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1
Grau, Torre-Marín Victor. "Estudi de l'3He bidimensional amb mètodes de Monte Carlo quàntics." Doctoral thesis, Universitat Politècnica de Catalunya, 2001. http://hdl.handle.net/10803/6574.
Full textAbstract:
de la tesi En aquest treball es presenta un estudi de l'3He a temperatura zero combinant les tècniques de Monte Carlo variacional (VMC) i la difusiva (DMC) amb nodes fixos (FN) i relaxació dels nodes (RN).
L'estudi comença amb una presentació de les característiques de l'heli i una revisió històrica tant del seu estudi com de les tècniques de Monte Carlo.
La primera part del treball exposa en detall els mètodes de càlcul emprats. Es fa un repàs dels mètodes variacional i difusiu així com de l'aplicació de condicions periòdiques de contorn i de la tècnica emprada per a calcular estimadors purs. Es proposa un càlcul de les cues que proporciona un valor final de l'energia molt proper a la del sistema vertaderament infinit. Això permet obtenir resultats numèrics pràcticament independents del nombre de partícules emprades en la simulació. A més, amb l'ús de la tècnica combinada FN-RN, es te una mesura de la proximitat al resultat exacte del valor FN trobat.
L'estudi variacional de l'3He tridimensional ocupa la segona part de la tesi. En ella s'analitza la influència sobre l'energia de cadascun dels mecanismes de correlació emprats, i es comparen amb altres resultats ja existents a la literatura. En destaca l'optimització de la funció de backflow, que condueix a uns resultats clarament millors. Es presenta també una anàlisi VMC en la que es valora la introducció de nous mecanismes de correlació a la funció d'ona, mostrant que la introducció de correccions d'ordre superior al backflow són irrellevants. Els resultats d'aquesta part, fàcilment comparables amb dades experimentals, serveixen com a banc de prova per als programes que seran adaptats després al sistema bidimensional.
La tercera part del treball s'ocupa del sistema d'3He bidimensional infinit en absència de qualsevol substrat de suport. Amb el mètode DMC es calcula l'equació d'estat del sistema a polarització variable, i s'avaluen els efectes que té en cadascun d'ells les interaccions de backflow. Els resultats mostren que el sistema no posseeix cap estat auto-lligat. Es calcula després el sistema a polarització variable i se'n analitzen algunes propietats físiques. Els valors obtinguts de la susceptibilitat magnètica apunten l'existència d'una transició de fase magnètica a polaritzacions de l'orde del 50%.
2
Vives, i. Santa-Eulàlia Eduard. "Simulació Monte Carlo de sistemes amb acoblament de graus de llibertat." Doctoral thesis, Universitat de Barcelona, 1991. http://hdl.handle.net/10803/1594.
Full textAbstract:
Els models microscòpics usuals que es proposen en Mecànica Estadística descriuen, únicament, un tipus de grau de llibertat. Aquests models permeten explicar algunes transicions de fase que es troben en els diagrames de fase de sistemes reals. Ara bé, aquests últims estan constituïts per elements que normalment presenten diferents tipus de graus de llibertat tals com els posicionals, orientacionals, magnètics, conformacionals, etc. L'estudi global de tot un diagrama de fases no pot fer-se mitjançant la simple superposició de models simples ja que, normalment, els diferents tipus de graus de llibertat interfereixen i s'acoblen. Cal, per tant, proposar i resoldre models microscòpics que descriguin la competició entre diferents graus de llibertat.D'entre d'altres exemples de sistemes amb fenòmens d'acoblament destaquen els aliatges binaris amb àtoms magnètics, els cristalls líquids, els cristalls plàstics, les barreges de líquids moleculars, etc... D'altres fenòmens que també poden englobar-se dins d'aquest marc de l'acoblament són la dependència amb l'ordre atòmic d'algunes transicions estructurals en aliatges binaris i, fins i tot, els sistemes de partícules adsorbides sobre un substrat.
Desde un punt de vista fenomenològic la teoria de Landau amb dos paràmetres d'ordre posa de manifest els principals efectes que es poden donar. Entre d'altres destaquen el desplaçament o desaparició de fases que hom esperaria si no existissin termes d'acoblament, l'existència de fases reentrants, punts tricritics I multicrítics, etc ... D'entre tots els possibles termes d'acoblament entre dos paràmetres d'ordre "x" i "y" a l'energia lliure que hom pot imaginar el més estudiat ha estat l'acoblament biquadràtic x(2)y(2), encara que termes com x(2)y també s'han mostrat útils en alguns casos com per exemple en l'estudi de diagrames de fase de cristalls líquids.
