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1
Keller, Peter, Sylvie Roelly, and Angelo Valleriani. "A quasi-random-walk to model a biological transport process." Universität Potsdam, 2013. http://opus.kobv.de/ubp/volltexte/2013/6358/.
Повний текст джерелаАнотація:
Transport Molecules play a crucial role for cell viability. Amongst others, linear motors transport cargos along rope-like structures from one location of
the cell to another in a stochastic fashion. Thereby each step of the motor, either forwards or backwards, bridges a fixed distance. While moving along the rope the motor can also detach and is lost. We give here a mathematical formalization of such dynamics as a random process which is an extension of Random Walks, to which we add an absorbing state to model the detachment of the motor from the rope. We derive particular properties of such processes that have not been available before. Our results include description of the maximal distance reached from the starting point and the position from which detachment takes place. Finally, we apply our theoretical results to a concrete established model of the transport molecule Kinesin V.
2
Auret, Lidia. "Process monitoring and fault diagnosis using random forests." Thesis, Stellenbosch : University of Stellenbosch, 2010. http://hdl.handle.net/10019.1/5360.
Повний текст джерелаАнотація:
Thesis (PhD (Process Engineering))--University of Stellenbosch, 2010.Dissertation presented for the Degree of DOCTOR OF PHILOSOPHY (Extractive Metallurgical Engineering) in the Department of Process Engineering at the University of Stellenbosch
ENGLISH ABSTRACT: Fault diagnosis is an important component of process monitoring, relevant in the greater context of developing safer, cleaner and more cost efficient processes. Data-driven unsupervised (or feature extractive) approaches to fault diagnosis exploit the many measurements available on modern plants. Certain current unsupervised approaches are hampered by their linearity assumptions, motivating the investigation of nonlinear methods. The diversity of data structures also motivates the investigation of novel feature extraction methodologies in process monitoring. Random forests are recently proposed statistical inference tools, deriving their predictive accuracy from the nonlinear nature of their constituent decision tree members and the power of ensembles. Random forest committees provide more than just predictions; model information on data proximities can be exploited to provide random forest features. Variable importance measures show which variables are closely associated with a chosen response variable, while partial dependencies indicate the relation of important variables to said response variable. The purpose of this study was therefore to investigate the feasibility of a new unsupervised method based on random forests as a potentially viable contender in the process monitoring statistical tool family. The hypothesis investigated was that unsupervised process monitoring and fault diagnosis can be improved by using features extracted from data with random forests, with further interpretation of fault conditions aided by random forest tools. The experimental results presented in this work support this hypothesis. An initial study was performed to assess the quality of random forest features. Random forest features were shown to be generally difficult to interpret in terms of geometry present in the original variable space. Random forest mapping and demapping models were shown to be very accurate on training data, and to extrapolate weakly to unseen data that do not fall within regions populated by training data. Random forest feature extraction was applied to unsupervised fault diagnosis for process data, and compared to linear and nonlinear methods. Random forest results were comparable to existing techniques, with the majority of random forest detections due to variable reconstruction errors. Further investigation revealed that the residual detection success of random forests originates from the constrained responses and poor generalization artifacts of decision trees. Random forest variable importance measures and partial dependencies were incorporated in a visualization tool to allow for the interpretation of fault conditions. A dynamic change point detection application with random forests proved more successful than an existing principal component analysis-based approach, with the success of the random forest method again residing in reconstruction errors. The addition of random forest fault diagnosis and change point detection algorithms to a suite of abnormal event detection techniques is recommended. The distance-to-model diagnostic based on random forest mapping and demapping proved successful in this work, and the theoretical understanding gained supports the application of this method to further data sets.
AFRIKAANSE OPSOMMING: Foutdiagnose is ’n belangrike komponent van prosesmonitering, en is relevant binne die groter konteks van die ontwikkeling van veiliger, skoner en meer koste-effektiewe prosesse. Data-gedrewe toesigvrye of kenmerkekstraksie-benaderings tot foutdiagnose benut die vele metings wat op moderne prosesaanlegte beskikbaar is. Party van die huidige toesigvrye benaderings word deur aannames rakende liniariteit belemmer, wat as motivering dien om nie-liniêre metodes te ondersoek. Die diversiteit van datastrukture is ook verdere motivering vir ondersoek na nuwe kenmerkekstraksiemetodes in prosesmonitering. Lukrake-woude is ’n nuwe statistiese inferensie-tegniek, waarvan die akkuraatheid toegeskryf kan word aan die nie-liniêre aard van besluitnemingsboomlede en die bekwaamheid van ensembles. Lukrake-woudkomitees verskaf meer as net voorspellings; modelinligting oor datapuntnabyheid kan benut word om lukrakewoudkenmerke te verskaf. Metingbelangrikheidsaanduiers wys watter metings in ’n noue verhouding met ’n gekose uitsetveranderlike verkeer, terwyl parsiële afhanklikhede aandui wat die verhouding van ’n belangrike meting tot die gekose uitsetveranderlike is. Die doel van hierdie studie was dus om die uitvoerbaarheid van ’n nuwe toesigvrye metode vir prosesmonitering gebaseer op lukrake-woude te ondersoek. Die ondersoekte hipotese lui: toesigvrye prosesmonitering en foutdiagnose kan verbeter word deur kenmerke te gebruik wat met lukrake-woude geëkstraheer is, waar die verdere interpretasie van foutkondisies deur addisionele lukrake-woude-tegnieke bygestaan word. Eksperimentele resultate wat in hierdie werkstuk voorgelê is, ondersteun hierdie hipotese. ’n Intreestudie is gedoen om die gehalte van lukrake-woudkenmerke te assesseer. Daar is bevind dat dit moeilik is om lukrake-woudkenmerke in terme van die geometrie van die oorspronklike metingspasie te interpreteer. Verder is daar bevind dat lukrake-woudkartering en -dekartering baie akkuraat is vir opleidingsdata, maar dat dit swak ekstrapolasie-eienskappe toon vir ongesiene data wat in gebiede buite dié van die opleidingsdata val. Lukrake-woudkenmerkekstraksie is in toesigvrye-foutdiagnose vir gestadigde-toestandprosesse toegepas, en is met liniêre en nie-liniêre metodes vergelyk. Resultate met lukrake-woude is vergelykbaar met dié van bestaande metodes, en die meerderheid lukrake-woudopsporings is aan metingrekonstruksiefoute toe te skryf. Verdere ondersoek het getoon dat die sukses van res-opsporing op die beperkte uitsetwaardes en swak veralgemenende eienskappe van besluitnemingsbome berus. Lukrake-woude-metingbelangrikheidsaanduiers en parsiële afhanklikhede is ingelyf in ’n visualiseringstegniek wat vir die interpretasie van foutkondisies voorsiening maak. ’n Dinamiese aanwending van veranderingspuntopsporing met lukrake-woude is as meer suksesvol bewys as ’n bestaande metode gebaseer op hoofkomponentanalise. Die sukses van die lukrake-woudmetode is weereens aan rekonstruksie-reswaardes toe te skryf. ’n Voorstel wat na aanleiding van hierde studie gemaak is, is dat die lukrake-woudveranderingspunt- en foutopsporingsmetodes by ’n soortgelyke stel metodes gevoeg kan word. Daar is in hierdie werk bevind dat die afstand-vanaf-modeldiagnostiek gebaseer op lukrake-woudkartering en -dekartering suksesvol is vir foutopsporing. Die teoretiese begrippe wat ontsluier is, ondersteun die toepassing van hierdie metodes op verdere datastelle.
3
Li, Zheng. "Approximation to random process by wavelet basis." View abstract/electronic edition; access limited to Brown University users, 2008. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3318378.
Повний текст джерела
4
Gupta, Resmi. "Flexible Multivariate Joint Model of Longitudinal Intensity and Binary Process for Medical Monitoring of Frequently Collected Data." University of Cincinnati / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1561393989215645.
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5
Mardoukhi, Yousof [Verfasser], and Ralf [Akademischer Betreuer] Metzler. "Random environments and the percolation model : non-dissipative fluctuations of random walk process on finite size clusters / Yousof Mardoukhi ; Betreuer: Ralf Metzler." Potsdam : Universität Potsdam, 2020. http://d-nb.info/1219580082/34.
