In computational science it is common to describe dynamic systems by mathematical models in forms of differential or integral equations. These models may contain parameters that have to be computed for the model to be complete. For the special type of ordinary differential equations studied in this thesis, the resulting parameter estimation problem is a separable nonlinear least squares problem with equality constraints. This problem can be solved by iteration, but due to complicated computations of derivatives and the existence of several local minima, so called short-cut methods may be an alternative. These methods are based on simplified versions of the original problem. An algorithm, called the modified Kaufman algorithm, is proposed and it takes the separability into account. Moreover, different kinds of discretizations and formulations of the optimization problem are discussed as well as the effect of ill-conditioning. Computation of parameters often includes as a part solution of linear system of equations Ax = b. The corresponding pseudoinverse solution depends on the properties of the matrix A and vector b. The singular value decomposition of A can then be used to construct error propagation matrices and by use of these it is possible to investigate how changes in the input data affect the solution x. Theoretical error bounds based on condition numbers indicate the worst case but the use of experimental error analysis makes it possible to also have information about the effect of a more limited amount of perturbations and in that sense be more realistic. It is shown how the effect of perturbations can be analyzed by a semi-experimental analysis. The analysis combines the theory of the error propagation matrices with an experimental error analysis based on randomly generated perturbations that takes the structure of A into account

We study the equilibrium solutions of an integrodifferential equation used to model one-dimensional biological swarms. We assume that the motion of the swarm is governed by pairwise interactions, or a convolution in the continuous setting, and derive a continuous model from conservation laws. The steady-state solution found for the model is compactly supported and is shown to be an attractive equilibrium solution via linear perturbation theory. Numerical simulations support that the steady-state solution is attractive for all initial swarm distributions. Some initial results for the model in higher dimensions are also presented.

Denna uppsats inriktar sig på rekvisitet verksam i betydande omfattning (verksamhetsrekvisitet) i relation till ”vanliga anställda” i personalägda fåmansföretag. Det framgår i förarbetena att verksamhetsrekvisitet anses vara uppfyllt när delägarens arbetsinsatser har stor betydelse för vinstgenereringen. Den avgörande faktorn här är om delägaren genom arbetsinsatser genererat intäkter till företaget. Arbetsinsatser av ”vanliga anställda”, dvs. anställda utan någon ledarbefattning eller utan kvalifikationer för företagets kärnverksamhet, anses i vanliga fall inte generera vinster till företaget. Det avgjordes dock några rättsfall där domstolen ansåg att ”vanliga anställda” var verksamma i betydande omfattning. Det är därför relevant att utreda om domstolens bedömningar i de här rättsfallen avviker från syftet bakom verksamhetsrekvisitet. Uppsatsens syfte är att utreda om domstolens bedömningar i rättspraxis som berör rekvisitet ”verksam i betydande omfattning” i relation till ”vanliga anställda” i personalägda företag avviker från lagstiftarens syfte bakom rekvisitet. Lagtexten ger ingen förklaring till hur verksamhetsrekvisitet ska tolkas. I uppsatsen läggs därför vikt vid analysen av förarbeten för att fastställa motivet till lagstiftningen. För att uppnå uppsatsens syfte görs därefter en jämförande analys av praxis med förarbetena. Författaren finner att domstolens bedömningar avviker från syftet bakom verksamhetsrekvisitet beträffande ”vanliga anställda” i personalägda företag. Uppsatsen visar att domstolen stegvis har slutat ta ställning till om arbetsinsatser av sådana anställda har någon betydelse för vinstgenereringen. Domstolen betraktar ”vanliga anställda” som aktivt verksamma utan att ge övertygande skäl till sitt avgörande. Det visas även att domstolens avgöranden påverkar framtida bedömningar i likartade mål. / This thesis focuses on the criterion significantly active in relation to ordinary employees in employee-owned private companies. Shareholders in close companies are considered to be significantly active when their undertakings are essential for the company’s profit. The decisive factor here is whether the shareholders contribute profits to the company. Ordinary employees usually are not concidered to generate profits to the company. Nevertheless, there have been several legal cases in which the Court stated that ordinary employees were significantly active. The question that arises is if the Court’s judgement in these cases deviates from what the legislator meant with the criterion “significantly active” concerning ordinary employees. The purpose of this thesis is to investigate whether the Courts’s judgement in the case law that concerns the criterion “significantly active” in relation to ordinary employees in employee-owned private companies deviates from what the legislator meant with this criterion. The law does not provide any guidance to how the criterion shoud be interpreted. The thesis is based therefore on the comparative analysis of the preparatory work with the relevant case law in order to answer the purpose of this thesis. The conclusion made in this thesis is that the Court’s judgement does deviate from what the legislator meant with the criterion “significantly active” concerning ordinary employees in employee-owned private companies. The analysis shows that the Court does not take into consideration whether such employees’ contribution is profitable to the company. The Court states that ordinary employees are significantly active without giving any convincing justification for its decision. Furthermore, the Court’s decisions affect future judgements in similar cases.

