La douleur sociale est une forme de douleur non physique dérivant de la perception de l'exclusion sociale. L'importance de la compréhension de ses modulations comportementales et neuronales est fondamentale, car ses conséquences sur le long terme peuvent être très néfastes. Dans ce travail de thèse, j'ai exploré ces aspects à travers une étude comportementale à l‟aide d‟enregistrements par SCR (Skin Conductance Recording), et trois études en iEEG (électro-encéphalographie intracrânienne) chez des patients épileptiques. La première étude comportementale a exploré la direction dans laquelle l'exclusion sociale est influencée par une récompense et ses réactions sur le long terme. Ainsi, la récompense monétaire altère l'équilibre social et augmente l‟activité électrodermale. La personne ayant été exclue met alors en oeuvre des mécanismes de vengeance en défavorisant la personne qui l‟a exclue précédemment. Les études en iEEG ont été une fenêtre unique d'exploration du cerveau lors de différentes types de modulation de l'exclusion. Dans la première étude en iEEG, nous avons observé que la douleur sociale produit une activation des oscillations thêta (3-7 Hz), lors de d'exclusion, dans l'insula, l'ACC, le cortex préfrontal et le gyrus fusiforme. La deuxième étude iEEG s'est intéressée aux modulations produites par la douleur sociale dans BA 19 et BA 17 présentant des P1 d'amplitude majeure lors de l'observation des photos du joueur qui exclut. La troisième étude en iEEG a exploré la réponse neuronale de l'influence d'une variable monétaire lors de l'exclusion. Nos résultats démontrent que l'insula postérieure présente une activation thêta indépendante du fait que l'exclusion soit positive (exclusion et gain d'argent) ou encore négative (exclusion et perte d'argent), à la différence de l'insula antérieure, active seulement lors d'une exclusion négative / Pain is a form of social non-physical pain arising from the perception of social exclusion. The importance of understanding its behavioral and neuronal modulations has a critical value, since its long lasting consequences can be extremely harmful. In this thesis I firstly explored these issues through a behavioral SCR study (Skin Conductance Recording), and successively through three iEEG studies in patients with epilepsy (intracranial EEG). The SCR study explored the direction in which social exclusion is influenced by a reward and its long lasting reactions. Money affects social equilibrium and increases the SCR pics. The excluded individual implements revenge attitudes toward the person who excluded in a previuous interaction. The iEEG studies were a unique window for exploring the brain during different types of social pain modulations. In the first iEEG study, we found that social pain produced activation of theta oscillations (3-7 Hz) during exclusion in the insula, in the ACC, in the prefrontal cortex and in the fusiform face area. The second iEEG study wanted to explore deeply the primitive modulations produced by social pain in visual area. We found in BA 19 and BA 17 greater P1 peak amplitude during excluder pictures presentation. The third iEEG study investigated the neuronal modulations produced by a monetary reward during social pain. These results demonstrated that the posterior insula has a theta activation independent of whether the exclusion is positive (excluded but gaining money) or more negative (excluded but losing money), whereas the anterior insula, has a theta activation only during a negative exclusion

Les processus d'apprentissage et de mémoire sont contrôlés par des circuits et éléments neuronaux spécifiques. De nombreuses études ont récemment mis en évidence que les circuits corticaux jouent un rôle important dans la régulation des comportements de peur, cependant, leurs caractéristiques anatomiques et fonctionnelles restent encore largement inconnues. Au cours de ma thèse, en utilisant des enregistrements unitaires et des approches optogénétiques chez la souris libre de se comporter, nous avons pu montrer que les interneurones inhibiteurs du cortex auditif et du cortex préfrontal médian forment un microcircuit désinhibiteur permettant respectivement l'acquisition et l'expression de la mémoire de peur conditionnée. Dans les deux cas, les interneurones parvalbuminergiques constituent l'élément central du circuit et sont inhibés de façon phasique. D’un point de vue fonctionnel, nous avons