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Consensus (agreement on a value) is regarded as a fundamental primitive in the design of fault tolerant distributed systems. A well-known solution to the consensus problem is Paxos. Extensions of the Paxos algorithm make it possible to reach agreement on a sequence of commands which can then be applied on a replicated state. However, concurrently proposed commands can create conflicts that must be resolved by ordering them. This thesis delivers an in-depth description of a Paxos-based algorithm to establish such command sequences, called Paxos Round Based Register (PRBR). In contrast to conventional approaches like Multi-Paxos, PRBR can manage multiple command sequences independently. Furthermore, each sequence is established in-place, which eliminates the need for managing multiple Paxos instances. PRBR is extended as part of this thesis to exploit the commutativity of concurrently proposed commands. As a result, conflict potential can be greatly reduced which increases the number of commands that can be handled by PRBR. This is shown for a number of workloads in an experimental evaluation.
Software for mixed-integer linear programming can return incorrect results for a number of reasons, one being the use of inexact floating-point arithmetic. Even solvers that employ exact arithmetic may suffer from programming or algorithmic errors, motivating the desire for a way to produce independently verifiable certificates of claimed results. Due to the complex nature of state-of-the-art MIP solution algorithms, the ideal form of such a certificate is not entirely clear. This paper proposes such a certificate format designed with simplicity in mind, which is composed of a list of statements that can be sequentially verified using a limited number of inference rules. We present a supplementary verification tool for compressing and checking these certificates independently of how they were created. We report computational results on a selection of MIP instances from the literature. To this end, we have extended the exact rational version of the MIP solver SCIP to produce such certificates.
Purpose: Despite the success of total knee arthroplasty there continues to be a significant proportion of patients who are dissatisfied. One explanation may be a shape mismatch between pre and post-operative distal femurs. The purpose of this study was to investigate a method to match a statistical shape model (SSM) to intra-operatively acquired point cloud data from a surgical navigation system, and to validate it against the pre-operative magnetic resonance imaging (MRI) data from the same patients.
Methods: A total of 10 patients who underwent navigated total knee arthroplasty also had an MRI scan less than 2 months pre-operatively. The standard surgical protocol was followed which included partial digitization of the distal femur. Two different methods were employed to fit the SSM to the digitized point cloud data, based on (1) Iterative Closest Points (ICP) and (2) Gaussian Mixture Models (GMM). The available MRI data were manually segmented and the reconstructed three-dimensional surfaces used as ground truth against which the statistical shape model fit was compared.
Results: For both approaches, the difference between the statistical shape model-generated femur and the surface generated from MRI segmentation averaged less than 1.7 mm, with maximum errors occurring in less clinically important areas.
Conclusion: The results demonstrated good correspondence with the distal femoral morphology even in cases of sparse data sets. Application of this technique will allow for measurement of mismatch between pre and post-operative femurs retrospectively on any case done using the surgical navigation system and could be integrated into the surgical navigation unit to provide real-time feedback.
We present a new strategy for the direct optimization of the values of policy functions. This approach is particularly well suited to model actors with a global perspective on the system and relies heavily on modern mathematical white-box optimization methods. We demonstrate our strategy on two classical models: market growth and World2. Each model is first transformed into an optimization problem by defining how the actor can influence the models' dynamics and by choosing objective functions to measure improvements. To improve comparability between different runs, we also introduce a comparison measure for possible interventions. We solve the optimization problems, discuss the resulting policies and compare them to the existing results from the literature. In particular, we present a run of the World2 model which significantly improves the published “towards a global equilibrium” run with equal cost of intervention.
Umsteigen ohne Warten
(2017)
Wir stellen einen mathematischen Optimierungsansatz zur Berechnung von periodischen Taktfahrplänen vor, bei dem die Umsteigezeiten unter Berücksichtigung des Passagierverhaltens minimiert werden. Wir untersuchen damit den Einfluss wichtiger Systemparameter und Verhaltensmuster auf die Beförderungsqualität.