A tutorial on interactive Markov chains

Interactive Markov chains (IMCs) constitute a powerful sto- chastic model that extends both continuous-time Markov chains and labelled transition systems. IMCs enable a wide range of modelling and analysis techniques and serve as a semantic model for many industrial and scientific formalisms, such as AADL, GSPNs and many more. Applications cover various engineering contexts ranging from industrial system-on-chip manufacturing to satellite designs. We present a survey of the state-of-the-art in modelling and analysis of IMCs.\ud We cover a set of techniques that can be utilised for compositional modelling, state space generation and reduction, and model checking. The significance of the presented material and corresponding tools is highlighted through multiple case studies

Can comprehensive background knowledge be incorporated into substitution models to improve phylogenetic analyses? A case study on major arthropod relationships

<p>Abstract</p> <p>Background</p> <p>Whenever different data sets arrive at conflicting phylogenetic hypotheses, only testable causal explanations of sources of errors in at least one of the data sets allow us to critically choose among the conflicting hypotheses of relationships. The large (28S) and small (18S) subunit rRNAs are among the most popular markers for studies of deep phylogenies. However, some nodes supported by this data are suspected of being artifacts caused by peculiarities of the evolution of these molecules. Arthropod phylogeny is an especially controversial subject dotted with conflicting hypotheses which are dependent on data set and method of reconstruction. We assume that phylogenetic analyses based on these genes can be improved further i) by enlarging the taxon sample and ii) employing more realistic models of sequence evolution incorporating non-stationary substitution processes and iii) considering covariation and pairing of sites in rRNA-genes.</p> <p>Results</p> <p>We analyzed a large set of arthropod sequences, applied new tools for quality control of data prior to tree reconstruction, and increased the biological realism of substitution models. Although the split-decomposition network indicated a high noise content in the data set, our measures were able to both improve the analyses and give causal explanations for some incongruities mentioned from analyses of rRNA sequences. However, misleading effects did not completely disappear.</p> <p>Conclusion</p> <p>Analyses of data sets that result in ambiguous phylogenetic hypotheses demand for methods, which do not only filter stochastic noise, but likewise allow to differentiate phylogenetic signal from systematic biases. Such methods can only rely on our findings regarding the evolution of the analyzed data. Analyses on independent data sets then are crucial to test the plausibility of the results. Our approach can easily be extended to genomic data, as well, whereby layers of quality assessment are set up applicable to phylogenetic reconstructions in general.</p

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

Molecular insights to crustacean phylogeny

This thesis aims to resolve internal relationships of the major crustacean groups inferring phylogenies with molecular data. New molecular and neuroanatomical data support the scenario that the Hexapoda might have evolved from Crustacea. Most molecular studies of crustaceans relied on single gene or multigene analyses in which for most cases partly sequenced rRNA genes were used. However, intensive data quality and alignment assessments prior to phylogenetic reconstructions are not conducted in most studies. One methodological aim in this thesis was to implement new tools to infer data quality, to improve alignment quality and to test the impact of complex modeling of the data. Two of the three phylogenetic analyses in this thesis are also based on rRNA genes. In analysis (A) 16S rRNA, 18S rRNA and COI sequences were analyzed. RY coding of the COI fragment, an alignment procedure that considers the secondary structure of RNA molecules and the exclusion of alignment positions of ambiguous positional homology was performed to improve data quality. Anyhow, by extensive network reconstructions it was shown that the signal quality in the chosen and commonly used markers is not suitable to infer crustacean phylogeny, despite the extensive data processing and optimization. This result draws a new light on previous studies relying on these markers. In analyses (B) completely sequenced 18S and 28S rRNA genes were used to reconstruct the phylogeny. Base compositional heterogeneity was taken into account based on the finding of analysis (A), additionally to secondary structure alignment optimization and alignment assessment. The complex modeling to compare time-heterogeneous versus time-homogenous processes in combination with mixed models for an implementation of secondary structures was only possible applying the Bayesian software package PHASE. The results clearly demonstrated that complex modeling counts and that ignoring time-heterogeneous processes can mislead phylogenetic reconstructions. Some results enlight the phylogeny of Crustaceans, for the first time the Cephalocarida (Hutchinsoniella macracantha) were placed in a clade with the Branchiopoda, which morphologically is plausible. Compared to the time-homogeneous tree the time-heterogeneous tree gives lower support values for some nodes. It can be suggested, that the incorporation of base compositional heterogeneity in phylogenetic analysis improves the reliability of the topology. The Pancrustacea are supported maximally in both approaches, but internal relations are not reliably reconstructed. One result of this analysis is that the phylogenetic signal in rRNA data might be eroded for crustaceans. Recent publications presented analyses based on phylogenomic data, to reconstruct mainly metazoan phylogeny. The supermatrix method seems to outperform the supertree approach. In this analysis the supermatrix approach was applied. Crustaceans were collected to conduct EST sequencing projects and to include the resulting sequences combined with public sequence data into a phylogenomic analysis (C). New and innovative reduction heuristics were performed to condense the dataset. The results showed that the matrix implementation of the reduced dataset ends in a more reliable topology in which most node values are highly supported. In analysis (C) the Branchiopoda were positioned as sister-group to Hexapoda, a differing result to analysis (A) and (B), but that is in line with other phylogenomic studies

