The automatic Algorithm ARI developed in this paper can generate variates from a large class of unimodal discrete distributions. It is only necessary to know the mode of the distribution and to have a subprogram available that can evaluate the probabilities. In a set up step the algorithm constructs a table mountain shaped hat function. Then rejection inversion, a new variant of the rejection method for discrete distributions that needs only one uniform random number per iteration, is used to sample from the desired distribution. It is shown that the expeceted number of iterations is uniformly bounded for all T-concave discrete distributions. Utilizing a simple squeeze or an auxiliary table of moderate size, which is initialized during generation and not in the set up, Algorithm ARI is fast, at least as fast as the fastest known methods designed for the Poisson, binomial and hypergeometric distributions. The set up time of the algorithm is not affected by the size of the domain of the distribution and is about ten times longer than the generation of one variate. Compared with the very fast and well known alias and indexed search methods the set up of Algorithm ARI is much faster but the generation time is about two times slower. More important than the speed is the fact that Algorithm ARI is the first automatic algorithm that can generate samples from discrete distributions with heavy tails. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

A sweep-plane algorithm by Lawrence for convex polytope computation is adapted to generate random tuples on simple polytopes. In our method an affine hyperplane is swept through the given polytope until a random fraction (sampled from a proper univariate distribution) of the volume of the polytope is covered. Then the intersection of the plane with the polytope is a simple polytope with smaller dimension. In the second part we apply this method to construct a black-box algorithm for log-concave and T-concave multivariate distributions by means of transformed density rejection. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

Different universal (also called automatic or black-box) methods have been suggested to sample from univariate log-concave distributions. The description of a universal generator for bivariate distributions has not been published up to now. The new algorithm for bivariate log-concave distributions is based on the method of transformed density rejection. In order to construct a hat function for a rejection algorithm the bivariate density is transformed by the logarithm into a concave function. Then it is possible to construct a dominating function by taking the minimum of several tangent planes which are by exponentiation transformed back into the original scale. The choice of the points of contact is automated using adaptive rejection sampling. This means that a point that is rejected by the rejection algorithm is used as additional point of contact until the maximal number of points of contact is reached. The paper describes the details how this main idea can be used to construct Algorithm ULC2D that can generate random pairs from bivariate log-concave distribution with a computable density. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

We give an algorithm that can be used to sample from any discrete log-concave distribution (e.g. the binomial and hypergeometric distributions). It is based on rejection from a discrete dominating distribution that consists of parts of the geometric distribution. The algorithm is uniformly fast for all discrete log-concave distributions and not much slower than algorithms designed for a single distribution. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

Thesis (doctoral)--Uppsala University, 1991"--T.p. verso. / Includes bibliographical references.

