Quantitative structure-retention relationships analysis of retention index of essential oils

Genetic algorithm and multiple linear regression (GA-MLR), partial least square (GA-PLS), kernel PLS (GA-KPLS) and Levenberg-Marquardt artificial neural network (L-M ANN) techniques were used to investigate the correlation between retention index (RI) and descriptors for 116 diverse compounds in essential oils of six Stachys species. The correlation coefficient LGO-CV (Q²) between experimental and predicted RI for test set by GA-MLR, GA-PLS, GA-KPLS and L-M ANN was 0.886, 0.912, 0.937 and 0.964, respectively. This is the first research on the QSRR of the essential oil compounds against the RI using the GA-KPLS and L-M ANN.

Application of GA-PLS and GA-KPLS calculations for the prediction of the retention indices of essential oils

Genetic algorithm and partial least square (GA-PLS) and kernel PLS (GA-KPLS) techniques were used to investigate the correlation between retention indices (RI) and descriptors for 117 diverse compounds in essential oils from 5 Pimpinella species gathered from central Turkey which were obtained by gas chromatography and gas chromatography-mass spectrometry. The square correlation coefficient leave-group-out cross validation (LGO-CV) (Q²) between experimental and predicted RI for training set by GA-PLS and GA-KPLS was 0.940 and 0.963, respectively. This indicates that GA-KPLS can be used as an alternative modeling tool for quantitative structure-retention relationship (QSRR) studies.

Innovations of ageing and societal transition : Dynamics of change of the socio-technical regime of ageing

The purpose of this dissertation is to examine the dynamics of the socio-technical system in the field of ageing. The study stems from the notion that the ageing of the population as a powerful megatrend has wide societal effects, and is not just a matter for the social and health sector. The central topic in the study is change: not only the age structures and structures of society are changing, but also at the same time there is constant development, for instance, in technologies, infrastructures and cultural perceptions. The changing concept of innovation has widened the understanding of innovations related to ageing from medical and assistive technological innovations to service and social innovations, as well as systemic innovations at different levels, which means the intertwined and co-evolutionary change in technologies, structures, services and thinking models. By the same token, the perceptions of older people and old age are becoming more multi-faceted: old age is no longer equated to illnesses and decline, but visions of active ageing and a third age have emerged, which are framed by choices, opportunities, resources and consumption in later life. The research task in this study is to open up the processes and mechanisms of change in the field of ageing, which are studied as a complex, multi-level and interrelated socio-technical system. The question is about co-effective elements consisting of macro-level landscape changes, the existing socio-technical regime (the rule system, practices and structures) and bottom-up niche-innovations. Societal transitions do not account for the things inside the regime alone, or for the long-term changes in the landscape, nor for the radical innovations, but for the interplay between all these levels. The research problem is studied through five research articles, which offer micro-level case studies to macro-level phenomenon. Each of the articles focus on different aspects related to ageing and change, and utilise various datasets. The framework of this study leans on the studies of socio-technical systems and multi-level perspective on transitions mainly developed by Frank Geels. Essential factors in transition from one socio-technological regime to another are the co-evolutionary processes between landscape changes, regime level and experimental niches. Landscape level changes, like the ageing of the population, destabilise the regime in the forms of coming pressures. This destabilization offers windows for opportunity to niche-innovations outside or at fringe of the regime, which, through their breakthrough, accelerate the transition process. However, the change is not easy because of various kinds of lock-ins and inertia, which tend to maintain the stability of the regime. In this dissertation, a constructionist approach of society is applied leaning mainly to the ideas of Anthony Giddens’ theory of structuration, with the dual nature of structures. The change is taking place in the interplay between actors and structures: structures shape people’s practices, but at the same time these practices constitute and reproduce social systems. Technology and other material aspects, as part of socio-technical systems, and the use of them, also take part in the structuration process. The findings of the study point out that co-evolutionary and co-effective relationships between economic, cultural, technological and institutional fields, as well as relationships between landscape changes, changes in the local and regime-level practices and rule systems, are a very complex and multi-level dynamic socio-technical phenomenon. At the landscape level of ageing, which creates the pressures and triggers to the regime change, there are three remarkable megatrends: demographic change, changes in the global economy and the development of technologies. These exert pressures to the socio-technical regime, which as a rule system is experiencing changes in the form of new markets and consumer habits, new ways of perceiving ageing, new models of organising the health care and other services and as new ways of considering innovation and innovativeness. There are also inner dynamics in the relationships between these aspects within the regime. These are interrelated and coconstructed: the prevailing perceptions of ageing and innovation, for instance, reflect the ageing policies, innovation policies, societal structures, organising models, technology and scientific discussion, and vice versa. Technology is part of the inner dynamics of the sociotechnological regime. Physical properties of the artefacts set limitations and opportunities with regard to their functions and uses. The use of and discussion about technology, contributes producing and reproducing the perceptions of old age. For societal transition, micro-level changes are also needed, in form of niche-innovations, for instance new services, organisational models or new technologies, Regimes, as stabilitystriven systems, tend to generate incremental innovations, but radically new innovations are generated in experimental niches protected from ‘normal’ market selection. The windows of opportunity for radical novelties may be opened if the circumstances are favourable for instance by tensions in the socio-technical regime affected by landscape level changes. This dissertation indicates that a change is taking place, firstly, in the dynamic interactionbetween levels, as a result of purposive action and governance to some extent. Breaking the inertia and using the window of opportunity for change and innovation offered by dynamics between levels, presupposes the actors’ special capabilities and actions such as dynamic capabilities and distance management. Secondly, the change is taking place the socio-technological negotiations inside the regime: interaction between technological and social, which is embodied in the use of technology. The use of technology includes small-level contextual scripts that also participate in forming broader societal scripts (for instance defining old age at the society level), which in their turn affect the formation of policies for innovation and ageing. Thirdly, the change is taking place by the means of active formation of the multi-actor innovation networks, where the role of distance management is crucial to facilitate the communication between actors coming from different backgrounds as well as to help the niches born outside the regime to utilise the window of opportunity offered by regime destabilisation. This dissertation has both theoretical and practical contributions. This study participates in the discussion of action-oriented view on transition by opening up of the socio-technological, coevolutionary processes of the multi-faceted phenomenon of ageing, which has lacked systematic analyses. The focus of this study, however, is not on the large-scale coordination and governance, but rather on opening up the incremental elements and structuration processes, which contribute to the transition little by little, and which can be affected to. This increases the practical importance of this dissertation, by highlighting the importance of very tiny, everyday elements in the change processes in the long run.

