Implementation and Evaluation of Algorithmic Skeletons: Parallelisation of Computer Algebra Algorithms

This thesis presents design and implementation approaches for the parallel algorithms of computer algebra. We use algorithmic skeletons and also further approaches, like data parallel arithmetic and actors. We have implemented skeletons for divide and conquer algorithms and some special parallel loops, that we call ‘repeated computation with a possibility of premature termination’. We introduce in this thesis a rational data parallel arithmetic. We focus on parallel symbolic computation algorithms, for these algorithms our arithmetic provides a generic parallelisation approach. The implementation is carried out in Eden, a parallel functional programming language based on Haskell. This choice enables us to encode both the skeletons and the programs in the same language. Moreover, it allows us to refrain from using two different languages—one for the implementation and one for the interface—for our implementation of computer algebra algorithms. Further, this thesis presents methods for evaluation and estimation of parallel execution times. We partition the parallel execution time into two components. One of them accounts for the quality of the parallelisation, we call it the ‘parallel penalty’. The other is the sequential execution time. For the estimation, we predict both components separately, using statistical methods. This enables very confident estimations, although using drastically less measurement points than other methods. We have applied both our evaluation and estimation approaches to the parallel programs presented in this thesis. We haven also used existing estimation methods. We developed divide and conquer skeletons for the implementation of fast parallel multiplication. We have implemented the Karatsuba algorithm, Strassen’s matrix multiplication algorithm and the fast Fourier transform. The latter was used to implement polynomial convolution that leads to a further fast multiplication algorithm. Specially for our implementation of Strassen algorithm we have designed and implemented a divide and conquer skeleton basing on actors. We have implemented the parallel fast Fourier transform, and not only did we use new divide and conquer skeletons, but also developed a map-and-transpose skeleton. It enables good parallelisation of the Fourier transform. The parallelisation of Karatsuba multiplication shows a very good performance. We have analysed the parallel penalty of our programs and compared it to the serial fraction—an approach, known from literature. We also performed execution time estimations of our divide and conquer programs. This thesis presents a parallel map+reduce skeleton scheme. It allows us to combine the usual parallel map skeletons, like parMap, farm, workpool, with a premature termination property. We use this to implement the so-called ‘parallel repeated computation’, a special form of a speculative parallel loop. We have implemented two probabilistic primality tests: the Rabin–Miller test and the Jacobi sum test. We parallelised both with our approach. We analysed the task distribution and stated the fitting configurations of the Jacobi sum test. We have shown formally that the Jacobi sum test can be implemented in parallel. Subsequently, we parallelised it, analysed the load balancing issues, and produced an optimisation. The latter enabled a good implementation, as verified using the parallel penalty. We have also estimated the performance of the tests for further input sizes and numbers of processing elements. Parallelisation of the Jacobi sum test and our generic parallelisation scheme for the repeated computation is our original contribution. The data parallel arithmetic was defined not only for integers, which is already known, but also for rationals. We handled the common factors of the numerator or denominator of the fraction with the modulus in a novel manner. This is required to obtain a true multiple-residue arithmetic, a novel result of our research. Using these mathematical advances, we have parallelised the determinant computation using the Gauß elimination. As always, we have performed task distribution analysis and estimation of the parallel execution time of our implementation. A similar computation in Maple emphasised the potential of our approach. Data parallel arithmetic enables parallelisation of entire classes of computer algebra algorithms. Summarising, this thesis presents and thoroughly evaluates new and existing design decisions for high-level parallelisations of computer algebra algorithms

Capillary networks and follicular marginal zones in human spleens : Three-dimensional models based on immunostained serial sections

We have reconstructed small parts of capillary networks in the human splenic white pulp using serial sections immunostained for CD34 alone or for CD34 and CD271. The three-dimensional (3D) models show three types of interconnected networks: a network with very few long capillaries inside the white pulp originating from central arteries, a denser network surrounding follicles plus periarterial T-cell regions and a network in the red pulp. Capillaries of the perifollicular network and the red pulp network have open ends. Perifollicular capillaries form an arrangement similar to a basketball net located in the outer marginal zone. The marginal zone is defined by MAdCAM-1+ marginal reticular stromal cells. Perifollicular capillaries are connected to red pulp capillaries surrounded by CD271+ stromal capillary sheath cells. The scarcity of capillaries inside the splenic white pulp is astonishing, as non-polarised germinal centres with proliferating B-cells occur in adult human spleens. We suggest that specialized stromal marginal reticular cells form a barrier inside the splenic marginal zone, which together with the scarcity of capillaries guarantees the maintenance of gradients necessary for positioning of migratory B- and T-lymphocytes in the human splenic white pulp

Registration of serial sections: An evaluation method based on distortions of the ground truths

Registration of histological serial sections is a challenging task. Serial sections exhibit distortions and damage from sectioning. Missing information on how the tissue looked before cutting makes a realistic validation of 2D registrations extremely difficult. This work proposes methods for ground-truth-based evaluation of registrations. Firstly, we present a methodology to generate test data for registrations. We distort an innately registered image stack in the manner similar to the cutting distortion of serial sections. Test cases are generated from existing 3D data sets, thus the ground truth is known. Secondly, our test case generation premises evaluation of the registrations with known ground truths. Our methodology for such an evaluation technique distinguishes this work from other approaches. Both under- and over-registration become evident in our evaluations. We also survey existing validation efforts. We present a full-series evaluation across six different registration methods applied to our distorted 3D data sets of animal lungs. Our distorted and ground truth data sets are made publicly available.Comment: Supplemental data available under https://zenodo.org/record/428244

Feature-based multi-resolution registration of immunostained serial sections - online material

This is the supplementary online material, including full data, evaluation, and executables, for the paper "Feature-based multi-resolution registration of immunostained serial sections" that appeared in Medical Image Analysis, Volume 35, January 2017, Pages 288–302. Same material was deposited online under https://gdv-server.inf.uni-bayreuth.de/gdvcloud/index.php/s/NnSov0O65n9Gp01 We also include here further supplementary files deposited at the journal page (http://www.sciencedirect.com/science/article/pii/S136184151630127X) under CC-BY licence. See there for the definite version of the paper or http://www.mathematik.uni-marburg.de/~lobachev/papers/lobachev-media16-registration-preprint.pdf for the preprint

Capillary networks and follicular marginal zones in the human spleen. Three-dimensional models based on immunostained serial sections - Supplementary videos

We regard ROI from a spleen specimen in single (four ROIs) and double (three ROIs) staining. The ROIs with same number correspond to each other. video_?a,b.mov - a temporal paging throgh the registered stack of serial sections, single (a) or double (b) staining video_?c.mov - video of the reconstruction, single staining, special blood vessels highlighted video_?d.mov - an overview video of the reconstruction, double staining colour-deconvolution.png - settings of colour deconvolution in Fiji for double staining comments to videos.odt - a commentary to Video 3. This data corresponds to a publication "Capillary networks and follicular marginal zones in the human spleen. Three-dimensional models based on immunostained serial sections" by B. S. Steiniger, C. Ulrich, M. Berthold, M. Guthe, and O. Lobachev, 2017

Three-dimensional arrangement of human bone marrow microvessels revealed by immunohistology in undecalcified sections - final data

<p>These are the meshes used to render the videos in 10.5281/zenodo.57834 and 10.5281/zenodo.57754</p> <p>The file names are:</p> <p>R[n]_[kind].ply</p> <p>where</p> <p>n is the ROI number, 1-4<br> kind is the diameter mesh or the overview mesh.</p> <p>The diameter meshes have additionally removed inner components and also other small non-connected components, as described in the paper.</p