Bloody fast blood collection

This thesis consists of four parts: The first part contains an introduction, the second presents approaches for the evaluation of waiting times at blood collection sites, the third uses these to present approaches that improve waiting times at blood collection sites. The final part shows the application of two of the approaches to data from real blood collection sites, followed by the conclusions that can be drawn from this thesis. Part I: Introduction, contains two chapters. Chapter 1 introduces the context for this thesis: blood banks in general, the Dutch blood bank Sanquin and blood collection sites. The chapter sketches some of the challenges faced with respect to blood collection sites. As blood donors are voluntary and non-remunerated, delays and waiting times within blood collection sites should be kept at acceptable levels. However, waiting times are currently not incorporated in staff planning or in other decisions with respect to blood collection sites. These blood collection sites will be the primary focus of this thesis. This thesis provides methods that do take waiting times into account, aiming to decrease waiting times at blood collection sites and leveling work pressure for staff members, without the need for additional staff. Chapter 2 then presents a technical methods that will be used most of the chapters in this thesis: uniformization. Uniformization can be used to transform Continuous Time Markov Chains (CTMCs) — that are very hard to analyze — into Discrete Time Markov Chains (DTMCs) — that are much easier to analyze. The chapter shows how the method works, provides an extensive overview of the literature related to the method, the (technical) intuition behind the method as well as several extensions and applications. Although not all of the extensions and applications are necessary for this thesis, it does provide an overview of one of the most valuable methods for this thesis. Part II: Evaluation, contains two chapters that propose and adapt several methods to compute waiting times and queues at blood collection sites. A blood collection site is best modeled as a time-dependent queueing network, requiring non-standard approaches. Chapter 3 considers a stationary, i.e. not time-dependent model of blood collection sites as a first step. A blood collection site consists of three main stations: Registration, Interview and Donation. All three of the stations can have their own queue. This means that even the stationary model is non-trivial for some computations. However, for the stationary model, an analytic so-called product form expression is derived. Based on this product form, two more results are shown. The first result is that the standard waiting time distributions from M|M|s queues are applicable, as if the queue is in isolation. It is then concluded that no closed form expression exist for the total waiting or delay time distribution, as the distributions of the three stations in tandem are not independent. Therefore a numerical approach is presented to compute the total delay time distribution of a collection site. All of the results are supported by numerical examples based on a Dutch blood collection site. The approach for the computation of the total delay time distribution can also be combined with the approach from Chapter 4 for an extension to a time-dependent setting. Chapter 4 shows an approach to deal with these time-dependent aspects in queueing systems, as often experienced by blood collection sites and other service systems, typically due to time-dependent arrivals and capacities. Easy and quick to use queueing expressions generally do not apply to time-dependent situations. A large number of computational papers has been written about queue length distributions for time-dependent queues, but these are mostly theoretical and based on single queues. This chapter aims to combine computational methods with more realistic time-dependent queueing networks, with an approach based on uniformization. Although uniformization is generally perceived to be too computationally prohibitive, we show that our method is very effective for practical instances, as shown with an example of a Dutch blood collection site. The objective of the results is twofold: to show that a time-dependent queueing network approach can be beneficial and to evaluate possible improvements for Dutch blood collection sites that can only be properly assessed with a time-dependent queueing method. Part III: Optimization, contains four chapters that aim to improve service levels at Sanquin. The first three chapters focus on three different methods to decrease queues at blood collection sites. Chapters 5 and 6 focus on improving the service by optimizing staff allocation to shifts and stations. Chapter 7 focuses on improving the arrival process with the same goal. Chapter 8 is focused at improving inventory management of red blood cells. Donors do not arrive to blood collection sites uniformly throughout the day, but show clear preferences for certain times of the day. However, the arrival patterns that are shown by historical data, are not used for scheduling staff members at blood collection sites. As a first significant step to shorten waiting times we can align staff capacity and shifts with walk-in arrivals. Chapter 