Some advances in mathematical models for preference relations

Preference relations, and their modeling, have played a crucial role in both social sciences and applied mathematics. A special category of preference relations is represented by cardinal preference relations, which are nothing other than relations which can also take into account the degree of relation. Preference relations play a pivotal role in most of multi criteria decision making methods and in the operational research. This thesis aims at showing some recent advances in their methodology. Actually, there are a number of open issues in this field and the contributions presented in this thesis can be grouped accordingly. The first issue regards the estimation of a weight vector given a preference relation. A new and efficient algorithm for estimating the priority vector of a reciprocal relation, i.e. a special type of preference relation, is going to be presented. The same section contains the proof that twenty methods already proposed in literature lead to unsatisfactory results as they employ a conflicting constraint in their optimization model. The second area of interest concerns consistency evaluation and it is possibly the kernel of the thesis. This thesis contains the proofs that some indices are equivalent and that therefore, some seemingly different formulae, end up leading to the very same result. Moreover, some numerical simulations are presented. The section ends with some consideration of a new method for fairly evaluating consistency. The third matter regards incomplete relations and how to estimate missing comparisons. This section reports a numerical study of the methods already proposed in literature and analyzes their behavior in different situations. The fourth, and last, topic, proposes a way to deal with group decision making by means of connecting preference relations with social network analysis.

From Fluid Dynamics to Human Psychology.What Drives Financial Markets Towards Extreme Events

For decades researchers have been trying to build models that would help understand price performance in financial markets and, therefore, to be able to forecast future prices. However, any econometric approaches have notoriously failed in predicting extreme events in markets. At the end of 20th century, market specialists started to admit that the reasons for economy meltdowns may originate as much in rational actions of traders as in human psychology. The latter forces have been described as trading biases, also known as animal spirits. This study aims at expressing in mathematical form some of the basic trading biases as well as the idea of market momentum and, therefore, reconstructing the dynamics of prices in financial markets. It is proposed through a novel family of models originating in population and fluid dynamics, applied to an electricity spot price time series. The main goal of this work is to investigate via numerical solutions how well theequations succeed in reproducing the real market time series properties, especially those that seemingly contradict standard assumptions of neoclassical economic theory, in particular the Efficient Market Hypothesis. The results show that the proposed model is able to generate price realizations that closely reproduce the behaviour and statistics of the original electricity spot price. That is achieved in all price levels, from small and medium-range variations to price spikes. The latter were generated from price dynamics and market momentum, without superimposing jump processes in the model. In the light of the presented results, it seems that the latest assumptions about human psychology and market momentum ruling market dynamics may be true. Therefore, other commodity markets should be analyzed with this model as well.

