This dissertation is focused on an algebraic approach of some many-valued generalizations of modal logics. The starting point is the definition of the [0,1]-valued and the Ł_n-valued Kripke models, where [0,1] denotes the well known MV-algebra and Ł_n its finite subalgebra {0, 1/n, ... , (n-1)/n,1} for any positive integer n. Two types of structures are used to define validity of formulas: the class of L-frames and the class of Ł_n-valued L-frames. The latter structures are L-frames in which we specify in each world u the set Ł_m (where m is a divisor of n) of the possible truth values of the formulas in u. These two classes of structures define two distinct notions of validity. We use these notions to study the problem of definability of classes of structures with modal formulas. We obtain for these two classes an equivalent of the Goldblatt-Thomason theorem. We are able to consider completeness problems with respect to these relational semantics thanks to the connections between relational and algebraic semantics. Our strongest results are about Ł_n-valued logics. We are indeed able to apply and develop algebraic tools (namely, canonical and strong canonical extensions) that allow to generate complete Ł_n-valued logics. / Nous consacrons cette dissertation à une étude algébrique de certaines généralisations multivaluées des logiques modales. Notre point de départ est la définition des modèle de Kripke [0,1]-valués et Ł_n-valués, où [0,1] désigne la MV-algèbre bien connue et Ł_n sa sous-algèbre {0, 1/n, ... , (n-1)/n,1} pour tout naturel non nul n. Nous utilisons deux types de structures pour définir une relation de validité: la classe des L-structures et celles des L-structures Ł_n-valuées. Ces dernières sont des L-structures dans lesquelles nous précisons pour chaque monde u l'ensemble Ł_m (où m est un diviseur de n) des valeurs de vérité que les formules sont autorisées à prendre en u. Ces deux classes de structures définissent deux notions distinctes de validité. Nous les utilisons pour étudier le problème de la définissabilité des classes de structures à l'aide du langage modal. Nous obtenons dans les deux cas l'équivalent du théorème de Goldblatt-Thomason. Nous considérons aussi les problèmes de complétude vis-à-vis de ces sémantiques relationnelles à l'aide des liens qui les lient à la sémantique algébrique. Les résultats les plus forts que nous obtenons concernent les logiques modales Ł_n-valuées. En effet, dans ce cas, nous pouvons appliquer et développer des outils algébriques (à savoir, les extensions canoniques et les extensions canoniques fortes) qui permettent de générer des logiques complètes.

Modern control theory is today an interdisciplinary area of research. Just as much as this can be problematic, it also provides a rich research environment where practice and theory meet. This Thesis is conducted in the borderline between computing science (numerical analysis) and applied control theory. The design and analysis of a modern control system is a complex problem that requires high qualitative software to accomplish. Ideally, such software should be based on robust methods and numerical stable algorithms that provide quantitative as well as qualitative information. The introduction of the Thesis is dedicated to the underlying control theory and to introduce the reader to the main subjects. Throughout the Thesis, the theory is illustrated with several examples, and similarities and differences between the terminology from mathematics, systems and control theory, and numerical linear algebra are highlighted. The main contributions of the Thesis are structured in two parts, dealing with two mainly unrelated subjects. Part I is devoted to the qualitative information which is provided by the stratification of orbits and bundles of matrices, matrix pencils and system pencils. Before the theory of stratification is established the reader is introduced to different canonical forms which reveal the system characteristics of the model under investigation. A stratification reveals which canonical structures of matrix (system) pencils are near each other in the sense of small perturbations of the data. Fundamental concepts in systems and control, like controllability and observability of linear continuous-time systems, are considered and it is shown how these system characteristics can be investigated using the stratification theory. New results are presented in the form of the cover relations (nearest neighbours) for controllability and observability pairs. Moreover, the permutation matrices which take a matrix pencil in the Kronecker canonical form to the corresponding