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6
Sarnoff, Tamar Jill. "METAPHOR, COGNITIVE ELABORATION AND PERSUASION." Diss., The University of Arizona, 2009. http://hdl.handle.net/10150/194626.
Повний текст джерелаАнотація:
Metaphors have long been a subject of interest to philosophers, scholars and researchers. Recent insights into the nature and function of metaphor have spurred new interest in the persuasive effects of metaphor. To date, research on the relation between metaphors and attitudes has produced mixed findings. This paper argues that there are several limitations in previous models and designs and this work attempted to resolve several of them. The rationale for the study is based on the Elaboration Likelihood Model (ELM) of persuasion, which argues that cognitive elaboration is a strong predictor of attitudes. Researchers have posited that metaphors should evoke more cognitive elaboration than literal counterparts. This paper reports the results of a study that tested the relationship between metaphors, cognitive elaboration, and attitudes. Participants were exposed to one of 72 message conditions and responded to a set of psychological and attitude scales. Many of the hypotheses were not supported, including tests of the amount of cognitive effort that subjects reported and results related to attitude change by metaphor type. Results indicated that attitudes were stable across time, which is consistent with the ELM.
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Shykula, Mykola. "Quantization of Random Processes and Related Statistical Problems." Doctoral thesis, Umeå : Department of Mathematics and Mathematical Statistics, Umeå University, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-883.
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Lutsyk, Nadiia. "Modeling and methods of biomechanical heart signals processing using the conditional cyclic random process." Thesis, Clermont-Ferrand 2, 2016. http://www.theses.fr/2016CLF22726.
Повний текст джерелаАнотація:
Ce travail a été réalisé en cotutelle entre l'Université Nationale de Technologie de Ternopil Ivan Pul'uj (TNTU, Ukraine) et l’Université Blaise Pascal (France). Il appartient au domaine scientifique de la biomécanique et de l'informatique. Le but de l'étude est de développer les modèles et les méthodes de traitement des signaux biomécaniques cardiaques par les systèmes de diagnostic assisté par ordinateur avec une précision accrue, informativité et de la complexité de calcul inférieure. La méthode d'analyse statistique du rythme cardiaque a été mise au point. Cette méthode possède une plus grande précision et informativité par rapport aux méthodes connues d'analyse du rythme cardiaque. Dans cette thèse, le logiciel existant de l'analyse des signaux cardiaques biomécaniques a été améliorée par l'ajout de nouveaux modules logiciels, qui mettent en œuvre les nouvelles méthodes de l'analyse du rythme cardiaque et de l'analyse morphologique des signaux cardiaques biomécaniquesThis work has been performed under the co-tutelle agreement between Ternopil Ivan Pul’uj National Technical University in Ternopil (TNTU, Ukraine) and the University Blaise Pascal in Clermont-Ferrand (France). It belongs to the scientific field of biomechanics and informatics. The aim of the study is to develop the mathematical models and methods of the processing of biomechanical heart signals in computer-based diagnostic systems with increased accuracy, informativeness and lower computational complexity. The method of statistical analysis of heart rhythm was developed, which is characterised by higher accuracy and informativeness compared with the known methods of heart rhythm analysis. In this thesis, the existing software of the analysis of biomechanical heart signals was improved by means of adding new software modules that implement the new methods of the analysis of heart rhythm and morphologic analysis of biomechanical heart signals
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Erich, Roger Alan. "Regression Modeling of Time to Event Data Using the Ornstein-Uhlenbeck Process." The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1342796812.
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Петранова, Марина Юрiївна. "Випадковi гауссовi процеси зi стiйкими кореляцiйними функцiями". Doctoral thesis, Київ, 2021. https://ela.kpi.ua/handle/123456789/40592.
Повний текст джерелаАнотація:
Робота виконана на кафедрi прикладної математики Донецького нацiонального унiверситету iменi Василя Стуса Мiнiстерства освiти i науки Українииссертационная работа посвящена изучению случайных гауссо вых процессов с устойчивыми корреляционными функциями и их свойств.
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Kreacic, Eleonora. "Some problems related to the Karp-Sipser algorithm on random graphs." Thesis, University of Oxford, 2017. http://ora.ox.ac.uk/objects/uuid:3b2eb52a-98f5-4af8-9614-e4909b8b9ffa.
Повний текст джерелаАнотація:
We study certain questions related to the performance of the Karp-Sipser algorithm on the sparse Erdös-Rényi random graph. The Karp-Sipser algorithm, introduced by Karp and Sipser [34] is a greedy algorithm which aims to obtain a near-maximum matching on a given graph. The algorithm evolves through a sequence of steps. In each step, it picks an edge according to a certain rule, adds it to the matching and removes it from the remaining graph. The algorithm stops when the remining graph is empty. In [34], the performance of the Karp-Sipser algorithm on the Erdös-Rényi random graphs G(n,M = [cn/2]) and G(n, p = c/n), c > 0 is studied. It is proved there that the algorithm behaves near-optimally, in the sense that the difference between the size of a matching obtained by the algorithm and a maximum matching is at most o(n), with high probability as n → ∞. The main result of [34] is a law of large numbers for the size of a maximum matching in G(n,M = cn/2) and G(n, p = c/n), c > 0. Aronson, Frieze and Pittel [2] further refine these results. In particular, they prove that for c < e, the Karp-Sipser algorithm obtains a maximum matching, with high probability as n → ∞; for c > e, the difference between the size of a matching obtained by the algorithm and the size of a maximum matching of G(n,M = cn/2) is of order Θlog n(n1/5), with high probability as n → ∞. They further conjecture a central limit theorem for the size of a maximum matching of G(n,M = cn/2) and G(n, p = c/n) for all c > 0. As noted in [2], the central limit theorem for c < 1 is a consequence of the result of Pittel [45]. In this thesis, we prove a central limit theorem for the size of a maximum matching of both G(n,M = cn/2) and G(n, p = c/n) for c > e. (We do not analyse the case 1 ≤ c ≤ e). Our approach is based on the further analysis of the Karp-Sipser algorithm. We use the results from [2] and refine them. For c > e, the difference between the size of a matching obtained by the algorithm and the size of a maximum matching is of order Θlog n(n1/5), with high probability as n → ∞, and the study [2] suggests that this difference is accumulated at the very end of the process. The question how the Karp-Sipser algorithm evolves in its final stages for c > e, motivated us to consider the following problem in this thesis. We study a model for the destruction of a random network by fire. Let us assume that we have a multigraph with minimum degree at least 2 with real-valued edge-lengths. We first choose a uniform random point from along the length and set it alight. The edges burn at speed 1. If the fire reaches a node of degree 2, it is passed on to the neighbouring edge. On the other hand, a node of degree at least 3 passes the fire either to all its neighbours or none, each with probability 1/2. If the fire extinguishes before the graph is burnt, we again pick a uniform point and set it alight. We study this model in the setting of a random multigraph with N nodes of degree 3 and α(N) nodes of degree 4, where α(N)/N → 0 as N → ∞. We assume the edges to have i.i.d. standard exponential lengths. We are interested in the asymptotic behaviour of the number of fires we must set alight in order to burn the whole graph, and the number of points which are burnt from two different directions. Depending on whether α(N) » √N or not, we prove that after the suitable rescaling these quantities converge jointly in distribution to either a pair of constants or to (complicated) functionals of Brownian motion. Our analysis supports the conjecture that the difference between the size of a matching obtained by the Karp-Sipser algorithm and the size of a maximum matching of the Erdös-Rényi random graph G(n,M = cn/2) for c > e, rescaled by n1/5, converges in distribution.
12
Starkloff, Hans-Jörg, Matthias Richter, Scheidt Jürgen vom, and Ralf Wunderlich. "On the convergence of random functions defined by interpolation." Universitätsbibliothek Chemnitz, 2004. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200401293.
Повний текст джерелаАнотація:
In the paper we study sequences of random functions which are defined by some
interpolation procedures for a given random function. We investigate the problem
in what sense and under which conditions the sequences converge to the prescribed
random function. Sufficient conditions for convergence of moment characteristics, of
finite dimensional distributions and for weak convergence of distributions in spaces
of continuous functions are given. The treatment of such questions is stimulated by
an investigation of Monte Carlo simulation procedures for certain classes of random
functions.
