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  • ddc:510
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  • 2010-2014  (24)
  • 2005-2009  (31)
  • 1995-1999  (134)
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  • 1
    Publication Date: 2020-12-11
    Description: Convexity is an important property in nonlinear optimization since it allows to apply efficient local methods for finding global solutions. We propose to apply symbolic methods to prove or disprove convexity of rational functions over a polyhedral domain. Our algorithms reduce convexity questions to real quantifier elimination problems. Our methods are implemented and publicly available in the open source computer algebra system REDUCE. Our long term goal is to integrate REDUCE as a workhorse'' for symbolic computations into a numerical solver.
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    Language: English
    Type: reportzib , doc-type:preprint
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  • 2
    Publication Date: 2016-06-30
    Description: Applications which need exclusive access to a shared resource in distributed systems require a fault-tolerant and scalable mechanism to coordinate this exclusive access. Examples of such applications include distributed file systems and master/slave data replication. We present Flease, an algorithm for decentralized and fault-tolerant lease coordination in distributed systems. Our algorithm allows the processes competing for a resource to coordinate exclusive access through leases among themselves without a central component. The resulting system easily scales with an increasing number of nodes and resources. We prove that Flease ensures exclusive access, i.e. guarantees that there is at most one valid lease at any time.
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    Language: English
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  • 3
    Publication Date: 2020-08-05
    Description: We propose an efficient column generation method to minimize the probability of delay propagations along aircraft rotations. In this way, delay resistant schedules can be constructed. Computational results for large-scale real-world problems demonstrate substantial punctuality improvements. The method can be generalized to crew and integrated scheduling problems.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
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  • 4
    Publication Date: 2022-01-07
    Description: In optimal control problems with nonlinear time-dependent 3D PDEs, full 4D discretizations are usually prohibitive due to the storage requirement. For this reason gradient and quasi-Newton methods working on the reduced functional are often employed. The computation of the reduced gradient requires one solve of the state equation forward in time, and one backward solve of the adjoint equation. The state enters into the adjoint equation, again requiring the storage of a full 4D data set. We propose a lossy compression algorithm using an inexact but cheap predictor for the state data, with additional entropy coding of prediction errors. As the data is used inside a discretized, iterative algorithm, lossy coding maintaining an error bound is sufficient.
    Keywords: ddc:510
    Language: English
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  • 5
    Publication Date: 2020-03-11
    Description: Bovine fertility is the subject of extensive research in animal sciences, especially because fertility of dairy cows has declined during the last decades. The regulation of estrus is controlled by the complex interplay of various organs and hormones. Mathematical modeling of the bovine estrous cycle could help in understanding the dynamics of this complex biological system. In this paper we present a mathematical model of the bovine estrous cycle that includes the processes of follicle and corpus luteum development and the key hormones that interact to control these processes. Focus in this paper is on development of the model, but also some simulation results are presented, showing that a set of equations and parameters is obtained that describes the system consistent with empirical knowledge. Even though the majority of the mechanisms that are included are only known qualitatively as stimulatory or inhibitory effects, the model surprisingly well features quantitative observations made in reality. This model of the bovine estrous cycle could be used as a basis for more elaborate models with the ability to study effects of external manipulations and genetic differences.
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    Language: English
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  • 6
    Publication Date: 2022-03-14
    Description: Learning during search allows solvers for discrete optimization problems to remember parts of the search that they have already performed and avoid revisiting redundant parts. Learning approaches pioneered by the SAT and CP communities have been successfully incorporated into the SCIP constraint integer programming platform. In this paper we show that performing a heuristic constraint programming search during root node processing of a binary program can rapidly learn useful nogoods, bound changes, primal solutions, and branching statistics that improve the remaining IP search.
    Keywords: ddc:510
    Language: English
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  • 7
    Publication Date: 2020-08-05
    Description: We propose a novel integer programming approach to transfer minimization for line planning problems in public transit. The idea is to incorporate penalties for transfers that are induced by “connection capacities” into the construction of the passenger paths. We show that such penalties can be dealt with by a combination of shortest and constrained shortest path algorithms such that the pricing problem for passenger paths can be solved efficiently. Connection capacity penalties (under)estimate the true transfer times. This error is, however, not a problem in practice. We show in a computational comparison with two standard models on a real-world scenario that our approach can be used to minimize passenger travel and transfer times for large-scale line planning problems with accurate results.
    Keywords: ddc:510
    Language: English
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  • 8
    Publication Date: 2016-06-09
    Description: The aim of this paper is to devise an adaptive timestep control in the contact--stabilized Newmark method (CONTACX) for dynamical contact problems between two viscoelastic bodies in the framework of Signorini's condition. In order to construct a comparative scheme of higher order accuracy, we extend extrapolation techniques. This approach demands a subtle theoretical investigation of an asymptotic error expansion of the contact--stabilized Newmark scheme. On the basis of theoretical insight and numerical observations, we suggest an error estimator and a timestep selection which also cover the presence of contact. Finally, we give a numerical example.
    Keywords: ddc:510
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  • 9
    Publication Date: 2020-08-05
    Description: Railway scheduling is based on the principle of the construction of a conflict-free timetable. This leads to a strict definition of capacity: in contrast with road transportation, it can be said in advance whether a given railway infrastructure can accommodate - at least in theory - a certain set of train requests. Consequently, auctions for railway capacity are modeled as auctions of discrete goods -- the train slots. We present estimates for the efficiency gain that may be generated by slot auctioning in comparison with list price allocation. We introduce a new class of allocation and auction problems, the feasible assignment problem, that is a proper generalization of the well-known combinatorial auction problem. The feasible assignment class was designed to cover the needs for an auction mechanism for railway slot auctions, but is of interest in its own right. As a practical instance to state and solve the railway slot allocation problem, we present an integer programming formulation, briefly the ACP, which turns out to be an instance of the feasible assignment problem and whose dual problem yields prices that can be applied to define a useful activity rule for the linearized version of the Ausubel Milgrom Proxy auction. We perform a simulation aiming to measure the impact on efficiency and convergence rate.
    Keywords: ddc:510
    Language: English
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  • 10
    Publication Date: 2022-01-07
    Description: This paper presents concepts and implementation of the finite element toolbox Kaskade 7, a flexible C++ code for solving elliptic and parabolic PDE systems. Issues such as problem formulation, assembly and adaptivity are discussed at the example of optimal control problems. Trajectory compression for parabolic optimization problems is considered as a case study.
    Keywords: ddc:510
    Language: English
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  • 11
    Publication Date: 2020-08-05
    Description: In this paper a bottom-up approach of automatic simplification of a railway network is presented. Starting from a very detailed, microscopic level, as it is used in railway simulation, the network is transformed by an algorithm to a less detailed level (macroscopic network), that is sufficient for long-term planning and optimization. In addition running and headway times are rounded to a pre-chosen time discretization by a special cumulative method, which we will present and analyse in this paper. After the transformation we fill the network with given train requests to compute an optimal slot allocation. Then the optimized schedule is re-transformed into the microscopic level and can be simulated without any conflicts occuring between the slots. The algorithm is used to transform the network of the very dense Simplon corridor between Swiss and Italy. With our aggregation it is possible for the first time to generate a profit maximal and conflict free timetable for the corridor across a day by a simultaneously optimization run.
    Keywords: ddc:510
    Language: English
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  • 12
    Publication Date: 2020-12-11
    Description: In solving large polynomial algebraic systems that are too big for standard Gröbner basis techniques one way to make progress is to introduce case distinctions. This divide and conquer technique can be beneficial if the algorithms and computer programs know how to take advantage of inequalities. A further hurdle is the form of the resulting general solutions which often have unnecessarily many branches. In this paper we discuss a procedure to merge solutions by dropping inequalities which are associated with them and, if necessary, by re-parametrizing solutions. In the appendix the usefulness of the procedure is demonstrated in the classification of quadratic Hamiltonians with a Lie-Poisson bracket $e(3)$. This application required the solution of algebraic systems with over 200 unknowns, 450 equations and between 5000 and 9000 terms.
    Keywords: ddc:510
    Language: English
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  • 13
    Publication Date: 2020-12-11
    Description: In the paper arguments are given why the concept of static evaluation (SE) has the potential to be a useful extension to Monte Carlo tree search. A new concept of modeling SE through a dynamical system is introduced and strengths and weaknesses are discussed. The general suitability of this approach is demonstrated. A Remark: Among users of the Internet Go server KGS the abbreviation SE is used for 'Score Estimator'. Although different from 'Static Evaluation' a score estimator is easily obtained from static evaluation by adding up probabilities of chains to be alive at the end of the game or points to be owned by White or Black
    Keywords: ddc:510
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  • 14
    Publication Date: 2020-12-11
    Description: Linear Poisson brackets on e(3) typical of rigid body dynamics are considered. All quadratic Hamiltonians of Kowalevski type having additional first integral of fourth degree are found. Quantum analogs of these Hamiltonians are listed.
    Keywords: ddc:510
    Language: English
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  • 15
    Publication Date: 2020-12-11
    Description: A classification problem is proposed for supersymmetric %scaling\/-\/in\-va\-ri\-ant evolutionary PDE that satisfy the assumptions of nonlinearity, nondegeneracy, and homogeneity. Four classes of nonlinear coupled boson\/-\/fermion systems are discovered under the weighting assumption $|f|=|b|=|D_t|=\oh$. The syntax of the \Reduce\ package \SsTools, which was used for intermediate computations, and the applicability of its procedures to the calculus of super\/-\/PDE are described.
    Keywords: ddc:510
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  • 16
    Publication Date: 2020-12-11
    Description: We consider the problem of constructing Gardner's deformations for the $N{=}2$ supersymmetric $a{=}4$--\/Korteweg\/--\/de Vries equation; such deformations yield recurrence relations between the super\/-\/Hamiltonians of the hierarchy. We prove the non\/-\/existence %P.~Mathieu's Open problem on constructing for of supersymmetry\/-\/invariant %Gardner's deformations that %solutions, retract to Gardner's formulas for the KdV equation %whenever it is assumed that, under the %respective component reduction. % in the $N{=}2$ super\/-\/field. the solutions . At the same time, we propose a two\/-\/step scheme for the recursive production of the integrals of motion for the $N{=}2$,\ $a{=}4$--\/SKdV. First, we find a new Gardner's deformation of the Kaup\/--\/Boussinesq equation, which is contained in the bosonic limit of the super\/-\/%$N{=}2$,\ $a{=}4$--\/SKdV hierarchy. This yields the recurrence relation between the Hamiltonians of the limit, whence we determine the bosonic super\/- /Hamiltonians of the full $N{=}2$, $a{=}4$--\/SKdV hierarchy.
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  • 17
    Publication Date: 2020-08-05
    Description: We provide an introduction into the mathematics of and with paths. Not on the shortest, but hopefully on an entertaining path!
    Keywords: ddc:510
    Language: English
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  • 18
    Publication Date: 2020-08-05
    Description: Wir stellen in dieser Arbeit ein mathematisches Optimierungsmodell zur Bestimmung eines optimalen Linienplans vor, das sowohl die Fahrzeiten und die Anzahl der Umstiege berücksichtigt als auch die Kosten des Liniennetzes. Dieses Modell deckt wichtige praktische Anforderungen ab, die in einem gemeinsamen Projekt mit den Verkehrsbetrieben in Potsdam (ViP) formuliert wurden. In diesem Projekt wurde der Linienplan 2010 für Potsdam entwickelt. Unsere Berechnungen zeigen, dass die mathematische Optimierung in nichts einer "Handplanung" des Liniennetzes nachsteht. Im Gegenteil, mit Hilfe des Optimierungsprogramms ist es möglich, durch Veränderung der Parameter mehrere verschiedene Szenarien zu berechnen, miteinander zu vergleichen und Aussagen über minimale Kosten und Fahrzeiten zu machen.
