En astronautique, une question importante est de contrôler le mouvement d’un satellite soumis à la gravitation des corps célestes de telle sorte que certains indices de performance soient minimisés (ou maximisés). Dans cette thèse, nous nous intéressons à la minimisation de la norme L¹ du contrôle pour le problème circulaire restreint des trois corps. Les conditions nécessaires à l’optimalité sont obtenues en utilisant le principe du maximum de Pontryagin, révélant l’existence de contrôles bang-bang et singuliers. En s’appuyant sur les résultats de Marchal [1] et Zelikin et al. [2], la présence du phénomène de Fuller est mise en évidence par l’analyse des es extrêmales singulières. La contrôlabilité pour le problème à deux corps (un cas dégénéré du problème circulaire restreint des trois corps) avec un contrôle prenant des valeurs dans une boule euclidienne est caractérisée dans le chapitre 2. Le résultat de contrôlabilité est facilement étendu au problème des trois corps puisque le champ de vecteurs correspondant à la dérive est récurrent. En conséquence, si les trajectoires contrôlées admissibles restent dans un compact fixé, l’existence des solutions du problème de minimisation L¹ peut être obtenu par une combinaison du théorème de Filippov (voir [4, chapitre 10]) et une procédure appropriée de convexification (voir [5]). En dimension finie, le problème de minimisation L¹ est bien connu pour générer des solutions où le contrôle s’annule sur certains intervalles de temps. Bien que le principe du maximum de Pontryagin soit un outil puissant pour identifier les solutions candidates pour le problème de minimisation L¹, il ne peut pas garantir que ces candidats sont au moins localement optimaux sauf si certaines conditions d’optimalité suffisantes sont satisfaites. En effet, il est une condition préalable pour établir (et pour être capable de vérifier) les conditions d’optimalité nécessaires et suffisantes pour résoudre le problème de minimisation L¹. Dans cette thèse, l’idée cruciale pour obtenir de telles conditions est de construire une famille paramétrée d’extrémales telle que l’extrémale de référence peut être intégrée dans un champ d’extrémales. Deux conditions de non-pliage pour la projection canonique de la famille paramétrée d’extrémales sont proposées. En ce qui concerne le cas de points terminaux fixés, ces conditions de non-pliage sont suffisantes pour garantir que l’extrémale de référence est localement minimisante tant que chaque point de commutation est régulier (cf. chapitre 3). Si le point terminal n’est pas fixe mais varie sur une sous-variété lisse, une condition suffisante supplémentaire impliquant la géométrie de variété de cible est établie (cf. chapitre 4). Bien que diverses méthodes numériques, y compris celles considérées comme directes [6, 7], indirectes [5, 8], et hybrides [11], dans la littérature sont en mesure de calculer des solutions optimales, nous ne pouvons pas attendre d’un satellite piloté par le contrôle optimal précalculé (ou le contrôle nominal) de se déplacer sur la trajectoire optimale précalculée (ou trajectoire nominale) en raison de perturbations et des erreurs inévitables. Afin d’éviter de recalculer une nouvelle trajectoire optimale une fois que la déviation de la trajectoire nominale s’est produite, le contrôle de rétroaction optimale voisin, qui est probablement l’application pratique la plus importante de la théorie du contrôle optimal [12, Chapitre 5], est obtenu en paramétrant les extrémales voisines autour de la nominale (cf. chapitre 5). Étant donné que la fonction de contrôle optimal est bang-bang, le contrôle optimal voisin comprend non seulement la rétroaction sur la direction de poussée, mais aussi celle sur les instants de commutation. En outre, une analyse géométrique montre qu’il est impossible de construire un contrôle optimal voisin une fois que le point conjugué apparaisse ou bien entre ou bien à des instants de commutation. / In astronautics, an important issue is to control the motion of a satellite subject to the gravitation of celestial bodies in such a way that certain performance indices are minimized (or maximized). In the thesis, we are interested in minimizing the L¹-norm of control for the circular restricted three-body problem. The necessary conditions for optimality are derived by using the Pontryagin maximum principle, revealing the existence of bang-bang and singular controls. Singular extremals are analyzed, and the Fuller phenomenon shows up according to the theories developed by Marchal [1] and Zelikin et al. [2, 3]. The controllability for the controlled two-body problem (a degenerate case of the circular restricted three-body problem) with control taking values in a Euclidean ball is addressed first (cf. Chapter 2). The controllability result is readily extended to the three-body problem since the drift vector field of the three-body problem is recurrent. As a result, if the admissible controlled trajectories remain in a fixed compact set, the existence of the solutions of the L¹-minimizaion problem can be obtained by a combination of Filippov theorem (see [4, Chapter 10], e.g.) and a suitable convexification procedure (see, e.g., [5]). In finite dimensions, the L¹-minimization problem is well-known to generate solutions where the control vanishes on some time intervals. While the Pontryagin maximum principle is a powerful tool to identify candidate solutions for L1-minimization problem, it cannot guarantee that the these candidates are at least locally optimal unless sufficient optimality conditions are satisfied. Indeed, it is a prerequisite to establish (as well as to be able to verify) the necessary and sufficient optimality conditions in order to solve the L¹-minimization problem. In this thesis, the crucial idea for establishing such conditions is to construct a parameterized family of extremals such that the reference extremal can be embedded into a field of extremals. Two no-fold conditions for the canonical projection of the parameterized family of extremals are devised. For the scenario of fixed endpoints, these no-fold conditions are sufficient to guarantee that the reference extremal is locally minimizing provided that each switching point is regular (cf. Chapter 3). If the terminal point is not fixed but varies on a smooth submanifold, an extra sufficient condition involving the geometry of the target manifold is established (cf. Chapter 4). Although various numerical methods, including the ones categorized as direct [6, 7], in- direct [5, 8, 9], and hybrid [10], in the literature are able to compute optimal solutions, one cannot expect a satellite steered by the precomputed optimal control (or nominal control) to move on the precomputed optimal trajectory (or nominal trajectory) due to unavoidable perturbations and errors. In order to avoid recomputing a new optimal trajectory once a deviation from the nominal trajectory occurs, the neighboring optimal feedback control, which is probably the most important practical application of optimal control theory [11, Chapter 5], is derived by parameterizing the neighboring extremals around the nominal one (cf. Chapter 5). Since the optimal control function is bang-bang, the neighboring optimal control consists of not only the feedback on thrust direction but also that on switching times. Moreover, a geometric analysis shows that it is impossible to construct the neighboring optimal control once a conjugate point occurs either between or at switching times.

