At an early age, i.e., up to about 1-2 years, humans learn to walk and subsequently develop a robust and flexible gait. This is learned by repetitively taking similar steps and the experience is stored in the muscle/reflexive memory. Over the last 30 years, a variety of humanoid bipedal robots have been developed to copy the human gait. However, walking/locomotion is still a relatively difficult control problem due to its complex hybrid nature because of non-smooth dynamics. Although, simple walking comprises of single support in which one leg swings forward, then it impacts with ground for a brief double support phase and further transition of the other support leg to start a new swing. The steps are repeated again and again in a similar manner for walking over an even surface. As the swinging leg strikes the ground, it is a non-linear impact which poses a challenge since it causes non-zero initial state errors for each step which depend on the error in the gait at last moment for previous step. The usual bipedal control relies on complex techniques based on inverse kinematics, ZMP (Zero-Moment Pole) and COP (Centre Of Pressure) to generate the required control inputs for the joints. However, a basic cognitive assumption is that walking is a relatively simple task which can be learned and the biological systems have achieved it by simple repetitions. This has been over-looked in these control techniques. In the past, ILC has been proposed to solve the repetitive learning problems. The Iterative Learning Controller learns to generate the desired set of input signals to compensate for the output tracking errors in a sequential manner such that in the initial iterations, the signals values at earlier time indices have faster rate than the later ones. So, at the last time index the convergence is achieved after all the earlier ones. ILC learns/adapts the joint control for repetitive gaits. In this thesis it has been proposed to be used as a muscle memory where control signals are learnt for a repetitive batch. Thus, ILC equates to “learning a sequence of action by muscles”. Due to the transfer of state error in a cyclic manner from the end of a previous step/repetition to the recent step/repetition, the convergence has to be established in joint control and state space. Similar is the case of continuous walking where the ground impacts transfer part of the error in the gait to the start of a new step representing an impacting Cyclic ILC scenario. Hence, the ILC problem is changed from finite to an infinite horizon. The second problem occurs with the non-constant length of the iteration due to change in step size. The two scenarios have been considered: Firstly, when the control input is updated using ILC with identical initial conditions at the start of each repetition. Secondly, control input update under varying initial conditions leading to Cyclic ILC. The batch to batch evolution of control inputs at each sample time within a batch is formulated. The sequential convergence of control input generated by ILC algorithms has been investigated. The exact relationship for the rate of convergence of the control input has been formulated down to the sample-time level. This provides deeper insight about the ILC algorithms and hence exact factors affecting the convergence could be established. Limits of the learning process have been clearly demonstrated as well. Although, simpler D-ILC converges for zero initial error but for cyclic non-zero initial errors, it has offset error which corresponds to the initial state error. With proportional part, the PD-ILC algorithm has eliminated the offset error which has been illustrated for a damped pendulum and further implemented to bipedal locomotion. For reasons of energy efficiency, passive dynamics has been chosen for the compass gait model of the biped. The walking problem for the compass gait robot has been solved using the modified PD-ILC which utilizes the acceleration error term as well. The steady gait has been achieved for the compass gait robot on flat surface which has been verified by the phase portraits.

This paper will be concerned with the convergence of complex power series.

Phasmatodea exhibit a variety of cryptic ecomorphs associated with various microhabitats. Multiple ecomorphs are present in the stick insect fauna from Papua New Guinea, including the tree lobster, spiny, and long slender forms. While ecomorphs have long been recognized in phasmids, there has yet to be an attempt to objectively define and study the evolution of these ecomorphs. Using principal component analysis, PERMANOVA, ANOVA, and phylogenetic reconstructions, we examined the evolution of ecomorphs in the Lonchodinae stick insects of Papua New Guinea. Phylogenetic reconstructions were performed via maximum likelihood and Bayesian methods and ecomorphs were mapped onto recovered topologies to assess patterns of ecomorph evolution. Statistical test supported a general tree lobster ecomorph grouping with overlap of the slender and spiny ecomorph groups. Phylogenetic reconstructions recovered predominantly congruent topologies, with indications of ecomorph convergence across Phasmatodea. Three independent origins of the tree lobster ecomorph were recovered within the subfamily Lonchodinae. When ecomorph evolution was examined across Phasmatodea, multiple origins of the slender, spiny, tree lobster, and large winged ecomorphs were also recovered.