    Keywords: ddc:510
    Language: German
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  • 19
    Publication Date: 2020-12-11
    Description: The paper gathers evidence showing different dimensions of the game of Go: the continuous and discrete nature of the game and different types of relations between state variables happening on ultra local, local, regional, and global scales. Based on these observations a new continuous local model for describing a board position is introduced. This includes the identification of the basic variables describing a board position and the formulation and solution of a dynamical system for their computation. To be usable as a static evaluation function for a game playing program at least group-wide (regional)aspects will have to be incorporated.
    Keywords: ddc:510
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  • 20
    Publication Date: 2020-08-05
    Description: The track allocation problem, also known as train routing problem or train timetabling problem, is to find a conflict-free set of train routes of maximum value in a railway network. Although it can be modeled as a standard path packing problem, instances of sizes relevant for real-world railway applications could not be solved up to now. We propose a rapid branching column generation approach that integrates the solution of the LP relaxation of a path coupling formulation of the problem with a special rounding heuristic. The approach is based on and exploits special properties of the bundle method for the approximate solution of convex piecewise linear functions. Computational results for difficult instances of the benchmark library TTPLIB are reported.
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  • 21
    Publication Date: 2020-08-05
    Description: This paper presents a case study on a railway timetable optimization for the very dense Simplon corridor, a major railway connection in the Alps between Switzerland and Italy. Starting from a detailed microscopic network as it is used in railway simulation, the data is transformed by an automatic procedure to a less detailed macroscopic network, that is sufficient for the purpose of capacity planning and amenable to state-of-the-art integer programming optimization methods. In this way, the macroscopic railway network is saturated with trains. Finally, the corresponding timetable is re-transformed to the microscopic level in such a way that it can be operated without any conflicts among the slots. Using this integer programming based micro-macro aggregation-disaggregation approach, it becomes for the first time possible to generate a profit maximal and conflict free timetable for the complete Simplon corridor over an entire day by a simultaneous optimization of all trains requests. This also allows to to undertake a sensitivity analysis of various problem parameters.
    Keywords: ddc:510
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  • 22
    Publication Date: 2016-06-09
    Description: The thesis presents the analysis of a reduced model for modulation of internal gravity waves by deep convective clouds. The starting point for the derivation are conservation laws for mass, momentum and energy coupled with a bulk micro-physics model describing the evolution of mixing ratios of water vapor, cloud water and rain water. A reduced model for the identified scales of the regime is derived, using multi-scale asymptotics. The closure of the model employs conditional averaging over the horizontal scale of the convective clouds. The resulting reduced model is an extension of the anelastic equations, linearized around a constant background state, which are well-known from meteorology. The closure of the model is achieved purely by analytical means and involves no additional physically motivated assumptions. The essential new parameter arising from the coupling to a micro-physics model is the area fraction of saturated regions on the horizontal scale of the convective clouds. It turns out that this parameter is constant on the employed short timescale. Hence the clouds constitute a constant background, modulating the characteristics of propagation of internal waves. The model is then investigated by analytical as well as numerical means. Important results are, among others, that in the model moisture (i) inhibits propagation of internal waves by reducing the modulus of the group velocity, (ii) reduces the angle between the propagation direction of a wave-packet and the horizontal, (iii) causes critical layers and (iv) introduces a maximum horizontal wavelength beyond which waves are no longer propagating but become evanescent. The investigated examples of orographically generated gravity waves also feature a significant reduction of vertical momentum flux by moisture. The model is extended by assuming systematically small under-saturation, that is saturation at leading order. The closure is similar to the original case but requires additional assumptions. The saturated area fraction in the obtained model is no longer constant but now depends nonlinearly on vertical displacement and thus on vertical velocity.
    Keywords: ddc:510
    Language: English
    Type: doctoralthesis , doc-type:doctoralThesis
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  • 23
    Publication Date: 2022-03-14
    Description: We propose a hybrid approach for solving the resource-constrained project scheduling problem which is an extremely hard to solve combinatorial optimization problem of practical relevance. Jobs have to be scheduled on (renewable) resources subject to precedence constraints such that the resource capacities are never exceeded and the latest completion time of all jobs is minimized. The problem has challenged researchers from different communities, such as integer programming (IP), constraint programming (CP), and satisfiability testing (SAT). Still, there are instances with 60 jobs which have not been solved for many years. The currently best known approach, lazyFD, is a hybrid between CP and SAT techniques. In this paper we propose an even stronger hybridization by integrating all the three areas, IP, CP, and SAT, into a single branch-and-bound scheme. We show that lower bounds from the linear relaxation of the IP formulation and conflict analysis are key ingredients for pruning the search tree. First computational experiments show very promising results. For five instances of the well-known PSPLIB we report an improvement of lower bounds. Our implementation is generic, thus it can be potentially applied to similar problems as well.
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    Language: English
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  • 24
    Publication Date: 2023-11-03
    Description: In contrast to the well known meshbased methods like the finite element method, meshfree methods do not rely on a mesh. However besides their great applicability, meshfree methods are rather time consuming. Thus, it seems favorable to combine both methods, by using meshfree methods only in a small part of the domain, where a mesh is disadvantageous, and a meshbased method for the rest of the domain. We motivate, that this coupling between the two simulation techniques can be considered as saddle point problem and show the stability of this coupling. Thereby a novel transfer operator is introduced, which interacts in the transition zone, where both methods coexist.
    Keywords: ddc:510
    Language: English
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  • 25
    Publication Date: 2019-01-29
    Description: We consider an optimal control problem from hyperthermia treatment planning and its barrier regularization. We derive basic results, which lay the groundwork for the computation of optimal solutions via an interior point path-following method. Further, we report on a numerical implementation of such a method and its performance at an example problem.
    Keywords: ddc:510
    Language: English
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  • 26
    Publication Date: 2016-06-09
    Description: Optical technologies are ubiquitously used in hi-tech devices. As a common feature of such devices one finds structures with dimensions in the order of the wavelength of the used light. To design and produce such devices, the wave nature of light must be taken into account. Accordingly, robust simulation tools are required which are based on rigorously solving Maxwell's equations, the governing equations of light propagation within macroscopic media. This thesis contributes to the modeling and the numerical computation of light scattering problems: Light scattering problems are typically posed on the entire space. The Perfectly-Matched -Layer method (PML) is widely used to restrict the simulation problem onto a bounded computational domain. We propose an adaptive PML method which exhibits a good convergence even for critical problems where standard PML implementations fail. Besides the computation of the near field, that is the electromagnetic field within the computational domain, it is of major interest to evaluate the electromagnetic field in the exterior domain and to compute the far field. So far, this was numerically only possible for simple geometries such as homogeneous exterior domains or layered media. To deal with more complicated devices, for example with waveguide inhomogeneities, we develop an evaluation formula based on the PML solution which allows for an exterior domain field evaluation in a half space above the device. Finally, we generalize the PML method to problems with multiply structured exterior domains. The term “multiply structured exterior domain” is defined in this thesis and means that the exterior domain exhibits several half-infinite structures. Mathematically, this gives rise to various complications. For example, no analytical solutions to Maxwell's equations for standard light sources are available in the exterior domain, which are needed to describe the incoming field in a light scattering problem. To tackle this we propose a new light scattering problem formulation which fits well into the PML method framework and which may be regarded as an extension of classical contributions by Sommerfeld, Wiener and Hopf. An exterior domain evaluation formula for multiply structured exterior domains with an extended illumination is derived as well.
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    Language: English
    Type: doctoralthesis , doc-type:doctoralThesis
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  • 27
    Publication Date: 2020-08-05
    Description: We introduce the coolest path problem, which is a mixture of two well-known problems from distinct mathematical fields. One of them is the shortest path problem from combinatorial optimization. The other is the heat conduction problem from the field of partial differential equations. Together, they make up a control problem, where some geometrical object traverses a digraph in an optimal way, with constraints on intermediate or the final state. We discuss some properties of the problem and present numerical solution techniques. We demonstrate that the problem can be formulated as a linear mixed-integer program. Numerical solutions can thus be achieved within one hour for instances with up to 70 nodes in the graph.
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    Language: English
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  • 28
    Publication Date: 2021-08-05
    Description: Given a general mixed integer program (MIP), we automatically detect block structures in the constraint matrix together with the coupling by capacity constraints arising from multi-commodity-flow formulations. We identify the underlying graph and generate cutting planes based on cuts in the detected network. Our implementation adds a separator to the branch-and-cut libraries of SCIP and CPLEX. We make use of the complemented mixed integer rounding framework (cMIR) but provide a special purpose aggregation heuristic that exploits the network structure. Our separation scheme speeds-up the computation for a large set of MIPs coming from network design problems by a factor of two on average.
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    Language: English
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  • 29
    Publication Date: 2022-03-14
    Description: Pseudo-Boolean problems lie on the border between satisfiability problems, constraint programming, and integer programming. In particular, nonlinear constraints in pseudo-Boolean optimization can be handled by methods arising in these different fields: One can either linearize them and work on a linear programming relaxation or one can treat them directly by propagation. In this paper, we investigate the individual strengths of these approaches and compare their computational performance. Furthermore, we integrate these techniques into a branch-and-cut-and-propagate framework, resulting in an efficient nonlinear pseudo-Boolean solver.
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  • 30
    Publication Date: 2020-08-05
    Description: Every day, millions of people are transported by buses, trains, and airplanes in Germany. Public transit (PT) is of major importance for the quality of life of individuals as well as the productivity of entire regions. Quality and efficiency of PT systems depend on the political framework (state-run, market oriented) and the suitability of the infrastructure (railway tracks, airport locations), the existing level of service (timetable, flight schedule), the use of adequate technologies (information, control, and booking systems), and the best possible deployment of equipment and resources (energy, vehicles, crews). The decision, planning, and optimization problems arising in this context are often gigantic and “scream” for mathematical support because of their complexity. This article sketches the state and the relevance of mathematics in planning and operating public transit, describes today’s challenges, and suggests a number of innovative actions. The current contribution of mathematics to public transit is — depending on the transportation mode — of varying depth. Air traffic is already well supported by mathematics. Bus traffic made significant advances in recent years, while rail traffic still bears significant opportunities for improvements. In all areas of public transit, the existing potentials are far from being exhausted. For some PT problems, such as vehicle and crew scheduling in bus and air traffic, excellent mathematical tools are not only available, but used in many places. In other areas, such as rolling stock rostering in rail traffic, the performance of the existing mathematical algorithms is not yet sufficient. Some topics are essentially untouched from a mathematical point of view; e.g., there are (except for air traffic) no network design or fare planning models of practical relevance. PT infrastructure construction is essentially devoid of mathematics, even though enormous capital investments are made in this area. These problems lead to questions that can only be tackled by engineers, economists, politicians, and mathematicians in a joint effort. Among other things, the authors propose to investigate two specific topics, which can be addressed at short notice, are of fundamental importance not only for the area of traffic planning, should lead to a significant improvement in the collaboration of all involved parties, and, if successful, will be of real value for companies and customers: • discrete optimal control: real-time re-planning of traffic systems in case of disruptions, • model integration: service design in bus and rail traffic. Work on these topics in interdisciplinary research projects could be funded by the German ministry of research and education (BMBF), the German ministry of economics (BMWi), or the German science foundation (DFG).