La fonctionnalisation des cycles concaves du symétrie Cn, en particulier leur post-fonctionnalisation, est importante pour leur nature et leurs applications. Au cours des dernières décennies, beaucoup de travail a été investi dans le développement de méthodes simples et efficaces pour ce fait. De grands progrès ont été réalisés concernant la fonctionnalisation des cyclodextrines, particulièrement depuis la découverte de la réaction de débenzylation utilisant DIBAL-H (l’hydrure de diisobutyl aluminium). Basés sur cette réaction et les méthodes de déprotection sélectives, divers motifs de l’hétéro- fonctionnalisation comportant de 2 à 3 fonctions differentes sont maintenant accessibles du façon sélective. Toutefois, les motifs plus complexes, comme l’hexadifférentiation de l’α-cyclodextrine et l’heptadifférentiation de la β-cyclodextrine, étaient encore inaccessibles. Tout d'abord, nous avons combiné les méthodes de déprotection sélectives établies précédemment, pour synthétiser, pour la première fois, l'α-cyclodextrine hexadifférenciée inédite sur laquel chaque unité de glucose possède une fonction différente. Cette réalisation ouvre la voie d’accès à toutes les 7826 combinaisons possibles de 6 fonctions sur une α-cyclodextrine. Ensuite, la réactivité du DIBAL-H a été étudiée sur des α-cyclodextrines fonctionnalisées avec des atoms de soufre et de selenium, et deux méthodes sélectives: la réaction tandem de debenzylation/reduction de thioester et une nouvelle stratégie de "frustration" ont été mise à jour, ce qui permettent l'accès à de nouveaux motifs de fonctionnalisation de cyclodextrines. Beaucoup d'efforts ont également été faits pour atteindre la β-cyclodextrine heptadifférenciée. La stratégie initiale utilisant les amines a seulement donné des motifs tétradifférenciées probablement à cause de la coordination entre les amines et les réactifs aluminium. Enfin, l'utilisation de la réaction tandem de débenzylation/réduction de thioester, nous a permis d'accéder à des cyclodextrines pentadifférenciées, qui doivent encore subir deux réactions de débenzylation successives pour atteindre la β-cyclodextrine heptadifférenciée avec des thioéthers différents sur sa couronne primaire. / Functionalization of Cn-symmetric concave cycles, especially their post-functionalization, has an important impact on their nature and their applications. In the past few decades, plenty of work has been invested in the development of simple and efficient methods. Great progress has been made concerning functionalization of cyclodextrins particularly since the discovery of the DIBAL-H-mediated debenzylation reaction. Based on this reaction and well-established site-directing rules, various cyclodextrin patterns are now accessible. However, the patterns with the higher level of complexity, i.e. hexadifferentiation of α-cyclodextrin and heptadifferentiation of β-cyclodextrin, were still out of reach. Firstly, we combined the previously delineated site-directing rules to synthesize, for the first time, the ultimate hexadifferentiated α-cyclodextrin on which each glucose unit possesses a different function. It opens the way to the synthesis of all 7826 possible combinations of 6 functions on α-cyclodextrin. Then the reactivity of DIBAL-H was studied on sulfur- and selenium-derived α-cyclodextrins, and two site-directing methods: tandem thioester-reduction/debenzylation and a new “frustration” strategy were disclosed, which enable the preparation of new patterns of cyclodextrins. Much efforts were also paid to reach heptadifferentiated β-cyclodextrin. The initial amine strategy only gave the tetradifferentiated patterns probably due to the coordination between amine and aluminum reagents. Finally, utilization of the uncovered tandem thioester-reduction/debenzylation method allowed us to access pentadifferentiated patterns, which still need to undergo two successive debenzylation reactions to reach the ultimate heptadifferentiated β-cyclodextrin with different thioethers on its primary rim.

A family of concave penalties, including the smoothly clipped absolute deviation (SCAD) and minimax concave penalties (MCP), has been shown to have attractive properties in variable selection. The computation of concave penalized solutions, however, is a difficult task. We propose a majorization minimization by coordinate descent (MMCD) algorithm to compute the solutions of concave penalized generalized linear models (GLM). In contrast to the existing algorithms that uses local quadratic or local linear approximation of the penalty, the MMCD majorizes the negative log-likelihood by a quadratic loss, but does not use any approximation to the penalty. This strategy avoids the computation of scaling factors in iterative steps, hence improves the efficiency of coordinate descent. Under certain regularity conditions, we establish the theoretical convergence property of the MMCD algorithm. We implement this algorithm in a penalized logistic regression model using the SCAD and MCP penalties. Simulation studies and a data example demonstrate that the MMCD works sufficiently fast for the penalized logistic regression in high-dimensional settings where the number of covariates is much larger than the sample size. Grouping structure among predictors exists in many regression applications. We first propose an l2 grouped concave penalty to incorporate such group information in a regression model. The l2 grouped concave penalty performs group selection and includes group Lasso as a special case. An efficient algorithm is developed and its theoretical convergence property is established under certain regularity conditions. The group selection property of the l2 grouped concave penalty is desirable in some applications; while in other applications selection at both group and individual levels is needed. Hence, we propose an l1 grouped concave penalty for variable selection at both individual and group levels. An efficient algorithm is also developed for the l1 grouped concave penalty. Simulation studies are performed to evaluate the finite-sample performance of the two grouped concave selection methods. The new grouped penalties are also used in analyzing two motivation datasets. The results from both the simulation and real data analyses demonstrate certain benefits of using grouped penalties. Therefore, the proposed concave group penalties are valuable alternatives to the standard concave penalties.