No description available.

The ordinary least squares (OLS) is one of the most widely used methods for modelling the functional relationship between variables. However, this estimation procedure counts on some assumptions and the violation of these assumptions may lead to nonrobust estimates. In this study, the simple linear regression model is investigated for conditions in which the distribution of the error terms is Generalised Logistic. Some robust and nonparametric methods such as modified maximum likelihood (MML), least absolute deviations (LAD), Winsorized least squares, least trimmed squares (LTS), Theil and weighted Theil are compared via computer simulation. In order to evaluate the estimator performance, mean, variance, bias, mean square error (MSE) and relative mean square error (RMSE) are computed.

Human T-lymphotropic virus type I (HTLV-I) is a persistent human retrovirus characterized by life-long infection and risk of developing HAM/TSP, a progressive neurological and inflammatory disease. Despite extensive studies of HTLV-I, a complete understanding of the viral dynamics has been elusive. Previous mathematical models are unable to fully explain experimental observations. Motivated by a new hypothesis for the mechanism of HTLV-I infection, a three dimensional compartmental model of ordinary differential equations is constructed that focusses on the highly dynamic interactions among populations of healthy, latently infected, and actively infected target cells. Results from mathematical and numerical investigations give rise to relevant biological interpretations. Comparisons of these results with experimental observations allow us to assess the validity of the original hypothesis. Our findings provide valuable insights to the infection and persistence of HTLV-I in vivo and motivate future mathematical and experimental work. / Applied Mathematics

在人口統計領域中，早期習慣將人口變化視為時間的函數，企圖以Deterministic Function來刻劃，例如：1798年Malthus提出的Malthusian Growth Model ；1825年Gompertz提出的Gompertz Model以及1838年Verhulst主張以Logistic Function描述人口成長。而近年來則是傾向於逐項分析各種因素的隨機性模型，例如：1983年Holford加入世代的APC模型；1992年Lee 和Carter提出的Lee-Carter死亡率模型以及2003年Renshaw與Haberman提出改善Lee-Carter死亡率模型的Reduction Factor模型。 人口變化主要分成自然增加與社會增加，而自然增加是為出生扣掉死亡，社會增加則為移入扣掉移出。首先，本文先不考慮遷移的部分，各別以出生與死亡人口的變化為研究對象，視其變化為一隨時間變動的動態系統，以常微分方程來刻劃。由台灣地區人口統計資料顯示，出生率或死亡率都有逐年下降的趨勢，而且隨著時間而變化加劇的傾向，使得以往使用的模型不易捕捉變化，因此我們提出「二次逼近法」，從出生、死亡人數對時間的變化率與曲度利用數值分析的方式來估計出生與死亡數，進而從中找出在此動態系統背後隱藏的規則。而後再同時考慮其他各種變項，以偏微分方程來刻劃，最後即可建立台灣地區人口變化模型。 / In early population statistics, the population changes were regarded as a function of time so that people tended to describe the variations by deterministic functions. For instance, Malthus proposed the Malthusian Growth Model in 1798; Gompertz presented Gompertz Model in 1825; Verhulst advocated using logistic function to describe an increase in population. In recent years, people tend to use the stochastic forecast method to analyse every factor term by term. For instance, the Age-Period-Cohort (APC) Model which was proposed by Holford in 1983; Lee and Carter proposed the Lee-Carter Mortality Model in 2003; and Renshaw and Haberman proposed the Reduction Factor Model in 2003 that improve the Lee-Carter Mortality Model. The population changes equal to nature and social increase, where the nature increase is the difference between birth and death population, and the social increase is the difference between immigrants and emigrants. First, we focus on natural increase rather than social increase. Moreover, we use ordinary differential equation to decribe the variation as a dynamic system over time. From the data obtained from the Ministry of Interior Taiwan, we know that the fertility and mortality has been decreasing, and the change is getting more violent year by year. Under the consideration that previous models are not able to accurately present the changes of birth and death, we proposed "second-order (or parabola) approximation method." From the variation rates and curvatures of birth and death population, we estimated the population size. Furthermore, we want to find the rule in the dynamic system. Later we will consider other factors simultaneously, and describe them by partial differential equation. Finally, the population model is constructed.