system pencil in (generalized) Brunovsky canonical form are derived. Two novel algorithms for determining the permutation matrices are provided. Part II deals with numerical methods for solving periodic Riccati differential equations (PRDE:s). The PRDE:s under investigation arise when solving the linear quadratic regulator (LQR) problem for periodic linear time-varying (LTV) systems. These types of (periodic) LQR problems turn up for example in motion planning of underactuated mechanical systems, like a humanoid robot, the Furuta pendulum, and pendulums on carts. The constructions of the nonlinear controllers are based on linear versions found by stabilizing transverse dynamics of the systems along cycles. Three different methods explicitly designed for solving the PRDE are evaluated on both artificial systems and stabilizing problems originating from experimental control systems. The methods are the one-shot generator method and two recently proposed methods: the multi-shot method (two variants) and the SDP method. As these methods use different approaches to solve the PRDE, their numerical behavior and performance are dependent on the nature of the underlying control problem. Such method characteristics are investigated and summarized with respect to different user requirements (the need for accuracy and possible restrictions on the solution time). / Modern reglerteknik är idag i högsta grad ett interdisciplinärt forskningsområde. Lika mycket som detta kan vara problematiskt, resulterar det i en stimulerande forskningsmiljö där både praktik och teori knyts samman. Denna avhandling är utförd i gränsområdet mellan datavetenskap (numerisk analys) och tillämpad reglerteknik. Att designa och analysera ett modernt styrsystem är ett komplext problem som erfordrar högkvalitativ mjukvara. Det ideala är att mjukvaran består av robusta metoder och numeriskt stabila algoritmer som kan leverera både kvantitativ och kvalitativ information.Introduktionen till avhandlingen beskriver grundläggande styr- och reglerteori samt ger en introduktion till de huvudsakliga problemställningarna. Genom hela avhandlingen illustreras teori med exempel. Vidare belyses likheter och skillnader i terminologin som används inom matematik, styr- och reglerteori samt numerisk linjär algebra. Avhandlingen är uppdelade i två delar som behandlar två i huvudsak orelaterade problemklasser. Del I ägnas åt den kvalitativa informationen som ges av stratifiering av mångfalder (orbits och bundles) av matriser, matrisknippen och systemknippen. Innan teorin för stratifiering introduceras beskrivs olika kanoniska former, vilka var och en avslöjar olika systemegenskaper hos den undersökta modellen. En stratifiering ger information om bl.a. vilka kanoniska strukturer av matrisknippen (systemknippen) som är nära varandra med avseende på små störningar i datat. Fundamentala koncept i styr- och reglerteori behandlas, så som styrbarhet och observerbarhet av linjära tidskontinuerliga system, och hur dessa systemegenskaper kan undersökas med hjälp av stratifiering. Nya resultat presenteras i form av relationerna för täckande (närmsta grannar) styrbarhets- och observerbarhets-par. Dessutom härleds permutationsmatriserna som tar ett matrisknippe i Kroneckers kanoniska form till motsvarande systemknippe i (generaliserade) Brunovskys kanoniska form. Två algoritmer för att bestämma dessa permutationsmatriser presenteras. Del II avhandlar numeriska metoder för att lösa periodiska Riccati differentialekvationer (PRDE:er). De undersökta PRDE:erna uppkommer när ett linjärt kvadratiskt regulatorproblem för periodiska linjära tidsvariabla (LTV) system löses. Dessa typer av (periodiska) regulatorproblem dyker upp till exempel när man planerar rörelser för understyrda (underactuated) mekaniska system, så som en humanoid (mänsklig) robot, Furuta-pendeln och en vagn med en inverterad (stående) pendel. Konstruktionen av det icke-linjära styrsystemet är baserat på en linjär variant som bestäms via stabilisering av systemets transversella dynamik längs med cirkulära banor. Tre metoder explicit konstruerade för att lösa PRDE:er evalueras på både artificiella system och stabiliseringsproblem av experimentella styrsystem. Metoderna är sk. en- och flerskotts metoder (one-shot, multi-shot) och SDP-metoden. Då dessa metoder använder olika tillvägagångssätt för att lösa en PRDE, beror dess numeriska egenskaper och effektivitet på det underliggande styrproblemet. Sådana metodegenskaper undersöks och sammanfattas med avseende på olika användares behov, t.ex. önskad noggrannhet och tänkbar begränsning i hur lång tid det får ta att hitta en lösning.

