On the Factor Refinement Principle and its Implementation on Multicore Architectures

The factor refinement principle turns a partial factorization of integers (or polynomi­ als) into a more complete factorization represented by basis elements and exponents, with basis elements that are pairwise coprime. There are lots of applications of this refinement technique such as simplifying systems of polynomial inequations and, more generally, speeding up certain algebraic algorithms by eliminating redundant expressions that may occur during intermediate computations. Successive GCD computations and divisions are used to accomplish this task until all the basis elements are pairwise coprime. Moreover, square-free factorization (which is the first step of many factorization algorithms) is used to remove the repeated patterns from each input element. Differentiation, division and GCD calculation op­ erations are required to complete this pre-processing step. Both factor refinement and square-free factorization often rely on plain (quadratic) algorithms for multipli­ cation but can be substantially improved with asymptotically fast multiplication on sufficiently large input. In this work, we review the working principles and complexity estimates of the factor refinement, in case of plain arithmetic, as well as asymptotically fast arithmetic. Following this review process, we design, analyze and implement parallel adaptations of these factor refinement algorithms. We consider several algorithm optimization techniques such as data locality analysis, balancing subproblems, etc. to fully exploit modern multicore architectures. The Cilk++ implementation of our parallel algorithm based on the augment refinement principle of Bach, Driscoll and Shallit achieves linear speedup for input data of sufficiently large size

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

Applications of fuzzy counterpropagation neural networks to non-linear function approximation and background noise elimination

An adaptive filter which can operate in an unknown environment by performing a learning mechanism that is suitable for the speech enhancement process. This research develops a novel ANN model which incorporates the fuzzy set approach and which can perform a non-linear function approximation. The model is used as the basic structure of an adaptive filter. The learning capability of ANN is expected to be able to reduce the development time and cost of the designing adaptive filters based on fuzzy set approach. A combination of both techniques may result in a learnable system that can tackle the vagueness problem of a changing environment where the adaptive filter operates. This proposed model is called Fuzzy Counterpropagation Network (Fuzzy CPN). It has fast learning capability and self-growing structure. This model is applied to non-linear function approximation, chaotic time series prediction and background noise elimination

Loop Transformations for the Optimized Generation of Reconfigurable Hardware

Current high-level design environments offer little support to implement data-intensive applications on heterogeneous-memory systems; they rather focus on parallelism. This thesis addresses the memory hierarchy problem to high-level transformations of loop structures. The composition of long transformation sequences by combining shorter subsequences is studied together with the influence of the order of applying transformation steps. Several methods are presented to estimate bounds on Ehrhart quasi-polynomials, which can be used to statically evaluate program properties, such as memory usage. Since loop transformations not only influence the data access pattern but also the control complexity we present a hardware loop controller architecture which supports hardware generation from the polyhedral representation used for loop transformations. The techniques are demonstrated by the semi-automatic generation of an FPGA implementation of an inverse discrete wavelet transform

Fear Classification using Affective Computing with Physiological Information and Smart-Wearables

Mención Internacional en el título de doctorAmong the 17 Sustainable Development Goals proposed within the 2030 Agenda and adopted by all of the United Nations member states, the fifth SDG is a call for action to effectively turn gender equality into a fundamental human right and an essential foundation for a better world. It includes the eradication of all types of violence against women. Focusing on the technological perspective, the range of available solutions intended to prevent this social problem is very limited. Moreover, most of the solutions are based on a panic button approach, leaving aside the usage and integration of current state-of-the-art technologies, such as the Internet of Things (IoT), affective computing, cyber-physical systems, and smart-sensors. Thus, the main purpose of this research is to provide new insight into the design and development of tools to prevent and combat Gender-based Violence risky situations and, even, aggressions, from a technological perspective, but without leaving aside the different sociological considerations directly related to the problem. To achieve such an objective, we rely on the application of affective computing from a realist point of view, i.e. targeting the generation of systems and tools capable of being implemented and used nowadays or within an achievable time-frame. This pragmatic vision is channelled through: 1) an exhaustive study of the existing technological tools and mechanisms oriented to the fight Gender-based Violence, 2) the proposal of a new smart-wearable system intended to deal with some of the current technological encountered limitations, 3) a novel fear-related emotion classification approach to disentangle the relation between emotions and physiology, and 4) the definition and release of a new multi-modal dataset for emotion recognition in women. Firstly, different fear classification systems using a reduced set of physiological signals are explored and designed. This is done by employing open datasets together with the combination of time, frequency and non-linear domain techniques. This design process is encompassed by trade-offs between both physiological considerations and embedded capabilities. The latter is of paramount importance due to the edge-computing focus of this research. Two results are highlighted in this first task, the designed fear classification system that employed the DEAP dataset data and achieved an AUC of 81.60% and a Gmean of 81.55% on average for a subjectindependent approach, and only two physiological signals; and the designed fear classification system that employed the MAHNOB dataset data achieving an AUC of 86.00% and a Gmean of 73.78% on average for a subject-independent approach, only three physiological signals, and a Leave-One-Subject-Out configuration. A detailed comparison with other emotion recognition systems proposed in the literature is presented, which proves that the obtained metrics are in line with the state-ofthe- art. Secondly, Bindi is presented. This is an end-to-end autonomous multimodal system leveraging affective IoT throughout auditory and physiological commercial off-theshelf smart-sensors, hierarchical multisensorial fusion, and secured server architecture to combat Gender-based Violence by automatically detecting risky situations based on a multimodal intelligence engine and then triggering a protection protocol. Specifically, this research is focused onto the hardware and software design of one of the two edge-computing devices within Bindi. This is a bracelet integrating three physiological sensors, actuators, power monitoring integrated chips, and a System- On-Chip with wireless capabilities. Within this context, different embedded design space explorations are presented: embedded filtering evaluation, online physiological signal quality assessment, feature extraction, and power consumption analysis. The reported results in all these processes are successfully validated and, for some of them, even compared against physiological standard measurement equipment. Amongst the different obtained results regarding the embedded design and implementation within the bracelet of Bindi, it should be highlighted that its low power consumption provides a battery life to be approximately 40 hours when using a 500 mAh battery. Finally, the particularities of our use case and the scarcity of open multimodal datasets dealing with emotional immersive technology, labelling methodology considering the gender perspective, balanced stimuli distribution regarding the target emotions, and recovery processes based on the physiological signals of the volunteers to quantify and isolate the emotional activation between stimuli, led us to the definition and elaboration of Women and Emotion Multi-modal Affective Computing (WEMAC) dataset. This is a multimodal dataset in which 104 women who never experienced Gender-based Violence that performed different emotion-related stimuli visualisations in a laboratory environment. The previous fear binary classification systems were improved and applied to this novel multimodal dataset. For instance, the proposed multimodal fear recognition system using this dataset reports up to 60.20% and 67.59% for ACC and F1-score, respectively. These values represent a competitive result in comparison with the state-of-the-art that deal with similar multi-modal use cases. In general, this PhD thesis has opened a new research line within the research group under which it has been developed. Moreover, this work has established a solid base from which to expand knowledge and continue research targeting the generation of both mechanisms to help vulnerable groups and socially oriented technology.Programa de Doctorado en Ingeniería Eléctrica, Electrónica y Automática por la Universidad Carlos III de MadridPresidente: David Atienza Alonso.- Secretaria: Susana Patón Álvarez.- Vocal: Eduardo de la Torre Arnan