Downscaling of technology causes signal integrity problems due to crosstalk between closely-spaced interconnect lines. Existing crosstalk estimation and optimization techniques operate at the layout-level of circuits and fail to utilize the efficient design-space exploration at the high-level. To address this, we propose word-level statistical techniques which estimate crosstalk between bus lines: (1) Given a data stream, the first technique simply counts the number of crosstalk events on each bus line. The drawback of this technique is that the execution time is proportional to the stream length. This is overcome by the second enumerative technique which is purely statistical in nature. (2) Given word-level statistics, we estimate the bit-level crosstalk probability of bus lines. (3) We further speedup the statistical method using a non-enumerative technique by linearizing its complexity with respect to the bus width. Average errors of less than 15% are obtained for bus-widths ranging from 8b to 32b while execution times are reduced by two orders of magnitude, compared to HSPICE. We then measure the crosstalk susceptibility of nets in the post global routing phase (performed using CADENCE Silicon Ensemble), prior to detailed routing using (1) Pt , the probability of crosstalk on victims in different regions along their route; and (2) Vpeak, the maximum crosstalk noise amplitude experienced by victims along their route. Pt is estimated using the fast and accurate statistical estimator we previously proposed. Vpeak is estimated by predicting the cross-coupling capacitances between neighboring wires, using their global routing information. Average errors are less than 8%, compared to HSPICE. We combine the crosstalk susceptibility values from individual regions along a victim wire’s route, to obtain a single susceptibility value for the entire wire. Further, we propose a register binding technique during high-level synthesis to minimize crosstalk at the register outputs in the RT-level design. It involves modification of the cliquepartitioning algorithm to make crosstalk-aware choices of edges to be mapped to the same register. RT-level comparisons between the regular and crosstalk-aware designs show upto 16% reduction in crosstalk activity at the register outputs.

Três ensembles, respectivamente relacionados com as distribuições Gaussiana, Lognormal e de Levy, são abordados neste trabalho primordialmente do ponto de vista da termodinâmica de seus espectros. Novas expressões para as grandezas termodinâmicas sao encontradas para os ensembles de Stieltjes e de Bertuola-Pato, e a conexão destes com os ensembles Gaussianos e estabelecida. Esta tese também se compromete com a continuação do desenvolvimento e aprimorarão do ensemble generalizado de Bertuola-Pato, estendendo alguns resultados para os ensembles simplifico e unitário generalizados, alem do ortogonal generalizado já introduzido anteriormente por A. C. Bertuola e M. P. Pato. / Three ensembles, related to the Gaussian, the Lognormal and the L´evy distributions respectively, have been studied in this work and were investigated most of all in what concerns their spectral thermodynamics. New expressions for the thermodynamics quantities were found for the Stieltjes and the Bertuola-Pato ensembles, and the connection with the gaussian ensembles is established. This work concerned with the development continuity and with the improvement of Bertuola-Pato generalized ensemble, extending some of the results to the simplectic and unitary generalized ensembles, besides the orthogonal generalized ensemble introduced before by A. C. Bertuola and M. P. Pato.

Três ensembles, respectivamente relacionados com as distribuições Gaussiana, Lognormal e de Levy, são abordados neste trabalho primordialmente do ponto de vista da termodinâmica de seus espectros. Novas expressões para as grandezas termodinâmicas sao encontradas para os ensembles de Stieltjes e de Bertuola-Pato, e a conexão destes com os ensembles Gaussianos e estabelecida. Esta tese também se compromete com a continuação do desenvolvimento e aprimorarão do ensemble generalizado de Bertuola-Pato, estendendo alguns resultados para os ensembles simplifico e unitário generalizados, alem do ortogonal generalizado já introduzido anteriormente por A. C. Bertuola e M. P. Pato. / Three ensembles, related to the Gaussian, the Lognormal and the L´evy distributions respectively, have been studied in this work and were investigated most of all in what concerns their spectral thermodynamics. New expressions for the thermodynamics quantities were found for the Stieltjes and the Bertuola-Pato ensembles, and the connection with the gaussian ensembles is established. This work concerned with the development continuity and with the improvement of Bertuola-Pato generalized ensemble, extending some of the results to the simplectic and unitary generalized ensembles, besides the orthogonal generalized ensemble introduced before by A. C. Bertuola and M. P. Pato.

O estudo de matrizes aleatórias na física tradicionalmente ocorre no contexto dos modelos de Wigner e na estatística por modelos de Wishart, que se conectam através do threefold way de Dyson para matrizes aleatórias reais, complexas e de quaternios indexadas respectivamente pelo índice B = 1; 2; 4 de Dyson. Estudos recentes mostraram o caminho para que estes modelos fossem generalizados para valores reais de B, permitindo o estudo de ensembles com índice arbitrário. Neste trabalho, estudamos as propriedades estatísticas destes sistemas e exploramos a física subjacente nos modelos de Wigner e Wishart e investigamos, através de cálculos numéricos, os efeitos de localização nos modelos de geral. Também introduzimos quebras na simetria desta nova forma e estudamos numericamente os resultados da estatística dos sistemas perturbados. / The study of random matrices in physics has traditionally occurred in the context of Wigner models and in statistics by Wishart models, which are connected through Dyson\'s threefold way for real, complex and quaternion random matrices index by the Dyson _ = 1; 2; 4 index, respectively. Recent studies have shown the way by which these models are generalized for real values of _, allowing for the study the ensembles with arbitrary index. In this work, we study the statistical properties of these systems and explore the underlying physics in Wigner\'s and Wishart\'s models through and investigate through numerical calculations the e_ects of localization in general _ models. We also introduce symmetry breaks in this new form and study numerically the results of the statistics of the disturbed systems.