Caracterização da estrutura fundiária do município de Bandeirantes - PR, utilizando geoprocessamento

As técnicas de sensoriamento remoto e o uso dos Sistemas de Informações Geográficas (SIG) facilitam a elaboração de mapas temáticos. Mapas com informações detalhadas são importantes instrumentos para que os municípios conheçam melhor sua realidade. O trabalho foi desenvolvido no município de Bandeirantes, Estado do Paraná, Brasil, visando a analisar sua estrutura fundiária, baseada nas classes de tamanho dos imóveis rurais. A partir de mapas de imóveis rurais e de cartas topográficas do IBGE, obteve-se o mapa fundiário digital do município. Imagens orbitais e fotografias aéreas foram utilizadas para o ajuste das linhas divisórias dos imóveis, cuja validação se deu por incursões a campo. O número e o tamanho dos imóveis de 1950 foram comparados com dados de 2006, e a distribuição e concentração dos imóveis foram analisadas utilizando o estimador de intensidade Kernel. Os imóveis com área menor que o módulo rural se concentram nas microbacias mais distantes da sede do município e correspondem a 60% do total. Dos demais, 31% são pequenas, 7% médias e 2% grandes propriedades, que ocupam, respectivamente, 16%, 27%, 25% e 32% da área do município.

Combustion properties of biomass residues rich in phosphorus

Tillgången på traditionella biobränslen är begränsad och därför behöver man ta fram nya, tidigare outnyttjade biobränslen för att möta de uppställda CO2 emissionsmålen av EU och det ständigt ökande energibehovet. Under de senare åren har intresset riktats mot termisk energiutvinning ur olika restfraktioner och avfall. Vid produktion av fordonsbränsle ur biomassa är den fasta restprodukten ofta den största procesströmmen i produktionsanläggningen. En riktig hantering av restprodukterna skulle göra produktionen mera lönsam och mer ekologiskt hållbar. Ett alternativ är att genom förbränning producera elektricitet och/eller värme eftersom dessa restprodukter anses som CO2-neutrala. Målsättningen med den här avhandlingen var att studera förbränningsegenskaperna hos några fasta restprodukter som uppstår vid framställning av förnybara fordonsbränslen. De fyra undersökta materialen är rapskaka, palmkärnskaka, torkad drank och stabiliserat rötslam. I studien används ett stort urval av undersökningsmetoder, från laboratorieskala till fullskalig förbränning, för att identifiera de huvudsakliga utmaningarna förknippade med förbränning av restprodukterna i pannor med fluidiserad bäddteknik. Med hjälp av detaljerad bränslekarakterisering kunde restprodukterna konstateras vara en värdefull källa för värme- och elproduktion. Den kemiska sammansättningen av restprodukterna varierar stort jämfört med mera traditionellt använda biobränslen. En gemensam faktor för alla de studerade restprodukterna är en hög fosforhalt. På grund av de låga fosforkoncentrationerna i de traditionella biobränslena har grundämnet hittills inte ansetts spela någon större roll i askkemin. Experimenten visade nu att fosfor inte mera kan försummas då man studerar kemin i förbränningsprocesser, då allt flera fosforrika bränslen tränger in på energimarknaden.