In an appendix basic facts concerning weak convergence of probability measures
in metric spaces are summarized.
13
Dirrler, Martin [Verfasser], and Martin [Akademischer Betreuer] Schlather. "Spatial point process models with applications to max-stable random fields / Martin Dirrler ; Betreuer: Martin Schlather." Mannheim : Universitätsbibliothek Mannheim, 2017. http://d-nb.info/1144178185/34.
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Christou, Christos [Verfasser], and Andreas [Gutachter] Schadschneider. "Non-Equilibrium Stochastic Models: Random Average Process and Diffusion with Resetting / Christos Christou ; Gutachter: Andreas Schadschneider." Köln : Universitäts- und Stadtbibliothek Köln, 2018. http://d-nb.info/1186251751/34.
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Mateluna, Diego Ignacio Gallardo. "Extensões em modelos de sobrevivência com fração de cura e efeitos aleatórios." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-24062014-202301/.
Повний текст джерелаАнотація:
Neste trabalho são apresentadas algumas extensões de modelos de sobrevivência com fração de cura, assumindo o contexto em que as observações estão agrupadas. Dois efeitos aleatórios são incorporados para cada grupo: um para explicar o efeito no tempo de sobrevida das observações suscetíveis e outro para explicar a probabilidade de cura. Apresenta-se uma abordagem clássica através dos estimadores REML e uma abordagem bayesiana através do uso de processos de Dirichlet. Discute-se alguns estudos de simulação em que avalia-se o desempenho dos estimadores propostos, além de comparar as duas abordagens. Finalmente, ilustram-se os resultados com dados reais.In this work some extensions in survival models with cure fraction are presented, assuming the context in which the observations are grouped into clusters. Two random effects are incorporated for each group: one to explain the effect on survival time of susceptible observations and another to explain the probability of cure. A classical approach through the REML estimators is presented as well as a bayesian approach through Dirichlet Process. Besides comparing both approaches, some simulation studies which evaluates the performance of the proposed estimators are discussed. Finally, the results are illustrated with a real database.
16
Leichsenring, Alexandre Ribeiro. "Não monotonicidade do parâmetro crítico no modelo dos sapos." Universidade de São Paulo, 2003. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-06042013-173920/.
Повний текст джерелаАнотація:
Estudamos um modelo de passeios aleatórios simples em grafos, conhecido como modelo dos sapos. Esse modelo pode ser descrito de maneira geral da seguinte forma: existem partículas ativas e partículas desativadas num grafo G. Cada partícula ativa desempenha um passeio aleatório simples a tempo discreto e a cada momento ela pode morrer com probabilidade 1-p. Quando uma partícula ativa entra em contato com uma partícula desativada, esta é ativada e também passa a realizar, de maneira independente, um passeio aleatório pelo grafo. Apresentamos limites superior e inferior para o parâmetro crítico de sobrevivência do modelo dos sapos na árvore, e demonstramos que este parâmetro crítico não é uma função monótona do grafo em que está definido.We study a system of simple random walks on graphs, known as frog model. This model can be described generally speaking as follows: there are active and sleeping particles living on some graph G. Each particle performs a simple random walk with discrete time and at each moment it may disappear with probability 1 - p. When an active particle hits a sleeping particle, the latter becomes active and starts to perform, independently, a simple random walk on the graph. We present lower and upper bounds for the surviving critical parameter on the tree, and we show that this parameter is not a monotonic function of the graph it is defined on.
17
Muwanguzi, Abraham Judah Bumalirivu. "Investigating the parameters that influence the behaviour of natural iron ores during the iron production process." Doctoral thesis, KTH, Tillämpad processmetallurgi, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-123063.
Повний текст джерелаАнотація:
In the iron production processes, sinters and pellets are mostly used as raw materials due to their consistency with respect to physical and chemical properties. However, natural iron ores, as mined, are rarely used directly as a feed material for iron processing. This is mainly due to the fact that they have small contents of iron and high concentration of impurities. Moreover, they swell and disintegrate during the descent in the furnace as well as due to low melting and softening temperatures. This work involves an investigation of the parameters that influence the use of natural iron ores as a direct feed material for iron production. Furthermore, it points out ways in which these can be mitigated so as to increase their direct use in iron production. Natural iron ore from Muko deposits in south-western Uganda was used in this study. Initially, characterisation of the physical and chemical properties was performed, to understand the natural composition of the ore. In addition, investigations were done to study the low temperature strength of the ore and its behaviour in the direct reduction zone. Also, simulations were performed with three models using the experimental data from the direct reduction experiments in order to determine the best model for predicting the direct reduction kinetics of natural iron ores. Chemical analyses showed that the Muko ore represents a high grade of hematite with an Fe content of 68% on average. The gangue content (SiO2+Al2O3) in 5 of the 6 investigated iron ore samples was < 4%, which is within the tolerable limits for the dominant iron production processes. The S and P contents were 0001-0.006% and 0.02-0.05% respectively. These can be reduced in the furnace without presenting major processing difficulties. With respect to the mechanical properties, the Muko ore was found to have a Tumble Index value of 88-93 wt%, an Abrasion Index value of 0.5-3.8 wt% and a Shatter Index value of 0.6-2.0 wt%. Therefore, the ore holds its form during the handling and charging processes. Under low temperature investigations, new parameters were discovered that influence the low temperature strength of iron oxides. It was discovered that the positioning of the samples in the reduction furnace together with the original weight (W0) of the samples, have a big influence on the low temperature strength of iron oxide. Higher mechanical degradation (MD) values were obtained in the top furnace reaction zone samples (3-25% at 500oC and 10-21% at 600oC). These were the samples that had the first contact with the reducing gas, as it was flowing through the furnace from top to bottom. Then, the MD values decreased till 5-16% at a 500oC temperature and 6-20% at a 600oC temperature in the middle and bottom reaction zones samples. It was found that the obtained difference between the MD values in the top and other zones can be more than 2 times, particularly at 500oC temperature. Furthermore, the MD values for samples with W0 < 5 g varied from 7-21% well as they decreased to 5-10% on average for samples with W0 ≥ 5 g. Moreover, the MD values for samples taken from the top reaction zone were larger than those from the middle and bottom zones. During direct reduction of the ores in a H2 and CO gas mixture with a ratio of 1.5 and a constant temperature, the reduction degree (RD) increased with a decreased flow rate until an optimum value was established. The RD also increased when the flow rate was kept constant and the temperature increased. An optimum range of 3-4g was found for natural iron ores, within which the highest RD values that are realised for all reduction conditions. In addition, the mechanical stability is greatly enhanced at RD values > 0.7. In the case of microstructure, it was observed that the original microstructure of the samples had no significant impact on the final RD value (only 2-4%). However, it significantly influenced the reduction rate and time of the DR process. The thermo-gravimetric data obtained from the reduction experiments was used to calculate the solid conversion rate. Three models: the Grain Model (GM), the Volumetric Model (VM) and the Random Pore Model (RPM), were used to estimate the reduction kinetics of natural iron ores. The random pore model (RPM) provided the best agreement with the obtained experimental results (r2 = 0.993-0.998). Furthermore, it gave a better prediction of the natural iron oxide conversion and thereby the reduction kinetics. The RPM model was used for the estimation of the effect of original microstructure and porosity of iron ore lumps on the parameters of the reduction process.QC 20130531
Sustainable Technology Development in the Lake Victoria Region
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Shi, Hongxiang. "Hierarchical Statistical Models for Large Spatial Data in Uncertainty Quantification and Data Fusion." University of Cincinnati / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1504802515691938.
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Ricciardi, Denielle E. "Uncertainty Quantification and Propagation in Materials Modeling Using a Bayesian Inferential Framework." The Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1587473424147276.
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Fang, Zaili. "Some Advanced Model Selection Topics for Nonparametric/Semiparametric Models with High-Dimensional Data." Diss., Virginia Tech, 2012. http://hdl.handle.net/10919/40090.