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  • 31
    Publication Date: 2020-08-05
    Description: The steel mill slab design problem from the CSPLib is a binpacking problem that is motivated by an application of the steel industry and that has been widely studied in the constraint programming community. Recently, several people proposed new models and methods to solve this problem. A steel mill slab library was created which contains 380 instances. A closely related binpacking problem called multiple knapsack problem with color constraints, originated from the same industrial problem, were discussed in the integer programming community. In particular, a simple integer programming for this problem has been given by Forrest et al. [3]. The aim of this paper is to bring these different studies together. Moreover, we adopt the model of [3] for the steel mill slab problem. Using a state of the art integer program solver, this model is capable to solve all instances of the steel mill slab library, mostly in less than one second, to optimality. We improved, thereby, the solution value of 76 instances.
    Keywords: ddc:510
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  • 32
    Publication Date: 2020-08-05
    Description: Nowadays most data networks use shortest path protocols such as OSPF or IS-IS to route traffic. Given administrative routing lengths for the links of a network, all data packets are sent along shortest paths with respect to these lengths from their source to their destination. One of the most fundamental problems in planning shortest path networks is to decide whether a given set of routing paths forms a valid routing and, if this is not the case, to find a small subset of the given paths that cannot be shortest paths simultaneously for any routing lengths. In this paper we show that it is NP-hard to approximate the size of the smallest shortest path conflict by a factor less than 7/6.
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  • 33
    Publication Date: 2020-08-05
    Description: The Vehicle Positioning Problem (VPP) consists of the assignment of vehicles (buses, trams or trains) of a public transport or railway company to parking positions in a depot and to timetabled trips. Such companies have many different types of vehicles, and each trip can be performed only by vehicles of some of these types. These assignments are non-trivial due to the topology of depots. The parking positions are organized in tracks, which work as one- or two-sided stacks or queues. If a required type of vehicle is not available in the front of any track, shunting movements must be performed in order to change vehicles' positions, which is undesirable and should be avoided. In this text we present integer linear and non-linear programming formulations for some versions of the problem and compare them from a theoretical and a computational point of view.
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  • 34
    Publication Date: 2020-03-11
    Description: The understanding of geometric structures and dynamical properties of molecular conformations gives insight into molecular long-term behavior. The identification of metastable conformations together with their life times and transition patterns is the intention of conformation dynamics. Conformation dynamics is a multi-scale approach that leads to a reduced description of the dynamical system in terms of a stochastic transition probability matrix. The present thesis deals with the error analysis of computed matrices and the resulting matrix functions. Since conformational membership vectors, as they are computed by the Robust Perron Cluster Analysis (PCCA+), form an invariant subspace of the transition matrix, subspace-based error estimators are of particular interest. The decomposition of the state space into basis functions and the approximation of integrals by Monte-Carlo quadrature give rise to row-wise correlated random matrices, for which stochastic norms are computed. Together with an appropriate statistical model for the distribution of matrix rows, this allows for the calculation of error bounds and error distributions of the invariant subspace and other variables of interest. Equilibration of errors among the basis functions can be achieved by enhanced sampling in regions where the trajectories are mixing slowly. Hierarchical refinement of such basis functions systematically improves the clustering into metastable conformations by reducing the error in the corresponding invariant subspace. These techniques allow for an evaluation of simulation results and pave the way for the analysis of larger molecules. Moreover, the extension of PCCA+ to non-reversible Markov chains, verified by the corresponding perturbation theory, and the modification of the objective function for the case of soft membership vectors represent a further generalization of the clustering method, thus continuing the development from PCCA over PCCA+ to PCCA++. The methods developed in this thesis are useful for but not limited to conformation dynamics. In fact, they are applicable to a broader class of problems which combine domain decomposition with Monte-Carlo quadrature. Possible application areas may include the chemical master equation or quantum dynamical systems.
    Description: Das Verständnis von geometrischen Strukturen und dynamischen Eigenschaften molekularer Konformationen ist essentiell für die Vorhersage des Langzeitverhaltens von Molekülen. Die Identifikation metastabiler Konformationen sowie die Bestimmung von Übergangswahrscheinlichkeiten und Haltezeiten sind Bestandteil der Konformationdynamik. Dabei handelt es sich um eine Mehrskalenmethode, die auf eine reduzierte Beschreibung des Systems mittels einer stochastischen Übergangsmatrix führt. In der vorliegenden Dissertation wurde untersucht, wie man die Genauigkeit der Matrizen sowie der daraus berechneten Größen quantifizieren kann. Im Mittelpunkt stehen dabei Fehlerschätzer für den invarianten Unterraum, da die rechten Eigenvektoren als Grundlage der Robusten Perron Cluster Analyse (PCCA+) zur Identifizierung der metastabilen Konformationen dienen. Die Zerlegung des Zustandsraumes in Basisfunktionen sowie die Approximation der Matrixeinträge mittels Monte-Carlo-Quadratur führen zu zeilenweise korrelierten Zufallsmatrizen. Mit Hilfe einer stochastischen Norm sowie einem geeigneten statistischen Modell für die Verteilung der Matrixzeilen können u.a. Fehlerschranken und -verteilungen für den invarianten Unterraum brechnet werden. Eine Equilibrierung des Fehlers zwischen den Basisfunktionen kann durch erweitertes Sampling in solchen Regionen erreicht werden, in denen die Trajektorien nur langsam mischen.Eine hierarchische Zerlegung dieser Basisfunktionen verbessert systematisch die Zerlegung in metastabile Konformationen, indem sie den Fehler im invarianten Unterraum reduziert. Diese Techniken gestatten eine Evaluierung der Simulationsergebnisse und ebnen den Weg zur Behandlung komplexerer Moleküle. Desweiteren wurden Verallgemeinerungen der PCCA+ untersucht. Die Erweiterung der PCCA+ auf nicht-reversible Markov-Ketten sowie die Modifizierung der Zielfunktion für den Fall der weichen Clusterung setzen die Entwicklung von der PCCA über PCCA+ zu PCCA++ fort. Somit können neue Anwendungsfelder für dieses Cluster-Verfahren erschlossen werden. Die Methoden wurden zwar in Rahmen der Konformationsdynamik entwickelt, jedoch lassen sie sich auf eine weite Problemklasse anwenden, in der Gebietszerlegungsverfahren mit Monte-Carlo-Quadratur kombiniert werden. Mögliche Anwendungsgebiete umfassen die chemische Master-Gleichung oder quantenchemische Systeme.
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    Type: doctoralthesis , doc-type:doctoralThesis
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  • 35
    Publication Date: 2020-08-05
    Description: The Vehicle Positioning Problem (VPP) is a classical combinatorial optimization problem in public transport planning. A number of models and approaches have been suggested in the literature, which work for small problems, but not for large ones. We propose in this article a novel set partitioning model and an associated column generation solution approach for the VPP. The model provides a tight linear description of the problem. The pricing problem, and hence the LP relaxation itself, can be solved in polynomial resp. pseudo-polynomial time for some versions of the problems.
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  • 36
    Publication Date: 2020-08-05
    Description: Since the initial application of mathematical optimisation methods to mine planning in 1965, the Lerchs-Grossmann algorithm for computing the ultimate pit limit, operations researchers have worked on a variety of challenging problems in the area of open pit mining. This thesis focuses on the open pit mining production scheduling problem: Given the discretisation of an orebody as a block model, determine the sequence in which the blocks should be removed from the pit, over the lifespan of the mine, such that the net present value of the mining operation is maximised. In practise, when some material has been removed from the pit, it must be processed further in order to extract the valuable elements contained therein. If the concentration of valuable elements is not sufficiently high, the material is discarded as waste or stockpiled. Realistically-sized block models can contain hundreds of thousands of blocks. A common approach to render these problem instances computationally tractable is the aggregation of blocks to larger scheduling units. The thrust of this thesis is the investigation of a new mixed-integer programming formulation for the open pit mining production scheduling problem, which allows for processing decisions to be made at block level, while the actual mining schedule is still computed at aggregate level. A drawback of this model in its full form is the large number of additional variables needed to model the processing decisions. One main result of this thesis shows how these processing variables can be aggregated efficiently to reduce the problem size significantly, while practically incurring no loss in net present value. The second focus is on the application of lagrangean relaxation to the resource constraints. Using a result of Möhring et al. (2003) for project scheduling, the lagrangean relaxation can be solved efficiently via minimum cut computations in a weighted digraph. Experiments with a bundle algorithm implementation by Helmberg showed how the lagrangean dual can be solved within a small fraction of the time required by standard linear programming algorithms, while yielding practically the same dual bound. Finally, several problem-specific heuristics are presented together with computational results: two greedy sub-MIP start heuristics and a large neighbourhood search heuristic. A combination of a lagrangean-based start heuristic followed by a large neighbourhood search proved to be effective in generating solutions with objective values within a 0.05% gap of the optimum.
    Keywords: ddc:510
    Language: English
    Type: masterthesis , doc-type:masterThesis
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  • 37
    Publication Date: 2019-01-29
    Description: In dieser Arbeit wird ein neuer Ansatz zur Modellierung von thermal signifikanten Gefäßsträngen im Hyperthermie-Kontext betrachtet. Ausgehend von einer Konvektions-Diffusions-Gleichung wird durch Reskalierung des Massenflussterms eine Reduktion des Adergebietes auf eine 1D-Struktur erreicht. Nach numerischen Vorbetrachtungen wird die Grenzgleichung innerhalb einer verallgemeinerten Sobolev-Algebra formuliert. Die Untersuchung der Lösungsfamilie in klassischen Funktionenräumen zeigt, dass deren schwacher Grenzwert die Lösung der korrespondierenden Diffusions-Gleichung ist. Die Diskretisierung einer formalen Grenzgleichung mit Linienstromanteil stellt jedoch eine gute Approximation an die Diskretisierung des ursprünglichen Problems dar, wenn man die lokale Maschenweite an die Gefäßradien koppelt und bei erhöhtem Genauigkeitsbedarf auf ein vollständiges 3D-Modell umschaltet.
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    Language: German
    Type: masterthesis , doc-type:masterThesis
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  • 38
    Publication Date: 2022-03-14
    Description: We present Undercover, a primal heuristic for mixed-integer nonlinear programming (MINLP). The heuristic constructs a mixed-integer linear subproblem (sub-MIP) of a given MINLP by fixing a subset of the variables. We solve a set covering problem to identify a minimal set of variables which need to be fixed in order to linearise each constraint. Subsequently, these variables are fixed to approximate values, e.g. obtained from a linear outer approximation. The resulting sub-MIP is solved by a mixed-integer linear programming solver. Each feasible solution of the sub-MIP corresponds to a feasible solution of the original problem. Although general in nature, the heuristic seems most promising for mixed-integer quadratically constrained programmes (MIQCPs). We present computational results on a general test set of MIQCPs selected from the MINLPLib.