démontré que cette inhibition était associée à la désinhibition des neurones pyramidaux par un mécanisme de réduction de l'inhibition continue exercée par les interneurones parvalbuminergiques. Ainsi, les interneurones parvalbuminergiques peuvent contrôler temporellement l'excitabilité des neurones pyramidaux. En particulier, nous avons montré que l'acquisition de la mémoire de peur conditionnée dépend du recrutement d'un microcircuit désinhibiteur localisé dans le cortex auditif. En effet, au cours du conditionnement de peur, la présentation du choc électrique induit l'inhibition des interneurones parvalbuminergiques, ce qui a pour conséquence de désinhiber les neurones pyramidaux du cortex auditif et de permettre l’apprentissage du conditionnement de peur. Dans leur ensemble, ces données suggèrent que la désinhibition est un mécanisme important dans l'apprentissage et le traitement de l'information dans les circuits corticaux. Dans un second temps, nous avons montré que l'expression de la peur conditionnée requière l'inhibition phasique des interneurones parvalbuminergiques du cortex préfrontal médian. En effet, leur inhibition désinhibe les cellules pyramidales préfrontales et synchronise leur activité en réinitialisant les oscillations thêta locales. Ces résultats mettent en évidence deux mécanismes neuronaux complémentaires induits par les interneurones parvalbuminergiques qui coordonnent et organisent avec précision l’activité neuronale des neurones pyramidaux du cortex préfrontal pour contrôler l'expression de la peur conditionnée. Ensemble, nos données montrent que la désinhibition joue un rôle important dans les comportements de peur en permettant l’association entre des informations comportementalement pertinentes, en sélectionnant les éléments spécifiques du circuit et en orchestrant l'activité neuronale des cellules pyramidales. / Learning and memory processes are controlled by specific neuronal circuits and elements. Numerous recent reports highlighted the important role of cortical circuits in the regulation of fear behaviour, however, the anatomical and functional characteristics of their neuronal components remain largely unknown. During my thesis, we used single unit recordings and optogenetic manipulations of specific neuronal elements in behaving mice, to show that both the auditory cortex and the medial prefrontal cortex contain a disinhibitory microcircuit required respectively for the acquisition and the expression of conditioned fear memory. In both cases, parvalbumin-expressing interneurons constitute the central element of the circuit and are phasically inhibited during the presentation of the conditioned tone. From a functional point of view, we demonstrated that this inhibition induced the disinhibition of cortical pyramidal neurons by releasing the ongoing perisomatic inhibition mediated by parvalbumin-expressing interneurons onto pyramidal neurons. Thereby, this disinhibition allows the precise temporal regulation of pyramidal neurons excitability. In particular, we showed that the acquisition of associative fear memories depend on the recruitment of a disinhibitory microcircuit in the auditory cortex. Fear-conditioning-associated disinhibition in auditory cortex is driven by foot-shock-mediated inhibition of parvalbumin-expressing interneurons. Importantly, pharmacological or optogenetic blockade of pyramidal neuron disinhibition abolishes fear learning. Together, these data suggest that disinhibition is an important mechanism underlying learning and information processing in cortical circuits. Secondly, in the medial prefrontal cortex, we demonstrated that expression of fear behaviour is causally related to the phasic inhibition of prefrontal parvalbumin-expressing interneurons. Inhibition of parvalbumin-expressing interneuron activity disinhibits prefrontal pyramidal neurons and synchronizes their firing by resetting local theta oscillations, leading to fear expression. These results identify two complementary neuronal mechanisms both mediated by prefrontal parvalbumin-expressing interneurons that precisely coordinate and enhance the neuronal efficiency of prefrontal pyramidal neurons to drive fear expression. Together these data highlighted the important role played by neuronal disinhibition in fear behaviour by binding behavioural relevant information, selecting specific circuit elements and orchestrating pyramidal neurons activity.

