegengesetzt war. Bei Reizfolgen entsprechend der Vorzugsrichtung entsprach die Gesamtreaktion der Summe der Einzelreizantworten. Dies läßt vermuten, daß die Richtungsspezifität durch unilaterale Hemmung bedingt ist.
    Notes: Summary Recordings were made from 80 single units in cat's Tectum opticum during visual stimulation with moving and stationary optic stimuli. The majority of units (89%) showed movement specific reactions, the rest behaved functionally similar to retinal or geniculate neurons. 70% of the movement specific units showed directional selective reactions. The receptive fields, as determined with stationary and moving stimuli were mostly circular with an average diameter of 8.1° (range 3–22°). Stimuli passing through the periphery of the field led to less pronounced reactions than those going through the center. In 10 out of 30 units, the relation between discharge rate and angular velocity in a restricted range from 1°–7.5°/sec could be approximated by a power function with an exponent of 0.67. Above 10°/sec irregular and unsystematic alterations of reactivity were observed. 68% of the tectal units recorded did not respond to diffuse light stimuli. The reactions to localized intermittent stationary light stimuli were mostly off (42%) or on-off-responses (19%) and were characterized by fast adaptation, change of reaction type during successive intermittent stimulation and by the absence of an antagonistic field-structure. Stimulation of adjacent points in a temporal sequence corresponding to movement opposite to the most sensitive direction of a directional specific neuron led to a reaction which was below the sum of the reaction of the two stimuli given alone. At a temporal sequence of the two stimuli such as to simulate the most sensitive direction, the resulting reaction corresponded to the sum of the reactions of both stimuli given alone. This suggests a mechanism of unilateral inhibition to be responsible for directional selectivity.
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  • 49
    ISSN: 1432-1912
    Keywords: Dopa formation ; Tyrosine hydroxylase ; Dopa decarboxylase ; Adrenal gland ; Cat ; Dopa-Bildung ; Tyrosin-Hydroxylase ; Dopa-Decarboxylase ; Nebenniere ; Katze
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Description / Table of Contents: Zusammenfassung Nach Injektion von H-3-Tyrosin wurde die Bildung von H-3-Dopa in verschiedenen Organen (Nebenniere, Hirnstamm, Herz, Leber, Niere, Milz, Pankreas und Blut) des Huhnes und der Katze gemessen. Die Isolierung von H-3-Dopa wurde wie folgt durchgeführt: 1. Die säurelösliche Fraktion wurde durch Papierhochspannungselektrophorese im Pyridin-Eisessig-Puffer vorgetrennt. 2. Die Tyrosin-Dopa-Bande wurde eluiert und papierchromatographisch aufgetrennt. 3. Die Dopa-Bande wurde erneut eluiert und Dopa wurde als Borat-Komplex durch Papierhochspannungselektrophorese in einem Borat-Puffer charakterisiert. Nach Hemmung der Dopa-Decarboxylase mit NSD-1034 [N-Methyl-N-(3-hydroxybenzyl)hydrazin-dihydrogenphosphat] betrug der Anteil des H-3-Dopa an der Gesamtaktivität der säurelöslichen Fraktion der Nebenniere beim Huhn 4% und bei der Katze 5%. Unter diesen Bedingungen konnte H-3-Dopa in allen anderen untersuchten Organen nicht nachgewiesen werden. Ohne NSD-1034 fand sich auch in der Nebenniere kein H-3-Dopa. Bei Versuchen an Katzen wurde die H-3-Dopa-Konzentration im venösen Blut der Nebenniere gemessen. In einigen Blutproben betrug die H-3-Dopa-Aktivität bis zu 3% der Gesamtaktivität. Nahezu die gesamte von der Nebenniere gebildete Menge an H-3-Dopa wurde an das venöse Blut abgegeben. Nur 5% des neugebildeten Dopa waren am Ende des Versuches in der Nebenniere nachweisbar. Das zeigt, daß Dopa von der Nebenniere nicht gespeichert wird. Im Blut anderer Organe fand sich hingegen kein Dopa. Die Dopa-Konzentration der Nebenniere betrug nach Blockierung der Dopa-Decarboxylase ca. 1 μg/g Naßgewebe und war ohne Hemmung 〈0,2 μg/g. Die Dopa-Neubildungsrate der Nebenniere wurde abgeschätzt aus dem H-3-Dopa-Gehalt der Nebenniere sowie aus dem zeitlichen Verlauf der H-3-Dopa-Aktivität und der spezifischen Aktivität des freien H-3-Tyrosins. Bei der Katze werden von einer einzelnen Nebenniere etwa $$\frac{{0,02{{\mu}}g}}{{\min /kg}}$$ Dopa gebildet $$\left( { = \frac{{1,2{{m\mu Mol}}}}{{\min /1{{gNebenniere}}}}} \right)$$ .
    Notes: Summary After injection of H-3-tyrosine the synthesis of H-3-dopa was measured in various organs (adrenal glands, brain stem, heart, liver, kidney, spleen, pancreas and blood) of fowl and cat. The isolation of H-3-dopa was carried out in the following way: 1. The acid soluble fraction was fractionated by high voltage paper electrophoresis in a pyridine-acetic acid-buffer. 2. The tyrosine-dopa-spot was eluated and descending paper chromatography was carried out. This system separated tyrosine from dopa. 3. The dopa-spot was eluated again, and dopa was characterized by its complex with boric acid in paper high voltage electrophoresis in a boric acid-sodium hydroxide-buffer. After inhibition of the dopa decarboxylase by NSD-1034 [N-methyl-N-(3-hydroxybenzyl)hydrazine dihydrogen phosphate] H-3-dopa represented in adrenal glands of domestic fowl 4% and in those of cats 5% of the total radioactivity. Under these conditions in all the other organs investigated H-3-dopa could not be detected. Without NSD-1034 H-3-dopa was undetectable in the adrenals, too. In experiments with cats the H-3-dopa concentration in the venous blood of the adrenals was measured. In some samples H-3-dopa represented up to 3% of the total radioactivity. Nearly the total amount of H-3-dopa formed in the adrenals was secreted into the venous blood, and only 5% of the total amount were detected in the gland at the end of the experiments. This demonstrates that dopa cannot be stored by the adrenals. We failed to detect H-3-dopa in blood from any other organ. The concentration of dopa in the adrenals was about 1 μg/g wet weight after inhibition of dopa decarboxylase and without inhibition it was 〈0.2 μg/g wet weight. The dopa synthesis rate in adrenals was calculated from the H-3-dopa activity in the gland and in the venous blood and from the specific activity of its precursor H-3-tyrosine. One adrenal of the cat synthetized 0.02 μg dopa/min·kg body weight (=1.2 mμMol/min·1 g adrenal).
    Type of Medium: Electronic Resource
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