Visible and near-infrared diffuse reflectance spectroscopy has been demonstrated to be a fast and cheap tool for estimating a large number of chemical and physical soil properties, and effective features extracted from spectra are crucial to correlating with these properties. We adopt a novel methodology for feature extraction of soil spectroscopy based on fractal geometry. The spectrum can be divided into multiple segments with different step–window pairs. For each segmented spectral curve, the fractal dimension value was calculated using variation estimators with power indices 0.5, 1.0 and 2.0. Thus, the fractal feature can be generated by multiplying the fractal dimension value with spectral energy. To assess and compare the performance of new generated features, we took advantage of organic soil samples from the large-scale European Land Use/Land Cover Area Frame Survey (LUCAS). Gradient-boosting regression models built using XGBoost library with soil spectral library were developed to estimate N, pH and soil organic carbon (SOC) contents. Features generated by a variogram estimator performed better than two other estimators and the principal component analysis (PCA). The estimation results for SOC were coefficient of determination (R2) = 0.85, root mean square error (RMSE) = 56.7 g/kg, the ratio of percent deviation (RPD) = 2.59; for pH: R2 = 0.82, RMSE = 0.49 g/kg, RPD = 2.31; and for N: R2 = 0.77, RMSE = 3.01 g/kg, RPD = 2.09. Even better results could be achieved when fractal features were combined with PCA components. Fractal features generated by the proposed method can improve estimation accuracies of soil properties and simultaneously maintain the original spectral curve shape.

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This diploma project is showen possibilities in classification of genomic sequences with CGR and FCGR methods in pictures. From this picture is computed classificator with BCM. Next here is written about the programme and its opportunities for classification. In the end is compared many of sequences computed in different options of programme.

Předkládaná dizertační práce se zabývá využitím techniky vysoce rozlišovací ultrazvukové spektroskopie (HRUS) při analýze huminových látek, za účelem získání hlubšího vhledu do problematiky vztahu mezi jejich primárními charakteristikami (elementární složení a rozložení uhlíku ve funkčních skupinách) a agregačními vlastnostmi. V literární rešerši jsou shrnuty nejnovější poznatky z oblasti studia huminových látek a představeny základní principy HRUS. Dále jsou uvedeny základní informace z oblasti fraktální analýzy a její aplikace na data získaná pomocí různých metod při studiu huminových látek. První úkol experimentální části je zaměřen na výhodné využití HRUS pro výzkum huminových látek, zde reprezentovaných standardy Mezinárodní společnosti pro huminové látky (IHSS) a to sodnými solemi huminových a fulvinových kyselin. Fulvinové kyseliny v jejich protonované formě byly taktéž zkoumány a to z důvodu objasnění vlivu sodného kationu. Pro popis chování vzorků byla použita mocninná funkce, jejíž empirické parametry byly korelovány s primárními charakteristikami. Byla vytvořena metoda fraktální analýzy a následně byla aplikována na data získána ultrazvukovou spektroskopií. Data získaná pomocí ultrazvukové spektroskopie byla zpracována i alternativní metodou. Ta spočívala v globálním pohledu na závislost ultrazvukové rychlosti na koncentraci a využití lineární regrese. Druhým z cílů práce je získání informací o vlivu teploty na stabilitu agregátů HS (IHSS standardy). Byl zkoumán vliv teplotních gradientů na chování agregátů při čtyřech různých koncentracích. V třetí části práce pak byly zkoumány koncentrační závislosti u vzorků pocházejících především z lokalit příliš nezasažených lidskou činností. HRUS data byla proložena mocninnou funkcí a zkoumána pomocí fraktální analýzy. Takto získané parametry byly korelovány s primárními vlastnostmi. Ze znalosti hustoty při dané koncentraci mohly být stanoveny velikosti hydratačních obálek. Jak se v současné době ukazuje, informace o agregačním chování huminových biomolekul mohou být v budoucnu velmi důležité pro navrhování průmyslových aplikací huminových látek, zejména v zemědělství a v ochraně životního prostředí, ale také například v medicíně.

The aim of the presented thesis is to create a compact publication which deals with properties, solution and examination of behavior of dynamical systems as models of mechanical structures. The opening portion of the theoretical part leads the reader through the subject of description of dynamical systems, offers solution methods and investigates solution stability. As the introduction proceeds, possible forms of structure loading, damping and response are presented. Following chapters discuss extensively the possible approaches to system behavior observation and identification of nonlinear and chaotic phenomena. The attention is also paid to displaying methods and color spaces as these are essential for the examination of complex and sensitive systems. The theoretical part of the thesis ends with an introduction to fractal geometry. As the theoretical background is laid down, the thesis proceeds with an application of the knowledge and shows the approach to numerical simulation and study of models of real structures. First, the reader is introduced to the single pendulum model, as the simplest model to exhibit chaotic behavior. The following double pendulum model shows the obstacles of observing systems with more state variables. The models of free rod and cantilever serve as examples of real structure models with many degrees of freedom. These models show even more that a definite or at least sufficiently relevant monitoring of behavior of such deterministic systems is a challenging task which requires sophisticated approach.

