5 resultados para Nonlinear time-delay systems

em Helda - Digital Repository of University of Helsinki


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This thesis studies quantile residuals and uses different methodologies to develop test statistics that are applicable in evaluating linear and nonlinear time series models based on continuous distributions. Models based on mixtures of distributions are of special interest because it turns out that for those models traditional residuals, often referred to as Pearson's residuals, are not appropriate. As such models have become more and more popular in practice, especially with financial time series data there is a need for reliable diagnostic tools that can be used to evaluate them. The aim of the thesis is to show how such diagnostic tools can be obtained and used in model evaluation. The quantile residuals considered here are defined in such a way that, when the model is correctly specified and its parameters are consistently estimated, they are approximately independent with standard normal distribution. All the tests derived in the thesis are pure significance type tests and are theoretically sound in that they properly take the uncertainty caused by parameter estimation into account. -- In Chapter 2 a general framework based on the likelihood function and smooth functions of univariate quantile residuals is derived that can be used to obtain misspecification tests for various purposes. Three easy-to-use tests aimed at detecting non-normality, autocorrelation, and conditional heteroscedasticity in quantile residuals are formulated. It also turns out that these tests can be interpreted as Lagrange Multiplier or score tests so that they are asymptotically optimal against local alternatives. Chapter 3 extends the concept of quantile residuals to multivariate models. The framework of Chapter 2 is generalized and tests aimed at detecting non-normality, serial correlation, and conditional heteroscedasticity in multivariate quantile residuals are derived based on it. Score test interpretations are obtained for the serial correlation and conditional heteroscedasticity tests and in a rather restricted special case for the normality test. In Chapter 4 the tests are constructed using the empirical distribution function of quantile residuals. So-called Khmaladze s martingale transformation is applied in order to eliminate the uncertainty caused by parameter estimation. Various test statistics are considered so that critical bounds for histogram type plots as well as Quantile-Quantile and Probability-Probability type plots of quantile residuals are obtained. Chapters 2, 3, and 4 contain simulations and empirical examples which illustrate the finite sample size and power properties of the derived tests and also how the tests and related graphical tools based on residuals are applied in practice.

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Large carnivore populations are currently recovering from past extirpation efforts and expanding back into their original habitats. At the same time human activities have resulted in very few wilderness areas left with suitable habitats and size large enough to maintain populations of large carnivores without human contact. Consequently the long-term future of large carnivores depends on their successful integration into landscapes where humans live. Thus, understanding their behaviour and interaction with surrounding habitats is of utmost importance in the development of management strategies for large carnivores. This applies also to brown bears (Ursus arctos) that were almost exterminated from Scandinavia and Finland at the turn of the century, but are now expanding their range with the current population estimates being approximately 2600 bears in Scandinavia and 840 in Finland. This thesis focuses on the large-scale habitat use and population dynamics of brown bears in Scandinavia with the objective to develop modelling approaches that support the management of bear populations. Habitat analysis shows that bear home ranges occur mainly in forested areas with a low level of human influence relative to surrounding areas. Habitat modelling based on these findings allows identification and quantification of the potentially suitable areas for bears in Scandinavia. Additionally, this thesis presents novel improvements to home range estimation that enable realistic estimates of the effective area required for the bears to establish a home range. This is achieved through fitting to the radio-tracking data to establish the amount of temporal autocorrelation and the proportion of time spent in different habitat types. Together these form a basis for the landscape-level management of the expanding population. Successful management of bears requires also assessment of the consequences of harvest on the population viability. An individual-based simulation model, accounting for the sexually selected infanticide, was used to investigate the possibility of increasing the harvest using different hunting strategies, such as trophy harvest of males. The results indicated that the population can sustain twice the current harvest rate. However, harvest should be changed gradually while carefully monitoring the population growth as some effects of increased harvest may manifest themselves only after a time-delay. The results and methodological improvements in this thesis can be applied to the Finnish bear population and to other large carnivores. They provide grounds for the further development of spatially-realistic management-oriented models of brow bear dynamics that can make projections of the future distribution of bears while accounting for the development of human activities.

