Building structure of wine-growing is situated in the countryside not far from the village Strachotin in South Moravia. Concerned area slopes wildly down to the level of the water reservoir. To the building of production concures parts of presentation, degustation, and distribution of wine. This area includes also leisure centre with possibility of accomodation , visit of wellness, seminary rooms, restaurant and coffee. Buildings for accomodation and some other are designed as energetically selfsufficient wooden structures using energy from renewable natural resources.

This paper contains four main ideas. First, it shows global existence for the steepest descent in the uniformly convex setting. Secondly, it shows existence of critical points for convex functions defined on uniformly convex spaces. Thirdly, it shows an isomorphism between the dual space of H^{1,p}[0,1] and the space H^{1,q}[0,1] where p > 2 and {1/p} + {1/q} = 1. Fourthly, it shows how the Beurling-Denny theorem can be extended to find a useful function from H^{1,p}[0,1] to L_{p}[1,0] where p > 2 and addresses the problem of using that function to establish a relationship between the ordinary and the Sobolev gradients. The paper contains some numerical experiments and two computer codes.

The descent algebra of a Coxeter group is a subalgebra of the group algebra with interesting representation theoretic properties. For instance, the natural map from the descent algebra of the symmetric group to the character ring is a surjective algebra homomorphism, so the descent algebra implicitly encodes information about the representations of the symmetric group. However, this property does not hold for other Coxeter groups. Moreover, a complete set of primitive idempotents in the descent algebra of the symmetric group leads to a decomposition of the group algebra as a direct sum of induced linear characters of centralizers of conjugacy class representatives. In this dissertation, I consider the hyperoctahedral group. When the descent algebra of a hyperoctahedral group is replaced with a generalization called the Mantaci-Reutenauer algebra, the natural map to the character ring is surjective. In 2008, Bonnafé asked whether a complete set of idempotents in the Mantaci-Reutenauer algebra could lead to a decomposition of the group algebra of the hyperoctahedral group as a direct sum of induced linear characters of centralizers. In this dissertation, I will answer this question positively and go through the construction of the idempotents, conjugacy class representatives, and linear characters required to do so.

Cette thèse traite des méthodes de descente d’ordre un pour les problèmes de minimisation. Elle comprend trois parties. Dans la première partie, nous apportons une vue d’ensemble des bornes d’erreur et les premières briques d’unification d’un concept. Nous montrons en effet la place centrale de l’inégalité du gradient de Lojasiewicz, en mettant en relation cette inégalité avec les bornes d’erreur. Dans la seconde partie, en usant de l’inégalité de Kurdyka-Lojasiewicz (KL), nous apportons un nouvel outil pour calculer la complexité des m´méthodes de descente d’ordre un pour la minimisation convexe. Notre approche est totalement originale et utilise une suite proximale “worst-case” unidimensionnelle. Ces résultats introduisent une méthodologie simple : trouver une borne d’erreur, calculer la fonction KL désingularisante quand c’est possible, identifier les constantes pertinentes dans la méthode de descente, et puis calculer la complexité en usant de la suite proximale “worst-case” unidimensionnelle. Enfin, nous étendons la méthode extragradient pour minimiser la somme de deux fonctions, la première étant lisse et la seconde convexe. Sous l’hypothèse de l’inégalité KL, nous montrons que la suite produite par la méthode extragradient converge vers un point critique de ce problème et qu’elle est de longueur finie. Quand les deux fonctions sont convexes, nous donnons la vitesse de convergence O(1/k) qui est classique pour la méthode de gradient. De plus, nous montrons que notre complexité de la seconde partie peut être appliquée à cette méthode. Considérer la méthode extragradient est l’occasion de d´écrire la recherche linéaire exacte pour les méthodes de décomposition proximales. Nous donnons des détails pour l’implémentation de ce programme pour le problème des moindres carrés avec régularisation ℓ1 et nous donnons des résultats numériques qui suggèrent que combiner des méthodes non-accélérées avec la recherche linéaire exacte peut être un choix performant. / This thesis focuses on first order descent methods in the minimization problems. There are three parts. Firstly, we give an overview on local and global error bounds. We try to provide the first bricks of a unified theory by showing the centrality of the Lojasiewicz gradient inequality. In the second part, by using Kurdyka- Lojasiewicz (KL) inequality, we provide new tools to compute the complexity of first-order descent methods in convex minimization. Our approach is completely original and makes use of a one-dimensional worst-case proximal sequence. This result inaugurates a simple methodology: derive an error bound, compute the KL esingularizing function whenever possible, identify essential constants in the descent method and finally compute the complexity using the one-dimensional worst case proximal sequence. Lastly, we extend the extragradient method to minimize the sum of two functions, the first one being smooth and the second being convex. Under Kurdyka-Lojasiewicz assumption, we prove that the sequence produced by the extragradient method converges to a critical point of this problem and has finite length. When both functions are convex, we provide a O(1/k) convergence rate. Furthermore, we show that our complexity result in the second part can be applied to this method. Considering the extragradient method is the occasion to describe exact line search for proximal decomposition methods. We provide details for the implementation of this scheme for the ℓ1 regularized least squares problem and give numerical results which suggest that combining nonaccelerated methods with exact line search can be a competitive choice.

