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

Extended SPI Bus

Serial peripheral interface (SPI) is a protocol that enables low-level machine communication between electronics subsystems, e.g., microcontrollers, peripherals, etc. In applying SPI to communications between devices of substantially differing performance characteristics, e.g., clock frequency, memory capacity, or response time, the original SPI has some disadvantages. For example, due to the streaming nature of SPI communication, errors are not detected; due to differing clock frequencies at two ends, synchronization is difficult; due to differing memory capacity at two ends, the buffers of the end with less memory overflow; etc. This disclosure describes an extension to SPI that features synchronization signaling and packet-splitting abilities to enable devices of differing abilities to communicate via SPI. The extension also enables asynchronous transaction execution over the SPI bus and adds error detection capabilities, both features that enable larger packet sizes and higher transmission/transaction rates

A Purely Functional Computer Algebra System Embedded in Haskell

We demonstrate how methods in Functional Programming can be used to implement a computer algebra system. As a proof-of-concept, we present the computational-algebra package. It is a computer algebra system implemented as an embedded domain-specific language in Haskell, a purely functional programming language. Utilising methods in functional programming and prominent features of Haskell, this library achieves safety, composability, and correctness at the same time. To demonstrate the advantages of our approach, we have implemented advanced Gr\"{o}bner basis algorithms, such as Faug\`{e}re's $F_4$ and $F_5$, in a composable way.Comment: 16 pages, Accepted to CASC 201

Mechanisms of Chromosomal Fragility and Rearrangements Triggered by Human Unstable Repeats

Kirill Lobachev, Assistant Professor, Department of Biology, Georgia Tech, presented a lecture at 11:00 AM, Tuesday, January 22, 2008, Klaus Advanced Computing Building, Room 1116WRuntime: 47:50 minutesResearch of my lab focuses on understanding how chromosomal rearrangements arise and lead to hereditary diseases and cancer. Chromosomes containing repeats that can adopt stable secondary structures are highly prone for double-strand breaks and various types of rearrangements. Molecular mechanisms for this type of genetic instability in eukaryotes are poorly understood. Using yeast, S. cerevisiae, we are investigating the chromosomal fragility mediated by two sequence motifs: cruciform-forming inverted repeats and H-DNA-forming GAA/TTC triplet repeats. Both types of repeats strongly induce breakage which results from the replication arrest by the secondary structures. However, genetic requirements for fragility, mode of breakage and consequences for the genome integrity are different for these two types of repeats. We propose that the nature of the secondary structure predisposes chromosomes for the specific pattern of gross chromosomal rearrangements. These rearrangements are strikingly similar to carcinogenic aberration suggesting that repeat-mediated instability might be a general phenomenon that operates not only in yeast but also in humans. I will present recent data from my lab on proteins that are involved into the fragility

Chromosome Fragmentation after Induction of a Double-Strand Break Is an Active Process Prevented by the RMX Repair Complex

Chromosome aberrations are common outcomes of exposure to DNA-damaging agents or altered replication events and are associated with various diseases and a variety of carcinomas, including leukemias, lymphomas, sarcomas, and epithelial tumors 1 and 2. The incidence of aberrations can be greatly increased as a result of defects in DNA repair pathways [3]. Although there is considerable information about the molecular events associated with the induction and repair of a double-strand break (DSB), little is known about the events that ultimately lead to translocations or deletions through the formation of chromosome breaks or the dissociation of broken ends. We describe a system for visualizing DNA ends at the site of a DSB in living cells. After induction of the break, DNA ends flanking the DSB site in wild-type cells remained adjacent. Loss of a functional RMX complex (Rad50/Mre11/Xrs2) or a mutation in the Rad50 Zn-hook structure resulted in DNA ends being dispersed in approximately 10%–20% of cells. Thus, the RMX complex holds broken ends together and counteracts mitotic spindle forces that can be destructive to damaged chromosomes

Checklist, distribution and bibliography of Mongolian Siphonaptera

Flea fauna in Mongolia is relatively unknown though the publications dealing with this problem are not few. The p·apers until 1966 are concerning ma.inly the territories delimited by natural plagua focis. Only in later periods, simu ltaneously with the intensive zoological research of the whole territory of the Mongolian People\u27s Republic, the more detailed research of flea fauna on the whole territory takes place. The systematic research began thanks to the Mongolian-German and MongolianHungarian expeditions, the members of which have collected considerable parasitological material covering the part of northern, eastern and western Mongolia. Since the year 1970 the Soviet-Mongolian academic expedition has been working on the territory of the Mongolian People\u27s Republic, as well as the Complex Chubsugul Mongolian-Soviet expedition, in which the members of the Comenius University in Bratislava have been working since the year 1974. On the basis of our own collections and the collections obtained from the Soviet-Mongolian academic expedition, from the Mongolian-German expedition, from the chair of Zoology Mongolian State University, from the Academy of science in Ulaan Baatar, and on the basis of literary data, on the territory of Mongolia there were recorded 157 species and subspecies of fleas. In future, many data (published) on the basis of single findings must be verified on some more materials from the viewpoint of progress in taxonomy in this group. There are concerned some species with cosmopolitan distribution (Xenopsylla cheopis, Ctenocephalides felis, Neopsylla teratura teratura, Rhadinopsylla li li, R. li ventricosa, subspecies Malaraeus penicilliger, Frontopsylla elata, Frontopsylla frontalis dubiosa, Citellophilus tesquorum mongolicus). The checklist contains: the sequence number of the taxon, the name of the taxon, the list of the publications mentioning the species in question. The publications are numbered as in the bibliography. Later, the localities are alleged, where the ajmaks are marked by the Roman figures and the localities in different ajmaks a.re marked by the Arabian figures. The division of ajmak and the localities are alleged on the map No. 1. The names of the localities are original Mongolian with the transcription into English

CHARACTERIZATION OF MOLECULAR MODE OF DNA SYNTHESIS DURING BREAK INDUCED REPLICATION

poster abstractAbnormal repair of DNA double strand breaks can lead to Gross Chromosomal Rearrangements (GCRs) that are the root cause for abnormal genetic and cellular functions that lead to cancer. DSBs left with only one of the two broken DNA ends must be repaired by Break Induced Replication (BIR). BIR requires extensive DNA replication which is very mutagenic. BIR model proposes that the junction made between the invading broken chromosome and the donor molecule substitutes for the origin of DNA replication. This initiates the assembly of a replication fork, which copies the donor sequence till the end of the donor chromosome. The as-sembly of a replication fork and the mode of DNA replication during BIR remains untested. Our study using 2-Dimensional electrophoresis demonstrates that BIR follows an unusual type of DNA synthesis forming “bubble” like replication inter-mediates. Also our result using molecular combing experiments demonstrates that BIR follows a “conservative mode” of DNA synthesis. This unusual kind of DNA replication could explain the highly mutagenic nature of BIR

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