En este trabajo de investigación se busca conocer cuáles son los cambios y continuidades de la versión impresa del diario ‘La República’ a la versión digital. Para ello, se tomó como pretexto los artículos del caso lavado de activos en Fuerza Popular para reconocer si el diario ha mantenido o cambiado las prácticas y herramientas comunicativas al exponer la noticia. Al analizar se encontró que ‘La República’ ha modificado o añadido algunas prácticas periodísticas y herramientas para producir la noticia, comunicarse con el consumidor y llamar su atención. Algunas de estas prácticas y elementos comunicativos que se modificaron son los siguientes: La manera de presentar la noticia y de demostrar su relevancia, la interacción del consumidor con la información y la forma de exponer datos relacionados a la noticia. Así como se identificaron los cambios del diario ‘La República’, también se identificaron las estrategias y herramientas que se han mantenido para exponer el contenido informativo, tanto en el medio impreso como en el digital. Algunas de estas actividades, estrategias y herramientas similares son los siguientes: La opinión del periodista dentro de los lineamientos del diario, la priorización de los datos que perjudican la imagen del partido Fuerza Popular, la verificación de la información, el uso de la fotografía como un discurso informativo y crítico sobre la noticia, la integración de elementos visuales y textuales en el contenido, además el orden de la información. / This research work seeks to know what the changes and continuities are from the printed version of the newspaper 'La República' to the digital version. For this, the articles of the money laundering case in Fuerza Popular were lost as a pretext to recognize if the newspaper has changed or the communication practices and tools when exposing the news. Upon analysis, it was found that ‘La República’ has modified or added some journalistic practices and tools to produce the news, communicate with the consumer and attract their attention. Some of these practices and communicative elements that were modified are the following: The way to present the news and to demonstrate its relevance, the interaction of the consumer with the information and the way to expose data related to the news. Just as the changes in the newspaper 'La República' were identified, the strategies and tools that have been maintained to expose the informative content, both in print and digital, were also identified. Some of these activities, strategies and similar tools are as follows: The journalist's opinion within the guidelines of the newspaper, the prioritization of data that harm the image of the Fuerza Popular party, the verification of information, the use of photography as an informative and critical discourse on the news, the integration of elements visual and textual in the content, as well as the order of the information. / Trabajo de investigación

The resource curse thesis states that countries with an abundance of natural resources tend to experience lower economic growth rates. However, does this theory apply also to the regional level? The purpose of this thesis is to both test the natural resources curse theory at the regional level in Sweden, as well to examine if different types of natural resource dependencies appear to have the same effect on regional income growth in the country. The methodological approach builds on an econometric (OLS) analysis using two different panel datasets over time intervals, 2000-2017 and 2007-2017, respectively. The results from one of the datasets suggest that the dependency on natural resources does not appear to affect Swedish counties' income growth, nor is there any difference in the impact on income growth from different types of natural resources. However, the corresponding results from the other dataset suggest a positive relationship, although these results are not robust across various model specifications. / Teorin om naturresursernas förbannelse förutspår att länder med ett överflöd av naturresurser kommer att ha en lägre ekonomisk tillväxt. Stämmer även denna teori på regional nivå? Syftet med denna studie är att undersöka om resursförbannelsen existerar på regional nivå i Sverige samt att undersöka om olika typer av naturresurser har olika påverkan på den regionala inkomstutvecklingen i landet. Metodiken för att besvara detta bygger på en ekonometrisk (OLS) analys med två olika paneldataset med skilda tidsintervaller, 2000–2017 och 2007–2017. De resultat som baseras på det ena datasetet visar att naturresurser inte har en påverkan på inkomstutvecklingen på svensk länsnivå, samt att olika typer av naturresurser inte heller har en påverkan på den regionala inkomstutvecklingen. Det andra datasetet påvisar dock att det finns ett positivt förhållande mellan regional inkomstutveckling och naturresurser, men detta resultat är inte robust.

