In recent years neuromorphic computing systems have achieved a lot of success due to its ability to process data much faster and using much less power compared to traditional Von Neumann computing architectures. There are two main types of Artificial Neural Networks (ANNs), Feedforward Neural Network (FNN) and Recurrent Neural Network (RNN). In this thesis we first study the types of RNNs and then move on to Spiking Neural Networks (SNNs). SNNs are an improved version of ANNs that mimic biological neurons closely through the emission of spikes. This shows significant advantages in terms of power and energy when carrying out data intensive applications by allowing spatio-temporal information processing. On the other hand, emerging non-volatile memory (eNVM) technology is key to emulate neurons and synapses for in-memory computations for neuromorphic hardware. A particular eNVM technology, memristors, have received wide attention due to their scalability, compatibility with CMOS technology and low power consumption properties. In this work we develop a spiking neural network by incorporating an inter-spike interval encoding scheme to convert the incoming input signal to spikes and use a memristive crossbar to carry out in-memory computing operations. We develop a novel input and output processing engine for our network and demonstrate the spatio-temporal information processing capability. We demonstrate an accuracy of a 100% with our design through a small-scale hardware simulation for digit recognition and demonstrate an accuracy of 87% in software through MNIST simulations. / M.S. / In recent years neuromorphic computing systems have achieved a lot of success due to its ability to process data much faster and using much less power compared to traditional Von Neumann computing architectures. Artificial Neural Networks (ANNs) are models that mimic biological neurons where artificial neurons or neurodes are connected together via synapses, similar to the nervous system in the human body. here are two main types of Artificial Neural Networks (ANNs), Feedforward Neural Network (FNN) and Recurrent Neural Network (RNN). In this thesis we first study the types of RNNs and then move on to Spiking Neural Networks (SNNs). SNNs are an improved version of ANNs that mimic biological neurons closely through the emission of spikes. This shows significant advantages in terms of power and energy when carrying out data intensive applications by allowing spatio-temporal information processing capability. On the other hand, emerging non-volatile memory (eNVM) technology is key to emulate neurons and synapses for in-memory computations for neuromorphic hardware. A particular eNVM technology, memristors, have received wide attention due to their scalability, compatibility with CMOS technology and low power consumption properties. In this work we develop a spiking neural network by incorporating an inter-spike interval encoding scheme to convert the incoming input signal to spikes and use a memristive crossbar to carry out in-memory computing operations. We demonstrate the accuracy of our design through a small-scale hardware simulation for digit recognition and demonstrate an accuracy of 87% in software through MNIST simulations.

The use of the discrete wavelet transform (DWT) for the JPEG2000 image compression standard has sparked interest in the design of fast, efficient hardware implementations of the perfect reconstruction filter bank used for computing the DWT. The accuracy and efficiency with which the filter coefficients are quantized in a multiplierless implementation impacts the image compression and hardware performance of the filter bank. A high precision representation ensures good compression performance, but at the cost of increased hardware resources and processing time. Conversely, lower precision in the filter coefficients results in smaller, faster hardware, but at the cost of poor compression performance. In addition to filter coefficient quantization, the filter bank structure also determines critical hardware properties such as throughput and power consumption. This thesis first investigates filter coefficient quantization strategies and filter bank structures for the hardware implementation of the biorthogonal 9/7 wavelet filters in a traditional convolution-based filter bank. Two new filter bank properties—"no-distortion-mse" and "deviation-at-dc"—are identified as critical to compression performance, and two new "compensating" filter coefficient quantization methods are developed to minimize degradation of these properties. The results indicate that the best performance is obtained by using a cascade form for the filters with coefficients quantized using the "compensating zeros" technique. The hardware properties of this implementation are then improved by developing a cascade polyphase structure that increases throughput and decreases power