Повний текст джерелаАнотація:
Model and variable selection have attracted considerable attention in areas of application where datasets usually contain thousands of variables. Variable selection is a critical step to reduce the dimension of high dimensional data by eliminating irrelevant variables. The general objective of variable selection is not only to obtain a set of cost-effective predictors selected but also to improve prediction and prediction variance. We have made several contributions to this issue through a range of advanced topics: providing a graphical view of Bayesian Variable Selection (BVS), recovering sparsity in multivariate nonparametric models and proposing a testing procedure for evaluating nonlinear interaction effect in a semiparametric model.
To address the first topic, we propose a new Bayesian variable selection approach via the graphical model and the Ising model, which we refer to the ``Bayesian Ising Graphical Model'' (BIGM). There are several advantages of our BIGM: it is easy to (1) employ the single-site updating and cluster updating algorithm, both of which are suitable for problems with small sample sizes and a larger number of variables, (2) extend this approach to nonparametric regression models, and (3) incorporate graphical prior information.
In the second topic, we propose a Nonnegative Garrote on a Kernel machine (NGK) to recover sparsity of input variables in smoothing functions. We model the smoothing function by a least squares kernel machine and construct a nonnegative garrote on the kernel model as the function of the similarity matrix. An efficient coordinate descent/backfitting algorithm is developed.
The third topic involves a specific genetic pathway dataset in which the pathways interact with the environmental variables. We propose a semiparametric method to model the pathway-environment interaction. We then employ a restricted likelihood ratio test and a score test to evaluate the main pathway effect and the pathway-environment interaction.Ph. D.
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Triampo, Wannapong. "Non-Equilibrium Disordering Processes In binary Systems Due to an Active Agent." Diss., Virginia Tech, 2001. http://hdl.handle.net/10919/26738.
Повний текст джерелаАнотація:
In this thesis, we study the kinetic disordering of systems
interacting with an agent or a walker. Our studies divide naturally into two
classes: for the first, the dynamics of the walker conserves the total
magnetization of the system, for the second, it does not. These distinct
dynamics are investigated in part I and II respectively.
In part I, we investigate the disordering of an initially
phase-segregated binary alloy due to a highly mobile vacancy which exchanges
with the alloy atoms. This dynamics clearly conserves the total
magnetization. We distinguish three versions of dynamic rules for the
vacancy motion, namely a pure random walk , an ``active' and a biased walk.
For the random walk case, we review and reproduce earlier work by Z.
Toroczkai et. al.,~cite{TKSZ} which will serve as our base-line. To test
the robustness of these findings and to make our model more accessible to
experimental studies, we investigated the effects of finite temperatures
(``active walks') as well as external fields (biased walks). To monitor the
disordering process, we define a suitable disorder parameter, namely the
number of broken bonds, which we study as a function of time, system size
and vacancy number. Using Monte Carlo simulations and a coarse-grained field
theory, we observe that the disordering process exhibits three well
separated temporal regimes. We show that the later stages exhibit dynamic
scaling, characterized by a set of exponents and scaling functions. For the
random and the biased case, these exponents and scaling functions are
computed analytically in excellent agreement with the simulation results.
The exponents are remarkably universal. We conclude this part with some
comments on the early stage, the interfacial roughness and other related
features.
In part II, we introduce a model of binary data corruption induced
by a Brownian agent or random walker. Here, the magnetization is not
conserved, being related to the density of corrupted bits }$
ho ${small .}
{small Using both continuum theory and computer simulations, we study the
average density of corrupted bits, and the
associated density-density correlation function, as well as several other
related quantities. In the second half, we
extend our investigations in three main directions which allow us to make
closer contact with real binary systems. These are i) a detailed analysis of
two dimensions, ii) the case of competing agents, and iii) the cases of
asymmetric and quenched random couplings. Our analytic results are in good
agreement with simulation results. The remarkable finding of this study is
the robustness of the phenomenological model which provides us with the tool,
continuum theory, to understand the nature of such a simple model.Ph. D.
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Souza, Wagner Barreto de. "Passeios aleatórios estáveis em Z com taxas não-homogêneas e os processos quase-estáveis." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-19022013-151640/.
Повний текст джерелаАнотація:
Seja $\\mathcal X=\\{\\mathcal X_t:\\, t\\geq0,\\, \\mathcal X_0=0\\}$ um passeio aleatório $\\beta$-estável em $\\mathbb Z$ com média zero e com taxas de saltos não-homogêneas $\\{\\tau_i^: i\\in\\mathbb Z\\}$, com $\\beta\\in(1,2]$ e $\\{\\tau_i: i\\in\\mathbb Z\\}$ sendo uma família de variáveis aleatórias independentes com distribuição marginal comum na bacia de atração de uma lei $\\alpha$-estável, com $\\alpha\\in(0,2]$. Nesta tese, obtemos resultados sobre o comportamento do processo $\\mathcal X_t$ para tempos longos, em particular, obtemos seu limite de escala. Quando $\\alpha\\in(0,1)$, o limite de escala é um processo $\\beta$-estável mudado de tempo pela inversa de um outro processo, o qual envolve o tempo local do processo $\\beta$-estável e um independente subordinador $\\alpha$-estável; chamamos o processo resultante de processo quase-estável. Para o caso $\\alpha\\in[1,2]$, o limite de escala é um ordinário processo $\\beta$-estável. Para $\\beta=2$ e $\\alpha\\in(0,1)$, o limite de escala é uma quase-difusão com medida de velocidade aleatória estudada por Fontes, Isopi e Newman (2002). Outros resultados sobre o comportamento de $\\mathcal X$ para tempos longos são envelhecimento e localização. Nós obtemos resultados de envelhecimento integrado e não-integrado para $\\mathcal X$ quando $\\alpha\\in(0,1)$. Relacionado à esses resultados, e possivelmente de interesse independente, consideramos o processo de armadilha definido por $\\{\\tau_{\\mathcal X_t}: t\\geq0\\}$, e obtemos seu limite de escala. Concluímos a tese com resultados sobre localização de $\\mathcal X$. Mostramos que ele pode ser localizado quando $\\alpha\\in(0,1)$, e que não pode ser localizado quando $\\alpha\\in(1,2]$, assim estendendo os resultados de Fontes, Isopi e Newman (1999) para o caso de passeios simples simétricos.Let $\\mathcal X=\\{\\mathcal X_t:\\, t\\geq0,\\, \\mathcal X_0=0\\}$ be a mean zero $\\beta$-stable random walk on $\\mathbb Z$ with inhomogeneous jump rates $\\{\\tau_i^: i\\in\\mathbb Z\\}$, with $\\beta\\in(1,2]$ and $\\{\\tau_i: i\\in\\mathbb Z\\}$ is a family of independent random variables with common marginal distribution in the basin of attraction of an $\\alpha$-stable law with $\\alpha\\in(0,2]$. In this thesis we derive results about the long time behavior of this process, in particular its scaling limit. When $\\alpha\\in(0,1)$, the scaling limit is a $\\beta$-stable process time-changed by the inverse of another process, involving the local time of the $\\beta$-stable process and an independent $\\alpha$-stable subordinator; the resulting process may be called a quasistable process. For the case $\\alpha\\in[1,2]$, the scaling limit is an ordinary $\\beta$-stable process. For $\\beta=2$ and $\\alpha\\in(0,1)$, the scaling limit is a quasidiffusion with random speed measure studied by Fontes, Isopi and Newman (2002). Other results about the long time behavior of $\\mathcal X$ concern aging and localization. We obtain integrated and non integrated aging results for $\\mathcal X$ when $\\alpha\\in(0,1)$. Related to these results, and possibly of independent interest, we consider the trap process defined as $\\{\\tau_{\\mathcal X_t}: t\\geq0\\}$, and derive its scaling limit. We conclude the thesis with results about localization of $\\mathcal X$. We show that it localizes when $\\alpha\\in(0,1)$, and does not localize when $\\alpha\\in(1,2]$, extending results of Fontes, Isopi and Newman (1999) for the simple symmetric case.
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Cheng, Lulu. "Statistical Methods for Genetic Pathway-Based Data Analysis." Diss., Virginia Tech, 2013. http://hdl.handle.net/10919/52039.