Cette thèse est consacrée à l'étude des propriétés de convergence forte du schéma de Ninomiya et Victoir. Les auteurs de ce schéma proposent d'approcher la solution d'une équation différentielle stochastique (EDS), notée $X$, en résolvant $d+1$ équations différentielles ordinaires (EDOs) sur chaque pas de temps, où $d$ est la dimension du mouvement brownien. Le but de cette étude est d'analyser l'utilisation de ce schéma dans une méthode de Monte-Carlo multi-pas. En effet, la complexité optimale de cette méthode est dirigée par l'ordre de convergence vers $0$ de la variance entre les schémas utilisés sur la grille grossière et sur la grille fine. Cet ordre de convergence est lui-même lié à l'ordre de convergence fort entre les deux schémas. Nous montrons alors dans le chapitre $2$, que l'ordre fort du schéma de Ninomiya-Victoir, noté $X^{NV,eta}$ et de pas de temps $T/N$, est $1/2$. Récemment, Giles et Szpruch ont proposé un estimateur Monte-Carlo multi-pas réalisant une complexité $Oleft(epsilon^{-2}right)$ à l'aide d'un schéma de Milstein modifié. Dans le même esprit, nous proposons un schéma de Ninomiya-Victoir modifié qui peut-être couplé à l'ordre fort $1$ avec le schéma de Giles et Szpruch au dernier niveau d'une méthode de Monte-Carlo multi-pas. Cette idée est inspirée de Debrabant et Rossler. Ces auteurs suggèrent d'utiliser un schéma d'ordre faible élevé au niveau de discrétisation le plus fin. Puisque le nombre optimal de niveaux de discrétisation d'une méthode de Monte-Carlo multi-pas est dirigé par l'erreur faible du schéma utilisé sur la grille fine du dernier niveau de discrétisation, cette technique permet d'accélérer la convergence de la méthode Monte-Carlo multi-pas en obtenant une approximation d'ordre faible élevé. L'utilisation du couplage à l'ordre $1$ avec le schéma de Giles-Szpruch nous permet ainsi de garder un estimateur Monte-Carlo multi-pas réalisant une complexité optimale $Oleft( epsilon^{-2} right)$ tout en profitant de l'erreur faible d'ordre $2$ du schéma de Ninomiya-Victoir. Dans le troisième chapitre, nous nous sommes intéressés à l'erreur renormalisée définie par $sqrt{N}left(X - X^{NV,eta}right)$. Nous montrons la convergence en loi stable vers la solution d'une EDS affine, dont le terme source est formé des crochets de Lie entre les champs de vecteurs browniens. Ainsi, lorsqu'au moins deux champs de vecteurs browniens ne commutent pas, la limite n'est pas triviale. Ce qui assure que l'ordre fort $1/2$ est optimal. D'autre part, ce résultat peut être vu comme une première étape en vue de prouver un théorème de la limite centrale pour les estimateurs Monte-Carlo multi-pas. Pour cela, il faut analyser l'erreur en loi stable du schéma entre deux niveaux de discrétisation successifs. Ben Alaya et Kebaier ont prouvé un tel résultat pour le schéma d'Euler. Lorsque les champs de vecteurs browniens commutent, le processus limite est nul. Nous montrons que dans ce cas précis, que l'ordre fort est $1$. Dans le chapitre 4, nous étudions la convergence en loi stable de l'erreur renormalisée $Nleft(X - X^{NV}right)$ où $X^{NV}$ est le schéma de Ninomiya-Victoir lorsque les champs de vecteurs browniens commutent. Nous démontrons la convergence du processus d'erreur renormalisé vers la solution d'une EDS affine. Lorsque le champ de vecteurs dritf ne commute pas avec au moins un des champs de vecteurs browniens, la vitesse de convergence forte obtenue précédemment est optimale / This thesis is dedicated to the study of the strong convergence properties of the Ninomiya-Victoir scheme, which is based on the resolution of $d+1$ ordinary differential equations (ODEs) at each time step, to approximate the solution to a stochastic differential equation (SDE), where $d$ is the dimension of the Brownian. This study is aimed at analysing the use of this scheme in a multilevel Monte Carlo estimator. Indeed, the optimal complexity of this method is driven by the order of convergence to zero of the variance between the two schemes used on the coarse and fine grids at each level, which is related to the strong convergence order between the two schemes. In the second chapter, we prove strong convergence with order $1/2$ of the Ninomiya-Victoir scheme $X^{NV,eta}$, with time step $T/N$, to the solution $X$ of the limiting SDE. Recently, Giles and Szpruch proposed a modified Milstein scheme and its antithetic version, based on the swapping of each successive pair of Brownian increments in the scheme, permitting to construct a multilevel Monte Carlo estimator achieving the optimal complexity $Oleft(epsilon^{-2}right)$ for the precision $epsilon$, as in a simple Monte Carlo method with independent and identically distributed unbiased random variables. In the same spirit, we propose a modified Ninomiya-Victoir scheme, which may be strongly coupled with order $1$ to the Giles-Szpruch scheme at the finest level of a multilevel Monte Carlo estimator. This idea is inspired by Debrabant and R"ossler who suggest to use a scheme with high order of weak convergence on the finest grid at the finest level of the multilevel Monte Carlo method. As the optimal number of discretization levels is related to the weak order of the scheme used in the finest grid at the finest level, Debrabant and R"ossler manage to reduce the computational time, by decreasing the number of discretization levels. The coupling with the Giles-Szpruch scheme allows us to combine both ideas. By this way, we preserve the optimal complexity $Oleft(epsilon^{-2}right)$ and we reduce the computational time, since the Ninomiya-Victoir scheme is known to exhibit weak convergence with order 2. In the third chapter, we check that the normalized error defined by $sqrt{N}left(X - X^{NV,eta}right)$ converges to an affine SDE with source terms involving the Lie brackets between the Brownian vector fields. This result ensures that the strong convergence rate is actually $1/2$ when at least two Brownian vector fields do not commute. To link this result to the multilevel Monte Carlo estimator, it can be seen as a first step to adapt to the Ninomiya-Victoir scheme the central limit theorem of Lindeberg Feller type, derived recently by Ben Alaya and Kebaier for the multilevel Monte Carlo estimator based on the Euler scheme. When the Brownian vector fields commute, the limit vanishes. We then prove strong convergence with order $1$ in this case. The fourth chapter deals with the convergence of the normalized error process $Nleft(X - X^{NV}right)$, where $X^{NV}$ is the Ninomiya-Victoir in the commutative case. We prove its stable convergence in law to an affine SDE with source terms involving the Lie brackets between the Brownian vector fields and the drift vector field. This result ensures that the strong convergence rate is actually $1$ when the Brownian vector fields commute, but at least one of them does not commute with the Stratonovich drift vector field