Made available in DSpace on 2016-05-17T16:51:23Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-08-17. Added 1 bitstream(s) on 2016-05-17T16:54:59Z : No. of bitstreams: 1 000864540.pdf: 1039983 bytes, checksum: 385664595ca05055e160d04f90391778 (MD5) / Russell Harrison (1994) reconhece a presença do chauvinismo machista na obra de Charles Bukowski e afirma que a redação de seus romances tem de ser vista no contexto da 'segunda onda do feminismo', época na qual Bukowski se consolidou como escritor, e como consequência recebeu influência. Esse momento da liberação feminina é representado por livros tais como Sexual Politics de Kate Millett (1969) e The Female Eunuch de Germaine Greer (1970). Bukowski, conhecido por apresentar a mulher como objeto do desejo masculino, demonstra uma sensibilidade diante da objetificação do corpo feminino no conto 'The Most Beautiful Woman in Town', no qual o autor retrata a protagonista Cass como vulnerável e carente de assistência. A dissertação situa esse conto no contexto dos 64 contos de Erections, Ejaculations, Exhibitions and Tales of Ordinary Madness (1972), para demonstrar a forma excepcional com que o autor mostra a sua sensibilidade em relação à figura feminina no contexto de uma coletânea caracterizada por sua misoginia / Russell Harrison (1994) recognises the male chauvinism of Charles Bukowski's work and argues that his novels must be seen in the context of the 'second wave of the feminism', a time in which Bukowski established himself as a writer, and which certainly influenced him. This point in the struggle for women's liberation is represented by books such as Sexual Politics, by Kate Millett (1969), and The Female Eunuch, by Germaine Greer (1970). Bukowski, known for his presentation of women as the objects of male desire, demonstrates a sensitivity concerning the objectification of the female body in the story 'The Most Beautiful Woman in Town', in which he depicts the protagonist, Cass, as vulnerable and in need of assistance. The dissertation situates this story in the context of the 64 stories of Erections, Ejaculations, Exhibitions and Tales of Ordinary Madness (1972) in order to demonstrate how exceptional its sensitivity with regard to women is in a collection characterised by its misogynism