A epilepsia do lobo temporal (ELT) é a forma mais comum de epilepsia e a mais resistente ao tratamento medicamentoso. Existem diversos tipos de drogas anti-epilépticas usadas no controle das crises. Entretanto, em alguns casos, esse tipo de tratamento não é eficaz e a cirurgia para remoção da zona epileptogênica (ZE) pode ser uma alternativa recomendada. A ZE é definida como aquela onde as crises são originadas. Trata-se de um conceito teórico e, atualmente, não existem técnicas capazes de delimitá-la precisamente. Na prática, exames de EEG, vídeo-EEG, MEG, SPECT, PET e diversas técnicas de MRI, em especial as funcionais, têm sido usados para mapear zonas relacionadas à ZE. Contudo, em alguns casos, os resultados permanecem não convergentes e a determinação da ZE inconclusiva. Desse modo, é evidente a importância do surgimento de novas metodologias para auxiliar a localização da ZE. Assim, pois, o objetivo deste trabalho foi desenvolver dois métodos para a avaliação da ZE, ambos baseados na imagem funcional por ressonância magnética. No primeiro, investigamos possíveis alterações da resposta hemodinâmica (HRF) quando da modulação da pressão parcial de CO2. Para tanto, fizemos um estudo sobre 22 pacientes com ELT e 10 voluntários assintomáticos modulando a pressão parcial de CO2 sanguíneo cerebral por um protocolo de manobra de pausa respiratória e outro de inalação passiva de CO2/ar. Os resultados mostram que o tempo de onset da HRF tende a ser maior e a amplitude da HRF tende a ser menor em áreas do lobo temporal de pacientes com ELT quando comparados com os dados de voluntários assintomáticos. Além disso, os resultados mostram mapas de onset individuais coincidentes com exames de SPECT ictal. O segundo estudo foi baseado em medidas de EEG-fMRI simultâneo. Neste, avaliamos a relação entres as potências dos ritmos cerebrais alfa e teta (EEG) e o contraste BOLD (fMRI) de 41 pacientes com ELT e 7 voluntários assintomáticos em estado de repouso. A análise da banda alfa mostrou correlações negativas nos lobos occipital, parietal e frontal tanto nos voluntários quanto nos pacientes com ELT. As correlações positivas nos voluntários foram dispersas e variáveis em ambos hemisférios cerebrais. Por outro lado, encontramos forte correlação positiva no tálamo e ínsula dos pacientes com ELT. Na análise da banda teta observamos correlações positivas bilaterais nos giros pré e pós central de voluntários. Ainda, foram observados clusters no cíngulo anterior, tálamo, ínsula, putamen, em regiões parietais superior, frontais e giros temporais. Também, utilizamos um cálculo de índice de lateralização (IL) no lobo temporal em confrontos entre pacientes com ELT à direita, pacientes com ELT à esquerda e voluntários assintomáticos. Verificamos que os ILs, utilizando os clusters obtidos nas análises em teta, foram coincidentes com o diagnóstico clínico prévio da localização da ZE em todas as análises dos grupos de pacientes com ELT à direita, e na maioria do grupo de pacientes com ELT à esquerda. De forma geral, verificamos que o método de hipercapnia se mostrou ferramenta interessante na localização da ZE comprovada pelos coincidentes achados pela avaliação de SPECT. Inferimos que o maior tempo de onset e menor amplitude da HRF observadas nos pacientes em relação a voluntários possam estar relacionados a um stress vascular devido à recorrência de crises. Já o método de ritmicidade alfa e teta proposto parece promissor para ser usado na determinação da lateralização da ZE em pacientes com ELT. / Temporal lobe epilepsy (TLE) is the most common and resistant form of epilepsy to anti-epileptic drug. There are several types of anti-epileptic drugs used in seizure control. However, in some cases drug treatment is not effective and surgery to remove the epileptogenic zone (EZ) is a recommended alternative. EZ is a theoretical concept and there are many techniques that have been applied to enclose it precisely. In practice, EEG, video-EEG, MEG, SPECT, PET and various MRI techniques, especially functional MRI (fMRI), have been used to map areas related to EZ. However, in some cases, the results remain non-convergent and the EZ, undefined. Therefore, the use of new methodologies to assist the location of EZ have been proposed. Herein, our goal was to develop two methods for assessing the EZ. The first one was designed to access changes in the hemodynamic response (HRF) of the EZ in response to hypercapnia. 