Climate driven changes in temperature, pH and food quality : effects on copepod reproduction

Increased emissions of greenhouse gases into the atmosphere are causing an anthropogenic climate change. The resulting global warming challenges the ability of organisms to adapt to the new temperature conditions. However, warming is not the only major threat. In marine environments, dissolution of carbon dioxide from the atmosphere causes a decrease in surface water pH, the so called ocean acidification. The temperature and acidification effects can interact, and create even larger problems for the marine flora and fauna than either of the effects would cause alone. I have used Baltic calanoid copepods (crustacean zooplankton) as my research object and studied their growth and stress responses using climate predictions projected for the next century. I have studied both direct temperature and pH effects on copepods, and indirect effects via their food: the changing phytoplankton spring bloom composition and toxic cyanobacterium. The main aims of my thesis were: 1) to find out how warming and acidification combined with a toxic cyanobacterium affect copepod reproductive success (egg production, egg viability, egg hatching success, offspring development) and oxidative balance (antioxidant capacity, oxidative damage), and 2) to reveal the possible food quality effects of spring phytoplankton bloom composition dominated by diatoms or dinoflagellates on reproducing copepods (egg production, egg hatching, RNA:DNA ratio). The two copepod genera used, Acartia sp. and Eurytemora affinis are the dominating mesozooplankton taxa (0.2 – 2 mm) in my study area the Gulf of Finland. The 20°C temperature seems to be within the tolerance limits of Acartia spp., because copepods can adapt to the temperature phenotypically by adjusting their body size. Copepods are also able to tolerate a pH decrease of 0.4 from present values, but the combination of warm water and decreased pH causes problems for them. In my studies, the copepod oxidative balance was negatively influenced by the interaction of these two environmental factors, and egg and nauplii production were lower at 20°C and lower pH, than at 20°C and ambient pH. However, presence of toxic cyanobacterium Nodularia spumigena improved the copepod oxidative balance and helped to resist the environmental stress, in question. In addition, adaptive maternal effects seem to be an important adaptation mechanism in a changing environment, but it depends on the condition of the female copepod and her diet how much she can invest in her offspring. I did not find systematic food quality difference between diatoms and dinoflagellates. There are both good and bad diatom and dinoflagellate species. Instead, the dominating species in the phytoplankton bloom composition has a central role in determining the food quality, although copepods aim at obtaining as a balanced diet as possible by foraging on several species. If the dominating species is of poor quality it can cause stress when ingested, or lead to non-optimal foraging if rejected. My thesis demonstrates that climate change induced water temperature and pH changes can cause problems to Baltic Sea copepod communities. However, their resilience depends substantially on their diet, and therefore the response of phytoplankton to the environmental changes. As copepods are an important link in pelagic food webs, their future success can have far reaching consequences, for example on fish stocks.

Análise espacial da prevalência de toxoplasmose em gestantes de Aracaju, Sergipe, Brasil

OBJETIVO:Analisar a distribuição espacial da prevalência de anticorpos antitoxoplasma em gestantes residentes em uma cidade do Nordeste do Brasil, e correlacionar a prevalência de anticorpos antitoxoplasma com a faixa etária materna e o local de residência.MÉTODOS:Estudo ecológico, descritivo e analítico, desenvolvido no período de 01 janeiro a 31 de dezembro de 2012. As informações foram obtidas retrospectivamente de um banco de dados, e processadas com o pacote estatístico Epi info (Epi 7, Centers for Disease Control and Prevention, Atlanta, EUA) e também em planilha do pacote Microsoft Office Excel, versão 2010. Para avaliar a associação entre a prevalência de anticorpos para a toxoplasmose e a faixa etária, foi aplicado o teste do X2. A análise espacial da prevalência dessa infecção foi realizada com o programa TerraView, versão 4.2.2, utilizando o estimador de intensidade Kernel, que permite estimar a quantidade de eventos em mapa para identificar áreas de maior concentração de casos no município.RESULTADOS:A soroprevalência encontrada para IgG foi de 68,5% (IC95% 67,2-69,8) e IgM de 0,36% (IC95% 0,23-0,6). Foi encontrado incremento da prevalência de IgG associado ao aumento da idade nos bairros mais antigos da capital. Entre as mulheres mais jovens, a maior prevalência foi nos bairros de periferia. Quanto ao anticorpo IgM, a concentração espacial foi mais elevada em bairros da periferia e não ocorreu associação significativa entre a soroprevalência e a idade.CONCLUSÃO:O geoprocessamento permitiu identificar as áreas de maior prevalência, assim como a faixa etária com maior suscetibilidade, servindo como instrumento de avaliação e implementação de medidas preventivas apropriadas para esse município e outras regiões do Brasil.