L’énergie apparaît comme un problème public majeur, dans la résolution duquel les pouvoirs publics s’engagent régulièrement. Mais, à l’autre bout de cette chaîne, comment les individus ordinaires s’approprient-ils le problème public de l’énergie ? Dans les mesures classiques de l’opinion publique, les questions énergétiques et environnementales sont souvent loin d’occuper les premières places dans la hiérarchie des priorités. Or, pour réduire la pression engendrée par nos modes de consommation sur les écosystèmes, le changement des comportements et des attitudes de consommation est présenté comme un levier majeur. La question énergétique est-elle alors un enjeu politique pour tous mais un problème pour personne ? Pour répondre à cette question nous nous interrogeons sur la fabrique des opinions ordinaires et nous proposons de considérer ces dernières comme des énoncés discursifs testés dans des situations sociales plus ou moins complexes, conflictuelles et publiques. En amont, bon nombre d'acteurs ayant accès à l'espace public contribue à orienter et promouvoir certaines injonctions normatives pour définir la « bonne » pratique. Mais ces injonctions ne sont ni stables, ni homogènes : elles font l'objet de controverses et donnent lieu à des reformulations discursives parfois dissonantes. Entre enjeux technologiques, économiques, écologiques, sociétaux, etc. l’énergie comme problème public est alors soumise à un cadrage par des ordres normatifs dynamiques définissant certaines déviances et se voit proposer des solutions reconnues comme légitimes sous l’effet, entre autres, de l’action publique. Mais, ce niveau de description fait l’économie de la parole des citoyens « ordinaires », couvrant ainsi un présupposé instrumental commun qui estime que les citoyens dotés de la « bonne » information agissent « correctement ». Ce présupposé est contestable. Certes, une majorité écrasante d’enquêtés souligne son accord de principe aux économies d’énergie, témoignant ainsi de sa connaissance – même partielle – de l’existence d’un « problème public de l’énergie » et d’un engagement – même limité – aux injonctions à la modération en termes de consommation énergétique. Mais cet accord tacite se heurte à d’autres injonctions, à la compétition des problèmes, des pratiques sociales et à la mise en œuvre pratique des solutions. Ni surcompétents, ni incompétents, les citoyens ordinaires construisent donc du sens à travers des ordres normatifs concurrentiels et cherchent à le rendre compatible avec leurs modes de vie. Pour ce faire, la confrontation de leurs opinions et l’ajustement collectif de leurs représentations sont nécessaires. En reprenant certaines notions du pragmatisme, nous interrogeons la manière dont les perceptions du problème de l’énergie varient selon les scènes sociales où il est discuté, leur publicité ou encore le degré de conflictualité qu’il génère, et nous montrons que des communautés locales interprétatives d’un problème – et éventuellement de solutions – peuvent émerger et contribuer à alimenter la légitimité du problème dans l’espace public. Par ce biais, nous soulignons qu’il existe des espaces adossés au politique mais qui ne répondent pas toujours aux critères de conflictualisation et montée en généralité. Ces espaces illustrent l’intérêt de prendre en compte l’ambivalence et la labilité des opinions dans l’appropriation d’un problème public et la normalisation de ses solutions. / Energy appears to be a major public problem, in which the public authorities regularly commit. But at the other end of this chain, how do ordinary individuals appropriate the public problem of energy? In the classical measures of public opinion, energy and environmental issues are often far from the top of the hierarchy of priorities. However, to reduce the pressure generated by our consumption patterns on ecosystems, the change in consumer behavior and attitudes is presented as a major lever. Is the energy issue then a political issue for all but a problem for no one? In order to answer this question, we question the fabric of ordinary opinions and propose to consider them as discursive statements tested in more or less complex, conflicting and public social situations.Upstream, many actors with access to public space help to guide and promote certain normative injunctions to define "good" practice. But these injunctions are neither stable nor homogeneous: they are the subject of controversies and give rise to discursive reformulations, sometimes dissonant. Between technological, economic, ecological, societal, etc. energy as a public problem is then subjected to a framing by dynamic normative orders defining certain deviations and is offered solutions recognized as legitimate under the influence of, inter alia, public action.But this level of description does not take "ordinary" citizens into account, and covers a common instrumental presupposition that citizens with "good" information act "correctly". This presupposition is questionable. Admittedly, an overwhelming majority of respondents stressed their agreement in principle to energy savings, thus demonstrating their knowledge - even partial - of the existence of a "public energy problem" and a commitment - even limited - to injunctions to moderate their energy consumption. But this tacit agreement comes up against other injunctions, competition between problems, social practices and the practical implementation of solutions.Neither overcompetent nor incompetent, ordinary citizens construct meaning through competitive normative norms and seek to make it compatible with their lifestyles. To do this, the confrontation of their opinions and the collective adjustment of their representations are necessary. By taking up some of the notions of pragmatism, we examine how the perceptions of the energy problem vary according to the social scenes in which it is discussed, their publicity or the degree of conflict that they generate, and we show that local communities with a common interpretation of a problem - and possibly solutions - can emerge and help fuel the legitimacy of the problem in public space. In this way, we emphasize that there are more or less public spaces but which do not always meet the criteria of conflictualization and rise in generality. These spaces illustrate the importance of taking into account the ambivalence and the lability of opinions in the appropriation of a public problem and the standardization of its solutions.