22 patients with TLE and 10 normal volunteers were evaluated by modulating the partial pressure of CO2 during the acquisition of fMRI in a breathing holding and a passive inhalation CO2/air protocols. The results show increased onset times and decreased amplitude of the HRF in the temporal lobe of TLE patients compared with asymptomatic volunteers. Moreover, most patients had onset maps coincident with ictal SPECT localizations. The second proposed study was based on simultaneous EEG-fMRI acquisitions. The relationship between powers of alpha and theta bands (EEG) and BOLD contrast (fMRI) was investigated in 41 TLE patients and 7 healthy controls. Alpha band results show a consistent negative correlation in the occipital, parietal and frontal lobes both in controls and TLE patients. In addition, controls show disperse positive correlations in both hemispheres. On the other hand, TLE patients presented strong positive correlations in the thalamus and insula. Theta band analysis, in controls, primarily show positive correlations in bilateral pre-and post-central gyri. In patients, robust positive correlations were observed in the anterior cingulate gyrus, thalamus, insula, putamen, superior parietal, frontal and temporal gyri. Moreover, the lateralization index (LI) indicates a coincidence between the side of the EZ evaluated by clinical diagnosis and clusters detected in the theta band. In conclusion, the hipercapnia study showed to be an interesting tool in locating EZ and the results are similar to SPECT findings. The longer onset and lower amplitude of the HRF observed in patients may be related to a vascular stress due to the recurrence of seizures. Furthermore, alpha and theta rhythms may be a promising tool to be used in determining the lateralization of EZ in patients with TLE.

[pt] Estudamos a variedade M3 de curvas de gênero três em característica dois. Para cada uma destas curvas calculamos seus possíveis números de pontos de Weierstrass, seus pesos, normalizações de muitos loci no espaço de moduli, entre outras coisas. Tratamos ainda do conceito de ponto de Galois. / [en] We study the variety M3 of curves of genus three in characteristic two. For each of the curves we compute the possible number of Weierstrass points, their weights, normalizations of many loci in the moduli space, and so on. We also deal with the concept of a Galois point.

The functions of sleep remain enigmatic. One of the dominant, yet more contentious hypotheses is that sleep is involved in memory consolidation. A large body of evidence supports the role of rapid eye movement (REM) sleep in memory consolidation, especially in rodents. In humans, the role of REM sleep in memory consolidation has also been investigated, however it is unclear if it supports only one type of memory, or consolidation for several memory systems. Recent evidence suggests that non-REM is also involved in memory consolidation. The role of theta activity during REM and sleep spindles during non-REM may provide electrophysiological signatures reflecting memory consolidation processes. The studies presented here attempt to further investigate the electrophysiological characteristics of the learning-dependent changes in REM and slow wave sleep (SWS) in rats. A 2-stage model of memory consolidation is outlined here, and both steps of the model were investigated. Consistent with previous studies, REM increases were observed following avoidance training. During this period, theta power during REM sleep was increased compared to non-learning rats. Increased sleep spindle density during SWS was observed following REM increases. When REM sleep was suppressed by infusing the GABAB agonist baclofen into the pedunculopontine nucleus, avoidance performance acquisition was impaired. Baseline sleep spindles predicted whether rats were able to learn to make avoidance responses. Results suggest that both REM and SWS may be sequentially involved in memory consolidation processes. Discrete periods (windows) exist for REM and SWS when memory consolidation processes appear to take place. Theta activity during REM sleep from 17- 20 h on the first post-training day and sleep spindles during SWS from 21-24 h on the first post- training day are increased in learning rats and are related to memory performance. / Thesis (Ph.D, Neuroscience Studies) -- Queen's University, 2009-10-26 12:07:47.515