The demand for outdoor precise location is increasing with the development of new applications such as autonomous vehicles, exploration robots and wireless sensor networks. Global Navigation Satellite System (GNSS) is the go-to system for outdoor localization. This thesis focuses on developing new methods for GNSS single-point positioning (SPP) model, where no access to a reference station or precise GNSS parameters is needed. We investigated the limitations of the standard method, least- squares adjustment (LSA), and we derived the Cramer-Rao bounds for the SPP estimation problem. We also investigated different techniques to formulate the positioning problem with the goal to increase the accuracy. A new method is developed by reformulating the problem as difference-of-convex program (DC program) and utilizing convex-concave procedure (CCCP) to solve the positioning problem without linearizing the observation equations. In addition, we examined the potential of multiple-receiver systems in increasing the accuracy. We formulated the multiple- receiver SPP estimation problem, and we proposed to configure the multiple receivers in a fixed equilateral triangle to exploit the symmetry and the geometrical constraints of the configuration. We extended the use of LSA in multiple-receiver system. We also developed a modification of LSA algorithm, named least-squares adjustment extension (LSAE), that utilizes attitude information and the constraints of the multiple-receiver system. In addition, we developed a new algorithm to optimizes the SPP estimates over the equilateral triangles Riemannian manifold, which enforces the geometrical constraints of the multiple-receiver system. Furthermore, we derived the constrained and the unconstrained Cramer-Rao bounds (CRB and CCRB) for the multiple-receiver SPP problem. Moreover, we investigated the influence of both attitude information and the equilateral triangle baseline length on the algorithms’ performances and the derived CCRB. Finally, we carried out a numerical analysis by implementing the algorithms and the bounds in MATLAB, where we tested the algorithms on simulated GNSS scenarios. The proposed multiple-receiver methods provide more precise estimates for the SPP problem in comparison to the single receiver methods.

<p> </p> <p>Formulating RL with MDPs work typically works for a single objective, and hence, they are not readily applicable where the policies need to optimize multiple objectives or to satisfy certain constraints while maximizing one or multiple objectives, which can often be conflicting. Further, many applications such as robotics or autonomous driving do not allow for violating constraints even during the training process. Currently, existing algorithms do not simultaneously combine multiple objectives and zero-constraint violations, sample efficiency, and computational complexity. To this end, we study sample efficient Reinforcement Learning with concave objective and convex constraints, where an agent maximizes a concave, Lipschitz continuous function of multiple objectives while satisfying a convex cost objective. For this setup, we provide a posterior sampling algorithm which works with a convex optimization problem to solve for the stationary distribution of the states and actions. Further, using our Bellman error based analysis, we show that the algorithm obtains a near-optimal Bayesian regret bound for the number of interaction with the environment. Moreover, with an assumption of existence of slack policies, we design an algorithm that solves for conservative policies which does not violate  constraints and still achieves the near-optimal regret bound. We also show that the algorithm performs significantly better than the existing algorithm for MDPs with finite states and finite actions.</p>

This report studies about optical convex and concavelenses, made of liquid materials. Design proposals of the liquidlenses and the required supporting structure (container), as wellas manufacturing method have been investigated. 8 lenses aredesigned: 4 convex and 4 concave. The theoretical expectationsare validated by simulation and experimental results. The methodhave both advantages and disadvantages. The materials in thelenses are water, syrup, benzyl benzoate and bromone naphtha-lene. / Undersökning gällande optiska linser konvexa och konkava, bestående av flytande material. Designförslag av linser och skall, samt tillverkningsmetod har undersökts. De teoretiska förväntningarna validerades genom simulering och experimentella resultat. Metoden visas har både fördelar och nackdelar. Material i de linserna som vi har undersökt är vatten, sockerlösning, bensylbensoat och Bromonaftalen. / Kandidatexjobb i elektroteknik 2020, KTH, Stockholm