<p>Harnessing the power of data has been a driving force for computing in recently years. However, the non-vectorized or even non-Euclidean nature of certain data with complex structures also poses new challenges to the data science community. Topological data analysis (TDA) has proven effective in several scenarios for alleviating the challenges, by providing techniques that can reveal hidden structures and high-order connectivity for data. A central technique in TDA is called persistent homology, which provides intervals tracking the birth and death of topological features in a growing sequence of topological spaces. In this dissertation, we study the representative problem for persistent homology, motivated by the observation that persistent homology does not pinpoint a specific homology class or cycle born and dying with the persistence intervals. Furthermore, studying the representatives also leads us to new findings for related problems such as persistence computation.<br> </p> <p>First, we look into the representative problem for (standard) persistence homology and term the representatives as persistent cycles. We define persistent cycles as cycles born and dying with given persistence intervals and connect the definition to interval decomposition for persistence modules. We also look into the computation of optimal (minimum) persistent cycles which have guaranteed quality. We prove that it is NP-hard to compute minimum persistent p-cycles for the two types of intervals in persistent homology in general dimensions (p>1). In view of the NP-hardness results, we then identify a special but important class of inputs called weak (p+1)-pseudomanifolds whose minimum persistent p-cycles can be computed in polynomial time. The algorithms are based on a reduction to minimum (s,t)-cuts on dual graphs.<br> </p> <p>Second, we propose alternative persistent cycles capturing the dynamic changes of homological features born and dying with persistence intervals, which the previous persistent cycles do not reveal. We focus on persistent homology generated by piecewise linear (PL) functions and base our definition on an extension of persistence called the levelset zigzag persistence. We define a sequence of cycles called levelset persistent cycles containing a cycle between each consecutive critical points within the persistence interval. Due to the NP-harness results proven previously, we propose polynomial-time algorithms computing optimal sequences of levelset persistent p-cycles for weak (p+1)-pseudomanifolds. Our algorithms draw upon the idea of relating optimal cycles to min-cuts in a graph that we exploited earlier for standard persistent cycles. Note that levelset zigzag poses non-trivial challenges for the approach because a sequence of optimal cycles instead of a single one needs to be computed in this case.<br> </p> <p>Third, we investigate the computation of zigzag persistence on graph inputs, motivated by the fact that graphs model real-world circumstances in many applications where they may constantly change to capture dynamic behaviors of phenomena. Zigzag persistence, an extension of the standard persistence incorporating both insertions and deletions of simplices, is one appropriate instrument for analyzing such changing graph data. However, unlike standard persistence which admits nearly linear-time algorithms for graphs, such results for the zigzag version improving the general $O(m^\omega)$ time complexity are not known, where $\omega< 2.37286$ is the matrix multiplication exponent. We propose algorithms for zigzag persistence on graphs which run in near-linear time. Specifically, given a filtration of length m on a graph of size n, the algorithm for 0-dimension runs in $O(m\log^2 n+m\log m)$ time and the algorithm for 1-dimension runs in $O(m\log^4 n)$ time. The algorithm for 0-dimension draws upon another algorithm designed originally for pairing critical points of Morse functions on 2-manifolds. The correctness proof of the algorithm, which is a major contribution, is achieved with the help of representatives. The algorithm for 1-dimension pairs a negative edge with the earliest positive edge so that a representative 1-cycle containing both edges resides in all intermediate graphs.</p>

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Ultra wide band (UWB) is an extremely promising wireless technology for researchers and industrials. One of the most interesting is its high data rate and fading robustness due to selective frequency fading. However, beside such advantages, UWB system performance is highly affected by existing narrowband interference (NBI), undesired UWB signals and tone/multi-tone noises. For this reason, research about NBI cancellation is still a challenge to improve the system performance vs. receiver complexity, power consumption, linearity, etc. In this work, the two major receiver sections, i.e., analog (radiofrequency or RF) and digital (digital signal processing or DSP), were considered and new techniques proposed to reduce circuit complexity and power consumption, while improving signal parameters. In the RF section, different multiband UWB low-noise amplifier key design parameters were investigated like circuit configuration, input matching and desired/undesired frequency band filtering, highlighting the most suitable filtering package for efficient UWB NBI cancellation. In the DSP section, due to pulse transmitter signals, different issues like modulation type and level, pulse variety, shape and color noise/tone noise assumptions, were addressed for efficient NBI cancelation. A comparison was performed in terms of bit-error rate, signal-to-interference ratio, signal-to-noise ratio, and channel capacity to highlight the most suitable parameters for efficient DSP design. The optimum number of filters that allows the filter bandwidth to be reduced by following the required low sampling rate and thus improving the system bit error rate was also investigated.