Les mécanismes cellulaires et moléculaires qui sous-tendent la mémoire et l’apprentissage chez les mammifères sont incomplètement compris. Le rythme thêta de l’hippocampe constitue l’état « en ligne » de cette structure qui est cruciale pour la mémoire déclarative. Dans la région CA1 de l’hippocampe, les interneurones inhibiteurs LM/RAD démontrent des oscillations de potentiel membranaire (OPM) intrinsèques qui pourraient se révéler importantes pour la génération du rythme thêta. Des travaux préliminaires ont suggéré que le courant K+ I(A) pourrait être impliqué dans la génération de ces oscillations. Néanmoins, peu de choses sont connues au sujet de l’identité des sous-unités protéiques principales et auxiliaires qui soutiennent le courant I(A) ainsi que l’ampleur de la contribution fonctionnelle de ce courant K+ dans les interneurones. Ainsi, cette thèse de doctorat démontre que le courant I(A) soutient la génération des OPM dans les interneurones LM/RAD et que des protéines Kv4.3 forment des canaux qui contribuent à ce courant. De plus, elle approfondit les connaissances sur les mécanismes qui régissent les interactions entre les sous-unités principales de canaux Kv4.3 et les protéines accessoires KChIP1. Finalement, elle révèle que la protéine KChIP1 module le courant I(A)-Kv4.3 natif et la fréquence de décharge des potentiels d’action dans les interneurones. Nos travaux contribuent à l’avancement des connaissances dans le domaine de la modulation de l’excitabilité des interneurones inhibiteurs de l’hippocampe et permettent ainsi de mieux saisir les mécanismes qui soutiennent la fonction de l’hippocampe et possiblement la mémoire chez les mammifères. / Cellular and molecular mechanisms underlying learning and memory in mammals are incompletely understood. The theta rhythm in the hippocampus constitutes the « on-line » state of this structure which is crucial for declarative memory. In the CA1 hippocampal area, LM/RAD inhibitory interneurons exhibit intrinsic membrane potential oscillations (MPOs) that could be important for the generation of theta rhythm. Preliminary work suggested that K+ current I(A) could be involved in the generation of these oscillations. Nevertheless, little is known about the identity of the principal and auxiliary protein subunits underlying I(A) current and the extent of the functional contribution of this K+ current in hippocampal interneurons. Thus, this Ph.D. thesis shows that I(A) current underlies MPO generation in LM/RAD interneurons and that Kv4.3 proteins form channels that contribute to this current. Also, it deepens the knowledge on the mechanism controlling the interactions between Kv4.3 channel-forming principal subunits and KChIP1 auxiliary proteins. Finally, it reveals that KChIP1 modulates native I(A)-Kv4.3 current and the action potential discharge frequency in interneurons. Our work takes part in advancing the knowledge on the field of modulation of excitability in hippocampal inhibitory interneurons and allows a better understanding of the mechanisms underlying the function of the hippocampus and possibly memory in mammals.

L'expérience Double Chooz utilise les antineutrinos émis par la centrale nucléaire de Chooz (France) pour mesurer l'angle de mélange θ13. La mesure précise de la disparition des antineutrinos se fera en utilisant deux détecteurs placés à différentes distances du réacteur. La prise de données avec le détecteur lointain se fait depuis avril 2011 alors que le détecteur proche est en cours de construction. Les données prise avec le détecteur lointain entre le 13 avril 2011 et le 30 mars 2012 ont été analysées. Une indication de la disparition d'antineutrinos électroniques, en accord avec l'hypothèse d'oscillation des neutrinos, a été trouvée. La valeur du paramètre de mélange mesurée est sin2 (2θ13) est 0,109 ± 0,030 (stat.) ± 0,025 (syst.). Cette thèse présente une description précise de l'expérience Double Chooz, avec une attention particulière portée sur le détecteur lointain et son système d'acquisition. Le principal objectif de la thèse est l'étude précise du bruit de fond corrélé affectant la sélection des antineutrinos et son impact sur la mesure de le paramètre de mélange. Une description générale du scénario expérimental actuel visant à la caractérisation de l'oscillation des neutrinos est également fournie, en se concentrant sur les résultats récents obtenus dans ce domaine.