Повний текст джерелаАнотація:
The wide application of the genomic microarray technology triggers a tremendous need in the development of the high dimensional genetic data analysis. Many statistical methods for the microarray data analysis consider one gene at a time, but they may miss subtle changes at the single gene level. This limitation may be overcome by considering a set of genes simultaneously where the gene sets are derived from the prior biological knowledge and are called "pathways". We have made contributions on two specific research topics related to the high dimensional genetic pathway data. One is to propose a semi- parametric model for identifying pathways related to the zero inflated clinical outcomes; the other is to propose a multilevel Gaussian graphical model for exploring both pathway and gene level network structures.
For the first problem, we develop a semiparametric model via a Bayesian hierarchical framework. We model the pathway effect nonparametrically into a zero inflated Poisson hierarchical regression model with unknown link function. The nonparametric pathway effect is estimated via the kernel machine and the unknown link function is estimated by transforming a mixture of beta cumulative density functions. Our approach provides flexible semiparametric settings to describe the complicated association between gene microarray expressions and the clinical outcomes. The Metropolis-within-Gibbs sampling algorithm and Bayes factor are used to make the statistical inferences. Our simulation results support that the semiparametric approach is more accurate and flexible than the zero inflated Poisson regression with the canonical link function, this is especially true when the number of genes is large. The usefulness of our approaches is demonstrated through its applications to a canine gene expression data set (Enerson et al., 2006). Our approaches can also be applied to other settings where a large number of highly correlated predictors are present.
Unlike the first problem, the second one is to take into account that pathways are not independent of each other because of shared genes and interactions among pathways. Multi-pathway analysis has been a challenging problem because of the complex dependence structure among pathways. By considering the dependency among pathways as well as genes within each pathway, we propose a multi-level Gaussian graphical model (MGGM): one level is for pathway network and the second one is for gene network. We develop a multilevel L1 penalized likelihood approach to achieve the sparseness on both levels. We also provide an iterative weighted graphical LASSO algorithm (Guo et al., 2011) for MGGM. Some asymptotic properties of the estimator are also illustrated. Our simulation results support the advantages of our approach; our method estimates the network more accurate on the pathway level, and sparser on the gene level. We also demonstrate usefulness of our approach using the canine genes-pathways data set.Ph. D.
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Kuoch, Kevin. "Processus de contact avec ralentissements aléatoires : transition de phase et limites hydrodynamiques." Thesis, Paris 5, 2014. http://www.theses.fr/2014PA05S020/document.
Повний текст джерелаАнотація:
Dans cette thèse, on étudie un système de particules en interaction qui généralise un processus de contact, évoluant en environnement aléatoire. Le processus de contact peut être interprété comme un modèle de propagation d'une population ou d'une infection. La motivation de ce modèle provient de la biologie évolutive et de l'écologie comportementale via la technique du mâle stérile, il s'agit de contrôler une population d'insectes en y introduisant des individus stérilisés de la même espèce: la progéniture d'une femelle et d'un individu stérile n'atteignant pas de maturité sexuelle, la population se voit réduite jusqu'à potentiellement s'éteindre. Pour comprendre ce phénomène, on construit un modèle stochastique spatial sur un réseau dans lequel la population suit un processus de contact dont le taux de croissance est ralenti en présence d'individus stériles, qui forment un environnement aléatoire dynamique. Une première partie de ce document explore la construction et les propriétés du processus sur le réseau Z^d. On obtient des conditions de monotonie afin d'étudier la survie ou la mort du processus. On exhibe l'existence et l'unicité d'une transition de phase en fonction du taux d'introduction des individus stériles. D'autre part, lorsque d=1 et cette fois en fixant l'environnement aléatoire initialement, on exhibe de nouvelles conditions de survie et de mort du processus qui permettent d'expliciter des bornes numériques pour la transition de phase. Une seconde partie concerne le comportement macroscopique du processus en étudiant sa limite hydrodynamique lorsque l'évolution microscopique est plus complexe. On ajoute aux naissances et aux morts des déplacements de particules. Dans un premier temps sur le tore de dimension d, on obtient à la limite un système d'équations de réaction-diffusion. Dans un second temps, on étudie le système en volume infini sur Z^d, et en volume fini, dans un cylindre dont le bord est en contact avec des réservoirs stochastiques de densités différentes. Ceci modélise des phénomènes migratoires avec l'extérieur du domaine que l'on superpose à l'évolution. À la limite on obtient un système d'équations de réaction-diffusion, auquel s'ajoutent des conditions de Dirichlet aux bords en présence de réservoirsIn this thesis, we study an interacting particle system that generalizes a contact process, evolving in a random environment. The contact process can be interpreted as a spread of a population or an infection. The motivation of this model arises from behavioural ecology and evolutionary biology via the sterile insect technique ; its aim is to control a population by releasing sterile individuals of the same species: the progeny of a female and a sterile male does not reach sexual maturity, so that the population is reduced or potentially dies out. To understand this phenomenon, we construct a stochastic spatial model on a lattice in which the evolution of the population is governed by a contact process whose growth rate is slowed down in presence of sterile individuals, shaping a dynamic random environment. A first part of this document investigates the construction and the properties of the process on the lattice Z^d. One obtains monotonicity conditions in order to study the survival or the extinction of the process. We exhibit the existence and uniqueness of a phase transition with respect to the release rate. On the other hand, when d=1 and now fixing initially the random environment, we get further survival and extinction conditions which yield explicit numerical bounds on the phase transition. A second part concerns the macroscopic behaviour of the process by studying its hydrodynamic limit when the microscopic evolution is more intricate. We add movements of particles to births and deaths. First on the d-dimensional torus, we derive a system of reaction-diffusion equations as a limit. Then, we study the system in infinite volume in Z^d, and in a bounded cylinder whose boundaries are in contact with stochastic reservoirs at different densities. As a limit, we obtain a non-linear system, with additionally Dirichlet boundary conditions in bounded domain
25
Houdebert, Pierre. "Continuum Random Cluster Model." Thesis, Lille 1, 2017. http://www.theses.fr/2017LIL10042/document.
Повний текст джерелаАнотація:
Cette thèse s'intéresse au Continuum Random Cluster Model (CRCM), modèle gibbsien de boules aléatoires où la densité dépend du nombre de composantes connexes de la structure. Ce modèle est une version continue du Random Cluster Model introduit pour unifier l'étude des modèles d'Ising et de Potts. Le CRCM fut introduit pour sa relation avec le modèle de Widom-Rowlinson, fournissant une nouvelle preuve de la transition de phase pour ce modèle. Dans cette thèse nous étudions dans un premier temps l'existence du CRCM en volume infinie. Dans le cas extrême des rayons non-intégrables, nous démontrons un résultat de non-unicité du CRCM en petite activité. Nous conjecturons de plus que l'unicité serait obtenue en grande activité. Une version faible de cette conjecture est démontré en dimension 1. Dans un second temps nous étudions la percolation du CRCM, qui s'intéresse aux propriétés de connectivité et en particulier à l'existence d'une composante connexe infinie. La percolation est d'autant plus cohérente pour le CRCM dont l'interaction dépend directement de la connectivité de la structure. Nous montrons dans cette thèse l'absence de percolation en petite activité et la percolation en grande activité. Ce résultat permet de généraliser la transition de phase du modèle de Widom-Rowlinson à des rayons non bornésThis thesis focuses on the Continuum Random Cluster Model (CRCM), defined as a Gibbs model of random balls where the density depends on the number of cluster in the structure. This model is a continuum version of the Random Cluster Model introduced to unify the study of the Ising and Potts model. The CRCM was introduced for its links with the Widom-Rowlinson model, which led to a new proof of the phase transition for this model. In this thesis we first study the existence of the model in the infinite volume regime. In the extreme setting of non integrable radii, we prove for small activities the non-uniqueness of a CRCM. We conjecture that the uniqueness would be revovered for large activities. A weak version of the conjecture is proved.We alson study the percolation of the CRCM, which is the existence of at least one unbounded connected component. Percolation is more relevant for the CRCM since the interaction depends on the connectivity of the structure. We prove the absence of percolation for small activities and percolation for large activities. This results leads to the phase transition of the Widom-Rowlinson model with unbounded radii
26
Loubaton, Philippe. "Prediction et representation markovienne des processus stationnaires vectoriels sur z::(2) : utilisation de techniques d'estimation spectrale 2-d en traitement d'antenne." Paris, ENST, 1988. http://www.theses.fr/1988ENST0012.