Le but de ce travail est de déterminer par méthodes optiques la distribution de taille (pdf) des nanoparticules de suie, agrégats de morphologie fractale. Après des études préliminaires qui utilisent DDSCAT pour valider la théorie RDG-FA et permettent de convertir un rayon de giration en rayon de mobilité, deux diagnostics optiques sont étudiés. Le premier consiste à exploiter une mesure d'extinction spectrale de la lumière. Nous montrons que pour exploiter ce signal, il faut connaître les propriétés optiques des suies, leur préfacteur et dimension fractale, la loi de distribution et le diamètre des sphérules primaires. Le second diagnostic tire parti de la mesure angulaire de la diffusion de la lumière. Nous montrons qu'il est possible de déterminer la pdf à l'aide de la mesure de diffusion à trois angles. Il faut supposer la loi de distribution et la dimension fractale. Cette deuxième approche, in-situ, est plus appropriée que la première pour déterminer optiquement la pdf des suies. / The objective of this thesis is to determine by optical methods the soot size distribution. Soot are fractal-like morphology nanoparticles aggregates. After preliminary studies which used DDSCAT to validate the RDG-FA theory and allow converting gyration radius to mobility radius, two optical approaches are considered. The first one is based on a measure of spectral light extinction by soot. To exploit this signal, the knowledge of soot optical properties, fractal prefactor, type of law distribution, fractal dimension and primary spheres diameters are needed. The second one exploits the measure of angular scattering by particles. It is possible to determine the size distribution by using scattering measurement at only three angles. However, it's necessary to assume the type of law distribution and the fractal dimension. This second approach is more appropriate than the first one to determine optically the size distribution of soot and hold the interest to be in-situ.

Classical partial transport barriers govern both classical and quantum dynamics of generic Hamiltonian systems. Chaotic eigenstates of quantum systems are known to localize on either side of a partial barrier if the flux connecting the two sides is not resolved by means of Heisenberg's uncertainty. Surprisingly, in open systems, in which orbits can escape, chaotic resonance states exhibit such a localization even if the flux across the partial barrier is quantum mechanically resolved. We explain this using the concept of conditionally invariant measures by introducing a new quantum mechanically relevant class of such fractal measures. We numerically find quantum-to-classical correspondence for localization transitions depending on the openness of the system and on the decay rate of resonance states. Moreover, we show that the number of long-lived chaotic resonance states that localize on one particular side of the partial barrier is described by an individual fractal Weyl law. For a generic phase space, this implies a hierarchy of fractal Weyl laws, one for each region of the hierarchical decomposition of phase space.

<div><br></div><div>Extreme heat is one of the deadliest health hazards that is projected to increase in intensity and persistence in the near future. Temperatures are further exacerbated in the urban areas due to the Urban Heat Island (UHI) effect resulting in increased heat-related mortality and morbidity. However, the spatial distribution of urban temperatures is highly heterogeneous. As a result, metrics such as UHI Intensity that quantify the difference between the average urban and non-urban air temperatures, often fail to characterize this spatial and temporal heterogeneity. My objective in this thesis is to understand and characterize the spatio-temporal dynamics of UHI for cities across the world. This has several applications, such as targeted heat mitigation, energy load estimation, and neighborhood-level vulnerability estimation.</div><div><br></div><div>Towards this end, I have developed a novel multi-scale framework of identifying emerging heat clusters at various percentile-based thermal thresholds T_thr and refer to them collectively as <i>intra-Urban Heat Islets</i>. Using the Land Surface Temperatures from Landsat for 78 cities representative of the global diversity, I have showed that the heat islets have a fractal spatial structure. They display properties analogous to that of a percolating system as T_thr varies. At the percolation threshold, the size distribution of these islets in all cities follows a power-law, with a scaling exponent = 1.88 and an aggregated Area-Perimeter Fractal Dimension =1.33. This commonality indicates that despite the diversity in urban form and function across the world, the urban temperature patterns are different realizations with the same aggregated statistical properties. In addition, analogous to the UHI Intensity, the mean islet intensity, i.e., the difference between mean islet temperature and thermal threshold, is estimated for each islet, and their distribution follows an exponential curve. This allows for a single metric (exponential rate parameter) to serve as a comprehensive measure of thermal heterogeneity and improve upon the traditional UHI Intensity as a bulk metric.</div><div><br></div><div><br></div><div>To study the impact of urban form on the heat islet characteristics, I have introduced a novel lacunarity-based metric, which quantifies the degree of compactness of the heat islets. I have shown that while the UHIs have similar fractal structure at their respective percolation threshold, differences across cities emerge when we shift the focus to the hottest islets (T_thr = 90^th percentile). Analysis of heat islets' size distribution demonstrates the emergence of two classes where the dense cities maintain a power law, whereas the sprawling cities show an exponential deviation at higher thresholds. This indicates a significantly reduced probability of encountering large heat islets for sprawling cities. In contrast, analysis of heat islet intensity distributions indicates that while a sprawling configuration is favorable for reducing the mean Surface UHI Intensity of a city, for the same mean, it also results in higher local thermal extremes. </div><div><br></div><div>Lastly, I have examined the impact of external forcings such as heatwaves (HW) on the heat islet characteristics. As a case study, the European heatwave of 2018 is simulated using the Weather Research Forecast model with a focus on Paris. My results indicate that the UHI Intensity under this HW reduces during night time by 1^oC on average. A surface energy budget analysis reveals that this is due to drier and hotter rural background temperatures during the HW period.</div><div>To analyze the response of heat islets at every spatial scale, power spectral density analysis is done. The results show that large contiguous heat islets (city-scale) persist throughout the day during a HW, whereas the smaller islets (neighborhood-scale) display a diurnal variability that is the same as non-HW conditions. </div><div><br></div><div>In conclusion, I have presented a new viewpoint of the UHI as an archipelago of intra-urban heat islets. Along the way, I have introduced several properties that enable a seamless comparison of thermal heterogeneity across diverse cities as well as under diverse climatic conditions. This thesis is a step towards a comprehensive characterization of heat from the spatial scales of an urban block to a megalopolis.</div><div><br></div>