In medicine, data are produced from different sources and continuously stored in data depositories. Examples of these growing databases are quality registries. In Sweden, there are many cancer registries where data on cancer patients are gathered and recorded and are used mainly for reporting survival analyses to high level health authorities. In this thesis, a breast cancer quality registry operating in South-East of Sweden is used as the data source for newer analytical techniques, i.e. data mining as a part of knowledge discovery in databases (KDD) methodology. Analyses are done to sift through these data in order to find interesting information and hidden knowledge. KDD consists of multiple steps, starting with gathering data from different sources and preparing them in data pre-processing stages prior to data mining. Data were cleaned from outliers and noise and missing values were handled. Then a proper subset of the data was chosen by canonical correlation analysis (CCA) in a dimensionality reduction step. This technique was chosen because there were multiple outcomes, and variables had complex relationship to one another. After data were prepared, they were analyzed with a data mining method. Decision tree induction as a simple and efficient method was used to mine the data. To show the benefits of proper data pre-processing, results from data mining with pre-processing of the data were compared with results from data mining without data pre-processing. The comparison showed that data pre-processing results in a more compact model with a better performance in predicting the recurrence of cancer. An important part of knowledge discovery in medicine is to increase the involvement of medical experts in the process. This starts with enquiry about current problems in their field, which leads to finding areas where computer support can be helpful. The experts can suggest potentially important variables and should then approve and validate new patterns or knowledge as predictive or descriptive models. If it can be shown that the performance of a model is comparable to domain experts, it is more probable that the model will be used to support physicians in their daily decision-making. In this thesis, we validated the model by comparing predictions done by data mining and those made by domain experts without finding any significant difference between them. Breast cancer patients who are treated with mastectomy are recommended to receive radiotherapy. This treatment is called postmastectomy radiotherapy (PMRT) and there is a guideline for prescribing it. A history of this treatment is stored in breast cancer registries. We analyzed these datasets using rules from a clinical guideline and identified cases that had not been treated according to the PMRT guideline. Data mining revealed some patterns of non-compliance with the PMRT guideline. Further analysis with data mining revealed some reasons for guideline non-compliance. These patterns were then compared with reasons acquired from manual inspection of patient records. The comparisons showed that patterns resulting from data mining were limited to the stored variables in the registry. A prerequisite for better results is availability of comprehensive datasets. Medicine can take advantage of KDD methodology in different ways. The main advantage is being able to reuse information and explore hidden knowledge that can be obtained using advanced analysis techniques. The results depend on good collaboration between medical informaticians and domain experts and the availability of high quality data.

Conserving structural and compositional diversity in Fescue Prairie requires reintroducing natural disturbances according to their historic regime. Fire is an important natural process that may be a source of spatial heterogeneity in Fescue Prairies. The effects of burning in all months of the year except January and February were evaluated in a Fescue Prairie in central Saskatchewan for 6 years following burning on 2 sites that had not been previously burned and 2 sites that had been burned 5 years earlier. Except for burning in March, burning reduced cover of litter (P<0.01) and <i>Festuca hallii </i> (Vasey) Piper (P=0.01) while increasing bare soil (P<0.01) for 1 to 5 years. Cover of <i>Elymus lanceolatus </i>(Scribn. & J.G. Sm.) Gould (P<0.01), graminoids (P=0.02), and species evenness (P=0.01) increased with burning frequency. Burning in late-summer reduced cover of graminoids (P=0.03), plants other than the dominant grasses (P=0.03), and total plant cover (P=0.02). Burning increased the spatial variance (s2) in litter cover (P<0.01) and bare soil (P<0.01) for 1 to 3 years. Aside from burning in early spring, burning reduced s2 in total standing crop (P=0.02) and <i>F. hallii</i> (P=0.01). Variability in the cover of <i>E. lanceolatus </i>(P<0.01) and graminoids (P=0.04) increased with burning frequency. Canonical correspondence analysis (CCA) indicated that pre-burn history had a dominant effect on plant community composition, explaining 13% of the variation (P<0.01). The cumulative effects of repeated burning, annual variability in weather, and exposure to temperature extremes may have caused a shift in the composition of the plant community. The first 4 ordination axes explained 22% of the variation in plant community composition after burning, indicating that many other environmental or site variables controlled community composition. A range of burning dates and frequencies should be reintroduced or maintained in Fescue Prairie to create a mosaic of plant communities in various stages of recovery after burning. A mosaic will increase the structural and compositional diversity in remnant Fescue Prairies.

Conserving structural and compositional diversity in Fescue Prairie requires reintroducing natural disturbances according to their historic regime. Fire is an important natural process that may be a source of spatial heterogeneity in Fescue Prairies. The effects of burning in all months of the year except January and February were evaluated in a Fescue Prairie in central Saskatchewan for 6 years following burning on 2 sites that had not been previously burned and 2 sites that had been burned 5 years earlier. Except for burning in March, burning reduced cover of litter (P<0.01) and <i>Festuca hallii </i> (Vasey) Piper (P=0.01) while increasing bare soil (P<0.01) for 1 to 5 years. Cover of <i>Elymus lanceolatus </i>(Scribn. & J.G. Sm.) Gould (P<0.01), graminoids (P=0.02), and species evenness (P=0.01) increased with burning frequency. Burning in late-summer reduced cover of graminoids (P=0.03), plants other than the dominant grasses (P=0.03), and total plant cover (P=0.02). Burning increased the spatial variance (s2) in litter cover (P<0.01) and bare soil (P<0.01) for 1 to 3 years. Aside from burning in early spring, burning reduced s2 in total standing crop (P=0.02) and <i>F. hallii</i> (P=0.01). Variability in the cover of <i>E. lanceolatus </i>(P<0.01) and graminoids (P=0.04) increased with burning frequency. Canonical correspondence analysis (CCA) indicated that pre-burn history had a dominant effect on plant community composition, explaining 13% of the variation (P<0.01). The cumulative effects of repeated burning, annual variability in weather, and exposure to temperature extremes may have caused a shift in the composition of the plant community. The first 4 ordination axes explained 22% of the variation in plant community composition after burning, indicating that many other environmental or site variables controlled community composition. A range of burning dates and frequencies should be reintroduced or maintained in Fescue Prairie to create a mosaic of plant communities in various stages of recovery after burning. A mosaic will increase the structural and compositional diversity in remnant Fescue Prairies.

