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Flow regime is a major determinant of the structure and functioning of aquatic ecosystems. Under climate change, flow intermittency is becoming more prevalent in glaciated alpine catchments, but the effects of increasing dryness on aquatic biodiversity remain largely unknown. We characterised flow intermittency patterns in 30 streams of a glaciated alpine catchment over 15 months and separated these streams into four intermittency categories: perennial streams, winter-drying streams, moderately intermittent streams with occasional drying in summer, and periodically intermittent streams with extensive dry periods throughout the year. We then examined how these drying patterns affected structural and functional properties of benthic macroinvertebrate communities, and whether these changes were primarily deterministic or stochastic. At the taxonomic level, we observed a response at the highest intermittency levels, with α diversity lower and β diversity higher in periodically intermittent streams than in other stream types. This result suggested that local biota were well adapted to intermediate intermittency levels (mostly during winter) but not to high intermittency during summer. In contrast, functional diversity indices at the α and β levels (based on trait abundances) did not differ across intermittency categories. Considering the moderate level of functional redundancy, we interpreted this as an indication that changes in taxonomic diversity may have resulted primarily from stochastic processes. Analysis of community and trait composition indicated that deterministic selection may indeed have occurred with increased intermittency, but this process was likely to be minor in comparison to stochastic extinctions. Notably, community evenness was highest in periodically intermittent streams and lowest in perennial streams, suggesting that frequent drying prevented competitive exclusion. Our results suggested that most macroinvertebrate populations are resilient to intermediate intermittency levels but are filtered at high intermittency, irrespective of their resilience capacities. However, more research is needed to clarify the specific roles of different facets of flow regimes, specifically frequency, duration, and timing of intermittency. Understanding the consequences of responses in diversity and community evenness with increasing intermittency on the functional properties of communities will allow better prediction of the future ecological status of alpine stream networks to ongoing environmental change.

The subject of random or stochastic processes analysis is a very important part of scientific inquire. The terms stochastic and random process are used interchangeably. Random processes are used as mathematical models for a large number of phenomena in physics, chemistry, biology, computer science, information theory, economics, environmental science and others. Each subject is described and problems are implemented in the R code, with real data collected in experiments performed by the authors or taken from the literature. With this intent, the reader can promptly apply the analysis to her or his own data, making the subject operational. Consistent with modern trends in university instruction, the book make readers active learners, with hands-on computer experiments directing readers through applications of random process analysis (RPA).

Presented is a new approach to aircraft crew intelligent support, which is based on comparing flight fragments (maneuvers) under study with the relevant patterns contained in the database and representing the system “empirical intelligence”. Principal components of this approach are four new metrics for comparing flight fragments, viz.: the Euclidean metric in the space of wavelet coefficients; the likelihood metric of eigenvalue trajectories for transformations of activity parameters; the Kohonen metric in the space of wavelet coefficients; the likelihood metric for comparing gaze trajectories. Features of the presented approach are: the presence of an “intelligent component” that is contained in empirical data and can be flexibly changed as they accumulate; the use of integral comparisons of the flight fragments under study and video oculography data with relevant patterns of various types and performance quality from a specialized database, with transferring characteristics of the nearest pattern from this specialized database to the fragment under study; applying a complex combination of the methods for stochastic processes analysis and multivariate statistical techniques.

This paper is a description of the evolution of long-term research work on two-phase flows using parallel studies of dynamic image analysis and stochastic processes analysis. The state of current knowledge on the research of gas-solid and gas-liquid systems as well as a review of research relating to these issues are also presented. The work grants the principles of videogrammetric surveys based on stochastic analysis for a series of photographs taken with video techniques. The method applies the analysis of changes in selected features and parameters in the time domain. Especially in application to multiphase gas-liquid and solid-gas mixture flows, which are characterized by strong variabilities. Parameters such as flow patterns of the mixture were determined as time-space distributions of phase concentration, displacement velocities of separated two-phase structures, volume partitions of phases, and velocity field distributions are evaluated. The changes of certain parameters characterizing the flow in the time domain often hide more useful information. The subject of this study covers the basics of videogrammetry with a description of two-phase mixture motion for co-current flow in channels, mapping of the phase velocity field, also across the tube bundle in shell-and-tube apparatus, phase motion at the flow of a two-phase gas-liquid mixture in mini-channels, transport of liquids in air-lift pump and fluidization of solid particles.