The way in which macroscopic transport results from microscopic dynamics is one of the important questions in statistical physics. Dynamical systems theory play a key role in a resent advance in this direction. Offering relatively simple models which are easy to study, dynamical systems theory became a standard branch of modern nonequilibrium statistical physics. In the present work the deterministic diffusion generated by simple dynamical systems is considered. The deterministic nature of these systems is more clearly expressed through the dependencies of the transport quantities as functions of systems parameters. For fully hyperbolic dynamical systems these dependencies were found to be highly irregular and, in fact, fractal. The main focus in this work is on nonhyperbolic and on intermittent dynamical systems. First, the climbing sine map is considered which is a nonhyperbolic system with many physical applications. Then we treat anomalous dynamics generated by a paradigmatic subdiffusive map. In both cases these systems display deterministic transport which, under variation of control parameters, is fractal. For both systems we give an explanation of the observed phenomena. The third part of the thesis is devoted to the relation between chaotic and transport properties of dynamical systems. This question lies at the heart of dynamical systems theory. For closed hyperbolic dynamical systems the Pesin theorem links the sum of positive Lyapunov exponents to the Kolmogorov-Sinai entropy. For open hyperbolic systems the escape rate formula is valid. In this work we have formulated generalizations of these formulas for a class of intermittent dynamical systems where the chaotic properties are weaker.

A fundamental challenge is to understand nonequilibrium statistical mechanics starting from microscopic chaos in the equations of motion of a many-particle system. In this thesis we summarize recent theoretical advances along these lines. We focus on two different approaches to nonequilibrium transport: One considers Hamiltonian dynamical systems under nonequilibrium boundary conditions, another one suggests a non-Hamiltonian approach to nonequilibrium situations created by external electric fields and by temperature or velocity gradients. A surprising result related to the former approach is that in simple low-dimensional periodic models the deterministic transport coefficients are typically fractal functions of control parameters. These fractal transport coefficients yield the first central theme of this thesis. We exemplify this phenomenon by deterministic diffusion in a simple chaotic map. We then construct an arsenal of analytical and numerical methods for computing further transport coefficients such as electrical conductivities andchemical reaction rates. These methods are applied to hierarchies of chaotic dynamical systems that are successively getting more complex, starting from abstract one-dimensional maps generalizing a simple random walk on the line up to particle billiards that should be directly accessible in experiments. In all cases, the resulting transport coefficients turn out to be either strictly fractal, or at least to be profoundly irregular. The impact of random perturbations on these quantities is also investigated. We furthermore provide some access roads towards a physical understanding of these fractalities. The second central theme is formed by a critical assessment of the non-Hamiltonian approach to nonequilibrium transport. Here we consider situations where the nonequilibrium constraints pump energy into a system, hence there must be some thermal reservoir that prevents the system from heating up. For this purpose a deterministic and time-reversible modeling of thermal reservoirs was proposed in form of Gaussian and Nose-Hoover thermostats. This approach yielded simple relations between fundamental quantities of nonequilibrium statistical mechanics and of dynamical systems theory. Our goal is to critically assesses the universality of these results. As a vehicle of demonstration we employ the driven periodic Lorentz gas, a toy model for the classical dynamics of an electron in a metal under application of an electric field. Applying different types of thermal reservoirs to this system we compare the resulting nonequilibrium steady states with each other. Along the same lines we discuss an interacting many-particle system under shear and heat. Finally, we outline an unexpected relationship between deterministic thermostats and active Brownian particles modeling biophysical cell motility.