論文(碩士)--香港中文大學,1968. / Manuscript. / Includes bibliographical references (leaves 300-309). / Thesis (M.A.)--Xianggang Zhong wen da xue, 1968. / Chapter (一) --- 引言 / Chapter (二) --- 東漢政權之本質及帝室與族之婚姻關係 / Chapter (甲) --- 東政權之本質 / Chapter (乙) --- 帝室與豪族之婚姻關係 / Chapter (丙) --- 親族之休戚相關 / Chapter (三) --- 東漢帝室嗣續與外戚勢力二者關聯之考察 / Chapter (甲) --- 郭陰馬三氏與帝室嗣續 / Chapter (乙) --- 臨朝諸后與帝室嗣續 / Chapter （丙） --- 諸帝嗣子之多寡有無 / Chapter （丁） --- 舊權之尊重 / Chapter （四） --- 東漢事規臺閣與權移外戚因果關係之論析 / Chapter （甲） --- 中朝與外朝之別 / Chapter （乙） --- 尚書權任與外戚擅政之關係 / Chapter （丙） --- 外戚以大將軍錄上書事 / Chapter （五） --- 東漢外戚勢力之淌長與京師柄及北官位置之關係 / Chapter （甲） --- 東漢京兵之重 / Chapter （乙） --- 外戚之操持兵柄與參決國政 / Chapter （丙） --- 外戚勢力消長之關鍵 / Chapter （丁） --- 北軍與北宮建置之形勢 / Chapter (六) --- 結語

We study optimization algorithms for the finite sum problems frequently arising in machine learning applications. First, we propose novel variants of stochastic gradient descent with a variance reduction property that enables linear convergence for strongly convex objectives. Second, we study distributed setting, in which the data describing the optimization problem does not fit into a single computing node. In this case, traditional methods are inefficient, as the communication costs inherent in distributed optimization become the bottleneck. We propose a communication-efficient framework which iteratively forms local subproblems that can be solved with arbitrary local optimization algorithms. Finally, we introduce the concept of Federated Optimization/Learning, where we try to solve the machine learning problems without having data stored in any centralized manner. The main motivation comes from industry when handling user-generated data. The current prevalent practice is that companies collect vast amounts of user data and store them in datacenters. An alternative we propose is not to collect the data in first place, and instead occasionally use the computational power of users' devices to solve the very same optimization problems, while alleviating privacy concerns at the same time. In such setting, minimization of communication rounds is the primary goal, and we demonstrate that solving the optimization problems in such circumstances is conceptually tractable.

In modern data and signal acquisition, one main challenge arises from the growing scale of data. The data acquisition devices, however, are often limited by physical and hardware constraints, precluding sampling with the desired rate and precision. It is thus of great interest to reduce the sensing complexity while retaining recovery resolution. And that is why we are interested in reconstructing a signal from a small number of randomly observed time domain samples. The main contributions of this thesis are as follows. First, we consider reconstructing a one-dimensional (1-D) spectrally sparse signal from a small number of randomly observed time-domain samples. The signal of interest is a linear combination of complex sinusoids at R distinct frequencies. The frequencies can assume any continuous values in the normalized frequency domain [0, 1). After converting the spectrally sparse signal into a low-rank Hankel structured matrix completion problem, we propose an efficient feasible point approach, named projected Wirtinger gradient descent (PWGD) algorithm, to efficiently solve this structured matrix completion problem. We give the convergence analysis of our proposed algorithms. We then apply this algorithm to a different formulation of structured matrix recovery: Hankel and Toeplitz mosaic structured matrix. The algorithms provide better recovery performance; and faster signal recovery than existing algorithms including atomic norm minimization (ANM) and Enhanced Matrix Completion (EMaC). We further accelerate our proposed algorithm by a scheme inspired by FISTA. Extensive numerical experiments are provided to illustrate the efficiency of our proposed algorithms. Different from earlier approaches, our algorithm can solve problems of very large dimensions very efficiently. Moreover, we extend our algorithms to signal recovery from noisy samples. Finally, we aim to reconstruct a two-dimension (2-D) spectrally sparse signal from a small size of randomly observed time-domain samples. We extend our algorithms to high-dimensional signal recovery from noisy samples and multivariate frequencies.