consumption. Next, this thesis investigates implementations of the lifting structure—an orthogonal structure that is more robust to coefficient quantization than the traditional convolution-based filter bank in computing the DWT. Novel, optimal filter coefficient quantization techniques are developed for a rational and an irrational set of lifting coefficients. The results indicate that the best quantized lifting coefficient set is obtained by starting with the rational coefficient set and using a "lumped scaling" and "gain compensation" technique for coefficient quantization. Finally, the image compression properties and hardware properties of the convolution and lifting based DWT implementations are compared. Although the lifting structure requires fewer computations, the cascaded arrangement of the lifting filters requires significant hardware overhead. Consequently, the results depict that the convolution-based cascade polyphase structure (with "<i>z</i>₁-compensated" coefficients) gives the best performance in terms of image compression performance and hardware metrics like throughput, latency and power consumption. / Master of Science

In this thesis we develop a system for recognition of strings of connected digits that can be used in a hands-free telephone system. We present a detailed description of the elements of the recognition system, such as an endpoint algorithm, the extraction of feature vectors from the speech samples, and the practical issues involved in training and recognition, in a Hidden Markov Model (HMM) based speech recognition system. We use continuous mixture densities to approximate the observation probability density functions (pdfs) in the HMM. While more complex in implementation, continuous (observation) HMMs provide superior performance to the discrete (observation) HMMs. Due to the nature of the application, ours is a speaker dependent recognition system and we have used a single speaker's speech to train and test our system. From the experimental evaluation of the effects of various model sizes on recognition performance, we observed that the use of HMMs with 7 states and 4 mixture density components yields average recognition rates better than 99% on the isolated digits. The level-building algorithm was used with the isolated digit models, which produced a recognition rate of better than 90% for 2-digit strings. For 3 and 4-digit strings, the performance was 83 and 64% respectively. These string recognition rates are much lower than expected for concatenation of single digits. This is most likely due to uncertainties in the location of the concatenated digits, which increases disproportionately with an increase in the number of digits in the string. / Master of Science

“Some numbers really are more popular than others.” Mark J. Nigrini (1998a:15) The above idea appears to defy common sense. In a random sequence of numbers drawn from a company’s financial books, every digit from 1 to 9 seems to have a one-in-nine chance of being the leading digit when used in a series of numbers. But, according to a mathematical formula of over 60 years old making its way into the field of accounting, certain numbers are actually more popular than others (Nigrini, 1998a:15). Accounting numbers usually follow a mathematical law, named Benford’s Law, of which the result is so unpredictable that fraudsters and manipulators, as a rule, do not succeed in observing the Law. With this knowledge, the forensic accountant is empowered to detect irregularities, anomalies, errors or fraud that may be present in a financial data set. The main objective of this study was to evaluate the effectiveness of Benford’s Law as a tool for forensic accountants. The empirical research used data from Company X to test the hypothesis that, in the context of financial fraud investigations, a significant difference between the actual and expected frequencies of Benford’s Law could be an indication of an error, fraud or irregularity. The effectiveness of Benford’s Law was evaluated according to findings from the literature review and empirical study. The results indicated that a Benford’s Law analysis was efficient in identifying the target groups in the data set that needed further investigation as their numbers did not match Benford’s Law. / MCom (Forensic Accountancy), North-West University, Potchefstroom Campus, 2014