Digital subscriber lines (DSL) have revolutionised the provision of high speed data over the ‘last mile’. Subscribers demand even more bandwidth and the penetration of the service is now nearly universal. While it is feasible to provide improved broadband services on the new very high speed DSL, such as VDSL2/3, one of the greatest challenges to further improvements in speed is the problem of crosstalk. Operating over the unused higher frequencies of the twisted pair network, this technology is subjected to electromagnetic coupling among the wires, limiting the DSL data rate and service reach. Crosstalk suppression methods such as zero-forcing or decision feedback mainly use block processing. However, to cope with the time-varying VDSL environment huge computational costs can be incurred. In contrast, adaptive processing approaches are much simpler and are more beneficial to track such a channel environment. An adaptive canceller uses a training sequence and the convergence speed depends on the number of crosstalk coefficients it has to estimate. In a populated DSL binder, only a few of the crosstalking neighbours to a particular user are significant. With the aim to reduce the computational complexity in such environments, this thesis introduces the concept of detection-guided adaptive crosstalk cancellation for DSL. We propose a least-squares test feature to detect and concentrate the adaptation only on the dominant crosstalking coefficients. In comparison to conventional adaptive cancellers, the cancellers proposed in this thesis demonstrate early convergence. Thus, by incorporating the test feature, these cancellers have to detect only the most significant canceller coefficients and therefore, the length of the training sequence is reduced. Together with enhanced adaptive cancellation with a low run-time complexity and improved convergence, the greatest advantage obtained here is in the bandwidth efficiency. While enhanced adaptive cancellation is a bandwidth-efficient approach, the frequent re-transmission of training sequences may still be required for a rapidly changing VDSL channel. Again, this can be a disadvantage in terms of bandwidth consumption. To overcome this difficulty, we propose fast-converging unsupervised cancellers with an aim to improve the bandwidth efficiency by not transmitting a training sequence. An added advantage obtained here is that this would enable Internet service providers to include multiple or improved broadband services within a single subscription. Certain properties of the DSL channel ensure the communication channel is properly conditioned. This ensures the basis vectors of the channel matrix are near-orthogonal and hence, the linear cancellers, such as zero-forcing perform near-optimally. However, this is not the case with wireless channels. We investigate user detection in wireless channels using the principle of lattice reduction. User detection can also be seen as a search for the closest vector point in the lattice of received symbols. Though a maximum likelihood (ML) detector facilitates optimal user-detection, it has exponential complexity. We identify that the closest vector problem can be cast as a non-linear optimisation problem. Using the periodicity of the maximum likelihood function, we first present a novel algorithm that approximates the ML function using the Taylor series expansion of a suitable cosine function. With the aim of minimising the approximation error, we represent the ML function as a Fourier Series expansion and later, propose another approximation using Jacobi theta functions. We study the performance of these approximations when subjected to a suitable unconstrained optimisation algorithm. Through simulations, we demonstrate that the newly-developed approximations perform better than the conventional cancellers, close to the ML and, importantly, converging in polynomial time.

Digital subscriber lines (DSL) have revolutionised the provision of high speed data over the ‘last mile’. Subscribers demand even more bandwidth and the penetration of the service is now nearly universal. While it is feasible to provide improved broadband services on the new very high speed DSL, such as VDSL2/3, one of the greatest challenges to further improvements in speed is the problem of crosstalk. Operating over the unused higher frequencies of the twisted pair network, this technology is subjected to electromagnetic coupling among the wires, limiting the DSL data rate and service reach. Crosstalk suppression methods such as zero-forcing or decision feedback mainly use block processing. However, to cope with the time-varying VDSL environment huge computational costs can be incurred. In contrast, adaptive processing approaches are much simpler and are more beneficial to track such a channel environment. An adaptive canceller uses a training sequence and the convergence speed depends on the number of crosstalk coefficients it has to estimate. In a populated DSL binder, only a few of the crosstalking neighbours to a particular user are significant. With the aim to reduce the computational complexity in such environments, this thesis introduces the concept of detection-guided adaptive crosstalk cancellation for DSL. We propose a least-squares test feature to detect and concentrate the adaptation only on the dominant crosstalking coefficients. In comparison to conventional adaptive cancellers, the cancellers proposed in this thesis demonstrate early convergence. Thus, by incorporating the test feature, these cancellers have to detect only the most significant canceller coefficients and therefore, the length of the training sequence is reduced. Together with enhanced adaptive cancellation with a low run-time complexity and improved convergence, the greatest advantage obtained here is in the bandwidth efficiency. While enhanced adaptive cancellation is a bandwidth-efficient approach, the frequent re-transmission of training sequences may still be required for a rapidly changing VDSL channel. Again, this can be a disadvantage in terms of bandwidth consumption. To overcome this difficulty, we propose fast-converging unsupervised cancellers with an aim to improve the bandwidth efficiency by not transmitting a training sequence. An added advantage obtained here is that this would enable Internet service providers to include multiple or improved broadband services within a single subscription. Certain properties of the DSL channel ensure the communication channel is properly conditioned. This ensures the basis vectors of the channel matrix are near-orthogonal and hence, the linear cancellers, such as zero-forcing perform near-optimally. However, this is not the case with wireless channels. We investigate user detection in wireless channels using the principle of lattice reduction. User detection can also be seen as a search for the closest vector point in the lattice of received symbols. Though a maximum likelihood (ML) detector facilitates optimal user-detection, it has exponential complexity. We identify that the closest vector problem can be cast as a non-linear optimisation problem. Using the periodicity of the maximum likelihood function, we first present a novel algorithm that approximates the ML function using the Taylor series expansion of a suitable cosine function. With the aim of minimising the approximation error, we represent the ML function as a Fourier Series expansion and later, propose another approximation using Jacobi theta functions. We study the performance of these approximations when subjected to a suitable unconstrained optimisation algorithm. Through simulations, we demonstrate that the newly-developed approximations perform better than the conventional cancellers, close to the ML and, importantly, converging in polynomial time.