The aim with this research is to investigate if there is a relationship between import of meat and the price on livestock in Sweden. It also investigates if the Swedish membership of the European Union has affected both the price on livestock and the quantity of import of meat to Sweden. The research is based on a publication from Swedish Board of Agriculture, which indicates that the membership of the European Union has affected the consumer price on agricultural products. This gave the idea that this could have happened on prices of livestock as well. The data is collected from Swedish Board of Agriculture and SCB, for the years of 1970-2019. Regression analysis and paired t-test were supposed to be used for data analysis. The results of stationarity tests implies that regression analysis should not be used regarding the non-stationary result. Therefor were only the stationarity tests and the t-test used. The result of t-test showed that the membership of European Union has affected both price and import in Sweden. To exclude other reasons for the price decrease and the increase of import than the membership is not possible. When comparing the data with other factors and literature the conclusion is that events in the end of the 20th century did affect the price level of livestock and the increased demand for imported meat. Key

Big data is an enabling technology in digital transformation. It perfectly complements ordinary linear models and generalized linear models, as training well-performed ordinary linear models and generalized linear models require huge amounts of data. With the help of big data, ordinary and generalized linear models can be well-trained and thus offer better services to human beings. However, there are still many challenges to address for training ordinary linear models and generalized linear models in big data. One of the most prominent challenges is the computational challenges. Computational challenges refer to the memory inflation and training inefficiency issues occurred when processing data and training models. Hundreds of algorithms were proposed by the experts to alleviate/overcome the memory inflation issues. However, the solutions obtained are locally optimal solutions. Additionally, most of the proposed algorithms require loading the dataset to RAM many times when updating the model parameters. If multiple model hyper-parameters needed to be computed and compared, e.g. ridge regression, parallel computing techniques are applied in practice. Thus, multiple learning with sufficient statistics arrays are proposed to tackle the memory inflation and training inefficiency issues.