“Some numbers really are more popular than others.” Mark J. Nigrini (1998a:15) The above idea appears to defy common sense. In a random sequence of numbers drawn from a company’s financial books, every digit from 1 to 9 seems to have a one-in-nine chance of being the leading digit when used in a series of numbers. But, according to a mathematical formula of over 60 years old making its way into the field of accounting, certain numbers are actually more popular than others (Nigrini, 1998a:15). Accounting numbers usually follow a mathematical law, named Benford’s Law, of which the result is so unpredictable that fraudsters and manipulators, as a rule, do not succeed in observing the Law. With this knowledge, the forensic accountant is empowered to detect irregularities, anomalies, errors or fraud that may be present in a financial data set. The main objective of this study was to evaluate the effectiveness of Benford’s Law as a tool for forensic accountants. The empirical research used data from Company X to test the hypothesis that, in the context of financial fraud investigations, a significant difference between the actual and expected frequencies of Benford’s Law could be an indication of an error, fraud or irregularity. The effectiveness of Benford’s Law was evaluated according to findings from the literature review and empirical study. The results indicated that a Benford’s Law analysis was efficient in identifying the target groups in the data set that needed further investigation as their numbers did not match Benford’s Law. / MCom (Forensic Accountancy), North-West University, Potchefstroom Campus, 2014

Hälso- och sjukvården befinner sig under ett allt större tryck av patienter som söker hjälp på grund av utmattningssyndrom. Kognitiva nedsättningar är en kärnkomponent i utmattningssyndrom och effektiva och korta screeninginstrument för att upptäcka dessa behövs för identifiera tillståndet tidigt. Syftet med föreliggande studie var att utveckla ett modifierat Symbol Digit Modalities Test. De totalt 90 deltagarna bestående av studenter delades in i två grupper efter självskattad utmattning. Tjugofyra individer identifierades i gruppen med låg utmattning och trettiofyra i gruppen med hög utmattning. De två grupperna jämfördes med prestation på testet. Testet bestod av tre block bestående av symboler, neutrala ord och hotfulla ord och vardera blocks testtid var 90 sekunder. Resultatet visade inga signifikanta skillnader mellan låg och hög utmattningsgrupp och prestation på testet. Däremot fanns signifikanta skillnader mellan blocken när samtliga deltagares prestation jämfördes. Det modifierade testet lyckas inte att differentiera mellan deltagare med låg och hög utmattning. Resultatet som visade att det fanns skillnader mellan blocken är intressant och visar på att det kan finnas en effekt av uppmärksamhetsvridning som framtida forskning kan bygga vidare på. / The Swedish healthcare system is under increasing pressure from patients seeking help due to fatigue syndrome. Cognitive impairments are a core symptom of the syndrome; effective screening tools to detect cognitive impairment related to fatigue are warranted to identify the condition. The aim of the present study was to develop a modified Symbol Digit Modalities. A total of 90 participants consisting of undergraduate students were divided into two groups after self-assessed fatigue. Twenty-four individuals were identified in the low fatigue group and thirty-four in the high fatigue group. The two groups’ test performance were compared. The test consisted of three blocks consisting of symbols, neutral words, and threat words; the duration of each test block was 90 seconds. The results showed no significant differences between low and high fatigue in terms of performance on the tests. However, there were significant differences across the blocks when comparing all participants' performance. The modified test failed to differentiate between low and high fatigue participants. The result indicating significant differences across the blocks is interesting and shows that there may be an effect of attentional bias that future research can build upon.

Muitas operações cognitivas requerem velocidade de processamento de informação (VPI) suficiente para serem executadas dentro do prazo permitido, sendo que VPI retardada geralmente está subjacente a déficits atencionais. A desaceleração no tempo de resposta é particularmente evidente em pacientes com traumatismo crânio-encefálico, doença de Parkinson, depressão, demência e esclerose múltipla (EM). A importância de compreender os déficits de VPI e o desenvolvimento de programas efetivos de reabilitação é, portanto, crítico. Devido à sua alta validade preditiva e à sua fácil administração, o Symbol Digit Modalities Test (SDMT) é um dos testes clínicos mais amplamente utilizados para a avaliação cognitiva de pacientes com menor VPI. No entanto, além de avaliar a presença e gravidade de seus déficits, é interessante determinar as regiões cerebrais responsáveis por essa função e sua integração. Devido à sua não invasividade e ao seu bom nível de confiabilidade, a técnica de Imagem de Ressonância Magnética Funcional Dependente do Nível de Oxigenação no Sangue (BOLD-fMRI) é a ferramenta mais apropriada para esse fim. Logo, o objetivo do presente estudo foi o mapeamento funcional cerebral de VPI durante o desempenho de uma tarefa (SDMT) adaptada para o ambiente da ressonância em um grupo de voluntários saudáveis jovens. 