La resolució exacta dels models complexos no pot fer-se analíticament. Els mètodes pertorbatius són adequats quan les energies d'acoblament són petites, però sovint aquest no és el cas. Per això la simulació de Monte CarIo és una eina indispensable per a aquests casos. Els principals problemes que presenta són que únicament podem simular sistemes finits durant un temps relativament curt. L'estudi de les transicions de fase, on el límit termodinàmic és indispensable i les correlacions temporals poden ésser molt llargues, requereix doncs de tècniques especifiques. Els efectes de mida finita es poden reduir mitjançant l'extrapolació a mida infinita a partir de l'estudi de sistemes de diferents mides o mitjançant la teoria del "Finite Size Scaling".
En aquest treball ens hem centrat en tres problemes concrets, relacionats amb l'acoblament de graus de llibertat.
En primer lloc hem proposat un model microscòpic per als cristalls líquids. Es basa en el model "lattice-gas" bidimensional i inclou graus de llibertat orientacionals de les partícules. La seva resolució s' ha fet mitjançant tècniques de camp mitjà i simulació de Monte Carlo. El model reprodueix qualitativament els diagrames de fase experimentals d'algunes barreges de cristalls líquids, així com l'existència d'un punt tricrític en la línea de transició Smèctica-Nemàtica i la variació dels exponents crítics efectius.
Un segon estudi s'ha centrat en el problema dels aliatges binaris amb estructura BCC que tenen una transició estructural cap a una fase més compacta a baixa temperatura. Aquesta transició involucra els graus de llibertat posicionals dels nusos de la zarza BCC que sofreixen l'acció d'una cisalla. Aquests aliatges presenten a temperatures més elevades fenòmens de reordenament dels àtoms en la.xarxa BCC. Aquests fenòmens de tipus difusiu poden estudiar-se prescindint dels detalls exactes de la dinàmica del moviment atòmic, mitjançant un model que inclogui graus de llibertat configuracionals (els nusos d'una xarxa poden ésser A o B). La temperatura a la qual es produeix la transició estructural (normalment de primer ordre) depèn de l'ordre configuracional dels àtoms. Aquesta ordenació pot vari.ar-se, de forma controlada, mitjançant trempes ràpides desde diferents temperatures dins la zona de reordenament atòmic. Mitjançant el mètode de Monte CarIo hem simulat amb un model molt simple els fenòmens de reordenament en un aliatge binari tipus BCC en funció de la temperatura. En particular s'han estudiat les transicions entre estructures D0(3) , B2 i A2. Estudiant com les constants elàstiques de la xarxa depenen de l'ordre configuracional hem pogut justificar qualitativament la dependència de la temperatura de transició estructural amb la temperatura des de la qual es fa la trempa. Hem estudiat també, mitjançant una energia lliure de Landau i un model microscòpic, com l'increment d'entropia de la transició estructural depèn de l'ordre configuracional.
Finalment hem estudiat el problema dels sistemes de partículas adsorbides sobre substrats. Hem proposat un model que separa els graus de llibertat posicionals de les partícules en dos: per un costat uns graus de llibertat discrets tipus "lattice-gas" que descriuen els salts de les partícules d'un pou de potencial ("corrugation potential") a un altre en el substrat i per altre uns graus de llibertat continus que descriuen el moviment de les partícules dins els pous. La simulació Monte CarIo d'aquest model ha permès estudiar la transició de fase sòlid-líquid en aquests sistemes per a diferents valors del "corrugation potential". En el límit de substrat pla els nostres resultats indiquen la presència d'una zona de coexistència entre la fase sòlida i la líquida amb propietats de tipus hexàtic. En el cas de que el "corrugation potential" sigui prou gran els factors d'estructura simulats coincideixen perfectament amb resultats teòrics trobats en la literatura. Ara bé, quan els pous del "corrugation potential" són molt petits es troben discrepàncies ja que les fluctuacions de les partícules són molt grans.
The particles that constitute the real systems have, normally, several degrees of freedom: positional, orientational, conformational, etc. The study of a complete phase diagram cannot be done by the mere superposition of simple models because the different degrees of freedom interfere and coupling phenomena appear. Several examples are: magnetic binary alloys, liquid crystals, etc.