Finite impulse response (FIR) digital filters are frequently used in many digital signal processing and communication applications, such as IS-95 CDMA, Digital Mobile Phone Systems (D-AMPS), etc. FIR filter achieves the frequency response of system requirement using a series of multiplications and additions. Previous papers on FIR hardware implementations usually focus on reducing area and delay of the multiple constant multiplications (MCM) through common sub-expression elimination (CSE) in the transpose FIR filter structure. In this thesis, we first perform optimization for the quantization of FIR filter coefficients that satisfy the target frequency response. Then suitable encoding methods are adopted to reduce the height of the partial products of the MCM in the direct FIR filter structure. Finally, by jointly considering the errors in the truncated multiplications and additions, we can design the hardware-efficient FIR filter that meets the bit accuracy requirement. Experimental results show that although CSE in the transpose FIR structure can reduce more area in MCM, the direct form takes smaller area in registers. Compared with previous approaches, the proposed FIR implementations with direct form has the minimum area cost.

Woody invasion into grasslands has been reported world-wide and has affected both the magnitude and spatial heterogeneity of soil carbon (C) and nitrogen (N). Since grasslands cover a large portion of the Earth's land surface, invasion of woody plants could have impacts on regional and global biogeochemistry. To understand large-scale ecological and policy implications of woody invasion, it is critical to understand the spatial pattern and uncertainty of soil C and N and their relationship with vegetation and soil attributes, as well as develop effective approaches to estimate soil C and N over large landscapes and regions. The goal of this study was to improve our understanding of the spatial pattern of soil organic carbon (SOC) and total nitrogen (TN) and their controlling factors in savanna landscapes and develop efficient sampling strategies for evaluating the effects of woody invasion. Specific objectives of this study were to: (1) Quantify the spatial pattern and uncertainty associated with SOC and develop efficient sampling strategies to estimate SOC storage; (2) Assess the influence of soil and vegetation factors on spatial distribution of SOC and TN; and (3) Determine the influence of physical variables related to landscape position and soil on woody vegetation structure. Conditional sequential indicator simulations indicated that woody encroachment into grassland increased both spatial heterogeneity and uncertainty of SOC, which increased errors in estimating SOC storage. Stratified random sampling with higher density in woody patches, plus structured sampling in cluster with strong spatial pattern, substantially increased estimation accuracy. Efficient sampling strategies for estimating SOC storage were developed based on these findings. Direct and spatial correlation and scaling analyses showed that SOC and TN were strongly correlated with litter and root biomass. Invaded woody vegetation has the most impact on spatial distribution of SOC and TN. Canonical correspondence analysis showed that variables related to landscape position were the primary factors determining the spatial distribution of woody species. These new insights will facilitate the estimation of soil C and N pools at landscape and regional scales, and will help evaluate the potential impacts of woody plant encroachment on the biogeochemistry of C and N.