Date:2022-06-02 Level:Master Thesis in Business Administration, 15cr Institution:School of Business, Society and Engineering, Mälardalen University Authors:Agostina Romano(92/08/23) Olivia Gurås (98/01/21) Title:Fashion shouldn’t cost the Earth: an exploratory study on small businesses driving sufficiency in the Swedish fashion industry Supervisor:Edward Gillmore Research Questions:RQ1: How do small firms management develop and implement strategies to promote sufficient consumption? RQ2: How do small firms implement stakeholder management to minimize the challenges caused by the promotion of sufficient consumption? Purpose:To provide a better understanding of the processes, factors and forces that enable companies to promote sufficient consumption, and how they manage to overcome challenges with internal and external stakeholders that are created by the implementation of sufficient consumption practices Methodology:Being an exploratory qualitative research, this study uses primary data collected through 6 semi-structured interviews with management roles of 4 sustainable companies, as well as secondary data obtained from official data bases, books, and websites. Conclusion:Small businesses in the fashion industry implement different sustainable strategies that promote sufficient consumption among others. Whether they are designed and implemented with sufficiency as a goal or not, these strategies bear challenges with multiple stakeholders that firms must face. Some of the main challenges are related to consumer and supplier resistance, as well as lack of awareness, challenging governance, and the internal sustainability vs. profitability debate. This study empirically contributes to past literature in terms of strategies and challenges, and it contributes theoretically in terms of solutions put in place through stakeholder management. Keywords:CSR, Stakeholder Management, Sustainability, Sufficiency, Sufficient Consumption, Sustainable Fashion

The purpose of this paper is to derive minimal sufficient statistics for the balanced incomplete block design and the group divisible partially balanced incomplete block design when the Eisenhart Model III (mixed model) is assumed. The results are identical to Hultquist and Graybill's (1965) and Hirotsu's (1965) for the same model without interaction, except for the addition of a statistic, ∑ijY2ij•.

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Advances in modern technologies have led to an abundance of high-dimensional time series data in many fields, including finance, economics, health, engineering, and meteorology, among others. This causes the “curse of dimensionality” problem in both univariate and multivariate time series data. The main objective of time series analysis is to make inferences about the conditional distributions. There are some methods in the literature to estimate the conditional mean and conditional variance functions in time series. However, most of those are inefficient, computationally intensive, or suffer from the overparameterization. We propose some dimension reduction techniques to address the curse of dimensionality in high-dimensional time series dataFor high-dimensional matrix-valued time series data, there are a limited number of methods in the literature that can preserve the matrix structure and reduce the number of parameters significantly (Samadi, 2014, Chen et al., 2021). However, those models cannot distinguish between relevant and irrelevant information and yet suffer from the overparameterization. We propose a novel dimension reduction technique for matrix-variate time series data called the "envelope matrix autoregressive model" (EMAR), which offers substantial dimension reduction and links the mean function and the covariance matrix of the model by using the minimal reducing subspace of the covariance matrix. The proposed model can identify and remove irrelevant information and can achieve substantial efficiency gains by significantly reducing the total number of parameters. We derive the asymptotic properties of the proposed maximum likelihood estimators of the EMAR model. Extensive simulation studies and a real data analysis are conducted to corroborate our theoretical results and to illustrate the finite sample performance of the proposed EMAR model.For univariate time series, we propose sufficient dimension reduction (SDR) methods based on some integral transformation approaches that can preserve sufficient information about the response. In particular, we use the Fourier and Convolution transformation methods (FM and CM) to perform sufficient dimension reduction in univariate time series and estimate the time series central subspace (TS-CS), the time series mean subspace (TS-CMS), and the time series variance subspace (TS-CVS). Using FM and CM procedures and with some distributional assumptions, we derive candidate matrices that can fully recover the TS-CS, TS-CMS, and TS-CVS, and propose an explicit estimate of the candidate matrices. The asymptotic properties of the proposed estimators are established under both normality and non-normality assumptions. Moreover, we develop some data-drive methods to estimate the dimension of the time series central subspaces as well as the lag order. Our simulation results and real data analyses reveal that the proposed methods are not only significantly more efficient and accurate but also offer substantial computational efficiency compared to the existing methods in the literature. Moreover, we develop an R package entitled “sdrt” to easily perform our program code in FM and CM procedures to estimate suffices dimension reduction subspaces in univariate time series.