Cette thèse est consacrée à l'étude de la dynamique des systèmes complexes. Nous construisons des réseaux couplés à partir de multiples instances de systèmes dynamiques déterministes, donnés par des équations différentielles ordinaires ou des équations aux dérivées partielles de type parabolique, qui décrivent un problème d'évolution. Nous étudions le lien entre la dynamique interne à chaque nœud du réseau, les éléments de la topologie du graphe portant ce réseau, et sa dynamique globale. Nous recherchons les conditions de couplage qui favorisent une dynamique globale particulière à l'échelle du réseau, et étudions l'impact des interactions sur les bifurcations identifiées sur chaque nœud. Nous considérons en particulier des réseaux couplés de systèmes de réaction-diffusion, dont nous étudions le comportement asymptotique, en recherchant des régions positivement invariantes, et en démontrant l'existence d'attracteurs exponentiels de dimension fractale finie, à partir d'estimations d'énergie qui révèlent la nature dissipative de ces réseaux de systèmes de réaction-diffusion. Ces questions sont étudiées dans le cadre de quelques applications. En particulier, nous considérons un modèle mathématique pour l'étude géographique des réactions comportementales d'individus, au sein d'une population en situation de catastrophe. Nous présentons les éléments de modélisation associés, ainsi que son étude mathématique, avec une analyse de la stabilité des équilibres et de leurs bifurcations. Nous établissons l'importance capitale des chemins d'évacuation dans les réseaux complexes construits à partir de ce modèle, pour atteindre l'équilibre attendu de retour au comportement du quotidien pour l'ensemble de la population considérée, tout en évitant une propagation du comportement de panique. D'autre part, la recherche de solutions périodiques émergentes dans les réseaux d'oscillateurs nous amène à considérer des réseaux complexes de systèmes hamiltoniens pour lesquels nous construisons des perturbations polynomiales qui provoquent l'apparition de cycles limites, problématique liée au XVIème problème de Hilbert. / This thesis is devoted to the study of the dynamics of complex systems. We consider coupled networks built with multiple instances of deterministicdynamical systems, defined by ordinary differential equations or partial differential equations of parabolic type, which describe an evolution problem.We study the link between the internal dynamics of each node in the network, its topology, and its global dynamics. We analyze the coupling conditions which favor a particular dynamics at the network's scale, and study the impact of the interactions on the bifurcations identified on each node. In particular, we consider coupled networks of reaction-diffusion systems; we analyze their asymptotic behavior by searching positively invariant regions, and proving the existence of exponential attractors of finite fractal dimension, derived from energy estimates which suggest the dissipative nature of those networks of reaction-diffusion systems.Our framework includes the study of multiple applications. Among them, we consider a mathematical model for the geographical analysis of behavioral reactions of individuals facing a catastrophic event. We present the modeling choices that led to the study of this evolution problem, and its mathematical study, with a stability and bifurcation analysis of the equilibria. We highlight the decisive role of evacuation paths in coupled networks built from this model, in order to reach the expected equilibrium corresponding to a global return of all individuals to the daily behavior, avoiding a propagation of panic. Furthermore, the research of emergent periodic solutions in complex networks of oscillators brings us to consider coupled networks of hamiltonian systems, for which we construct polynomial perturbationswhich provoke the emergence of limit cycles, question which is related to the sixteenth Hilbert's problem.