Substitution-Newton-Raphson method applied to the modeling of a vapour compression refrigeration system using different representations of the thermodynamic properties of R-134a

This paper gives a detailed presentation of the Substitution-Newton-Raphson method, suitable for large sparse non-linear systems. It combines the Successive Substitution method and the Newton-Raphson method in such way as to take the best advantages of both, keeping the convergence features of the Newton-Raphson with the low requirements of memory and time of the Successive Substitution schemes. The large system is solved employing few effective variables, using the greatest possible part of the model equations in substitution fashion to fix the remaining variables, but maintaining the convergence characteristics of the Newton-Raphson. The methodology is exemplified through a simple algebraic system, and applied to a simple thermodynamic, mechanical and heat transfer modeling of a single-stage vapor compression refrigeration system. Three distinct approaches for reproducing the thermodynamic properties of the refrigerant R-134a are compared: the linear interpolation from tabulated data, the use of polynomial fitted curves and the use of functions derived from the Helmholtz free energy.

Forest cover and its change in Unguja Island, Zanzibar

Tropical forests are sources of many ecosystem services, but these forests are vanishing rapidly. The situation is severe in Sub-Saharan Africa and especially in Tanzania. The causes of change are multidimensional and strongly interdependent, and only understanding them comprehensively helps to change the ongoing unsustainable trends of forest decline. Ongoing forest changes, their spatiality and connection to humans and environment can be studied with the methods of Land Change Science. The knowledge produced with these methods helps to make arguments about the actors, actions and causes that are behind the forest decline. In this study of Unguja Island in Zanzibar the focus is in the current forest cover and its changes between 1996 and 2009. The cover and changes are measured with often used remote sensing methods of automated land cover classification and post-classification comparison from medium resolution satellite images. Kernel Density Estimation is used to determine the clusters of change, sub-area –analysis provides information about the differences between regions, while distance and regression analyses connect changes to environmental factors. These analyses do not only explain the happened changes, but also allow building quantitative and spatial future scenarios. Similar study has not been made for Unguja and therefore it provides new information, which is beneficial for the whole society. The results show that 572 km2 of Unguja is still forested, but 0,82–1,19% of these forests are disappearing annually. Besides deforestation also vertical degradation and spatial changes are significant problems. Deforestation is most severe in the communal indigenous forests, but also agroforests are decreasing. Spatially deforestation concentrates to the areas close to the coastline, population and Zanzibar Town. Biophysical factors on the other hand do not seem to influence the ongoing deforestation process. If the current trend continues there should be approximately 485 km2 of forests remaining in 2025. Solutions to these deforestation problems should be looked from sustainable land use management, surveying and protection of the forests in risk areas and spatially targeted self-sustainable tree planting schemes.

Effects of weed "Reestablishment" after hoeing on corn yields

Some growers and researchers sustain the idea that regrowth or root setting of some weeds may occur after hoeing, with detrimental effects over corn. The objective of this study was to evaluate the effects of weed removal from the field, removal after each hoeing, and corn intercropped with gliricidia on weed control and corn yield values. The experimental design consisted of blocks with split-plots and six replicates. Cultivars AG 1051 and BM 2022, planted in the plots, were submitted to the following treatments: no hoeing, two hoeings (at 20 and 40 days after planting), and intercropped with gliricidia. The hoed plots were either submitted to weed removal after the first, second, or both hoeings, or remained without weed removal. In the intercropped treatment, gliricidia was sown by broadcasting at corn planting between the corn rows, at a density of 15 seeds m-2. Twenty-five weed species occurred in the experiment; the most frequent was Digitaria sanguinalis (family Poaceae). The weed control methods tested had similar effects on the cultivars, which were not different from one another with respect to the evaluated traits, except for one-hundred-kernel weight, with cultivar AG 1051 being superior. Weed removal did not influence green corn yield or grain yield. However, the number of kernels/ear was higher in plots where weeds were removed in relation to plots without weed removal, suggesting that weed removal might be beneficial to corn. Besides, a higher dry matter weight was obtained for the above-ground part of weeds removed from the field after the first and second hoeings than the weight of weeds removed after the second hoeing only which, in turn, was higher than the weight of weeds removed after the first hoeing only. Green ear yield, grain yield, and dry matter of the above-ground part of the weeds did not show differences in hoed plots and were superior to the non-weeded plots and the intercropped plots, which were not different from each other; therefore, intercropping with gliricidia did not improve corn yield values.