The air that humans exhale contains various chemical markers whose levels have been associated with various respiratory disorders. Therefore, measurement of these markers offers a potential method of examining airway disease status. Furthermore, exhaled breath offers the advantage of being easy to collect and non-invasive. Hence, these exhaled breath markers are potentially of significant clinical use in examining airways. Therefore, examination of exhaled breath has become the subject of intense study. Current research is targeting the development of methods and parameters for looking at these markers. The goal of this cross-sectional pilot study was to consider the variability in the measurement of these exhaled breath markers between members of different ethnic populations. Specifically, measurements of the exhaled breath marker Nitric Oxide (NO) were compared between two ethnic groups (Caucasian men versus men of African descent). Ten healthy men in each group were studied to examine whether baseline NO measurements differed between them. In this study, a cross-sectional design was used. The study sample consisted of young, healthy men with no history of environmental allergies, asthma, or lung diseases and no significant smoking history. A total of twenty-five men volunteered for the study, including fourteen men of Caucasian descent and eleven men of African descent. Because four men were excluded and one withdrew, ten men in each ethnic group were included in the final analysis. The source population from which the sample was drawn included students and workers. All participants were residing in Florida at the time of study. Ideally, the target population for this study was young, healthy, working men. Large inter-measurement variation was seen between the participants of each ethnic group. This was hypothesized to be attributed to a tri-modal distribution due to the existence of 3 populations of subjects: (1) asymptomatic with normal airways, where NO levels were under 30 parts per billion (ppb); (2) asymptomatic with airway pathology, where NO levels were over 30 ppb; and (3) asymptomatic just before the onset of an upper respiratory tract infection, where NO levels were over 60 ppb. This pilot study did not find statistically significant evidence that there is a difference in the baseline exhaled breath NO measurements between the two ethnic groups studied. Nonetheless, in participants with NO levels under 30 ppb the mean of the African group was found to be 7.6 ppb lower than the mean of the Caucasian group when attempts were made to exclude individuals with underlying airway pathology or imminent upper respiratory tract infection. In order to find statistical significance in the results, a power analysis using the standard deviation of 7.7 ppb that was found in this study indicates that at least thirty-two eligible participants with NO levels under 30 ppb would be required. Only 13 such participants were examined in this study, Thus, at least fifty eligible participants would be required to find significant results. The implication is that even though statistical significance was not achieved, the crude mean averages differed between the two groups in participants with NO levels under 30 ppb. This implies that a larger-scale well-designed study is warranted before NO is used in clinical settings in the diagnosis and monitoring of patients.

After hundreds of years of contact, the relationships between the people of Native Nations and the Canadian Nation are still filled with turmoil. This is common knowledge. What isn't well known, are the personal consequences for children who have Native and non-Native ancestors. This thesis is written with the assistance of eight people of mixed ancestry, who share their experiences, ideas, strategies and dreams, to help others who are dealing with similar issues. This thesis has been organized around the dominant themes and commonalities that have emerged out of eight interviews, into four sections: CONTEXT, CHALLENGES, STRATEGIES & GIFTS. The context that mixed ancestry individuals are born into is complex. Euro-Canadian designs on Native lands and resources resulted in policies that had, and continue to have, a devastating effect on Native people. Legal manipulations of Native identity, in particular, have resulted in the emergence of hierarchies of belonging. Such hierarchies are maintained by enduring stereotypes of "Indianness" and "Whiteness". For some mixed ancestry individuals, negotiating the polarized hierarchies of Native and Canadian societies can result in feelings of being split, and the need to harmonize aspects of the self, with varying social environments. Various strategies are used to deal with such issues, internally and externally. Ultimately, through choices, strategies and transformations, it is possible to transcend the challenges of mixed ancestry, and to lead more fulfilling lives. My hope is that this thesis will be of assistance to people of mixed ancestry and to those trying to understand the complexities of Native- Canadian relations, at least to the point of inspiring more discussions and research.

The goals of the pelvis include maintaining the center of mass of the body, assisting in foot clearance and absorb forces from the lower extremities using muscles and ligaments to stabilize the joint. A better understanding of the influence of muscle strength on controlling pelvic obliquity in a healthy population will help in understanding low back pain and overuse lower extremity injuries. Thirteen females (22 ±2 yrs) participated in isokinetic strength testing of the hip abductors, adductors, internal rotators and external rotators on a Biodex dynamometer. The subjects also underwent gait analysis during self selected pace walking and stair descent. For each muscle group subjects were divided into weaker and stronger groups based on the mean. Independent t-test revealed a significantly greater amount of pelvic obliquity in the stronger group for abductors, adductors, and internal rotators during stair descent. Subjects may be compensating for more pelvic obliquity with less movement of the hip, knee and ankle. During walking weaker external rotators was the only muscle group that significantly increased pelvic obliquity. Our study supports the finding of other studies that the external rotators contribute to pelvic stabilization during walking (Powers, 2003).