Повний текст джерела
27
Krajenbrink, Alexandre. "Beyond the typical fluctuations : a journey to the large deviations in the Kardar-Parisi-Zhang growth model." Thesis, Paris Sciences et Lettres (ComUE), 2019. http://www.theses.fr/2019PSLEE021.
Повний текст джерелаАнотація:
Cette thèse de doctorat porte sur l'étude du modèle de croissance stochastique Kardar-Parisi-Zhang (KPZ) en 1+1 dimensions et en particulier de l'équation qui le régit. Cette thèse est d'une part destinée à effectuer un état de l'art et dresser un portrait moderne de la recherche des solutions exactes de l'équation KPZ, de leurs propriétés en terme de théorie des grandes déviations et également de leurs applications (en théorie des matrices aléatoires ou en calcul stochastique notamment). D'autre part cette thèse a pour but de formuler un certain nombre de questions ouvertes à l'interface avec la théorie de l'intégrabilité, la théorie des matrices aléatoires et la théorie des gaz de Coulomb.Cette thèse est divisée en trois parties distinctes portant (i) sur les solutions exactes de l'équation KPZ, (ii) sur les solutions à temps court sous la forme d'un principe grandes déviations et (iii) sur les solutions à temps long et leurs extensions aux statistiques linéaires au bord de spectre de matrice aléatoire.Nous présenterons les résultats de cette thèse comprenant notamment (a) une nouvelle solution de l'équation KPZ à tout temps dans un demi-espace, (b) une méthodologie générale pour établir à temps court un principe de grandes déviations pour les solutions de KPZ à partir de leur représentation sous forme de déterminant de Fredholm et (c) une unification de quatre méthodes permettant d'obtenir à temps long un principe de grandes déviations pour les solutions de l'équation KPZ et de manière plus générale d'étudier des statistiques linéaires au bord du spectre de matrices aléatoiresThroughout this Ph.D thesis, we will study the Kardar-Parisi-Zhang (KPZ) stochastic growth model in 1+1 dimensions and more particularly the equation which governs it. The goal of this thesis is two-fold. Firstly, it aims to review the state of the art and to provide a detailed picture of the search of exact solutions to the KPZ equation, of their properties in terms of large deviations and also of their applications to random matrix theory or stochastic calculus. Secondly, is it intended to express a certain number of open questions at the interface with integrability theory, random matrix theory and Coulomb gas theory.This thesis is divided in three distinct parts related to (i) the exact solutions to the KPZ equation, (ii) the short time solutions expressed by a Large Deviation Principle and the associated rate functions and (iii) the solutions at large time and their extensions to linear statistics at the edge of random matrices.We will present the new results of this thesis including (a) a new solution to the KPZ equation at all times in a half-space, (b) a general methodology to establish at short time a Large Deviation Principle for the solutions to the KPZ equation from their representation in terms of Fredholm determinant and (c) the unification of four methods allowing to obtain at large time a Large Deviation Principle for the solution to the KPZ equation and more generally to investigate linear statistics at the soft edge of random matrices
28
Kasinos, Stavros. "Seismic response analysis of linear and nonlinear secondary structures." Thesis, Loughborough University, 2018. https://dspace.lboro.ac.uk/2134/33728.
Повний текст джерелаАнотація:
Understanding the complex dynamics that underpin the response of structures in the occurrence of earthquakes is of paramount importance in ensuring community resilience. The operational continuity of structures is influenced by the performance of nonstructural components, also known as secondary structures. Inherent vulnerability characteristics, nonlinearities and uncertainties in their properties or in the excitation pose challenges that render their response determination as a non-straightforward task. This dissertation settles in the context of mathematical modelling and response quantification of seismically driven secondary systems. The case of bilinear hysteretic, rigid-plastic and free-standing rocking oscillators is first considered, as a representative class of secondary systems of distinct behaviour excited at a single point in the primary structure. The equations governing their full dynamic interaction with linear primary oscillators are derived with the purpose of assessing the appropriateness of simplified analysis methods where the secondary-primary feedback action is not accounted for. Analyses carried out in presence of pulse-type excitation have shown that the cascade approximation can be considered satisfactory for bilinear systems provided the secondary-primary mass ratio is adequately low and the system does not approach resonance. For the case of sliding and rocking systems, much lighter secondary systems need to be considered if the cascade analysis is to be adopted, with the validity of the approximation dictated by the selection of the input parameters. Based on the premise that decoupling is permitted, new analytical solutions are derived for the pulse driven nonlinear oscillators considered, conveniently expressing the seismic response as a function of the input parameters and the relative effects are quantified. An efficient numerical scheme for a general-type of excitation is also presented and is used in conjunction with an existing nonstationary stochastic far-field ground motion model to determine the seismic response spectra for the secondary oscillators at given site and earthquake characteristics. Prompted by the presence of uncertainty in the primary structure, and in line with the classical modal analysis, a novel approach for directly characterising uncertainty in the modal shapes, frequencies and damping ratios of the primary structure is proposed. A procedure is then presented for the identification of the model parameters and demonstrated with an application to linear steel frames with uncertain semi-rigid connections. It is shown that the proposed approach reduces the number of the uncertain input parameters and the size of the dynamic problem, and is thus particularly appealing for the stochastic assessment of existing structural systems, where partial modal information is available e.g. through operational modal analysis testing. Through a numerical example, the relative effect of stochasticity in a bi-directional seismic input is found to have a more prominent role on the nonlinear response of secondary oscillators when compared to the uncertainty in the primary structure. Further extending the analyses to the case of multi-attached linear secondary systems driven by deterministic seismic excitation, a convenient variant of the component-mode synthesis method is presented, whereby the primary-secondary dynamic interaction is accounted for through the modes of vibration of the two components. The problem of selecting the vibrational modes to be retained in analysis is then addressed for the case of secondary structures, which may possess numerous low frequency modes with negligible mass, and a modal correction method is adopted in view of the application for seismic analysis. The influence of various approaches to build the viscous damping matrix of the primary-secondary assembly is also investigated, and a novel technique based on modal damping superposition is proposed. Numerical applications are demonstrated through a piping secondary system multi-connected on a primary frame exhibiting various irregularities in plan and elevation, as well as a multi-connected flexible secondary system. Overall, this PhD thesis delivers new insights into the determination and understanding of the response of seismically driven secondary structures. The research is deemed to be of academic and professional engineering interest spanning several areas including seismic engineering, extreme events, structural health monitoring, risk mitigation and reliability analysis.
29
Vojta, T., R. A. Römer, and M. Schreiber. "Two interfacing particles in a random potential: The random model revisited." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801028.
Повний текст джерелаАнотація:
We reinvestigate the validity of mapping the problem of two onsite interacting particles in a random potential onto an effective random matrix model. To this end we first study numerically how the non-interacting basis is coupled by the interaction. Our results indicate that the typical coupling matrix element decreases significantly faster with increasing single-particle localization length than is assumed in the random matrix model. We further show that even for models where the dependency of the coupling matrix element on the single-particle localization length is correctly described by the corresponding random matrix model its predictions for the localization length can be qualitatively incorrect. These results indicate that the mapping of an interacting random system onto an effective random matrix model is potentially dangerous. We also discuss how Imry's block-scaling picture for two interacting particles is influenced by the above arguments.
30
Taramasco, Ollivier. "Modélisation non paramétrique du comportement des cours boursiers." Grenoble 1, 1993. http://www.theses.fr/1993GRE10038.
Повний текст джерелаАнотація:
Ce travail a pour objet d'eclairer le comportement des cours d'actions et indices de valeurs. Le processus des rentabilites boursieres est d'abord examine a l'aide des outils statistiques classiques puis des techniques empruntees a la theorie du chaos. L'etude se focalise ensuite sur la nature de la dependance entre les rentabilites consecutives. Celle-ci est decrite par l'analyse factorielle des correspondances et par l'analyse canonique entre deux vecteurs aleatoires. Les resultats montrent qu'il existe, outre la correlation lineaire, une dependance d'allure parabolique, que ces deux formes de dependance restent relativement stables dans le temps et qu'elles ont une interpretation financiere possible. Ces constats conduisent alors a une representation de type arch non parametrique du processus des rentabilites dont les moments conditionnels peuvent etre exprimes a l'aide des fonctions canoniques
31
Akkermans, Éric. "Propagation d'ondes dans les milieux désordonnés." Grenoble 1, 1986. http://www.theses.fr/1986GRE10050.