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  • 39
    Publication Date: 2020-08-05
    Description: We consider a system with Poisson arrivals and i.i.d. service times. The requests are served according to the state-dependent processor sharing discipline, where each request receives a service capacity which depends on the actual number of requests in the system. The linear systems of PDEs describing the residual and attained sojourn times coincide for this system, which provides time reversibility including sojourn times for this system, and their minimal non negative solution gives the LST of the sojourn time $V(\tau)$ of a request with required service time $\tau$. For the case that the service time distribution is exponential in a neighborhood of zero, we derive a linear system of ODEs, whose minimal non negative solution gives the LST of $V(\tau)$, and which yields linear systems of ODEs for the moments of $V(\tau)$ in the considered neighborhood of zero. Numerical results are presented for the variance of $V(\tau)$. In case of an M/GI/2-PS system, the LST of $V(\tau)$ is given in terms of the solution of a convolution equation in the considered neighborhood of zero. For bounded from below service times, surprisingly simple expressions for the LST and variance of $V(\tau)$ in this neighborhood of zero are derived, which yield in particular the LST and variance of $V(\tau)$ in M/D/2-PS.
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  • 40
    Publication Date: 2020-12-11
    Description: Eigentlich war der erste Autor nur zu einem Grußwort zur Tagung „GML² 2009 - Grundfragen Multi¬medialen Lehrens und Lernens“ eingeladen. Daraus wurde ein E-Learning-bezogener Vortrag, der – basierend auf Erfahrungen im Fach Mathematik – einen kritischen Blick auf die E-Learning-Szene in Deutschland wirft und diese mit entsprechenden Aktivitäten weltweit vergleicht. Dies ist die in seinen mathematischen Teilen gekürzte, in den E-Learning-Anteilen ein wenig erweiterte schriftliche Fassung des Vortrags. Der Artikel stammt nicht von E-Learning-Spezialisten sondern von Personen, die sich seit fast zwanzig Jahren mit elektronischer Information und Kommunikation (kurz: IuK) – insbesondere in der Mathematik – beschäftigen. Nach einer Definition von Michael Kerres kennzeichnet der Begriff E-Learning (electronic learning – elektronisch unterstütztes Lernen) alle Formen von Lernen, bei denen digitale Medien für die Präsentation und Distribution von Lernmaterialien und/oder zur Unterstützung zwischenmenschlicher Kommunikation zum Einsatz kommen, siehe z.B. http://de.wikipedia.org/wiki/E-Learning. IuK und E-Learning haben nach dieser Begriffsbildung viele Berührungspunkte. Deswegen wagen wir es, unsere positiven und negativen Erfahrungen im Bereich IuK in diesem Eröffnungsvortrag zu berichten, einige Entwicklungslinien zu vergleichen und eine eigene Kurzversion der Definition von E-Learning (besser E-Teaching and -Learning) voranzustellen: „Lehren und Lernen mit Unterstützung elektronischer Hilfsmittel“.
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    Language: German
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  • 41
    Publication Date: 2020-08-05
    Description: Telecommunication transport networks consist of a stack of technologically different subnetworks, so-called layers, which are strongly interdependent. For example, one layer may correspond to an Internet (IP) backbone network whose links are realized by lightpath connections in an underlying optical fiber layer. To ensure that the network can fulfill its task of routing all communication requests, the inter-layer dependencies have to be taken into account already in the planning phase of the network. This is particularly important with survivability constraints, where connections in one layer have to be protected against cable cuts or equipment failures in another layer. The traditional sequential planning approach where one layer is optimized after the other cannot properly take care of the inter-layer dependencies; this can only be achieved with an integrated planning of several network layers at the same time. This thesis provides mathematical models and algorithmic techniques for the integrated optimization of two network layers with survivability constraints. We describe a multi-layer network design problem which occurs in various technologies, and model it mathematically using mixed-integer programming (MIP) formulations. The presented models cover many important practical side constraints from different technological contexts. In contrast to previous models from the literature, they can be used to design large two-layer networks with survivability requirements. We discuss modeling alternatives for various aspects of a multi-layer network and compare different routing formulations under multi-layer survivability constraints. We solve our models using a branch-and-cut-and-price approach with various problemspecific enhancements. This includes a presolving technique based on linear programming to reduce the problem size, combinatorial and sub-MIP-based primal heuristics to compute feasible network configurations, cutting planes which take the multi-layer survivability constraints into account to improve the lower bound on the optimal network cost, and column generation to generate flow variables dynamically during the algorithm. We develop techniques to speed up computations in a Benders decomposition approach and compare this approach to the standard formulation with a single MIP. We use the developed techniques to design large survivable two-layer networks by means of linear and integer programming methods. On realistic test instances with up to 67 network nodes and survivability constraints, we investigate the algorithmic impact of our techniques and show how to use them to compute good network configurations with quality guarantees. Most of the smaller test instances with up to 17 nodes can be solved to near-optimality. Moreover, we can compute feasible solutions and dual bounds even for large networks with survivability constraints, which has not been possible before.
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    Language: English
    Type: doctoralthesis , doc-type:doctoralThesis
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  • 42
    Publication Date: 2020-08-05
    Description: In the simplex algorithm, solving linear systems with the basis matrix and its transpose accounts for a large part of the total computation time. We investigate various methods from modern numerical linear algebra to improve the computation speed of the basis updates arising in LPs. The experiments are executed on a large real-world test set. The most widely used solution technique is sparse LU factorization, paired with an updating scheme that allows to use the factors over several iterations. Clearly, small number of fill-in elements in the LU factors is critical for the overall performance. Using a wide range of LPs we show numerically that after a simple permutation the non-triangular part of the basis matrix is so small, that the whole matrix can be factorized with (relative) fill-in close to the optimum. This permutation has been exploited by simplex practitioners for many years. But to our knowledge no systematic numerical study has been published that demonstrates the effective reduction to a surprisingly small non-triangular problem, even for large scale LPs. For the factorization of the non-triangular part most existing simplex codes use some variant of dynamic Markowitz pivoting, which originated in the late 1950s. We also show numerically that, in terms of fill-in and in the simplex context, dynamic Markowitz is quite consistently superior to other, more recently developed techniques.
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  • 43
    Publication Date: 2020-03-11
    Description: We compute expectation values for the solution of the nuclear Schrödinger equation. The proposed particle method consists of three steps: sampling of the initial Wigner function, classical transport of the sampling points, weighted phase space summation for the final computation of the expectation values. The Egorov theorem guarantees that the algorithm is second order accurate with respect to the semiclassical parameter. We present numerical experiments for a two-dimensional torsional potential with three different sets of initial data and for a six-dimensional Henon-Heiles potential. By construction, the computing times scale linearly with the number of initial sampling points and range between three seconds and one hour.
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  • 44
    Publication Date: 2022-03-14
    Description: This paper discusses how to build a solver for mixed integer quadratically constrained programs (MIQCPs) by extending a framework for constraint integer programming (CIP). The advantage of this approach is that we can utilize the full power of advanced MIP and CP technologies. In particular, this addresses the linear relaxation and the discrete components of the problem. For relaxation, we use an outer approximation generated by linearization of convex constraints and linear underestimation of nonconvex constraints. Further, we give an overview of the reformulation, separation, and propagation techniques that are used to handle the quadratic constraints efficiently. We implemented these methods in the branch-cut-and-price framework SCIP. Computational experiments indicates the potential of the approach.
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  • 45
    Publication Date: 2016-06-09
    Description: Supercomputers can simulate complex molecular systems. However, there is a very large gap between the fastest oscillations of covalent bonds of a molecule and the time-scale of the dominant processes. In order to extract the dominant time-scales and to identify the dominant processes, a clustering of information is needed. This thesis shows that only the subspace-based Robust Perron Cluster Analysis (PCCA+) can solve this problem correctly by the construction of a Markov State Model. PCCA+ allows for time-extrapolation in molecular kinetics. This thesis shows the difference between molecular dynamics and molecular kinetics. Only in the molecular kinetics framework a definition of transition rates is possible. In this context, the existence of an infinitesimal generator of the dynamical processes is discussed. If the existence is assumed, the Theorem of Gauß can be applied in order to compute transition rates efficiently. Molecular dynamics, however, is not able to provide a suitable statistical basis for the determination of the transition pattern.
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  • 46
    Publication Date: 2020-08-05
    Description: We consider a system with Poisson arrivals and general service times, where the requests are served according to the State-Dependent Processor Sharing (SDPS) discipline (Cohen's generalized processor sharing discipline), where each request receives a service capacity which depends on the actual number of requests in the system. For this system, denoted by $M/GI/SDPS$, we derive approximations for the squared coefficients of variation of the conditional sojourn time of a request given its service time and of the unconditional sojourn time by means of two-moment fittings of the service times. The approximations are given in terms of the squared coefficients of variation of the conditional and unconditional sojourn time in related $M/D/SDPS$ and $M/M/SDPS$ systems, respectively. The numerical results presented for $M/GI/m-PS$ systems illustrate that the proposed approximations work well.
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  • 47
    Publication Date: 2020-08-05
    Description: We consider a system with Poisson arrivals and i.i.d. service times and where the requests are served according to the state-dependent (Cohen's generalized) processor sharing discipline, where each request in the system receives a service capacity which depends on the actual number of requests in the system. For this system we derive asymptotically tight upper bounds for the moments of the conditional sojourn time of a request with given required service time. The bounds generalize corresponding results, recently given for the single-server processor sharing system by Cheung et al. and for the state-dependent processor sharing system with exponential service times by the authors. Analogous results hold for the waiting times.
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  • 48
    Publication Date: 2020-11-13
    Description: The Dynamic Multi-Period Routing Problem DMPRP introduced by Angelelli et al. gives a model for a two-stage online-offline routing problem. At the beginning of each time period a set of customers becomes known. The customers need to be served either in the current time period or in the following. Postponed customers have to be served in the next time period. The decision whether to postpone a customer has to be done online. At the end of each time period, an optimal tour for the customers assigned to this period has to be computed and this computation can be done offline. The objective of the problem is to minimize the distance traveled over all planning periods assuming optimal routes for the customers selected in each period. We provide the first randomized online algorithms for the DMPRP which beat the known lower bounds for deterministic algorithms. For the special case of two planning periods we provide lower bounds on the competitive ratio of any randomized online algorithm against the oblivious adversary. We identify a randomized algorithm that achieves the optimal competitive ratio of $\frac{1+\sqrt{2}}{2}$ for two time periods on the real line. For three time periods, we give a randomized algorithm that is strictly better than any deterministic algorithm.
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  • 49
    Publication Date: 2021-08-05
    Description: This thesis introduces the novel paradigm of "constraint integer programming" (CIP), which integrates constraint programming (CP) and mixed integer programming (MIP) modeling and solving techniques. It is supplemented by the software SCIP, which is a solver and framework for constraint integer programming that also features SAT solving techniques. SCIP is freely available in source code for academic and non-commercial purposes. Our constraint integer programming approach is a generalization of MIP that allows for the inclusion of arbitrary constraints, as long as they turn into linear constraints on the continuous variables after all integer variables have been fixed. The constraints, may they be linear or more complex, are treated by any combination of CP and MIP techniques: the propagation of the domains by constraint specific algorithms, the generation of a linear relaxation and its solving by LP methods, and the strengthening of the LP by cutting plane separation. The current version of SCIP comes with all of the necessary components to solve mixed integer programs. In the thesis, we cover most of these ingredients and present extensive computational results to compare different variants for the individual building blocks of a MIP solver. We focus on the algorithms and their impact on the overall performance of the solver. In addition to mixed integer programming, the thesis deals with chip design verification, which is an important topic of electronic design automation. Chip manufacturers have to make sure that the logic design of a circuit conforms to the specification of the chip. Otherwise, the chip would show an erroneous behavior that may cause failures in the device where it is employed. An important subproblem of chip design verification is the property checking problem, which is to verify whether a circuit satisfies a specified property. We show how this problem can be modeled as constraint integer program and provide a number of problem-specific algorithms that exploit the structure of the individual constraints and the circuit as a whole. Another set of extensive computational benchmarks compares our CIP approach to the current state-of-the-art SAT methodology and documents the success of our method.