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Kirjallisuusosa: Alzheimerin taudin hoitoon olisi tarvetta uusille taudinkulkuun vaikuttaville lääkeaineille. Niiden kehittämiseksi tarvitaan eläinmalleja, joissa esiintyy taudin patofysiologisia piirteitä. Rottamalleista vanhemmat skopolamiini- tai MK-801-häirintä sekä ikääntyneiden rottien käyttö eivät kovin hyvin vastaa taudin patofysiologiaa, vaikka niissä eläimen muisti käyttäytymiskokeissa onkin heikentynyt. Uudemmat transgeeniset rottamallit ja mallit, joissa annetaan Aβ:a aivoihin, ilmentävät huomattavasti paremmin Alzheimerin taudin kaltaista tilaa aivoissa ainakin Aβ:n osalta. Taupatofysiologiaa ei silti kummassakaan näistä malleista juuri esiinny. Toisaalta Aβ:lla näyttäisi olevan huomattavasti tau:ta suurempi rooli taudissa, joten sen ilmeneminen mallissa onkin keskeisempi tekijä. Nämä mallit ilmentävät melko suurelti osin yhtä hyvin Alzheimerin taudin patofysiologiaa. Aβ:n antaminen on hieman yksinkertaisempi suorittaa käytännössä, sillä siinä ei tarvitse luoda transgeenista kantaa. Toisaalta transgeenisessa mallissa Aβ-patofysiologia syntyy enemmän Alzheimerin taudin kaltaisesti solujen sisällä eikä valmiita aggregoituvia Aβ-peptidejä anneta ulkopuolelta aivoihin. Molemmat mallit ovat kuitenkin käyttökelpoisia, ja soveltuvat erityisesti Aβ:an vaikuttavien lääkeaineiden kehittämiseen. Kokeellinen osa: Kokeen tarkoituksena oli validoida kohotettu ristikko-sokkelo (elevated plus-maze, EPM) hiirillä kognitiomallina. Kokeessa käytettiin kahden koekerran (trial, T) menetelmää, jossa koekertojen pituus oli viisi minuuttia. Näin saatiin useita oppimista kuvaavia parametreja. Hiirille yritettiin saada muistihäiriö aikaviiveen avulla (koekertojen väli 1-18 vrk) tai antamalla muskariinireseptoriantagonistia skopolamiinia (0,1-0,8 mg/kg i.p.) 30 minuuttia ennen T1:tä. Nämä kokeet suoritettiin sekä C57BL/6J- että ICR:(CD-1)-hiirillä. Aikaviivekokeissa ainut ryhmä, jolla oli viitettä unohtamisesta, oli ICR:(CD-1)-hiirien 18 vrk:n ryhmä. Tämän perusteella tutkittiin vielä 21 vuorokauden aikaväli, mutta selvää muistihäiriötä ei esiintynyt. Skopolamiini ei häirinnyt muistia ICR:(CD-1)-hiirillä, mutta C57BL/6J-hiirillä 0,2 mg/kg:n annoksesta ylöspäin merkitsevä muistihäiriö esiintyi. Näin ollen jatkokokeissa käytettäväksi valittiin skopolamiinin annos 0,2 mg/kg C57BL/6J-hiirillä, ja siinä tutkittiin donepetsiilin (0,3, 0,8 ja 1,5 mg/kg s.c), memantiinin (5,0 ja 10,0 mg/kg s.c) ja kokeellisen 5-HT6-antagonistin SB742457:n (1,5 ja 6,0 mg/kg s.c) muistia parantavia vaikutuksia. Tutkittavat lääkeaineet annettiin 40 minuuttia ennen T1:tä ja skopolamiini 30 minuuttia ennen. Memantiinilla (5,0 mg/kg) oli selkeä skopolamiinin heikentämää kognitiota parantava vaikutus ja donepetsiilillakin (1,5 mg/kg) suuntaus tähän. Tulosten perusteella malli näyttäisi soveltuvan muisti- ja oppimisvaikutusten tutkimiseen käytettäväksi malliksi.

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The paradigm of computational vision hypothesizes that any visual function -- such as the recognition of your grandparent -- can be replicated by computational processing of the visual input. What are these computations that the brain performs? What should or could they be? Working on the latter question, this dissertation takes the statistical approach, where the suitable computations are attempted to be learned from the natural visual data itself. In particular, we empirically study the computational processing that emerges from the statistical properties of the visual world and the constraints and objectives specified for the learning process. This thesis consists of an introduction and 7 peer-reviewed publications, where the purpose of the introduction is to illustrate the area of study to a reader who is not familiar with computational vision research. In the scope of the introduction, we will briefly overview the primary challenges to visual processing, as well as recall some of the current opinions on visual processing in the early visual systems of animals. Next, we describe the methodology we have used in our research, and discuss the presented results. We have included some additional remarks, speculations and conclusions to this discussion that were not featured in the original publications. We present the following results in the publications of this thesis. First, we empirically demonstrate that luminance and contrast are strongly dependent in natural images, contradicting previous theories suggesting that luminance and contrast were processed separately in natural systems due to their independence in the visual data. Second, we show that simple cell -like receptive fields of the primary visual cortex can be learned in the nonlinear contrast domain by maximization of independence. Further, we provide first-time reports of the emergence of conjunctive (corner-detecting) and subtractive (opponent orientation) processing due to nonlinear projection pursuit with simple objective functions related to sparseness and response energy optimization. Then, we show that attempting to extract independent components of nonlinear histogram statistics of a biologically plausible representation leads to projection directions that appear to differentiate between visual contexts. Such processing might be applicable for priming, \ie the selection and tuning of later visual processing. We continue by showing that a different kind of thresholded low-frequency priming can be learned and used to make object detection faster with little loss in accuracy. Finally, we show that in a computational object detection setting, nonlinearly gain-controlled visual features of medium complexity can be acquired sequentially as images are encountered and discarded. We present two online algorithms to perform this feature selection, and propose the idea that for artificial systems, some processing mechanisms could be selectable from the environment without optimizing the mechanisms themselves. In summary, this thesis explores learning visual processing on several levels. The learning can be understood as interplay of input data, model structures, learning objectives, and estimation algorithms. The presented work adds to the growing body of evidence showing that statistical methods can be used to acquire intuitively meaningful visual processing mechanisms. The work also presents some predictions and ideas regarding biological visual processing.