Repeated emergence of similar adaptations is often explained by parallel evolution of underlying genes. However, evidence of parallel evolution at amino acid level is limited. When the analyzed species are highly divergent, this can be due to epistatic interactions underlying the dynamic nature of the amino acid preferences: The same amino acid substitution may have different phenotypic effects on different genetic backgrounds. Distantly related species also often inhabit radically different environments, which makes the emergence of parallel adaptations less likely. Here, we hypothesize that parallel molecular adaptations are more prevalent between closely related species. We analyze the rate of parallel evolution in genome-size sets of orthologous genes in three groups of species with widely ranging levels of divergence: 46 species of the relatively recent lake Baikal amphipod radiation, a species flock of very closely related cichlids, and a set of significantly more divergent vertebrates. Strikingly, in genes of amphipods, the rate of parallel substitutions at nonsynonymous sites exceeded that at synonymous sites, suggesting rampant selection driving parallel adaptation. At sites of parallel substitutions, the intraspecies polymorphism is low, suggesting that parallelism has been driven by positive selection and is therefore adaptive. By contrast, in cichlids, the rate of nonsynonymous parallel evolution was similar to that at synonymous sites, whereas in vertebrates, this rate was lower than that at synonymous sites, indicating that in these groups of species, parallel substitutions are mainly fixed by drift.

No / Convergence properties are established for the piecewise linear heat balance integral solution of a benchmark moving boundary problem, thus generalising earlier results [Numer. Heat Transfer 8 (1985) 373]. A convergence rate of O(n¿1) is identified with minor effects at large values of the Stefan number ß (slow interface movement). The correct O(n¿1/2) behaviour for incident heat flux is recovered for ß ¿ 0 (pure heat conduction) as previously found [Numer. Heat Transfer 8 (1985) 373¿382]. Numerical illustrations support the theoretical findings.

<p> The various criteria and methods suggested in the literature for choosing the optimum sequence of calculation are compared. They are then analysed using the results of runs on three different simulations. Two techniques of convergence are used, and it is found that Geometric Convergence Promotion will improve the rate of convergence compared to Direct Substitution for any feasible sequence. It is also shown that the optimal sequences of calculation are different for the two techniques. </p> <p> It is concluded that the Minimum Cut Streams criterion is the best to use for Direct Substitution, but that the use of the feasible Set criterion and Convergence Promotion will yield better convergence. The iterative improvement of convergence is discussed, and it is concluded that the available time is best spent on improving the starting point and the Convergence Promotion technique rather than on changing the sequence of calculation. </p> / Thesis / Master of Engineering (MEngr)

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