    Description: Diese Arbeit stellt einen integrierten Ansatz aus "Constraint Programming" (CP) und Gemischt-Ganzzahliger Programmierung ("Mixed Integer Programming", MIP) vor, den wir "Constraint Integer Programming" (CIP) nennen. Sowohl Modellierungs- als auch Lösungstechniken beider Felder fließen in den neuen integrierten Ansatz ein, um die unterschiedlichen Stärken der beiden Gebiete zu kombinieren. Als weiteren Beitrag stellen wir der wissenschaftlichen Gemeinschaft die Software SCIP zur Verfügung, die ein Framework für Constraint Integer Programming darstellt und zusätzlich Techniken des SAT-Lösens beinhaltet. SCIP ist im Source Code für akademische und nicht-kommerzielle Zwecke frei erhältlich. Unser Ansatz des Constraint Integer Programming ist eine Verallgemeinerung von MIP, die zusätzlich die Verwendung beliebiger Constraints erlaubt, solange sich diese durch lineare Bedingungen ausdrücken lassen falls alle ganzzahligen Variablen auf feste Werte eingestellt sind. Die Constraints werden von einer beliebigen Kombination aus CP- und MIP-Techniken behandelt. Dies beinhaltet insbesondere die "Domain Propagation", die Relaxierung der Constraints durch lineare Ungleichungen, sowie die Verstärkung der Relaxierung durch dynamisch generierte Schnittebenen. Die derzeitige Version von SCIP enthält alle Komponenten, die für das effiziente Lösen von Gemischt-Ganzzahligen Programmen benötigt werden. Die vorliegende Arbeit liefert eine ausführliche Beschreibung dieser Komponenten und bewertet verschiedene Varianten in Hinblick auf ihren Einfluß auf das Gesamt-Lösungsverhalten anhand von aufwendigen praktischen Experimenten. Dabei wird besonders auf die algorithmischen Aspekte eingegangen. Ein weiterer Hauptteil der Arbeit befasst sich mit der Chip-Design-Verifikation, die ein wichtiges Thema innerhalb des Fachgebiets der "Electronic Design Automation" darstellt. Chip-Hersteller müssen sicherstellen, dass der logische Entwurf einer Schaltung der gegebenen Spezifikation entspricht. Andernfalls würde der Chip fehlerhaftes Verhalten aufweisen, dass zu Fehlfunktionen innerhalb des Gerätes führen kann, in dem der Chip verwendet wird. Ein wichtiges Teilproblem in diesem Feld ist das Eigenschafts-Verifikations-Problem, bei dem geprüft wird, ob der gegebene Schaltkreisentwurf eine gewünschte Eigenschaft aufweist. Wir zeigen, wie dieses Problem als Constraint Integer Program modelliert werden kann und geben eine Reihe von problemspezifischen Algorithmen an, die die Struktur der einzelnen Constraints und der Gesamtschaltung ausnutzen. Testrechnungen auf Industrie-Beispielen vergleichen unseren Ansatz mit den bisher verwendeten SAT-Techniken und belegen den Erfolg unserer Methode.
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    Language: English
    Type: doctoralthesis , doc-type:doctoralThesis
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  • 50
    Publication Date: 2020-08-05
    Description: In this paper we investigate the fare planning model for public transport, which consists in designing a system of fares maximizing the revenue. We discuss a discrete choice model in which passengers choose between different travel alternatives to express the demand as a function of fares. Furthermore, we give a computational example for the city of Potsdam and discuss some theoretical aspects.
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  • 51
    Publication Date: 2020-08-05
    Description: This extended abstract is about algorithms for controlling elevator systems employing destination hall calls, i.e. the passenger provides his destination floor when calling an elevator. We present the first exact algorithm for controlling a group of elevators and report on simulation results indicating that destination hall call systems outperform conventional systems.
    Keywords: ddc:510
    Language: English
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  • 52
    Publication Date: 2019-01-29
    Description: The paper proposes goal-oriented error estimation and mesh refinement for optimal control problems with elliptic PDE constraints using the value of the reduced cost functional as quantity of interest. Error representation, hierarchical error estimators, and greedy-style error indicators are derived and compared to their counterparts when using the all-at-once cost functional as quantity of interest. Finally, the efficiency of the error estimator and generated meshes are demonstrated on numerical examples.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
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  • 53
    Publication Date: 2016-06-09
    Description: The paper considers the time integration of frictionless dynamical contact problems between viscoelastic bodies in the frame of the Signorini condition. Among the numerical integrators, interest focuses on the contact-stabilized Newmark method recently suggested by Deuflhard et al., which is compared to the classical Newmark method and an improved energy dissipative version due to Kane et al. In the absence of contact, any such variant is equivalent to the Störmer-Verlet scheme, which is well-known to have consistency order 2. In the presence of contact, however, the classical approach to discretization errors would not show consistency at all because of the discontinuity at the contact. Surprisingly, the question of consistency in the constrained situation has not been solved yet. The present paper fills this gap by means of a novel proof technique using specific norms based on earlier perturbation results due to the authors. The corresponding estimation of the local discretization error requires the bounded total variation of the solution. The results have consequences for the construction of an adaptive timestep control, which will be worked out subsequently in a forthcoming paper.
    Keywords: ddc:510
    Language: English
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  • 54
    Publication Date: 2020-08-05
    Description: The mathematical treatment of planning problems in public transit has made significant advances in the last decade. Among others, the classical problems of vehicle and crew scheduling can nowadays be solved on a routine basis using combinatorial optimization methods. This is not yet the case for problems that pertain to the design of public transit networks, and for the problems of operations control that address the implementation of a schedule in the presence of disturbances. The article gives a sketch of the state and important developments in these areas, and it addresses important challenges. The vision is that mathematical tools of computer aided scheduling (CAS) will soon play a similar role in the design and operation of public transport systems as CAD systems in manufacturing.
    Description: Die mathematische Behandlung von Planungsproblemen im öffentlichen Verkehr hat im letzten Jahrzehnt große Fortschritte gemacht. Klassische Probleme wie die Umlauf- und die Dienstplanung können heutzutage routinemäßig mit kombinatorischen Optimierungsmethoden gelöst werden. Die Behandlung von Problemen der Angebotsplanung und der Betriebssteuerung sind dagegen noch nicht ganz auf diesem Stand. Dieser Artikel gibt einen Überblick über den Stand der Forschung, über wichtige Entwicklungen und einige Herausforderungen in diesem Gebiet. Die Vision ist, dass mathematische Planungswerkzeuge im öffentlichen Verkehr (Computer Aided Scheduling, CAS) in Zukunft eine ähnliche Rolle spielen werden wie CAD-Systeme in der industriellen Fertigung.
    Keywords: ddc:510
    Language: English
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  • 55
    Publication Date: 2022-07-19
    Description: The reconstruction of geometric shapes plays an important role in many biomedical applications. One example is the patient-specific, computer-aided planning of complex interventions, which requires the generation of explicitly represented geometric models of anatomical structures from medical image data. Only solutions that require minimal interaction by medical personnel are likely to enter clinical routine. Another example is the planning of surgical corrections of deformities where the target shape is unknown. Surgeons are often forced to resort to subjective criteria. These applications still pose highly challenging reconstruction problems, which are addressed in this thesis. The fundamental hypothesis, pursued in this thesis, is that the problems can be solved by incorporating a-priori knowledge about shape and other application-specific characteristics. Here, we focus mainly on the aspect of geometric shape analysis. The basic idea is to capture the most essential variations of a certain class of geometric objects via statistical shape models, which model typical features contained in a given population, and restrict the outcome of a reconstruction algorithm (more or less) to the space spanned by such models. A fundamental prerequisite for performing statistical shape analysis on a set of different objects is the identification of corresponding points on their associated surfaces. This problem is particularly difficult to solve if the shapes stem from different individuals. The reason lies in the basic difficulty of defining suitable measures of similarity. In this thesis, we divide the correspondence problem into feature and non-feature matching. The feature part depends on the application, while the non-feature part can be characterized by a purely geometric description. We propose two different approaches. The first approach has proved useful in many applications. Yet, it suffers from some practical limitations and does not yield a measure of similarity. Our second, variational, approach is designed to overcome these limitations. In it, we propose to minimize an invariant stretching measure, constrained by previously computed features. An important property, which sets our method apart from previous work, is that it does not require the computation of a global surface parameterization.
    Keywords: ddc:510
    Language: English
    Type: doctoralthesis , doc-type:doctoralThesis
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  • 56
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    Diseases of the colon & rectum 41 (1998), S. 1062-1066 
    ISSN: 1530-0358
    Keywords: Colonic neoplasms, complication ; Hemangioma, cavernous ; Magnetic resonance imaging ; Tomography, x-ray computed
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract PURPOSE: We present two cases of diffuse cavernous hemangioma of the rectum that invaded the pelvic structures. METHODS: Two young women suffering from intermittent rectal bleeding were studied using computed tomography and magnetic resonance imaging. RESULTS: Beside the rectal hemangioma, computed tomography and magnetic resonance imaging revealed that the pelvic ureter and the iliac vessels were each eroded by the tumor that produced symptoms in these two patients. CONCLUSION: Computed tomography and magnetic resonance imaging permit direct visualization for tumor staging and also for recognition of any pelvic structure invasion, which facilitate preoperative assessment of diffuse cavernous hemangioma of the rectum.
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  • 57
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    Diseases of the colon & rectum 41 (1998), S. 514-516 
    ISSN: 1530-0358
    Keywords: Angiomyxoma ; Intraoperative radiation therapy ; Magnetic resonance imaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract Aggressive angiomyxomas are rare soft tissue tumors found mainly in the female reproductive mesenchyme and pelvis. They are low-grade sarcomas that have a propensity to recur locally. These tumors are encapsulated and have the same consistency as normal connective tissue, thus making wide excision difficult. We report a case of a large aggressive angiomyxoma in the perirectal tissues treated with preoperative angiographic embolization, causing ischemia of the tumor and, thus, improved visualization of the lesion. In addition, preoperative external beam irradiation and intraoperative electron beam radiotherapy were used to decrease the chances of local recurrence.
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  • 58
    ISSN: 1534-4681
    Keywords: Magnetic resonance imaging ; Breast cancer ; Locoregional recurrence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract Background: Dynamic contrast-enhanced magnetic resonance imaging (MRI) of the breast is highly sensitive for the diagnosis of primary breast malignancy. We investigated the clinical application of dedicated dynamic breast MR for routine screening for local recurrence following breast-conserving therapy. Methods: Patients underwent a single dynamic MR of the breast routinely in the period 1 to 2 years following treatment, or earlier if recurrence was suspected. A biopsy was performed if there was suspicion of recurrence on MR. Results: One hundred and five patients with a median age of 58 years (range 50 to 65 years) were recruited for the study. Sixteen biopsies were performed and nine recurrences were confirmed histologically. Patients not undergoing biopsy have been followed up for a median of 341 days (range 168 to 451 days) following the MR. The sensitivity for clinical examination, mammography, examination combined with mammography, and MRI alone for the detection of recurrent cancer were 89%, 67%, 100%, and 100%, respectively, and the specificity was 76%, 85%, 67%, and 93%. Conclusion: Combined clinical examination and mammography are as sensitive as dedicated dynamic MR of the breast for the detection of locoregional recurrence, but breast MRI is associated with a far greater specificity. Therefore, dedicated dynamic breast MRI should be used when there is clinical or mammographic suspicion of recurrence to confirm or refute its presence.