Повний текст джерелаАнотація:
Les phenomenes etudies font intervenir la phase de l'onde et la dimensionalite de l'espace de propagation. Dans le cas des systemes uni et bidimensionnels, les ondes subissant des collisions multiples elastiques interferent fortement et conduisent a des modes propres exponentiellement localises. Leur structure est etudiee sur la base d'un modele particulier de potentiel incommensurable. Le transport des phonons et des electrons dans les systemes unidimensionnels desordonnes a ete plus generalement caracterise
32
Bui, Hoai Thang Computer Science & Engineering Faculty of Engineering UNSW. "Guided random-walk based model checking." Awarded by:University of New South Wales. Computer Science & Engineering, 2009. http://handle.unsw.edu.au/1959.4/44829.
Повний текст джерелаАнотація:
The ever increasing use of computer systems in society brings emergent challenges to companies and system designers. The reliability of software and hardware can be financially critical, and lives can depend on it. The growth in size and complexity of software, and increasing concurrency, compounds the problem. The potential for errors is greater than ever before, and the stakes are higher than ever before. Formal methods, particularly model checking, is an approach that attempts to prove mathematically that a model of the behaviour of a product is correct with respect to certain properties. Certain errors can therefore be proven never to occur in the model. This approach has tremendous potential in system development to provide guarantees of correctness. Unfortunately, in practice, model checking cannot handle the enormous sizes of the models of real-world systems. The reason is that the approach requires an exhaustive search of the model to be conducted. While there are exceptions, in general model checkers are said not to scale well. In this thesis, we deal with this scaling issue by using a guiding technique that avoids searching areas of the model, which are unlikely to contain errors. This technique is based on a process of model abstraction in which a new, much smaller model is generated that retains certain important model information but discards the rest. This new model is called a heuristic. While model checking using a heuristic as a guide can be extremely effective, in the worst case (when the guide is of no help), it performs the same as exhaustive search, and hence it also does not scale well in all cases. A second technique is employed to deal with the scaling issue. This technique is based on the concept of random walks. A random walk is simply a `walk' through the model of the system, carried out by selecting states in the model randomly. Such a walk may encounter an error, or it may not. It is a non-exhaustive technique in the sense that only a manageable number of walks are carried out before the search is terminated. This technique cannot replace the conventional model checking as it can never guarantee the correctness of a model. It can however, be a very useful debugging tool because it scales well. From this point of view, it relieves the system designer from the difficult task of dealing with the problem of size in model checking. Using random walks, the effort goes instead into looking for errors. The effectiveness of model checking can be greatly enhanced if the above two techniques are combined: a random walk is used to search for errors, but the walk is guided by a heuristic. This in a nutshell is the focus of this work. We should emphasise that the random walk approach uses the same formal model as model checking. Furthermore, the same heuristic technique is used to guide the random walk as a guided model checker. Together, guidance and random walks are shown in this work to result in vastly improved performance over conventional model checking. Verification has been sacrificed of course, but the new technique is able to find errors far more quickly, and deal with much larger models.
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Rosser, Gabriel A. "Mathematical modelling and analysis of aspects of bacterial motility." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:1af98367-aa2f-4af3-9344-8c361311b553.
Повний текст джерелаАнотація:
The motile behaviour of bacteria underlies many important aspects of their actions, including pathogenicity, foraging efficiency, and ability to form biofilms. In this thesis, we apply mathematical modelling and analysis to various aspects of the planktonic motility of flagellated bacteria, guided by experimental observations. We use data obtained by tracking free-swimming Rhodobacter sphaeroides under a microscope, taking advantage of the availability of a large dataset acquired using a recently developed, high-throughput protocol. A novel analysis method using a hidden Markov model for the identification of reorientation phases in the tracks is described. This is assessed and compared with an established method using a computational simulation study, which shows that the new method has a reduced error rate and less systematic bias. We proceed to apply the novel analysis method to experimental tracks, demonstrating that we are able to successfully identify reorientations and record the angle changes of each reorientation phase. The analysis pipeline developed here is an important proof of concept, demonstrating a rapid and cost-effective protocol for the investigation of myriad aspects of the motility of microorganisms. In addition, we use mathematical modelling and computational simulations to investigate the effect that the microscope sampling rate has on the observed tracking data. This is an important, but often overlooked aspect of experimental design, which affects the observed data in a complex manner. Finally, we examine the role of rotational diffusion in bacterial motility, testing various models against the analysed data. This provides strong evidence that R. sphaeroides undergoes some form of active reorientation, in contrast to the mainstream belief that the process is passive.
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Andreou, Pantelis. "A random reordering stochastic process for regression residuals." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape10/PQDD_0003/NQ42492.pdf.
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Mussini, Filipe. "Random cover times using the Poisson cylinder process." Licentiate thesis, Uppsala universitet, Analys och sannolikhetsteori, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-329351.
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Ezepue, P. O. "The dual process and renewal theory in the random environment branching process." Thesis, University of Sheffield, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.312812.
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Brown, A. S. "Critical phenomena in the Random Ising Model." Thesis, University of Edinburgh, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.370906.
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Wheeler, Christopher Timothy. "Boundary corrections to the random wave model." Thesis, University of Bristol, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.425189.
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Brody, Justin. "On the model theory of random graphs." College Park, Md. : University of Maryland, 2009. http://hdl.handle.net/1903/9291.
Повний текст джерелаАнотація:
Thesis (Ph.D.) -- University of Maryland, College Park, 2009.Thesis research directed by: Dept. of Mathematics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Dostaler, Marc. "Multi-level random data based correlator model." Thesis, University of Ottawa (Canada), 2005. http://hdl.handle.net/10393/26893.
Повний текст джерелаАнотація:
The thesis proposes to develop a virtual prototyping environment (VPE) allowing the study of multi-level random data processing. This VPE allows to experimentally study the effect of different quantization levels and dither signal parameters on the performance of generalized random data correlator architectures.
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Kandler, Anne, Matthias Richter, Scheidt Jürgen vom, Hans-Jörg Starkloff, and Ralf Wunderlich. "Moving-Average approximations of random epsilon-correlated processes." Universitätsbibliothek Chemnitz, 2004. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200401266.
Повний текст джерелаАнотація:
The paper considers approximations of time-continuous epsilon-correlated random
processes by interpolation of time-discrete Moving-Average processes. These approximations
are helpful for Monte-Carlo simulations of the response of systems
containing random parameters described by
epsilon-correlated processes. The paper focuses
on the approximation of stationary
epsilon-correlated processes with a prescribed
correlation function. Numerical results are presented.
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Sidenko, Sergiy. "Kac's random walk and coupon collector's process on posets." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/43781.
Повний текст джерелаАнотація:
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.Includes bibliographical references (p. 100-104).
In the first part of this work, we study a long standing open problem on the mixing time of Kac's random walk on SO(n, R) by random rotations. We obtain an upper bound mix = O (n2.5 log n) for the weak convergence which is close to the trivial lower bound [Omega] (n2). This improves the upper bound O (n4 log n) by Diaconis and SaloffCoste 1131. The proof is a variation on the coupling technique we develop to bound the mixing time for compact Markov chains, which is of independent interest. In the second part, we consider a generalization of the coupon collector's problem in which coupons are allowed to be collected according to a partial order. Along with the discrete process, we also study the Poisson version which admits a tractable parametrization. This allows us to prove convexity of the expected completion time E T with respect to sample probabilities, which has been an open question for the standard coupon collector's problem. Since the exact computation of E - is formidable, we use convexity to establish the upper and the lower bound (these bounds differ by a log factor). We refine these bounds for special classes of posets. For instance, we show the cut-off phenomenon for shallow posets that are closely connected to the classical Dixie Cup problem. We also prove the linear growth of the expectation for posets whose number of chains grows at most exponentially with respect to the maximal length of a chain. Examples of these posets are d-dimensional grids, for which the Poisson process is usually referred as the last passage percolation problem. In addition, the coupon collector's process on a poset can be used to generate a random linear extension.
