Investigating mechanisms that regulate genes and the genes' functions are essential to understand a biological system. This dissertation is consists of two specific research projects under these aims, which are for understanding piRNA's regulation mechanism and predicting genes' function computationally. The first project shows a piRNA regulation landscape in C. elegans. piRNAs (Piwi-interacting small RNAs) form a complex with Piwi Argonautes to maintain fertility and silence transposons in animal germlines. In C. elegans, previous studies have suggested that piRNAs tolerate mismatched pairing and in principle could target all transcripts. In this project, by computationally analyzing the chimeric reads directly captured by cross-linking piRNA and their targets in vivo, piRNAs are found to target all germline mRNAs with microRNA-like pairing rules. The number of targeting chimeric reads correlates better with binding energy than with piRNA abundance, suggesting that piRNA concentration does not limit targeting. Further more, in mRNAs silenced by piRNAs, secondary small RNAs are found to be accumulating at the center and ends of piRNA binding sites. Whereas in germline-expressed mRNAs, reduced piRNA binding density and suppression of piRNA-associated secondary small RNAs targeting correlate with the CSR-1 Argonaute presence. These findings reveal physiologically important and nuanced regulation of piRNA targets and provide evidence for a comprehensive post-transcriptional regulatory step in germline gene expression. The second project elaborates a computational model to predict gene function. Predicting genes involved in a biological function facilitates many kinds of research, such as prioritizing candidates in a screening project. Following the “Guilt By Association” principle, multiple datasets are considered as biological networks and integrated together under a multi-label learning framework for predicting gene functions. Specifically, the functional labels are propagated and smoothed using a label propagation method on the networks and then integrated using an “Error correction of code” multi-label learning framework, where a “codeword” defines all the labels annotated to a specific gene. The model is then trained by finding the optimal projections between the code matrix and the biological datasets using canonical correlation analysis. Its performance is benchmarked by comparing to a state-of-art algorithm and a large scale screen results for piRNA pathway genes in D.melanogaster. Finally, piRNA targeting's roles in epigenetics and physiology and its cross-talk with CSR-1 pathway are discussed, together with a survey of additional biological datasets and a discussion of benchmarking methods for the gene function prediction.

Error-control codes provide a mechanism to increase the reliability of digital data being processed, transmitted, or stored under noisy conditions. Cyclic codes constitute an important class of error-control code, offering powerful error detection and correction capabilities. They can easily be generated and verified in hardware, which makes them particularly well suited to the practical use as error detecting codes.A cyclic code is based on a generator polynomial which determines its properties including the specific error detection strength. The optimal choice of polynomial depends on many factors that may be influenced by the underlying application. It is therefore advantageous to employ programmable cyclic code hardware that allows a flexible choice of polynomial to be applied to different requirements. A novel method is presented in this thesis to realise programmable cyclic code circuits that are fast, energy-efficient and minimise implementation resources.It can be shown that the correction of a single-bit error on the basis of a cyclic code is equivalent to the solution of an instance of the discrete logarithm problem. A new approach is proposed for computing discrete logarithms; this leads to a generic deterministic algorithm for analysed group orders that equal Mersenne numbers with an exponent of a power of two. The algorithm exhibits a worst-case runtime in the order of the square root of the group order and constant space requirements.This thesis establishes new relationships for finite fields that are represented as the polynomial ring over the binary field modulo a primitive polynomial. With a subset of these properties, a novel approach is developed for the solution of the discrete logarithm in the multiplicative groups of these fields. This leads to a deterministic algorithm for small group orders that has linear space and linearithmic time requirements in the degree of defining polynomial, enabling an efficient correction of single-bit errors based on the corresponding cyclic codes.

This thesis describes barcodes which are used in postal services. Specifically, it is concerned with Intelligent Mail Barcode, the GS1-128 code, the C128 code of Ceska posta (Czech Postal Services) and the QR code. The thesis attempts to analyze methods of encoding information into barcodes and error detection algorithms used for error correction during the decoding processes. Most importantly, there is described Reed-Solomon error correction in the QR code. There are presented and evaluated different methods of code detecting which are suggested by authors of various academic articles. The thesis also describes the method of creating test sets of images and proposed appearances of the scanning scene. Additionally, there are described algorithms for detection and decoding barcodes GS1-128, C128 and IMB in the image which was created during the work on this thesis. Finally, there is the evaluation of the percentage success of algorithms.