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  • 59
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    Surgical and radiologic anatomy 20 (1998), S. 299-302 
    ISSN: 1279-8517
    Keywords: Magnetic resonance imaging ; Anatomical variant ; Hook of hamate ; Wrist ; Carpal tunnel
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract Normal skeletal variants are a common occurrence in clinical practice and may lead to misinterpretation. As part of a case control study investigating the carpal tunnel, our asymptomatic and voluntary participant underwent magnetic resonance (MR) imaging of both wrists from the metacarpal bases to the distal radiocarpal joint. The imaging techniques included spin echo (SE), turbo spin echo (TSE) and fast field echo (FFE) sequences using 4 mm-slice thickness. As an incidental finding bipartite hamulus was detected bilaterally. The anomaly was evident in both hamuli with similar MRI characteristics. The congenital origin was further supported by the absence of trauma or surgery to the wrists. In this case report the authors discuss the anatomical variant, bilateral bipartite hook of the hamate, and demonstrate the reliability of contiguous slices of MR axial slices in displaying an anatomical variant of the carpus. This normal variant of the hamate is not commonly encountered in MR imaging of the wrist and can be misinterpreted as fracture or post-traumatic sequelae. Images of the normal hamulus are presented for comparison.
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  • 60
    ISSN: 1279-8517
    Keywords: Ocular development ; Orbit ; Fetus ; Eye ; Magnetic resonance imaging ; Anatomy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract The aim of this study was to measure fetal ocular development and to determine a growth curve by means of measurements in utero. Fetal ocular development was recorded by analysis of the results of magnetic resonance imaging (MRI). An anatomic study allowed definition of the best contrasted MRI sequences for calculation of the ocular surface. Biometric analysis of the values of the ocular surface in the neuro-ocular plane in 35 fetuses allowed establishment of a linear model of ocular growth curve in utero. Evaluation of ocular development may allow the detection and confirmation of malformational ocular anomalies such as microphthalmia.
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  • 61
    Electronic Resource
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    Surgical and radiologic anatomy 20 (1998), S. 299-302 
    ISSN: 1279-8517
    Keywords: Magnetic resonance imaging ; Anatomical variant ; Hook of hamate ; Wrist ; Carpal tunnel
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Description / Table of Contents: Résumé Les variations squelettiques normales sont fréquemment rencontrées en pratique clinique et peuvent conduire à des erreurs d'interprétation. Lors d'une étude contrôle concernant le canal carpien, des sujets asymptomatiques et volontaires ont subi une imagerie par résonance magnétique (IRM) des deux poignets depuis les bases des métacarpiens jusqu'à l'interligne radio-carpien. Les techniques d'imagerie utilisaient des coupes de 4 mm en spin-écho (SE), en turbo spin-écho (TSE) et en écho de champ rapide (FFE). Fortuitement, nous avons trouvé un hamulus bipartite bilatéral. L'anomalie était évidente sur les deux hamulus et présentait les mêmes caractéristiques IRM. L'origine congénitale a été retenue en l'absence de traumatisme ou de chirurgie des poignets. Dans le cas rapporté, les auteurs discutent la variante anatomique, un hamulus bipartite de l'hamatum, et montrent la fiabilité des coupes axiales IRM contiguës pour décrire une variante anatomique du carpe. Cette variante normale de l'hamatum est rarement rencontrée en IRM du poignet et pourrait être prise par erreur comme une fracture ou une séquelle post-traumatique. Les images d'un hamulus normal sont présentées pour comparaison.
    Notes: Summary Normal skeletal variants are a common occurrence in clinical practice and may lead to misinterpretation. As part of a case control study investigating the carpal tunnel, our asymptomatic and voluntary participant underwent magnetic resonance (MR) imaging of both wrists from the metacarpal bases to the distal radiocarpal joint. The imaging techniques included spin echo (SE), turbo spin echo (TSE) and fast field echo (FFE) sequences using 4 mm-slice thickness. As an incidental finding bipartite hamulus was detected bilaterally. The anomaly was evident in both hamuli with similar MRI characteristics. The congenital origin was further supported by the absence of trauma or surgery to the wrists. In this case report the authors discuss the anatomical variant, bilateral bipartite hook of the hamate, and demonstrate the reliability of contiguous slices of MR axial slices in displaying an anatomical variant of the carpus. This normal variant of the hamate is not commonly encountered in MR imaging of the wrist and can be misinterpreted as fracture or post-traumatic sequelae. Images of the normal hamulus are presented for comparison.
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  • 62
    ISSN: 1437-160X
    Keywords: Key words Myositis ; Diagnosis ; Biopsy ; 99mtechnetium-pyrophosphate scintigraphy ; Magnetic resonance imaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract Our objective was to study the value of 99mtechnetium-pyrophosphate (99mTc-PYP) muscle scintigraphy and magnetic resonance imaging (MRI) in detecting areas of likely muscle inflammation and in increasing the rate of positive muscle biopsies in patients with suspected myositis. The results showed that in 13 out of 13 patients with clinical and/or signs of inflammatory muscle disease, increased 99mTc-PYP uptake was demonstrated at different muscle sites 3 h after isotope injection. Subsequent MRI of symmetric muscle areas with enhanced 99mTc-PYP uptake revealed signal patterns suggesting inflammation in all cases. Biopsy of these targeted muscles demonstrated characteristic histopathologic signs of muscle inflammation in 9 out of 13 patients. Four of these 9 patients had clinically atypical disease or did not show elevated creatine phosphokinase levels. Seven of these 9 patients had not been pretreated with corticosteroids. In 4 patients only muscle fiber atrophy and/or necrosis without cellular infiltrations was seen. These 4 patients had received either high doses of corticosteroids or low doses over longer periods of time before muscle biopsy. In conclusion, the combination of 99mTc-PYP muscle scintigraphy and MRI demonstrated muscle areas with maximum inflammatory signal patterns. Targeting of muscles by MRI only will probably yield reliable results of muscle biopsy in cases of clinically and serologically characteristic myositis. 99mTc-PYP muscle scintigraphy may provide useful initial information about localization of inflamed muscle tissue, especially in atypical disease. Treatment with corticosteroids prior to histologic diagnosis may abolish inflammatory infiltrations in affected muscle tissue.
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  • 63
    ISSN: 1437-9813
    Keywords: Key words Myofibromatosis ; Fibromatosis ; Soft-tissue tumor ; Interspinous ligament ; Magnetic resonance imaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract The authors describe an extremely rare presentation of congenital infantile myofibromatosis. A full-term newborn boy presented with a thumb-sized subcutaneous mass on the mid-spinal line between the 2nd and 3rd lumbar spinous processes. A solid tumor arising from the interspinous ligament was resected. Microscopic and immunohistochemical studies revealed myofibromatosis.
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  • 64
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    Pediatric surgery international 13 (1998), S. 442-444 
    ISSN: 1437-9813
    Keywords: Key words Lymphangioma ; Scrotum ; Magnetic resonance imaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract A 7-year-old boy who presented with a painful left hemiscrotal mass was diagnosed with acquired lymphangioma of the scrotum. Chronic friction from a cast for Perthes' disease might have been the cause of sudden enlargement of a congenital lymphangioma of the scrotum. Magnetic resonance imaging (MRI) was useful for preoperative diagnosis and determining the extent of the scrotal lesions. Total excision of the mass leaving the overlying skin was successfully performed. The clinical significance of MRI for preoperative diagnosis and planning surgical resection of this lesion is discussed.
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  • 65
    ISSN: 1437-9813
    Keywords: Key words Accessory hepatic lobe ; Torsion ; Ultrasonography ; Computed tomography ; Magnetic resonance imaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract A case of acute epigastric pain resulting from torsion of an accessory hepatic lobe is reported. Sonographic, computerized tomographic, and magnetic resonance findings are illustrated and the surgical management is discussed.
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  • 66
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    Skeletal radiology 27 (1998), S. 13-17 
    ISSN: 1432-2161
    Keywords: Key words Silicone implants ; Synovitis ; Magnetic resonance imaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract  Silicone synovitis is a known complication of silicone implants used in orthopedic surgery for joint reconstruction. It has been studied with routine radiography; however, no report on magnetic resonance imaging abnormalities of this condition exist in the literature. This article reports on five patients with silicone synovitis studied by magnetic resonance imaging. All patients showed hypointense implants that were deformed, fragmented or subluxed, and intra- and periarticular silicone particles were evident on T1- and T2-weighted images.
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  • 67
    ISSN: 1432-2161
    Keywords: Key words Lipoma arborescens ; Synovial membrane ; Magnetic resonance imaging ; Hip
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract  Objective. The imaging characteristics of lipoma arborescens using plain radiographs, computed tomography (CT), and magnetic resonance imaging (MRI) are described. Design and patients. Five patients with a diagnosis of lipoma arborescens are presented. Three had monoarticular involvement of the knee joint. In the remaining two patients both knees and both hips, respectively, were affected. All patients were examined using plain radiographs and MRI. CT was employed in two cases. Results and conclusions. A conclusive diagnosis with exclusion of other synovial pathologies having similar clinical and radiological behaviour can be achieved on the basis of the MRI characteristics of lipoma arborescens. The aetiology of lipoma arborescens remains unknown, but its association with previous pathology of the affected joints in all our patients supports the theory of a non-neoplastic reactive process involving the synovial membrane.
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  • 68
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    Acta neuropathologica 96 (1998), S. 537-540 
    ISSN: 1432-0533
    Keywords: Key words Central pontine myelinolysis ; AIDS ; Magnetic resonance imaging ; Autopsy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract Central pontine myelinolysis (CPM) is an uncommon complication in sick patients with severe underlying disorders such as chronic alcoholism, malignancy, malnutrition and hyponatraemia. We report two patients with advanced HIV infection who developed CPM. In one case the diagnosis was not suspected in life, in the other the diagnosis was made just before death, on the basis of magnetic resonance (MR) imaging appearances. At post mortem there was a close correlation between the MR abnormalities and the anatomic changes in the pons.
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  • 69
    ISSN: 1432-0584
    Keywords: Key words High-grade non-Hodgkin's lymphoma ; Methotrexate ; Leukoencephalopathy ; Neurotoxicity ; Magnetic resonance imaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract  Aggressive polychemotherapy, intrathecal cytostatic prophylaxis and cranial irradiation have contributed to the remarkable improvement in the prognosis of acute lymphoblastic leukemia (ALL) and subtypes of high-grade non-Hodgkin's lymphoma (NHL) and the reduction of central nervous system (CNS) relapses. Early and late neurologic changes have been observed after different CNS-directed therapies. We report on the rare event of an acute tetraparesis after methotrexate (MTX) without other CNS-directed therapy. A young female with a diffuse large B-cell lymphoma developed signs of meningeal irritation a few hours after intrathecal prophylaxis with MTX, cytosine-arabinoside and dexamethasone. She recovered quickly. Ten days after her last course of systemic chemotherapy including high dose MTX she was admitted with a tetraparesis and motoric aphasia. A computer assisted tomography (CT) scan was normal. On magnetic resonance imaging (MRI) hyperintense white matter lesions were visible in the periventricular white matter. Initially, the radiologic signs were progressive while the patient's clinical condition improved. MRI controls after complete neurologic normalization revealed delayed partial regression of the white matter abnormalities. The patient has now been free of neurologic symptoms for 16 months. This case report demonstrates acute and subacute neurotoxic effects of MTX in the same patient and illustrates that radiologic CNS changes can persist irrespective of the disappearance of clinical symptoms.