(cont.) We show that for forests of rooted directed trees it is possible to assign sample probabilities such that the induced distribution over all linear extensions will be uniform. Finally, we show the connection of the process with some combinatorial properties of posets.
by Sergiy Sidenko.
Ph.D.
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Urry, Matthew. "Learning curves for Gaussian process regression on random graphs." Thesis, King's College London (University of London), 2013. https://kclpure.kcl.ac.uk/portal/en/theses/learning-curves-for-gaussian-process-regression-on-random-graphs(c1f5f395-0426-436c-989c-d0ade913423e).html.
Повний текст джерелаАнотація:
Gaussian processes are a non-parametric method that can be used to learn both regression and classification rules from examples for arbitrary input spaces using the ’kernel trick’. They are well understood for inputs from Euclidean spaces, however, much less research has focused on other spaces. In this thesis I aim to at least partially resolve this. In particular I focus on the case where inputs are defined on the vertices of a graph and the task is to learn a function defined on the vertices from noisy examples, i.e. a regression problem. A challenging problem in the area of non-parametric learning is to predict the general-isation error as a function of the number of examples or learning curve. I show that, unlike in the Euclidean case where predictions are either quantitatively accurate for a few specific cases or only qualitatively accurate for a broader range of situations, I am able to derive accurate learning curves for Gaussian processes on graphs for a wide range of input spaces given by ensembles of random graphs. I focus on the random walk kernel but my results generalise to any kernel that can be written as a truncated sum of powers of the normalised graph Laplacian. I begin first with a discussion of the properties of the random walk kernel, which can be viewed as an approximation of the ubiquitous squared exponential kernel in continuous spaces. I show that compared to the squared exponential kernel, the random walk kernel has some surprising properties which includes a non-trivial limiting form for some types of graphs. After investigating the limiting form of the kernel I then study its use as a prior. I propose a solution to this in the form of a local normalisation, where the prior scale at each vertex is normalised locally as desired. To drive home the point about kernel normalisation I then examine the differences between the two kernels when they are used as a Gaussian process prior over functions defined on the vertices of a graph. I show using numerical simulations that the locally normalised kernel leads to a probabilistically more plausible Gaussian process prior. After investigating the properties of the random walk kernel I then discuss the learning curves of a Gaussian process with a random walk kernel for both kernel normalisations in a matched scenario (where student and teacher are both Gaussian processes with matching hyperparameters). I show that by using the cavity method I can derive accu-rate predictions along the whole length of the learning curve that dramatically improves upon previously derived approximations for continuous spaces suitably extended to the discrete graph case. The derivation of the learning curve for the locally normalised kernel required an addi-tional approximation in the resulting cavity equations. I subsequently, therefore, investi-gate this approximation in more detail using the replica method. I show that the locally normalised kernel leads to a highly non-trivial replica calculation, that eventually shows that the approximation used in the cavity analysis amounts to ignoring some consistency requirements between incoming cavity distributions. I focus in particular on a teacher distribution that is given by a Gaussian process with a random walk kernel but different hyperparameters. I show that in this case, by applying the cavity method, I am able once more to calculate accurate predictions of the learning curve. The resulting equations resemble the matched case over an inflated number of variables. To finish this thesis I examine the learning curves for varying degrees of model mismatch.
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Elstro, Stephanie Jo. "25 Random Things About Me." Miami University / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=miami1250637568.
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Finch, Sam. "The random cluster model on the tree : Markov chains, random connections and boundary conditions." Thesis, University of Warwick, 2010. http://wrap.warwick.ac.uk/47385/.
Повний текст джерелаАнотація:
The Fortuin-Kasteleyn random cluster model was adapted to the tree by Häggström [38] who considered a Gibbs specification corresponding to "wired boundary conditions" on the tree. Grimmett and Janson [36] generalized this idea by considering boundary conditions defined by equivalence relations on the set of rays of the tree. In this thesis we continue this project by defining a new object, a "random connection;" a type of random equivalence relation that allows us to redefine what is meant by a cluster of edges on the tree. Our definition is general enough to include Grimmett and Janson's boundary conditions. The random connection approach allows us to reconnect the random cluster model on the tree with Bernoulli bond percolation and we define two critical probabilities for bond percolation on a tree associated with each random connection that allow us to identify three behavioral phases of the associated random cluster model. We consider some examples of random connections defined by equivalence relations, including the "open" boundary conditions described in [36] where we are able to describe the behaviour of the random cluster model exactly and "Mandelbrot" bondary conditions described by a map from the boundary of a tree to the unit square that defines fractal percolation. In addition we adapt work of Zachary [66] to the wired random cluster model on a tree so as to prove a conjecture of Häggström concerning uniqueness of the Gibbs measure for large bond strengths.
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Khoshbin, Ehteram. "Modelling two stage duration process." Thesis, Lancaster University, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.310460.
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Putcha, Venkata Rama Prasad. "Random effects in survival analysis." Thesis, University of Reading, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.312431.
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Susarla, Prameela. "A generalized model for crystallization in random copolymers." Diss., Georgia Institute of Technology, 2001. http://hdl.handle.net/1853/8294.
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Chen, Guo-Huei. "Image segmentation using a multiresolution random field model." Thesis, University of Warwick, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.269395.
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Silva, Maurício Banaszeski da. "A physics-based statistical random telegraph noise model." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2016. http://hdl.handle.net/10183/150171.
Повний текст джерелаАнотація:
O Ruído de Baixa Frequência (LFN), tais como o ruído flicker e o Random Telegraph Noise (RTN), são limitadores de performance em muitos circuitos analógicos e digitais. Para transistores diminutos, a densidade espectral de potência do ruído pode variar muitas ordens de grandeza, impondo uma séria limitação na performance do circuito e também em sua confiabilidade. Nesta tese, nós propomos um novo modelo de RTN estatístico para descrever o ruído de baixa frequência em MOSFETs. Utilizando o modelo proposto, pode-se explicar e calcular o valor esperado e a variabilidade do ruído em função das polarizações, geometrias e dos parâmetros físicos do transistor. O modelo é validado através de inúmeros resultados experimentais para dispositivos com canais tipo n e p, e para diferentes tecnologias CMOS. É demonstrado que a estatística do ruído LFN dos dispositivos de canal tipo n e p podem ser descritos através do mesmo mecanismo. Através dos nossos resultados e do nosso modelo, nós mostramos que a densidade de armadilhas dos transistores de canal tipo p é fortemente dependente do nível de Fermi, enquanto para o transistor de tipo n a densidade de armadilhas pode ser considerada constante na energia. Também é mostrado e explicado, através do nosso modelo, o impacto do implante de halo nas estatísticas do ruído. Utilizando o modelo demonstra-se porque a variabilidade, denotado por σ[log(SId)], do RTN/LFN não segue uma dependência 1/√área; e fica demonstrado que o ruído, e sua variabilidade, encontrado em nossas medidas pode ser modelado utilizando parâmetros físicos. Além disso, o modelo proposto pode ser utilizado para calcular o percentil do ruído, o qual pode ser utilizado para prever ou alcançar certo rendimento do circuito.Low Frequency Noise (LFN) and Random Telegraph Noise (RTN) are performance limiters in many analog and digital circuits. For small area devices, the noise power spectral density can easily vary by many orders of magnitude, imposing serious threat on circuit performance and possibly reliability. In this thesis, we propose a new RTN model to describe the statistics of the low frequency noise in MOSFETs. Using the proposed model, we can explain and calculate the Expected value and Variability of the noise as function of devices’ biases, geometry and physical parameters. The model is validated through numerous experimental results for n-channel and p-channel devices from different CMOS technology nodes. We show that the LFN statistics of n-channel and p-channel MOSFETs can be described by the same mechanism. From our results and model, we show that the trap density of the p-channel device is a strongly varying function of the Fermi level, whereas for the n-channel the trap density can be considered constant. We also show and explain, using the proposed model, the impact of the halo-implanted regions on the statistics of the noise. Using this model, we clarify why the variability, denoted by σ[log(SId)], of RTN/LFN doesn't follow a 1/√area dependence; and we demonstrate that the noise, and its variability, found in our measurements can be modeled using reasonable physical quantities. Moreover, the proposed model can be used to calculate the percentile quantity of the noise, which can be used to predict or to achieve certain circuit yield.