Weed management boosts yield in fine rice under system of rice intensification

The system of rice intensification has emerged as a promising rice production package but weed infestation could lead to incomplete benefits from the system. A two-year field study was performed to determine an appropriate method of weed management in SRI. Weed management treatments were manual hoeing 20, 40 and 60 days after transplanting (DAT), hoeing with rotary hoe at 20, 40 and 60 DAT, hoeing with rotary hoe at 20 DAT + spray with sorghum and sunflower water extracts at 15 L ha-1 40 DAT, manual hoeing 20 DAT + spray with sorghum and sunflower water extracts, both in equal amount, at 15 L ha-1 40 DAT, orthosulfamuron at 145 g a.i. ha-1 7 DAT, weedy check and weed free. Manual hoeing at 20, 40 and 60 DAT was the treatment that exhibited the maximum kernel yield i.e. 5.34 and 4.99 t ha-1., which was 8.4 and 7.2% higher than orthosulfamuron and 61.0 and 64.9% higher than weedy check, during both years of study, respectively. The highest weed suppression was also achieved by manual hoeing at 20, 40 and 60 DAT with weed control efficiency of 87.89 and 82.32% during 2010 and 2011, respectively. Manual hoeing at 20, 40 and 60 DAT is an eco-friendly, non-chemical weed control method to increase kernel yield of fine rice under SRI.

Changes in the behavioral and immunological parameters of the mollusk Biomphalaria tenagophila induced by disruption of the circadian cycle as a consequence of continuous illumination

In the present investigation we studied some behavioral and immunological parameters of adult gastropod mollusk, Biomphalaria tenagophila, which have been reproducing for several generations under laboratory conditions. One group of gastropods was kept on a 14-h light/10-h dark cycle, corresponding to a regular circadian cycle, and another group was exposed to continuous light for 48 h. Animals were studied along (behavioral groups) or immediately after (immunological groups) 48 h of regular circadian cycle or continuous light conditions. Stopping/floating, dragging and sliding were the behavioral aspects considered (N = 20 for regular cycle; N = 20 for continuous illumination) and number of hemocytes/µl hemolymph was the immunological parameter studied (N = 15 for regular cycle, N = 14 for continuous illumination). Animals under continuous illumination were more active (sliding = 33 episodes, dragging = 48 episodes) and displayed a lower number of hemocytes (78.0 ± 24.27/µl) when compared with mollusks kept on a regular circadian cycle (sliding = 18 episodes, dragging = 27 episodes; hemocytes = 157.6 ± 53.27/µl). The data are discussed in terms of neural circuits and neuroimmunological relations with the possible stressful effect of continuous illumination.

Efficient Optimization Algorithms for Nonlinear Data Analysis

Identification of low-dimensional structures and main sources of variation from multivariate data are fundamental tasks in data analysis. Many methods aimed at these tasks involve solution of an optimization problem. Thus, the objective of this thesis is to develop computationally efficient and theoretically justified methods for solving such problems. Most of the thesis is based on a statistical model, where ridges of the density estimated from the data are considered as relevant features. Finding ridges, that are generalized maxima, necessitates development of advanced optimization methods. An efficient and convergent trust region Newton method for projecting a point onto a ridge of the underlying density is developed for this purpose. The method is utilized in a differential equation-based approach for tracing ridges and computing projection coordinates along them. The density estimation is done nonparametrically by using Gaussian kernels. This allows application of ridge-based methods with only mild assumptions on the underlying structure of the data. The statistical model and the ridge finding methods are adapted to two different applications. The first one is extraction of curvilinear structures from noisy data mixed with background clutter. The second one is a novel nonlinear generalization of principal component analysis (PCA) and its extension to time series data. The methods have a wide range of potential applications, where most of the earlier approaches are inadequate. Examples include identification of faults from seismic data and identification of filaments from cosmological data. Applicability of the nonlinear PCA to climate analysis and reconstruction of periodic patterns from noisy time series data are also demonstrated. Other contributions of the thesis include development of an efficient semidefinite optimization method for embedding graphs into the Euclidean space. The method produces structure-preserving embeddings that maximize interpoint distances. It is primarily developed for dimensionality reduction, but has also potential applications in graph theory and various areas of physics, chemistry and engineering. Asymptotic behaviour of ridges and maxima of Gaussian kernel densities is also investigated when the kernel bandwidth approaches infinity. The results are applied to the nonlinear PCA and to finding significant maxima of such densities, which is a typical problem in visual object tracking.