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Statistikoje ir jos taikyme vienas dažniausiai sprendžiamų uždavinių yra daugiamačių tankių vertinimas.Tankių vertinimas skirstomas į parametrinį ir neparametrinį vertinimą. Parametriniame vertinime daroma prielaida, kad tankio funkcija f, apibūdinanti duomenis yi, kai i kinta nuo 1 iki n, priklauso tam tikrai gan siaurai funkcijų šeimai f(•;θ), kuri priklauso nuo nedidelio kiekio parametrų θ=(θ1, θ2, …, θk). Tankis, apskaičiuojamas pagal parametrinį vertinimą, gaunamas iš pradžių apskaičiavus parametro θ įvertį θ0 ir f0=f(•;θ). Toks traktavimas statistiniu požiūriu yra labai efektyvus, tačiau jeigu nei vienas šeimos f(•;θ) narys nėra artimas funkcijai f, rezultatai gali būti gauti labai netikslūs. Neparametriniam tankio vertinimui jokios parametrinės prielaidos apie f nėra reikalingos, tačiau vietoj to daromos kitos prielaidos, pavyzdžiui, apie funkcijos f tolydumą arba, kad f yra integruojama. Tankio funkcijos forma yra nustatoma iš turimų duomenų.Turint dideles imtis, tankis f gali būti apskaičiuotas pakankamai tiksliai. Šiuolaikinėje duomenų analizėje naudojama daugybė neparametrinių metodų, skirtų daugiamačių atsitiktinių dydžių pasiskirstymo tankio statistiniam vertinimui. Ypač plačiai paplitę branduoliniai įvertiniai, populiarūs ir splaininiai bei pusiau parametriniai algoritmai. Taikant daugumą populiarių neparametrinio įvertinimo procedūrų praktikoje susiduriama su jų parametrų optimalaus parinkimo problema. Branduolinių įvertinių konstrukcijos svarbiausiu... [toliau žr. visą tekstą] / Most algorithms work properly if the probability densities of the multivariate vectors are known. Unfortunately, in reality these densities are usually not available, and parametric or non-parametric estimation of the densities becomes critically needed. In parametric estimation one assumes that the density f underlying the data yi where i varies from 1 to n, belongs to some rather restricted family of functions f(•;θ) indexed by a small number of parameters θ=(θ1, θ2, …, θk). An example is the family of multivariate normal densities which is parameterized by the mean vector and the covariance matrix. A density estimate in the parametric approach is obtained by computing from the data an estimate θ0 of θ and setting f0=f(•;θ). Such an approach is statistically and computationally very efficient but can lead poor results if none of the family members f(•;θ) is close to f. In nonparametric density estimation no parametric assumptions about f are made and one assumes instead that f, for example, has some smoothness properties (e.g. two continuous derivatives) or that it is square integrable. The shape of the density estimate is determined by the data and, in principle, given enough data, arbitrary densities f can be estimated accurately. Most popular methods are the kernel estimator based on local smoothing of the data. Quite popular are histospline, semiparametric and projection pursuit algorithms. While constructing various probability density estimation methods the most... [to full text]

De récentes découvertes montrent le rôle important que joue l’acide ribonucléique (ARN) au sein des cellules, que ce soit le contrôle de l’expression génétique, la régulation de plusieurs processus homéostasiques, en plus de la transcription et la traduction de l’acide désoxyribonucléique (ADN) en protéine. Si l’on veut comprendre comment la cellule fonctionne, nous devons d’abords comprendre ses composantes et comment ils interagissent, et en particulier chez l’ARN. La fonction d’une molécule est tributaire de sa structure tridimensionnelle (3D). Or, déterminer expérimentalement la structure 3D d’un ARN s’avère fort coûteux. Les méthodes courantes de prédiction par ordinateur de la structure d’un ARN ne tiennent compte que des appariements classiques ou canoniques, similaires à ceux de la fameuse structure en double-hélice de l’ADN. Ici, nous avons amélioré la prédiction de structures d’ARN en tenant compte de tous les types possibles d’appariements, dont ceux dits non-canoniques. Cela est rendu possible dans le contexte d’un nouveau paradigme pour le repliement des ARN, basé sur les motifs cycliques de nucléotides ; des blocs de bases pour la construction des ARN. De plus, nous avons dévelopées de nouvelles métriques pour quantifier la précision des méthodes de prédiction des structures 3D des ARN, vue l’introduction récente de plusieurs de ces méthodes. Enfin, nous avons évalué le pouvoir prédictif des nouvelles techniques de sondage de basse résolution des structures d’ARN. / Recent findings show the important role of ribonucleic acid (RNA) within the cell, be it the control of gene expression, the regulation of several homeostatic processes, in addition to the transcription and translation of deoxyribonucleic acid (DNA) into protein. If we wish to understand how the cell works, we first need to understand its components and how they interact, and in particular for RNA. The function of a molecule is tributary of its three-dimensional (3D) structure. However, experimental determination of RNA 3D structures imparts great costs. Current methods for RNA structure prediction by computers only take into account the classical or canonical base pairs, similar to those found in the well-celebrated DNA double helix. Here, we improved RNA structure prediction by taking into account all possible types of base pairs, even those said non-canonicals. This is made possible in the context of a new paradigm for the folding of RNA, based on nucleotide cyclic motifs (NCM): basic blocks for the construction of RNA. Furthermore, we have developed new metrics to quantify the precision of RNA 3D structure prediction methods, given the recent introduction of many of those methods. Finally, we have evaluated the predictive power of the latest low-resolution RNA structure probing techniques.