16 controles saudáveis destros foram recrutados e submetidos à avaliação cognitiva com a versão oral do SDMT antes da aquisição de imagens. IRM foi adquirida em um sistema de 3T (Philips Achieva). Imagens funcionais (BOLD) foram adquiridas com uma sequência EPI. O experimento consistiu de seis blocos de 30 s de controle intercalados com cinco blocos de 30 segundos de tarefa (SDMT). Durante os blocos de tarefa, um símbolo foi apresentado a cada 2 segundos e ao participante foi requerido que associasse o número correspondente ao símbolo apresentado baseando-se em uma chave de resposta. Durante os blocos de controle, um número foi apresentado a cada 2 segundos e ao participante foi requerido que lesse silenciosamente o número em questão. Mapas paramétricos estatísticos foram obtidos para estudo de localização funcional utilizando o Modelo Linear Geral com um regressor boxcar convoluído com uma função de resposta hemodinâmica canônica (p-FDR < 0,01). Foi realizada a correlação bivariada entre as séries temporais médias das regiões associadas à tarefa para estudo de integração funcional (p-FDR < 0.0001). As informações de localização e integração funcionais foram inseridas em analise de conectividade efetiva. Ativações foram observadas na rede frontoparietal e no córtex occipital para análises individual e em grupo. Análise de conectividade efetiva para a arquitetura do sistema revelou o declive em posição serial com o giro lingual, o cúneo e duas regiões paralelas (pré-cúneo e lóbulo parietal superior), a partir do qual a informação converge para o giro frontal inferior e se bifurca para os giros frontais médios esquerdo e direito. Um modelo de rede envolvendo áreas relacionadas à VPI foi obtido e pode servir como referência para investigações futuras deste processo cognitivo em grupos clínicos, combinadas com estudos de neuroplasticidade cerebral. / Many cognitive operations require sufficient information processing speed (IPS) to be executed within the allowed time frame, with delayed IPS often underlining attentional deficits. The deceleration in response time is particularly evident in patients with traumatic brain injury, Parkinson\'s disease, depression, dementia and multiple sclerosis (MS). The importance of understanding IPS deficits and developing effective rehabilitation programs is therefore critical. Because of its high predictive validity and easy administration, the Symbol Digit Modalities Test (SDMT) is one of the most widely used clinical tests for the cognitive assessment of patients with lower IPS. However, in addition to evaluating the presence and severity of its deficits, it is interesting to determine the brain regions responsible for this function and its integration. Because of its non-invasiveness and its good level of reliability, the BOLD-fMRI technique is the most appropriate tool for this purpose. Therefore, the aim of the present study was the functional brain function mapping of IPS during the performance of a task (SDMT) adapted to the resonance environment in a group of healthy young volunteers. 16 healthy right controls were recruited and submitted to cognitive assessment with the oral version of SDMT prior to image acquisition. MRI was acquired in a 3T system (Philips Achieva). Functional images (BOLD) were acquired with an EPI sequence. The experiment consisted of six blocks of 30 s of control intercalated with five blocks of 30 seconds of task (SDMT). During the task blocks, a symbol was displayed every 2 seconds and the participant was required to associate the number corresponding to the displayed symbol based on a response key. During the control blocks, a number was displayed every 2 seconds and the participant was required to silently read the number in question. Statistical parametric maps were obtained for functional localization study using the General Linear Model with a boxcar regressor convolved with a canonical hemodynamic response function (p-FDR <0.01). The bivariate correlation between the mean time series of the regions associated with the task for functional integration study (p-FDR <0.0001) was performed. The functional location and integration information was inserted into effective connectivity analysis. Activations were observed in the frontoparietal network and in the occipital cortex for individual and group analyzes. Effective connectivity analysis for the system architecture revealed the declive in serial position with the lingual gyrus, the cuneus and two parallel regions (precuneus and superior parietal lobule), from which the information converges to the inferior frontal gyrus and bifurcates to the left and right middle turns. A network model involving areas related to IPS has been obtained and may serve as a reference for future investigations of this cognitive process in clinical groups, combined with studies of cerebral neuroplasticity.