Electric arc furnaces (EAFs) are important appliances in steelmaking industry, but they are characterized by nonlinear, dynamic and stochastic nature. Due to this fact, EAFs can have a negative influence on power systems. Measures for mitigation of such problems can be designed properly only with the knowledge of the load influence on the system. Therefore, it is necessary to have accurate models of EAFs, reflecting the complicated character of such loads. Researchers use different approaches for EAF modelling, such as stochastic processes analysis, differential equation models or neural networks. This paper presents the application of three artificial neural network (ANN) based models in EAF modelling. The goal was to provide ANN models which are simple in structure in comparison to deep learning methods used by other researchers. First two models are built on multilayer perceptron networks and the third applies a nonlinear autoregressive exogenous model with the help of a differential equation transformed into Hammerstein-Wiener model. The paper describes the measurement data, a design for each approach and the results of EAF modelling.

A class of infinite dimensional Ornstein-Uhlenbeck processes that arise as solutions of stochastic partial differential equations with noise generated by measure-valued catalytic processes is investigated. It will be shown that the catalytic Ornstein-Uhlenbeck process with super-Brownian catalyst in one dimension arises as a high density fluctuation limit of a super-Brownian motion in a super-Brownian catalyst with immigration. The main tools include Laplace transformations of stochastic processes, analysis of a non-linear partial differential equation and techniques on continuity and regularity based on properties of the Sobolev spaces.

Dissertação de mestrado em Estatística, Uma série temporal é um conjunto de observações ordenadas no tempo. Os dados que resultam de observações desta natureza são muito comuns em diversas áreas como a Economia, o Ambiente, a Biologia, a Física e a Meteorologia, entre outras. A previsão de valores futuros em séries temporais, de um dado fenómeno ou de uma variável em estudo, é um dos principais objectivos da aplicação dos modelos de séries temporais. A escolha do modelo de previsão depende da estrutura dos dados e dos objetivos do estudo. Os métodos de alisamento exponencial são os mais utilizados na modelação e previsão em séries temporais, devido à sua versatilidade e à vasta opção de modelos que integram. Também, na área da estatística computacional, a metodologia de Bootstrap é muito aplicada na inferência estatística no âmbito de séries temporais. Assim, este estudo teve como principal objectivo analisar o desempenho do método de alisamento exponencial Holt-Winters associado à metodologia Bootstrap, como um procedimento alternativo na modelação e previsão de séries temporais. Neste trabalho apresentam-se, sucintamente, os conceitos básicos da análise de processos estocásticos no domínio do tempo, os principais métodos de alisamento exponencial, em particular o método não paramétrico de Holt-Winters, a metodologia Bootstrap e algumas das metodologias mais frequentemente aplicadas na modelação/previsão de séries temporais. Posteriormente, é apresentada a aplicação a um caso de estudo de séries temporais relativas a uma variável ambiental de qualidade da água de superfície, o Oxigénio Dissolvido, medida mensalmente desde março de 2000 a dezembro de 2011, em oito estações de amostragem de qualidade da bacia hidrográfica do Rio Ave. Com o procedimento proposto são obtidas previsões que são comparadas com os valores reais do período observado e deixado para previsão. São utilizadas medidas para avaliar o desempenho da metodologia adotada quanto à qualidade das previsões dos dois métodos de previsão considerados (o método Holt-Winters usual e a combinação deste método com a abordagem Bootstrap). O estudo comparativo mostrou que a aplicação do Bootstrap em associação ao método Holt-Winters permite obter intervalos de confiança das previsões com menor amplitude do que os obtidos pelos métodos usuais., A time series is a set of observations ordered in time. The resulting data from this type of observations is very common in several areas such as Economics, Environment, Biology, Physics, and Meteorology, among others. The forecasting in time series, of a certain phenomenon or variable under study, is one of the main purposes of applying time series models. The choice of the forecasting model depends on the data structure and study objectives. Exponential smoothing methods are the most used in time series modeling and forecasting, due to their versatility and the vast model option they integrate. Also, within the computing statistical area, Bootstrap methodology is widely applied in statistical inference concerning time series. Therefore, this study’s main objective is to analyze Holt-Winters exponential smoothing method’s performance associated to Bootstrap methodology, as an alternative procedure of modeling and forecasting in time series. This work briefly presents the basic concepts of stochastic processes analysis in time domain, the main exponential smoothing methods, particularly the Holt- Winters nonparametric method, Bootstrap methodology, and some of the most frequently applied methodologies in time series modeling/forecasting. Subsequently, the methodology is applied to a study case of time series related to an environment variable of surface water quality, Dissolved Oxygen, monthly measured from March 2000 to December 2011, in eight sampling sites of water quality in river Ave’s watershed. Following the proposed procedure are obtained forecasting estimates that are then compared with the real values of the observed period left to forecasting. Some measures are used to evaluate the adopted methodology’s performance concerning the forecasting quality of the two forecasting methods under consideration (Holt-Winters usual method and the combination of this method with Bootstrap approach). The comparative study showed that Bootstrap application in association with Holt-Winters method allows to obtain forecasts intervals with less amplitude than those obtained by means of the usual methods.