O estudo de matrizes aleatórias na física tradicionalmente ocorre no contexto dos modelos de Wigner e na estatística por modelos de Wishart, que se conectam através do threefold way de Dyson para matrizes aleatórias reais, complexas e de quaternios indexadas respectivamente pelo índice B = 1; 2; 4 de Dyson. Estudos recentes mostraram o caminho para que estes modelos fossem generalizados para valores reais de B, permitindo o estudo de ensembles com índice arbitrário. Neste trabalho, estudamos as propriedades estatísticas destes sistemas e exploramos a física subjacente nos modelos de Wigner e Wishart e investigamos, através de cálculos numéricos, os efeitos de localização nos modelos de geral. Também introduzimos quebras na simetria desta nova forma e estudamos numericamente os resultados da estatística dos sistemas perturbados. / The study of random matrices in physics has traditionally occurred in the context of Wigner models and in statistics by Wishart models, which are connected through Dyson\'s threefold way for real, complex and quaternion random matrices index by the Dyson _ = 1; 2; 4 index, respectively. Recent studies have shown the way by which these models are generalized for real values of _, allowing for the study the ensembles with arbitrary index. In this work, we study the statistical properties of these systems and explore the underlying physics in Wigner\'s and Wishart\'s models through and investigate through numerical calculations the e_ects of localization in general _ models. We also introduce symmetry breaks in this new form and study numerically the results of the statistics of the disturbed systems.

Ce mémoire est composé de deux articles portant respectivement sur les chaînes de spin–1/2 critiques quantiques d’Ising–Kawasaki et de Fredkin. La première chaîne provient d’une chaîne d’Ising classique couplée à un bain thermique par une dynamique de Kawasaki. La deuxième chaîne est une généralisation de la chaîne fortement intriquée de Motzkin. Les deux chaînes sont étudiées avec des conditions frontière périodiques. L’objectif principal est de caractériser la dynamique de ces deux chaînes. D’abord, les exposants critiques dynamiques obtenus suggèrent que, à basse énergie, les deux systèmes comportent de multiples dynamiques. Dans les secteurs à un et deux magnons, nous obtenons un exposant z = 2 pour les deux chaînes. Pour la chaîne d’Ising–Kawasaki, à fort couplage, l’exposant dynamique global est plutôt z = 3. Pour la chaîne de Fredkin, l’exposant dépend de la parité de la longueur de la chaîne. Nous obtenons z = 3.23 ± 0.20 dans le cas pair et z = 2.71 ± 0.09 dans le cas impair. Ensuite, les symétries des systèmes permettent d’obtenir les états propres comme solutions d’ondes de spin dans les secteurs à un et deux magnons. Ces solutions sont présentées pour les deux chaînes et nous étudions leurs continuums de dispersion. Cependant, l’étude de la statistique des niveaux d’énergie indique que de telles solutions ne peuvent être obtenues dans les secteurs de polarisation plus basse. En effet, la distribution des espacements des niveaux d’énergie normalisés dans les secteurs faiblement polarisés correspond à une distribution de Wigner. Selon la conjecture de Berry-Tabor, cela indique que les deux systèmes ne sont pas intégrables. Finalement, pour la chaîne de Fredkin, nous étudions la dispersion des états faiblement excités. Cette dispersion est anomale puisqu’elle dépend de la longueur de la chaîne. En combinant le facteur d’échelle de l’amplitude des branches avec l’exposant dynamique à impulsion fixée, on trouve un exposant dynamique critique z = 2.8. / This thesis is composed of two scientific articles studying respectively the critial quantum spin-1/2 chains of Ising–Kawasaki and Fredkin. The first chain comes from a classical Ising chain coupled to a thermal bath via the Kawasaki dynamic. The second chain is a generalization of the strongly entangled Motzkin chain. The two chains are studied with periodic boundary conditions. The main objective is to characterize the dynamics of these two chains. First, the dynamical critical exponents obtained suggest that, at low energy, the two systems host multiple dynamics. In the one and two magnon sectors, we get an exponent z = 2 for the two chains. For the Ising–Kawasaki chain, at strong coupling, the global dynamical exponent is rather z = 3. For the Fredkin chain, the exponent depends on the parity of the length of the chain. We get z = 3.23 ± 0.20 in the even case and z = 2.71 ± 0.09 in the odd case. Afterwards, the symmetries of the systems make it possible to obtain the eigenstates as spin wave solutions in the one- and two- magnon sectors. These solutions are presented for the two chains and their dispersion continua is studied. However, the study of the statistics of energy levels indicates that such solutions cannot be obtained in lower polarization sectors. Indeed, the distribution of the spacings of the normalized energy levels in the weakly polarized sectors corresponds to a Wigner distribution. According to the Berry-Tabor conjecture, this indicates that the two systems are not integrable. Finally, for the Fredkin chain, we study the dispersion of weakly excited states. This dispersion is anomalous since it depends on the length of the chain. By combining the branch amplitude scaling with the fixed momentum dynamic exponent, we find a dynamical critical exponent z = 2.8.