Muitas operações cognitivas requerem velocidade de processamento de informação (VPI) suficiente para serem executadas dentro do prazo permitido, sendo que VPI retardada geralmente está subjacente a déficits atencionais. A desaceleração no tempo de resposta é particularmente evidente em pacientes com traumatismo crânio-encefálico, doença de Parkinson, depressão, demência e esclerose múltipla (EM). A importância de compreender os déficits de VPI e o desenvolvimento de programas efetivos de reabilitação é, portanto, crítico. Devido à sua alta validade preditiva e à sua fácil administração, o Symbol Digit Modalities Test (SDMT) é um dos testes clínicos mais amplamente utilizados para a avaliação cognitiva de pacientes com menor VPI. No entanto, além de avaliar a presença e gravidade de seus déficits, é interessante determinar as regiões cerebrais responsáveis por essa função e sua integração. Devido à sua não invasividade e ao seu bom nível de confiabilidade, a técnica de Imagem de Ressonância Magnética Funcional Dependente do Nível de Oxigenação no Sangue (BOLD-fMRI) é a ferramenta mais apropriada para esse fim. Logo, o objetivo do presente estudo foi o mapeamento funcional cerebral de VPI durante o desempenho de uma tarefa (SDMT) adaptada para o ambiente da ressonância em um grupo de voluntários saudáveis jovens. 16 controles saudáveis destros foram recrutados e submetidos à avaliação cognitiva com a versão oral do SDMT antes da aquisição de imagens. IRM foi adquirida em um sistema de 3T (Philips Achieva). Imagens funcionais (BOLD) foram adquiridas com uma sequência EPI. O experimento consistiu de seis blocos de 30 s de controle intercalados com cinco blocos de 30 segundos de tarefa (SDMT). Durante os blocos de tarefa, um símbolo foi apresentado a cada 2 segundos e ao participante foi requerido que associasse o número correspondente ao símbolo apresentado baseando-se em uma chave de resposta. Durante os blocos de controle, um número foi apresentado a cada 2 segundos e ao participante foi requerido que lesse silenciosamente o número em questão. Mapas paramétricos estatísticos foram obtidos para estudo de localização funcional utilizando o Modelo Linear Geral com um regressor boxcar convoluído com uma função de resposta hemodinâmica canônica (p-FDR < 0,01). Foi realizada a correlação bivariada entre as séries temporais médias das regiões associadas à tarefa para estudo de integração funcional (p-FDR < 0.0001). As informações de localização e integração funcionais foram inseridas em analise de conectividade efetiva. Ativações foram observadas na rede frontoparietal e no córtex occipital para análises individual e em grupo. Análise de conectividade efetiva para a arquitetura do sistema revelou o declive em posição serial com o giro lingual, o cúneo e duas regiões paralelas (pré-cúneo e lóbulo parietal superior), a partir do qual a informação converge para o giro frontal inferior e se bifurca para os giros frontais médios esquerdo e direito. Um modelo de rede envolvendo áreas relacionadas à VPI foi obtido e pode servir como referência para investigações futuras deste processo cognitivo em grupos clínicos, combinadas com estudos de neuroplasticidade cerebral. / Many cognitive operations require sufficient information processing speed (IPS) to be executed within the allowed time frame, with delayed IPS often underlining attentional deficits. The deceleration in response time is particularly evident in patients with traumatic brain injury, Parkinson\'s disease, depression, dementia and multiple sclerosis (MS). The importance of understanding IPS deficits and developing effective rehabilitation programs is therefore critical. Because of its high predictive validity and easy administration, the Symbol Digit Modalities Test (SDMT) is one of the most widely used clinical tests for the cognitive assessment of patients with lower IPS. However, in addition to evaluating the presence and severity of its deficits, it is interesting to determine the brain regions responsible for this function and its integration. Because of its non-invasiveness and its good level of reliability, the BOLD-fMRI technique is the most appropriate tool for this purpose. Therefore, the aim of the present study was the functional brain function mapping of IPS during the performance of a task (SDMT) adapted to the resonance environment in a group of healthy young volunteers. 