5 aims to optimize shift scheduling for blood collection sites. The chapter proposes a two-step procedure. First, the arrival patterns and methods from queueing theory are used to determine the required number of staff members for every half hour. Second, an integer linear program is used to compute optimal shift lengths and starting times, based on the required number of staff members. The chapter is concluded with numerical experiments that show, depending on the scenario, a reduction of waiting times, a reduction of staff members or a combination of both. At a blood collection site three stations (Registration, Interview and Donation) can roughly be distinguished. Staff members at Dutch blood collection sites are often trained to work at any of these stations, but are usually allocated to one of the stations for large fractions of a shift. If staff members change their allocation this is based on an ad hoc decision. Chapter 6 aims to take advantage of this mostly unused allocation flexibility to reduce queues at blood collection sites. As a collection site is a highly stochastic process, both in arrivals and services, an optimal allocation of staff members to the three stations is unknown, constantly changing and a challenge to determine. Chapter 6 provides and applies a so-called Markov Decision Process (MDP) to compute optimal staff assignments. Extensive numerical and simulation experiments show the potential reductions of queues when the reallocation algorithm would be implemented. Based on Dutch blood collection sites, reductions of 40 to 80% on the number of waiting donors seem attainable, depending on the scenario. Chapter 7 also aims to align the arrival of donors with scheduled staff, similarly to Chapter 5. Chapter 7 tries to achieve this by changing the arrivals of donors. By introducing appointments for an additional part of donors, arrivals can be redirected from the busiest times of the day to quiet times. An extended numerical queueing model with priorities is introduced for blood collection sites, as Sanquin wants to incentive donors to make appointments by prioritizing donors with appointments over donors without appointments. Appointment slots are added if the average queue drops below certain limits. The correct values for these limits, i.e. the values that plan the correct number of appointments, are then determined by binary search. Numerical results show that the method succeeds in decreasing excessive queues. However, the proposed priorities might result in unacceptably high waiting times for donors without appointments, and caution is therefore required before implementation. Although this thesis mainly focuses on blood collection sites, many more logistical challenges are present at a blood bank. One of these challenges arises from the expectation that Sanquin can supply hospitals with extensively typed red blood cell units directly from stock. Chapter 8 deals with this challenge. Currently, all units are issued according to the first-in-first-out principle, irrespective of their specific typing. These kind of issuing policies lead to shortages for rare blood units. Shortages for rare units could be avoided by keeping them in stock for longer, but this could also lead to unnecessary wastage. Therefore, to avoid both wastage and shortages, a trade-off between the age and rarity of a specific unit in stock should be made. For this purpose, we modeled the allocation of the inventory as a circulation flow problem, in which decisions about which units to issue are based on both the age and rarity of the units in stock. We evaluated the model for several settings of the input parameters. It turns out that, especially if only a few donors are typed for some combinations of antigens, shortages can be avoided by saving rare blood products. Moreover, the average issuing age remains unchanged. Part IV: Practice and Outlook concludes this thesis. The first of two chapters in this part shows the combined application of two approaches from this thesis to data from three collection sites in the Netherlands. The final chapter of this thesis presents the conclusions that can be drawn from this thesis and discusses an outlook for further research. Chapter 9 shows the combined application of the methods in Chapters 5 and 6 to three real collection sites in Dutch cities: Nijmegen, Leiden and Almelo. The collection sites in Nijmegen and Leiden are both large fixed collection sites. The collection site in Almelo is a mobile collection site. The application of each one of the methods individually reduce waiting times significantly, and the combined application of the methods reduces waiting times even further. Simultaneously, small reductions in the number of staff hours are attainable. The results from Chapter 9 summarize the main message of this thesis: waiting time for blood donors at blood collection sites can be reduced without the need for more staff members when the working times of staff members are used more effectively and efficiently, and controlling the arrival process of donors. The approaches presented in this thesis can be used for this purpose. This is not only beneficial for blood donors, but will also result in more balanced workload for staff members, as fluctuations in this workload are reduced significantly