Accompanying the advances in computer technology is an increase collection of high dimensional data in many scientific and social studies. Sufficient dimension reduction (SDR) is a statistical method that enable us to reduce the dimension ofpredictors without loss of regression information. In this dissertation, we introduce principal asymmetric least squares (PALS) as a unified framework for linear and nonlinear sufficient dimension reduction. Classical methods such as sliced inverse regression (Li, 1991) and principal support vector machines (Li, Artemiou and Li, 2011) often do not perform well in the presence of heteroscedastic error, while our proposal addresses this limitation by synthesizing different expectile levels. Through extensive numerical studies, we demonstrate the superior performance of PALS in terms of both computation time and estimation accuracy. For the asymptotic analysis of PALS for linear sufficient dimension reduction, we develop new tools to compute the derivative of an expectation of a non-Lipschitz function. PALS is not designed to handle symmetric link function between the response and the predictors. As a remedy, we develop expectile-assisted inverse regression estimation (EA-IRE) as a unified framework for moment-based inverse regression. We propose to first estimate the expectiles through kernel expectile regression, and then carry out dimension reduction based on random projections of the regression expectiles. Several popular inverse regression methods in the literature including slice inverse regression, slice average variance estimation, and directional regression are extended under this general framework. The proposed expectile-assisted methods outperform existing moment-based dimension reduction methods in both numerical studies and an analysis of the Big Mac data. / Statistics

The ADtree, a data structure useful for caching sufficient statistics, has been successfully adapted to grow lazily when memory is limited and to update sequentially with an incrementally updated dataset. However, even these modified forms of the ADtree still exhibit inefficiencies in terms of both space usage and query time, particularly on datasets with very high dimensionality and with high arity features. We propose five modifications to the ADtree, each of which can be used to improve size and query time under specific types of datasets and features. These modifications also provide an increased ability to precisely control how an ADtree is built and to tune its size given external memory or speed requirements.

Potato production requires high phosphorus (P) application with potential negative environmental or nutritional consequences for potato as well as for subsequent crops. Impacts of high available P on yield and plant nutrition of species in potato cropping rotations are inadequately understood, and could result in antagonistic interactions with cationic micronutrients such as zinc (Zn) and manganese (Mn). Three hydroponic experiments were conducted with Russet Burbank potato to elucidate P and Zn relationships and associated interactions with other nutrients. In the first experiment, P solution concentration was constant at 256 µM while Zn concentration varied: 0.1, 2, 6, 18, 54, 162 and 456 µM Zn. In the second, Zn solution concentration was constant at 6 µM while P concentration varied: 32, 64, 128, 256, 512, 1024 and 2048 µM P. In the third, three levels of P and Zn varied in all possible combinations: 32, 128 and 1024 µM P and 0.1, 54 and 486 µM Zn. As expected, Zn increased in all plant parts with increasing old shoots while root P increased. This suggests a P-Zn complex formation in roots preventing movement of P to the shoots of plants under high Zn. This was confirmed under variable P and Zn. Contrary to expectations, a direct impact of increased solution P on Zn uptake or distribution in potato was not observed except at 486 µM Zn in the third experiment. Increased solution P at low Zn levels resulted in a steep increase of P in new and old shoot growth and an accumulation of Mn in potato roots—factors that might indirectly impact Zn nutrition in potato. Although high P levels in potato did not directly reduce Zn content or cause Zn deficiency, excessive P accumulation with insufficient Zn may reduce the activity of Zn by interacting with other micronutrients such as Mn.