The theory of infinite multiplication has been studied in the case of the Hawaiian earring group, and has been seen to simplify the description of that group. In this paper we try to extend the theory of infinite multiplication to other groups and give a few examples of how this can be done. In particular, we discuss the theory as applied to symmetric groups and braid groups. We also give an equivalent definition to K. Eda's infinitary product as the fundamental group of a modified wedge product.

Shuffled linear regression concerns itself with linear models with an unknown correspondence between the input and the output. This correspondence is usually represented by a permutation matrix II*. The model we are interested in has one more complication which is that the design matrix is itself latent and is observed with noise. This is considered as a type of errors-in-variables (EIV) model. Our interest lies in the recovery of the permutation matrix. We propose an estimator for II* based on the total least squares (TLS) technique, a common method of estimation used in EIV model. The estimation problem can be viewed as approximating one matrix by another of lower rank and the quantity it seeks to minimize is the sum of the smallest singular values squared. Due to identifiability issue, we evaluate the proposed estimator by the normalized Procrustes quadratic loss which allows for an orthogonal rotation of the estimated design matrix. Our main result provides an upper bound on this quantity which states that it is required that the signal-to-noise ratio to go to infinity in order for the loss to go to zero. On the computational front, since the problem of permutation recovery is NP-hard to solve, we propose a simple and efficient algorithm named alternating LAP/TLS algorithm (ALTA) to approximate the estimator, and we use it to empirically examine the main result. The main idea of the algorithm is to alternate between estimating the unknown coefficient matrix using the TLS method and estimating the latent permutation matrix by solving a linear assignment problem (LAP) which runs in polynomial time. Lastly, we propose a hypothesis testing procedure based on graph matching which we apply in the field of digital humanities, on character social networks constructed from novel series.

This paper suggests that a reconceptualization of the structuralist framework of story anddiscourse, the foundational concept of narrative theory, is needed in order to account for postmodernist texts. It reframes story and discourse as an “intra-textual” approach, wherein individual narrative strata are understood as equal and interrelated voices within a text, thus refusing to privilege any one aspect over another. In other words, I work to build a method of narrative analysis that interrogates form as it manifests across various levels of narrative, uncovering the patterns, connections, fissures and inconsistencies that emerge within and between the various levels in order to produce meaning. The paper then employs this method through a reading of Samuel Beckett’s postwar Trilogy that argues against traditional critical interpretations of the text, thus presenting a new possibility for historicizing Beckett at the midcentury mark.

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Noncoherent modulation is an important technique in wireless communication systems. Although noncoherent modulation usually does not perform as well as its coherent counterpart it is practical and useful in some applications, such as paging systems. In this thesis we investigate ways to improve the performance of noncoherent FSK in narrowband channels. It is shown that FSK permutation modulation has better spectral efficiency than conventional FSK modulation" but with the tradeoff on reduced energy efficiency. To overcome this problem, we apply trellis-coded modulation (TCM) , which is a combined technology of convolutional coding and modulation, to FSK permutation. TCM was originally designed for coherent modulation. The application of TCM to permutation modulation retains the fundamental concepts of TCM. The simulation results show that trellis-coded permutation modulation provides a better combination of energy efficiency and spectral efficiency than conventional FSK noncoherent demodulation. / Master of Science

Digital signal processing systems demand higher computational performance and more operations per second than ever before, and this trend is not expected to end any time soon. Processing architectures must adapt in order to meet these demands. The two techniques most prevalent for achieving throughput constraints are parallel processing and stream processing. By combining these techniques, significant throughput improvements have been achieved. These preliminary results apply to specific applications, and general tools for automation are in their infancy. In this dissertation techniques are developed to automatically generate efficient parallel streaming hardware architectures. / Ph. D.