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  • 70
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    European radiology 8 (1998), S. 66-68 
    ISSN: 1432-1084
    Keywords: Key words: Heart angiosarcoma ; Computed tomography ; Magnetic resonance imaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract. We report a case of primary heart angiosarcoma and its appearance on plain and post-contrast computed tomography and magnetic resonance imaging in 21-year-old woman. The tumour involved the right atrium, expanded superiorly among the superior vena cava, ascending aorta and innominate vein, and infiltrated the pericardium. The tumour was disseminated into lungs, liver and bones at the time of its clinical presentation.
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  • 71
    ISSN: 1432-1920
    Keywords: Key words Stroke recurrent ; Diffusion-weighted imaging ; Magnetic resonance imaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract We performed MRI, including diffusion-weighted imaging, in 15 patients with recurrent strokes with acute ischaemia and at least one old lesion according to the clinical history and/or CT. Routine MRI showed similar signal intensity changes in both situations. Diffusion-weighted images, however, were positive in all acute or subacute infarcts. The high signal of acutely disturbed diffusion due to intracellular oedema could also be identified in small brain stem lesions. Spatial resolution was increased by applying separate gradients in each axis instead of creating anisotropy-independent trace images.
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  • 72
    ISSN: 1432-1920
    Keywords: Key words Creutzfeldt-Jakob disease ; Prion disease ; Magnetic resonance imaging ; Dementia
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract To ascertain whether increased grey matter signal intensity on T2-weighted images in patients with sporadic Creutzfeldt-Jakob disease (CJD) corresponds to the stage and severity of this disease, we correlated MRI findings in four of our own and previously reported patients with sporadic CJD with the clinical variants, neuropathological changes at autopsy, duration of the disease and survival time after MRI examination. Of 15 patients with the extrapyramidal type of CJD, 10 showed increased signal in the basal ganglia on T2-weighted images. One of seven patients with the Heidenhain variant had increased signal in the occipital cortex. Patients without increased grey matter signal intensity had a longer overall duration of CJD (P = 0.035). Although the interval between onset of neurological symptoms and MRI was not different, patients without increased grey matter signal also survived longer after MRI examination (P = 0.022).
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  • 73
    ISSN: 1432-1920
    Keywords: Key words Pituitary ; Adenohypophysitis ; Magnetic resonance imaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract We report the skull radiograph, CT and MRI findings in three patients with lymphocytic adenohypophysitis mimicking pituitary adenoma. All cases were associated with pregnancy. CT demonstrated a pituitary mass but did not differentiate lymphocytic adenohypophysitis from pituitary adenoma. The skull radiographs showed either a normal sella turcica or minimal abnormalities; they did not show ballooning or destruction. The MRI appearances were distinctive: relatively low signal on T1-weighted images; preservation of the bright posterior pituitary lobe despite the presence of a relatively large pituitary mass, less common in macroadenomas; marked contrast enhancement compared with pituitary macroadenomas; and dural enhancement adjacent to a pituitary mass.
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  • 74
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    Neuroradiology 40 (1998), S. 126-127 
    ISSN: 1432-1920
    Keywords: Key words Lyme disease ; Spinal cord ; Magnetic resonance imaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract We report a child with Borrelia burgdorferi meningoradiculitis. This entity, also known as Bannwarth syndrome, is rare and its presentation with low back pain only is even more unusual. The MRI findings can suggest the diagnosis.
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  • 75
    ISSN: 1432-1920
    Keywords: Key words Methanol ; intoxication ; Magnetic resonance imaging ; Putaminal necrosis ; Putaminal haemorrhage ; Toxic encephalopathy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract Methanol, a highly toxic substance, is used as an industrial solvent and in automobile antifreeze. Acute methanol poisoning produces severe metabolic acidosis and serious neurologic sequelae. We describe a 50-year-old woman with accidental methanol intoxication who was in a vegetative state. MRI showed haemorrhagic necrosis of the putamina and oedema in the deep white matter.
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  • 76
    ISSN: 1432-1920
    Keywords: Key words Spinocerebellar ataxia type 6 ; Cerebellar cortical atrophy ; Magnetic resonance imaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract We describe the MRI findings in three Japanese patients with spinocerebellar ataxia type 6 (SCA6) in which a polymorphic CAG repeat was identified in the gene encoding the α1A voltage-dependent P/Q-type Ca2+ channel subunit (CACNL1A4). All showed slowly progressive cerebellar ataxia and mild pyramidal signs. Neuroradiologically, they had moderate cerebellar atrophy, most prominently in the superior vermis, whereas the brain stem appeared to be spared. No abnormal signal intensity was identified.
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  • 77
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    Neuroradiology 40 (1998), S. 238-241 
    ISSN: 1432-1920
    Keywords: Key words Leiomyoma ; brain ; Magnetic resonance imaging ; Computed tomography
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract We present a case of intracranial parenchymal leiomyoma in a 20-year-old woman with a chief complaint of numbness and a painful sensation over the right limbs for several years. CT and MRI revealed an intensely enhancing calcified mass. The patient was well, without recurrence, 2 years after surgery.
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  • 78
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    Neuroradiology 40 (1998), S. 255-257 
    ISSN: 1432-1920
    Keywords: Key words Behçet's disease ; Spinal cord ; Magnetic resonance imaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract MRI demonstrated well-defined areas of signal change and moderate contrast enhancement in the thoracic spinal cord of a patient with Behçet's disease presenting with subacute myelopathy. The patient improved after intravenous steroids, and MRI 5 months later showed a normal spinal cord.
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  • 79
    ISSN: 1432-1920
    Keywords: Key words Central nervous system diseases ; Temporal bone ; Magnetic resonance imaging ; Siderosis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract We present a 50-year-old man who was investigated for sensorineural hearing loss. On MRI of the brain superficial siderosis of the central nervous system was seen, while MRI of the spine revealed an ependymoma of the cauda equina. This case illustrates the importance of performing T2-weighted imaging of the brain and posterior fossa when sensorineural hearing loss is present. Spine imaging is mandatory when superficial siderosis of the brain is diagnosed without identification of a bleeding source in the brain.
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  • 80
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    Neuroradiology 40 (1998), S. 734-738 
    ISSN: 1432-1920
    Keywords: Key words Unilateral megalencephaly ; Myelination ; Magnetic resonance imaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract We reviewed the MRI of 17 patients with hemimegalencephaly to investigate abnormal myelination in this condition. On images of seven patients aged 18 months or less, the white matter on the affected side suggested advanced myelination for the age. On T1-weighted images of three patients aged 1 month, the anterior limb of the internal capsule in the affected hemisphere was myelinated, and T1 shortening was not clearly seen in the pre- and postcentral gyri. The cortical grey matter and subcortical white matter was isointense in two patients. Images of two patients aged 4 to 5 months and of five patients aged 8–18 months showed myelination that extended more peripherally in the white matter of the affected hemisphere.
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  • 81
    ISSN: 1432-1920
    Keywords: Key words Brain metastases ; Magnetic resonance imaging ; Magnetisation transfer ; Contrast enhancement
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract Our purpose was to compare prospectively the sensitivity of contrast-enhanced magnetisation transfer (MT) MRI and gradient-echo (GE) T1-weighted images in metastatic disease of the brain. We studied 52 patients with brain metastases, using conventional T1-weighted GE and MT spin-echo (SE) images after the same standard dose of gadolinium. Axial 5-mm reconstructions of GE data were compared with 5-mm MT images in the same plane. Metastases were counted independently by two neuroradiologists. In 12 patients (23 %) MT imaging showed more metastases than GE images (P = 0.03). We detected 68 more metastases with the former technique.
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  • 82
    ISSN: 1432-1920
    Keywords: Key words Multiple sclerosis ; Spinal cord ; Magnetic resonance imaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract We report assessment of a new three-dimensional fast spin echo (3D FSE) sequence in ten patients with clinically definite multiple sclerosis, comparing it with standard 2D FSE, and in ten normal controls. We saw 29 focal lesions on the 2D images and 53 on the 3D FSE imgages (P = 0.05); none were seen in controls. Lesion length was significantly smaller on the 3D FSE than on to the 2D FSE images (3D: 1.36; 2D 2,0; P = 0.03). This may relate in part to separation into several lesions on the 3D images of confluent abnormal signal seen on 2D and in part to detection of small lesions missed by the thicker 2D FSE slices (3 mm compared to 1.5 mm). The 3D FSE sequence looks promising in improving spinal cord imaging.
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  • 83
    ISSN: 1432-1920
    Keywords: Key words Radiation injury ; Optic chiasm ; Magnetic resonance imaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract We report a case of radiation-induced optic neuropathy in a 32-year-old man with Cushing's disease and a recurrent tumour of the left cavernous sinus. The patient experienced rapid, painless loss of vision 4 years after treatment without recurrence of tumour or other visual disorder. MRI showed enlargement and contrast enhancement of the optic chiasm. A year later the patient was almost blind and MRI showed atrophy and persistent contrast enhancement of the chiasm.
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  • 84
    ISSN: 1432-1920
    Keywords: Key words Sinuses ; dural ; Epidermoid cyst ; skull ; Magnetic resonance imaging ; Tinnitus
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract We report an intradiploic epidermoid cyst of the skull responsible for transverse sinus compression and presenting with nonpulsatile tinnitus. Plain films and CT both demonstrated the tumour. Cerebral angiography showed best the degree of narrowing of the right transverse sinus, accompanied with turbulent flow probably leading to tinnitus. MRI demonstrated accurately both the tumour and the dural sinus compression. The tumour was totally removed, cranioplasty was performed, and the patient was discharged free of symptoms.
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  • 85
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    Neuroradiology 40 (1998), S. 477-482 
    ISSN: 1432-1920
    Keywords: Key words Brain ; anatomy ; Brain ; white matter ; Brain ; oedema ; Magnetic resonance imaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract MRI was obtained in eight normal volunteers and seven patients with brain oedema around the trigone. In addition to the conventional sequences, diffusion-weighted and intravoxel-incoherent-motion images using motion-proving anteroposterior and/or lateral direction gradients were obtained to show the white matter pathways better. Coronal proton-density-weighted images showed three thin relatively high-intensity layers in addition to the tapetum and the internal and external sagittal strata. Although they have not been confirmed anatomically, the thin layer between the internal and the external sagittal strata was corroborated by diffusion-weighted and intravoxel-incoherent-motion images, and by characteristics of the spread of oedema into the sagittal stratum. We propose that this layer be named the central sagittal lamina. The other two layers medial and lateral to the sagittal stratum were outside, but in contact with the medial and lateral parts of the sagittal stratum, respectively. We provisionally named them medial and lateral sagittal laminae; they were not evident on any other images. The low-intensity layer on T2-weighting was the internal sagittal stratum. The optic radiation, comprising the external sagittal stratum, appeared as an intermediate to slightly high-intensity layer on T2-weighted images and a low-intensity layer on T1-weighted images as did the corticospinal tract in the posterior internal capsule.