In March 1933, the administration of United States President Franklin D. Roosevelt initiated a national relief program aimed at alleviating the disastrous effects ofthe Great Depression. The Civilian Conservation Corp (CCC) began as one of these programs designed to employ young men from all over the country and put them "back to work". The CCC provided these young men with training, a monthly stipend, and basic supplies such as food, clothing, and accommodations. After 1942, CCC camps were closed and many of these sites were abandoned or destroyed, leaving little historical documentation as to the experiences ofthe people involved. This project revolves around the archaeological investigations and data recovery of a CCC camp that was in operation from 1933-1942 in Zigzag, Oregon. This research analyzes the remains of the camp in order to gain further knowledge about this important period in American history, and more specifically, Oregon history. In assessing the material culture left behind, combined with the historical documents and oral history interviews, the goal of this project was to expand the historical and archaeological narrative of the CCC experience. More specifically, the aim of this research was to reveal the unwritten record of CCC camp life in a pivotal period of American history. The results of the historical archaeological research indicates that Camp Zigzag represents a community that participated in resistance related activities, such as drinking alcohol on camp property, but one that also adhered to the regulations of camp policy. Military-style order and training permeated even the surrounding architectural environment. The rituals of daily life in the structured order of the camp appear to have developed and formulated a strong sense of cohesion among the men. However, resistance-related items, such as alcohol bottles, suggest that Camp Zigzag enrollees resisted the authoritarian dynamic of the camp. Social drinking would have provided the men with a sense of solidarity and commonality that would have been maintained beyond the ideals of camp uniformity. This communal familiarity may have influenced the men's behaviour in daily camp routines, rituals, and work. Overall, the archaeological evidence depicts the Camp Zigzag community as united through the bonds of formality and in its resistance to it. Camp Zigzag offered a unique and unusually expansive window into not only the history of Oregon State, but into the history of our nation as a whole. The camp's archaeological assemblage remains as an important learning tool and its value far exceeds the humble nature of its material contents. It is a collection of untold stories representing the lives of young men and their families at a tumultuous turning point in American history.

Une des caractéristiques les plus remarquables des fluides géophysiques est la présence de stratification, c'est-à dire d'un gradient vertical de densité, qui induit une structure en couches horizontales. Lindborg (1999) et Billant & Chomaz (2001) ont proposé que la dynamique au sein de ces couches est tridimensionnelle et non bidimensionnelle comme cela était supposé auparavant. Les derniers ont aussi proposé un mécanisme de sélection de l' épaisseur de ces couches : l'instabilité zigzag qu'ils ont observée dans le cas particulier d'une paire de tourbillons contra-rotatifs. Cependant, les paires de tourbillons contra-rotatifs sont rarement observées dans l'océan et l'atmosphère contrairement aux couples de tourbillons co-rotatifs. De plus, l'appariement de tourbillons co-rotatifs est le processus dominant en turbulence bidimensionnelle responsable du transfert d'énergie des petites vers les grandes échelles. Au cours de ma thèse, je me suis donc intéressée à la dynamique de tourbillons co-rotatifs verticaux dans un fluide stratifié. Une instabilité associée au même effet physique que l'instabilité zigzag a été découverte. Elle décorrèle verticalement l'appariement de ces tourbillons, suggérant que l' instabilité zigzag est générique et affecte tout écoulement stratifié constitué de plus d'un tourbillon. L'analyse numérique de stabilité linéaire a montré que cette instabilité consiste en un mode déplacement et sélectionne une échelle verticale proportionnelle à l' échelle de flottabilité définie comme Fb, où F est le nombre de Froude horizontal et b la distance entre les deux tourbillons. Son taux de croissance est proportionnel au champ d'étirement créé par un tourbillon sur son compagnon. L'origine physique de cette instabilité a été identifiée grâce à une étude asymptotique : elle provient du couplage entre le mode de déplacement d'un tourbillon et le champ d'étirement généré par l'autre tourbillon. Observations expérimentales et Simulations Numériques Directes montrent que les non-linéarités n'inhibent pas le développement de l'instabilité zigzag qui entraîne bien une décorrelation verticale de l'écoulement selon une échelle proportionnelle à l'échelle de flottabilité. Enfin, l'effet de la rotation de la Terre a été étudié et nous avons montré que l'instabilité Zigzag reste active en présence de la force de Coriolis. Son taux de croissance est indépendant du taux de rotation. En régime fortement tournant, on retrouve l'approximation quasi-géostrophique : l'instabilité zigzag est similaire à l'instabilité ''tall-column'' découverte par Dritschel & de la Torre Juàrez (1996) et la longueur d'onde la plus instable est proportionnelle à Fb/Ro, où Ro est le nombre de Rossby. Cette instabilité affecte donc les écoulements géophysiques sur une large gamme d' échelles aussi bien dans l'océan que dans l'atmosphère.