S'il fallait résumer le sujet de cette thèse en une expression, cela pourrait être quelque chose comme: phénomènes de grande dimension (mais néanmoins finie) en théorie quantique de l'information. Cela étant dit, essayons toutefois de développer brièvement. La physique quantique a inéluctablement affaire à des objets de grande dimension. Partant de cette observation, il y a, en gros, deux stratégies qui peuvent être adoptées: ou bien essayer de ramener leur étude à celle de situations de plus petite dimension, ou bien essayer de comprendre quels sont les comportements universels précisément susceptibles d'émerger dans ce régime. Nous ne donnons ici notre préférence à aucune de ces deux attitudes, mais au contraire oscillons constamment entre l'une et l'autre. Notre but dans la première partie de ce manuscrit (Chapitres 5 et 6) est de réduire autant que possible la complexité de certains processus quantiques, tout en préservant, évidemment, leurs caractéristiques essentielles. Les deux types de processus auxquels nous nous intéressons sont les canaux quantiques et les mesures quantiques. Dans les deux cas, la complexité d'une transformation est mesurée par le nombre d'opérateurs nécessaires pour décrire son action, tandis que la proximité entre la transformation d'origine et son approximation est définie par le fait que, quel que soit l'état d'entrée, les deux états de sortie doivent être proches l'un de l'autre. Nous proposons des solutions universelles (basées sur des constructions aléatoires) à ces problèmes de compression de canaux quantiques et d'amenuisement de mesures quantiques, et nous prouvons leur optimalité. La deuxième partie de ce manuscrit (Chapitres 7, 8 et 9) est, au contraire, spécifiquement dédiée à l'analyse de systèmes quantiques de grande dimension et certains de leurs traits typiques. L'accent est mis sur les systèmes multi-partites et leurs propriétés ayant un lien avec l'intrication. Les principaux résultats auxquels nous aboutissons peuvent se résumer de la façon suivante: lorsque les dimensions des espaces sous-jacents augmentent, il est générique pour les états quantiques multi-partites d'être à peine distinguables par des observateurs locaux, et il est générique pour les relaxations de la notion de séparabilité d'en être des approximations très grossières. Sur le plan technique, ces assertions sont établies grâce à des estimations moyennes de suprema de processus gaussiens, combinées avec le phénomène de concentration de la mesure. Dans la troisième partie de ce manuscrit (Chapitres 10 et 11), nous revenons pour finir à notre état d'esprit de réduction de dimensionnalité. Cette fois pourtant, la stratégie est plutôt: pour chaque situation donnée, tenter d'utiliser au maximum les symétries qui lui sont inhérentes afin d'obtenir une simplification qui lui soit propre. En reliant de manière quantitative symétrie par permutation et indépendance, nous nous retrouvons en mesure de montrer le comportement multiplicatif de plusieurs quantités apparaissant en théorie quantique de l'information (fonctions de support d'ensembles d'états, probabilités de succès dans des jeux multi-joueurs non locaux etc.). L'outil principal que nous développons dans cette optique est un résultat de type de Finetti particulièrement malléable / If a one-phrase summary of the subject of this thesis were required, it would be something like: miscellaneous large (but finite) dimensional phenomena in quantum information theory. That said, it could nonetheless be helpful to briefly elaborate. Starting from the observation that quantum physics unavoidably has to deal with high dimensional objects, basically two routes can be taken: either try and reduce their study to that of lower dimensional ones, or try and understand what kind of universal properties might precisely emerge in this regime. We actually do not choose which of these two attitudes to follow here, and rather oscillate between one and the other. In the first part of this manuscript (Chapters 5 and 6), our aim is to reduce as much as possible the complexity of certain quantum processes, while of course still preserving their essential characteristics. The two types of processes we are interested in are quantum channels and quantum measurements. In both cases, complexity of a transformation is measured by the number of operators needed to describe its action, and proximity of the approximating transformation towards the original one is defined in terms of closeness between the two outputs, whatever the input. We propose universal ways of achieving our quantum channel compression and quantum measurement sparsification goals (based on random constructions) and prove their optimality. Oppositely, the second part of this manuscript (Chapters 7, 8 and 9) is specifically dedicated to the analysis of high dimensional quantum systems and some of their typical features. Stress is put on multipartite systems and on entanglement-related properties of theirs. We essentially establish the following: as the dimensions of the underlying spaces grow, being barely distinguishable by local observers is a generic trait of multipartite quantum states, and being very rough approximations of separability itself is a generic trait of separability relaxations. On the technical side, these statements stem mainly from average estimates for suprema of Gaussian processes, combined with the concentration of measure phenomenon. In the third part of this manuscript (Chapters 10 and 11), we eventually come back to a more dimensionality reduction state of mind. This time though, the strategy is to make use of the symmetries inherent to each particular situation we are looking at in order to derive a problem-dependent simplification. By quantitatively relating permutation symmetry and independence, we are able to show the multiplicative behavior of several quantities showing up in quantum information theory (such as support functions of sets of states, winning probabilities in multi-player non-local games etc.). The main tool we develop for that purpose is an adaptable de Finetti type result

Un code de permutations G(n,d) un sous-ensemble C de Sym(n) tel que la distance de Hamming D entre deux éléments de C est supérieure ou égale à d. Dans cette thèse, le groupe des isométries de (Sym(n),D) est déterminé et il est prouvé que ces isométries sont des automorphismes du schéma d'association induit sur Sym(n) par ses classes de conjugaison. Ceci mène, par programmation linéaire, à de nouveaux majorants de la taille maximale des G(n,d) pour n et d fixés et n compris entre 11 et 13. Des algorithmes de génération avec rejet d'objets isomorphes sont développés. Pour classer les G(n,d) non isométriques, des invariants ont été construits et leur efficacité étudiée. Tous les G(4,3) et les G(5,4) ont été engendrés à une isométrie près, il y en a respectivement 61 et 9445 (dont 139 sont maximaux et décrits explicitement). D’autres classes de G(n,d) sont étudiées. A permutation code G(n,d) is a subset C of Sym(n) such that the Hamming distance D between two elements of C is larger than or equal to d. In this thesis, we characterize the isometry group of the metric space (Sym(n),D) and we prove that these isometries are automorphisms of the association scheme induced on Sym(n) by the conjugacy classes. This leads, by linear programming, to new upper bounds for the maximal size of G(n,d) codes for n and d fixed and n between 11 and 13. We develop generating algorithms with rejection of isomorphic objects. In order to classify the G(n,d) codes up to isometry, we construct invariants and study their efficiency. We generate all G(4,3) and G(4,5)codes up to isometry; there are respectively 61 and 9445 of them. Precisely 139 out of the latter codes are maximal and explicitly described. We also study other classes of G(n,d)codes.