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  • 86
    ISSN: 1432-1920
    Keywords: Key words Vascular dementia ; Subcortical arteriosclerotic encephalopathy ; Magnetic resonance imaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract Previous cross-sectional studies in patients with subcortical vascular encephalopathy (SVE) have shown little or no correlation between brain lesion load and clinical disability, which could be due to the low specificity of T2-weighted MRI. Recent studies have indicated that T1-weighted MRI may be more specific than T2-weighted MRI for severe tissue destruction. We studied 37 patients with a diagnosis of SVE and 11 normal controls with standardised T1- and T2-weighted MRI. All patients underwent detailed clinical assessment including a neuropsychological test battery and computerised gait analysis. Both the T2- and T1-weighted total MRI lesion loads different between patients and controls different, particularly T1. The ratio of T2-/T1-weighted lesion load was lower in controls than in patients. There was no overall correlation of T1- or T2-weighted lesion load with clinical disability, but group comparison of patients with severe and mild clinical deficits showed different lesion loads. We suggest that T1- and T2-weighted MRI lesion loads demonstrate relevant structural abnormality in patients with SVE.
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  • 87
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    Neuroradiology 40 (1998), S. 512-515 
    ISSN: 1432-1920
    Keywords: Key words Behçet's disease ; Magnetic resonance imaging ; Meninges
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract Behçet's disease is a multisystem disease that involves the central nervous system up to half of cases. Presentation with neurologic symptoms occurs in 5 % of cases and cerebral venous thrombosis is one of its major manifestations. A feature not previously reported is progressive meningeal thickening with involvement of both optic nerves. We report a patient with cerebral venous thrombosis, meningeal thickening and contrast enhancement on MRI. This patient had two other unusual features: positive antineutrophil cytoplasmic antibodies and later development of central diabetes insipidus.
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  • 88
    ISSN: 1432-1920
    Keywords: Key words Brain ; Calcification ; perivenous ; Lupus erythematosus ; Computed tomography ; Magnetic resonance imaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract We present a case of neuropsychiatric lupus erythematosus with granular calcification in the basal ganglia and cerebral white matter on CT. Histopathologically, these were identified as perivenous necrotising lesions, with loss of axons and myelin sheaths and prominent dystrophic calcification.
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  • 89
    ISSN: 1432-1920
    Keywords: Key words Dysequilibrium syndrome ; Osmotic demyelination syndrome ; Magnetic resonance imaging ; Haemodialysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract Neurological disorders may be seen in end-stage renal disease patients due to uraemia or to complications of dialysis. A dysequilibrium syndrome may be seen, usually soon after or towards the end of haemodialysis. This group of patients has no particular findings on MRI. On the other hand, the osmotic demyelination syndrome has definitive MRI findings, not to date reported with the dysequilibrium syndrome. We report a patient with end-stage renal disease and the dysequilibrium syndrome who showed findings of osmotic demyelination on MRI. The patient had a convulsion after a first haemodialysis, with quadriparesis and hyperactive deep tendon reflexes and bilateral Babinski signs. The upper motor neurone signs lasted for a week. Meanwhile, he was also dysarthric and had dysphagia. He recovered neurologically without any residuum following appropriate treatment and there was improvement on MRI.
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  • 90
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    Neuroradiology 40 (1998), S. 303-307 
    ISSN: 1432-1920
    Keywords: Key words Choroid plexus ; infection ; Magnetic resonance imaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract Four cases of choroid plexitis of the brain (two with cryptococcosis and two with tuberculosis) are presented. The four patients showed either unilateral enlargement (3) or bilateral enlargement (1) and dense enhancement of the choroid plexus in the lateral ventricles (4) and fourth ventricle (1) in association with clinical findings of leptomeningitis. All patients had unilateral cystic dilatation of the temporal horn of the lateral ventricle presumably secondary to entrapment of the temporal horn and extensive oedema around the ipsilateral ventricle.
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  • 91
    ISSN: 1432-1920
    Keywords: Key words Neurenteric cyst ; Posterior cranial fossa ; Magnetic resonance imaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract Neurenteric cysts are cystic masses lined by a columnar epithelium of endodermal origin. They are rare in the central nervous system. We report two neurenteric cysts in the posterior cranial fossa and describe their neuroradiological features. The lesions were of low density on CT and more accurately delineated on MRI. They gave the same signal as cerebrospinal fluid on all sequences. There was no contrast enhancement.
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  • 92
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    Neuroradiology 40 (1998), S. 383-384 
    ISSN: 1432-1920
    Keywords: Key words Brucellosis ; intracranial ; Magnetic resonance imaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract We report a rare case of neurobrucellosis in a 25-year-old woman with visual impairment, bilateral hearing loss, hyperprolactinaemia and meningitis. MRI revealed a sellar and suprasellar mass with enlargement of the optic chiasm.
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  • 93
    ISSN: 1432-1920
    Keywords: Key words Brain ; basal ganglia ; Pituitary gland ; Manganese ; Parenteral nutrition ; Magnetic resonance imaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract Hypermanganesaemia is reported in patients on long-term parenteral nutrition. Deposition of manganese, giving high signal on T1-weighted images, may involve the basal ganglia. MRI in nine patients (mean age 51 years, range 31–75 years) on long-term parenteral nutrition (mean duration 30 months, range 6–126 months), demonstrated high signal in the anterior pituitary gland on T1-weighted sagittal and coronal images. The gland appeared normal on T2-weighted images. Signal intensity in the basal ganglia on T1-weighted images was increased in all patients. Endocrine assessment showed no significant abnormality. Neurological examination showed a mild parkinsonian movement disorder in one patient. Hypermanganaesemia was present in all nine (1.3–2.8 μmol/l, mean 1.87 μmol/l). The high signal in the anterior pituitary gland was probably related to deposition of paramagnetic substances, especially manganese.
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  • 94
    ISSN: 1432-1920
    Keywords: Key words Cervical spine ; trauma ; Magnetic resonance imaging ; Children
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract We carried out a retrospective analysis of imaging and clinical findings in 52 children with a history of cervical spinal trauma. No patient had evidence of a fracture on plain films or CT. All had MRI at 1.5 T because of persistent or delayed symptoms, unexplained findings of injury or instability, or as further assessment of the extent of soft-tissue injury. Clinical follow-up ranged from 6 months to 3.5 years. MRI was evaluated for its influence on therapy and outcome. MRI was positive in 16 (31 %) of 52 patients. Posterior soft-tissue or ligamentous injury was the most common finding in the 10 patients with mild to moderate trauma, while acute disc bulges and longitudinal ligament disruption, each seen in one case, were uncommon. MRI was superior to CT for assessment of the extent of soft-tissue injury and for identification of spinal cord injuries and intracanalicular hemorrhage in the six patients with more severe trauma. MRI specifically influenced the management of all four patients requiring surgery by extending the level of posterior stabilization. No patients with normal MRI or any of the 10 with radiographically stable soft-tissue injury on MRI, developed delayed clinical or radiographic evidence of instability or deformity.
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  • 95
    ISSN: 1432-1920
    Keywords: Key words Myotonic dystrophy ; Magnetic resonance imaging ; Fluid-attenuated inversion-recovery pulse sequence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract We compared the fluid-attenuated inversion recovery (FLAIR) sequence with conventional spin-echo (SE) imaging for detection of involvement of the central nervous system in five patients with myotonic dystrophy (MD). The diagnosis was made based on clinical features and DNA analysis. All patients showed abnormal high-intensity lesions in the white matter on T2-weighted images, although these were more clearly visible using FLAIR.
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  • 96
    ISSN: 1432-1920
    Keywords: Key words Spontaneous intracranial hypotension ; Headache ; Magnetic resonance imaging ; Radionuclide cisternography
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract Spontaneous intracranial hypotension is an unusual syndrome of postural headache and low cerebrospinal fluid pressure without an established cause. We present four cases, analyze those previously reported in the literature, examine the MRI, CT, angiographic and cisternographic finding and discuss the clinical picture, proposed pathophysiologic mechanisms and potential treatment.
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  • 97
    ISSN: 1432-1920
    Keywords: Key words Inner ear ; Aqueduct ; vestibular ; Endolymphatic duct ; Hearing loss ; Computed tomography ; Magnetic resonance imaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract We studied ten inner ears of five patients with a bilateral large vestibular aqueduct syndrome, using CT and MRI. Although the large vestibular aqueduct varied in size, a markedly dilated endolymphatic sac extending to the sigmoid sinus was demonstrated bilaterally on MRI in all patients. The cause of hearing loss in this syndrome is unclear. However, it is suggested that reflux of the protein-rich, hyperosmolar endolymph from the enlarged endolymphatic sac (EES) into the cochlea through a widely patent endolymphatic duct may damage the neuroepithelium. CT density and spin-echo MRI signal intensity of the endolymph in EES were markedly higher than those of CSF in eight inner ears of four patients. Increased density and high signal may indicate protein-rich, hyperosmolar endolymph. In some patients with sensorineural hearing loss and EES, the vestibular aqueduct may not appear dilated on CT. MRI is therefore necessary for correct diagnosis of this syndrome, which should more correctly be termed “large endolymphatic duct and sac syndrome”. Prominent EES may predict poor prognosis in this syndrome.
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  • 98
    ISSN: 1432-1920
    Keywords: Key words Aneurysm intracranial ; Magnetic resonance imaging ; Embolisation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract To determine when and how intracranial aneurysms causing mass effect change following endovascular treatment, we used MRI to assess patients for 2–3 years after the interventional procedure. Nine patients who had aneurysms compressing the surrounding structures underwent endovascular treatment. Proximal occlusion of the parent artery was performed in seven cases, and in two the aneurysm was embolised with microcoils. After embolisation, signal intensity within aneurysms tended to be high on both T1- and T2-weighted images. When there was rapid reduction in size high-signal zones within aneurysms became isointense or gave low signal on T1-weighted images. On T2-weighted images, isointense or low-signal foci appeared within high-signal areas in the aneurysm, giving mixed intensity. In typical cases, the mean volume of the aneurysm fell to approximately 30 % of its initial value 2–12 months after treatment. After this, no additional reduction was observed. The aneurysms which showed little signal intensity change tended to shrink more slowly and to a lesser degree than the more typical cases. Aneurysms which gave high signal on both T1- and T2-weighted images early following embolisation shrank more quickly than those showing little signal change.
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  • 99
    ISSN: 1432-1920
    Keywords: Key words Amyloid ; Cerebral amyloid angiopathy ; Congophilic angiopathy ; Magnetic resonance imaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract The case of a 70-year-old woman with cerebral amyloid angiopathy (CAA) is presented. MRI of the head showed widespread miliary foci of haemorrhage within the cerebrum and cerebellum, with some additional linear lesions within the cerebral cortex and patchy lesions in the white matter. This is in contrast to the more usual pattern of intracranial haemorrhage in CAA, i. e., a lobar haematoma.
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  • 100
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    Neuroradiology 40 (1998), S. 401-403 
    ISSN: 1432-1920
    Keywords: Key words Amyloidosis ; larynx ; Laryngocele ; Magnetic resonance imaging ; Computed tomography
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract A case of laryngeal amyloidosis associated with a laryngocele is reported. Preoperative CT showed diffuse thickening of the epiglottis, aryepiglottic folds and false vocal cords with well-defined calcific foci. MRI revealed contrast enhancement and increased signal intensity on T2-weighted images.
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