Digital subscriber lines (DSL) have revolutionised the provision of high speed data over the ‘last mile’. Subscribers demand even more bandwidth and the penetration of the service is now nearly universal. While it is feasible to provide improved broadband services on the new very high speed DSL, such as VDSL2/3, one of the greatest challenges to further improvements in speed is the problem of crosstalk. Operating over the unused higher frequencies of the twisted pair network, this technology is subjected to electromagnetic coupling among the wires, limiting the DSL data rate and service reach. Crosstalk suppression methods such as zero-forcing or decision feedback mainly use block processing. However, to cope with the time-varying VDSL environment huge computational costs can be incurred. In contrast, adaptive processing approaches are much simpler and are more beneficial to track such a channel environment. An adaptive canceller uses a training sequence and the convergence speed depends on the number of crosstalk coefficients it has to estimate. In a populated DSL binder, only a few of the crosstalking neighbours to a particular user are significant. With the aim to reduce the computational complexity in such environments, this thesis introduces the concept of detection-guided adaptive crosstalk cancellation for DSL. We propose a least-squares test feature to detect and concentrate the adaptation only on the dominant crosstalking coefficients. In comparison to conventional adaptive cancellers, the cancellers proposed in this thesis demonstrate early convergence. Thus, by incorporating the test feature, these cancellers have to detect only the most significant canceller coefficients and therefore, the length of the training sequence is reduced. Together with enhanced adaptive cancellation with a low run-time complexity and improved convergence, the greatest advantage obtained here is in the bandwidth efficiency. While enhanced adaptive cancellation is a bandwidth-efficient approach, the frequent re-transmission of training sequences may still be required for a rapidly changing VDSL channel. Again, this can be a disadvantage in terms of bandwidth consumption. To overcome this difficulty, we propose fast-converging unsupervised cancellers with an aim to improve the bandwidth efficiency by not transmitting a training sequence. An added advantage obtained here is that this would enable Internet service providers to include multiple or improved broadband services within a single subscription. Certain properties of the DSL channel ensure the communication channel is properly conditioned. This ensures the basis vectors of the channel matrix are near-orthogonal and hence, the linear cancellers, such as zero-forcing perform near-optimally. However, this is not the case with wireless channels. We investigate user detection in wireless channels using the principle of lattice reduction. User detection can also be seen as a search for the closest vector point in the lattice of received symbols. Though a maximum likelihood (ML) detector facilitates optimal user-detection, it has exponential complexity. We identify that the closest vector problem can be cast as a non-linear optimisation problem. Using the periodicity of the maximum likelihood function, we first present a novel algorithm that approximates the ML function using the Taylor series expansion of a suitable cosine function. With the aim of minimising the approximation error, we represent the ML function as a Fourier Series expansion and later, propose another approximation using Jacobi theta functions. We study the performance of these approximations when subjected to a suitable unconstrained optimisation algorithm. Through simulations, we demonstrate that the newly-developed approximations perform better than the conventional cancellers, close to the ML and, importantly, converging in polynomial time.