Quasistationary states are long-lived nonequilibrium states, observed in some systems with long-range interactions under deterministic Hamiltonian evolution. These intriguing non-Boltzmann states relax to equilibrium over times which diverge algebraically with the system size. To test the robustness of this phenomenon to non-deterministic dynamical processes, we have generalized the paradigmatic model exhibiting such a behavior, the Hamiltonian Mean-Field model, to include energy-conserving stochastic processes. Analysis, based on the Boltzmann equation, a scaling approach and numerical studies, demonstrates that in the long time limit, the system relaxes to the equilibrium state on timescales which do not diverge algebraically with the system size. Thus, quasistationarity takes place only as a crossover phenomenon on times determined by the strength of the stochastic process., 4+ pages, 1 figure; v2: minor changes, published version

Większość ekonometrycznych modeli rynków finansowych konstruowanych jest w oparciu o wielkie i rozwinięte gospodarki światowe. Podejście takie nie zawsze znajduje zastosowanie w przypadku młodych i wschodzących rynków. Wynika to po pierwsze z dostępności, a po drugie z charakteru danych tworzących finansowe szeregi czasowe (skupiska danych, grube ogony, autokorelacja). Celem pracy jest zastosowanie modelu M-GARCH do analizy poziomu zmienności stóp zwrotu aktywów finansowych w przypadku, gdy badaniu poddane są portfele inwestycyjne (o więcej niż dwóch składnikach). Przedstawione zostaną różne podejścia do analizy warunkowej wariancji (modyfikacje M-GARCH). Wynikiem będzie ocena stosowalności tej klasy modeli. The majority of econometric financial market models are based on well run and highly developed economies and available financial time series are very wide, numerous, reporting some specific features as clustering of variance and outliers. Thus, the application of classical methods of the stochastic processes analysis can be biased. The purpose of this paper is to present the review of M-GARCH model to examine the volatility of asset returns in financial market. The analysis includes both individual stocks and portfolios. The most popular approaches of multivariate GARCH models estimation are considered. As a result, the applicability assessment of this class of models within emerging markets will be presented. Zadanie pt. „Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki” nr 885/P-DUN/2014 dofinansowane zostało ze środków MNiSW w ramach działalności upowszechniającej naukę.

Using the methods of multiplicative stochastic processes, a thorough analysis of “non-Markovian,” generalized Langevin equations is presented. For the Gaussian case, these methods are used to show that the nonstationary Fokker-Planck equation already found by Adelman and others is also obtainable from van Kampen's lemma for stochastic probability flows. Here, results applicable to an arbitraryn-component process are obtained and the specific two-component case of the Brownian harmonic oscillator is presented in detail in order to explicitly exhibit the matrix algebraic methods. The non-Gaussian case is presented at the end of the paper and shows that the methods already used in the Gaussian case lead directly to results for the non-Gaussian case. In order to use the methods of multiplicative stochastic processes analysis, it is necessary to transform the “non-Markovian,” generalized Langevin equation using a stochastic extension of a transformation discussed by Adelman. This transformation removes the “memory kernel” term in the usual generalized Langevin equation and in the Gaussian case leads to the result that the original process was in fact not “non-Markovian” but actually nonstationary,Markovian.

The paper addresses the concept of multicointegration in panel data frame- work. The proposal builds upon the panel data cointegration procedures developed in Pedroni (2004), for which we compute the moments of the parametric statistics. When individuals are either cross-section independent or cross-section dependence can be re- moved by cross-section demeaning, our approach can be applied to the wider framework of mixed I(2) and I(1) stochastic processes analysis. The paper also deals with the issue of cross-section dependence using approximate common factor models. Finite sample performance is investigated through Monte Carlo simulations. Finally, we illustrate the use of the procedure investigating inventories, sales and production relationship for a panel of US industries., Aquest article estèn el concepte de multicointegració a l'entorn de dades de panell. La proposta es basa en els procediments de contrast de cointegració en dades de panell desenvolupats per Pedroni (2004), pels quals es calculen els moments dels estadístics paramètrics. Quan els individus són o bé independents entre si, o bé la dependencia transversal es pot eliminar treient la mitjana del tall transversal, la nostra aproximació es pot aplicar a l'àmbit a on es consideren processos estocàstics I(2) i I(1) de manera conjunta. El treball també considera aquella situació en què la dependència transversal es pot recollir mitjançant models de factors comuns. El comportament en mostra finita dels estadístics de prova és estudiat a través de simulacions de Monte Carlo. Finalment, el treball il·lustra l'ús del procediment analitzant la relació entre existències, vendes i producció per a un panell d'indústries dels Estats Units.