16 healthy right controls were recruited and submitted to cognitive assessment with the oral version of SDMT prior to image acquisition. MRI was acquired in a 3T system (Philips Achieva). Functional images (BOLD) were acquired with an EPI sequence. The experiment consisted of six blocks of 30 s of control intercalated with five blocks of 30 seconds of task (SDMT). During the task blocks, a symbol was displayed every 2 seconds and the participant was required to associate the number corresponding to the displayed symbol based on a response key. During the control blocks, a number was displayed every 2 seconds and the participant was required to silently read the number in question. Statistical parametric maps were obtained for functional localization study using the General Linear Model with a boxcar regressor convolved with a canonical hemodynamic response function (p-FDR <0.01). The bivariate correlation between the mean time series of the regions associated with the task for functional integration study (p-FDR <0.0001) was performed. The functional location and integration information was inserted into effective connectivity analysis. Activations were observed in the frontoparietal network and in the occipital cortex for individual and group analyzes. Effective connectivity analysis for the system architecture revealed the declive in serial position with the lingual gyrus, the cuneus and two parallel regions (precuneus and superior parietal lobule), from which the information converges to the inferior frontal gyrus and bifurcates to the left and right middle turns. A network model involving areas related to IPS has been obtained and may serve as a reference for future investigations of this cognitive process in clinical groups, combined with studies of cerebral neuroplasticity.

This M.S. thesis introduces new modulus scaling techniques for transforming a class of primes into special forms which enable efficient arithmetic. The scaling technique may be used to improve multiplication and inversion in finite fields. We present an efficient inversion algorithm that utilizes the structure of a scaled modulus. Our inversion algorithm exhibits superior performance to the Euclidean algorithm and lends itself to efficient hardware implementation due to its simplicity. Using the scaled modulus technique and our specialized inversion algorithm we develop an elliptic curve processor architecture. The resulting architecture successfully utilizes redundant representation of elements in GF(p) and provides a low-power, high speed, and small footprint specialized elliptic curve implementation. We also introduce a unified Montgomery multiplier architecture working on the extension fields GF(p), GF(2) and GF(3). With the increasing research activity for identity based encryption schemes, there has been an increasing need for arithmetic operations in field GF(3). Since we based our research on low-power and small footprint applications, we designed a unified architecture rather than having a seperate hardware for GF{3}. To the best of our knowledge, this is the first time a unified architecture was built working on three different extension fields.

This study aims to find out the relationship between Working Memory Capacity and Verbal and Mathematical Achievement. The participants were 60 students at Hacettepe University School of Foreign Languages Department of Basic English. For measuring working memory capacity, one simple (Digit Span Task) and one complex (Reading Span Task) were used. Verbal achievement of the participants was measured both in their native language (Turkish) and their foreign language (English). For measuring their native language achievement, the participants&rsquo / Turkish scores in Y&uuml / ksek&ouml / gretime Ge&ccedil / is Sinavi 2010 (Transition to Higher Education Examination) / and for measuring their foreign language achievement, the participants&rsquo / scores in Hacettepe University School of Foreign Languages Department of Basic English Elementary Groups Achievement Exams I and II were used. For measuring their mathematical achievement, the participants&rsquo / Mathematic scores in Y&uuml / ksek&ouml / gretime Ge&ccedil / is Sinavi 2010 (Transition to Higher Education Examination) were used. The data was analyzed using a statistical package program (SPSS Version 18.0). The data analysis results revealed that there is a relationship between working memory capacity and verbal and mathematical achievements of the participants. It was tentatively concluded that, as the working memory capacity of the participants increase, so might their achievement in verbal and mathematical subjects. This result was discussed in terms of its implications, which may be that, if working memory capacity could be improved / the cognitive processes which the working memory is responsible for might also improve.