Ultra wide band (UWB) is an extremely promising wireless technology for researchers and industrials. One of the most interesting is its high data rate and fading robustness due to selective frequency fading. However, beside such advantages, UWB system performance is highly affected by existing narrowband interference (NBI), undesired UWB signals and tone/multi-tone noises. For this reason, research about NBI cancellation is still a challenge to improve the system performance vs. receiver complexity, power consumption, linearity, etc. In this work, the two major receiver sections, i.e., analog (radiofrequency or RF) and digital (digital signal processing or DSP), were considered and new techniques proposed to reduce circuit complexity and power consumption, while improving signal parameters. In the RF section, different multiband UWB low-noise amplifier key design parameters were investigated like circuit configuration, input matching and desired/undesired frequency band filtering, highlighting the most suitable filtering package for efficient UWB NBI cancellation. In the DSP section, due to pulse transmitter signals, different issues like modulation type and level, pulse variety, shape and color noise/tone noise assumptions, were addressed for efficient NBI cancelation. A comparison was performed in terms of bit-error rate, signal-to-interference ratio, signal-to-noise ratio, and channel capacity to highlight the most suitable parameters for efficient DSP design. The optimum number of filters that allows the filter bandwidth to be reduced by following the required low sampling rate and thus improving the system bit error rate was also investigated.

Ultra wide band (UWB) is an extremely promising wireless technology for researchers and industrials. One of the most interesting is its high data rate and fading robustness due to selective frequency fading. However, beside such advantages, UWB system performance is highly affected by existing narrowband interference (NBI), undesired UWB signals and tone/multi-tone noises. For this reason, research about NBI cancellation is still a challenge to improve the system performance vs. receiver complexity, power consumption, linearity, etc. In this work, the two major receiver sections, i.e., analog (radiofrequency or RF) and digital (digital signal processing or DSP), were considered and new techniques proposed to reduce circuit complexity and power consumption, while improving signal parameters. In the RF section, different multiband UWB low-noise amplifier key design parameters were investigated like circuit configuration, input matching and desired/undesired frequency band filtering, highlighting the most suitable filtering package for efficient UWB NBI cancellation. In the DSP section, due to pulse transmitter signals, different issues like modulation type and level, pulse variety, shape and color noise/tone noise assumptions, were addressed for efficient NBI cancelation. A comparison was performed in terms of bit-error rate, signal-to-interference ratio, signal-to-noise ratio, and channel capacity to highlight the most suitable parameters for efficient DSP design. The optimum number of filters that allows the filter bandwidth to be reduced by following the required low sampling rate and thus improving the system bit error rate was also investigated.

La turbulence fortement influencée par une stratification stable en densité est étudiée expérimentalement, numériquement et théoriquement. Ce type de turbulence est rencontré dans l'atmosphère et les océans dans une gamme d'échelles intermédiaires où la force de Coriolis est négligeable. Dans une première partie, la transition à la turbulence d'un écoulement simple : une paire de tourbillons colonnaires contra-rotatifs est étudiée. Des Simulations Numériques Directes (DNS) montrent que lorsque la dissipation est suffisamment faible, deux instabilités secondaires, de cisaillement et gravitationnelle, se développent après l'instabilité zigzag. La taille caractéristique des tourbillons de Kelvin-Helmholtz est de l'ordre de l'échelle de flottabilité. Ces deux instabilités mènent à une transition à la turbulence qui présente des spectres anisotropes similaires à ceux associés à la turbulence stratifiée pleinement développée. Pour la première fois, un retour à l'isotropie est observé pour des échelles inférieures à l'échelle d'Ozmidov. Dans une deuxième partie, un écoulement pleinement turbulent forcé par plusieurs générateurs de dipoles est étudié. Les expériences aux plus grands nombres de Reynolds de flottabilité ont permis pour la première fois de quasiment atteindre le régime de turbulence fortement stratifié. Les simulations numériques forcées dans l'espace physique avec le même type de forcage ont permis de reproduire les résultats expérimentaux et de les étendre aux grands nombres de Reynolds de flottabilité. Elles révèlent que la plus grande échelle des retournements est de l'ordre de l'échelle de flottabilité. Enfin, une généralisation de la loi des 4/5 de Kolmogorov est proposée pour la turbulence stratifiée.