Other systems whose behaviours can also be regarded as the result of coupling are alloys undergoing structural phase transitions and systems of adsorbed molecules on substrates. In this work we have focused our attention in three problems related to coupling between degrees of freedom: (a) First of all we have developed a microscopic model for Liquid Crystals. It is based on a lattice-gas 2-dimensional model that includes orientational degrees of freedom for the molecules. It reproduces qualitatively well the experimental phase diagrams of a number of liquid crystal mixtures, the existence of a tri-critical point in the Smectic-Nematic transition line, and a continuous variation of the effective critical exponents. (b) A second work has been the study of BCC binary alloys that undergo structural phase transitions to packed phases at low temperature, and also exhibit atomic reordering phenomena at higher temperatures. Coupling phenomena between the structural degrees of freedom and the configurational atomic order can appear by means of quenches starting at temperatures in the range where atomic reordering is operative. We have studied how the elastic constants depend on the configurational order and we have justified the dependence of the structural transition temperature upon the starting temperature of the quench. (c) Finally we have studied systems of adsorbed molecules on substrates. We have proposed a model that splits the positional degrees of freedom of the particles: on the one hand it considers variables associated with the jumps of the particles between neighbouring wells of the corrugation potential and on the other hand it considers continuous degrees of freedom associated with the movement of particles inside the wells. Monte Carlo simulation allows the study of the solid-liquid phase transition for different values of the corrugation potential. In the limit of flat substrate our results show a coexisting zone with hexatic properties between the solid and liquid phases. For big enough corrugation potential the simulated structure factors are in agreement with the results of previous theorie s found in the literature.
3
Vegas, Lozano Esteban. "Optimización en estudios de Monte Carlo en Estadística: Aplicaciones al Contraste de Hipótesis." Doctoral thesis, Universitat de Barcelona, 1996. http://hdl.handle.net/10803/1565.
Full textAbstract:
El principal resultado es la presentación de una técnica de optimización en estudios de Monte Carlo en Estadística. Se obtiene un estimador de la esperanza de una variable dicotómica (Y), que tiene una varianza menor que el estimador habitual, la frecuencia relativa. Este estimador optimizado se basa en el conocimiento de otra variable dicotómica (de control), C, correlacionada con Y y de esperanza conocida, E(C). La aplicación de esta técnica es sencilla de implementar. En simulación de Monte Carlo en es relativamente frecuente disponer de tales variables de control. Así, por ejemplo, en estudios de simulación de la potencia de un nuevo test no paramétrico se puede utilizar en ocasiones un test paramétrico comparable, de potencia conocida.Se demuestra que este estimador es insesgado y se obtiene la expresión de su varianza. Se estudiaron varios estimadores de esta varianza, escogiendo a uno de ellos como el más adecuado. Además, se estudia el tanto por ciento de reducción de la varianza del nuevo estimador en comparación con el estimador habitual (frecuencia relativa). Se observan unos valores entre un 40% a un 90% según se incremente el valor de la correlación entre la variable de control (C) y la variable de estudio (Y).
Para validar los resultados teóricos anteriores e ilustrar la técnica propuesta se realizaron dos estudios de simulación. El primero sirve para obtener una estimación de la potencia de un nuevo test. Mientras que el segundo es un estudio de simulación general sin ninguna finalidad concreta.
Se propuso un nuevo test para resolver el problema de Behrens-Fisher, basado en la distancia de Hao, al cual se le aplica la anterior técnica para conocer su potencia y robustez. Se obtiene una potencia y robustez óptimas.
Por último, se exponen dos casos reales, dentro del entorno médico-biológico, donde surge el problema de Behrens-Fisher. En ambos estudios, se realiza un análisis crítico ya que las verdaderas probabilidades de error son distintas de las supuestas debido a ignorar probables diferencias entre varianzas.
The main purpose is the presentation of an optimization technique in Monte-Carlo studies in statistics and subsequent study of some statistical properties of the estimator associated with this technique. An estimator of the expectation of a dichotomous variable, Y, with variance less than the most obvious unbiased estimator, relative frequency, is obtained. This new estimator is based on the availability of another dichotomous variable (control), C, correlated with Y and expectation, E(C), which is known. The availability of this control variable is relatively common in Monte-Carlo simulations. So, for example, simulation studies of the power of a new nonparametric test may sometimes use a comparable parametric test, with known power.
Moreover, a new test for the Behrens-Fisher problem, based on geodesic distance criteria, is proposed. The power and robustness of this test are estimated through Monte-Carlo simulation using the previous optimization technique.
4
Lecina, Casas Daniel. "Studying protein-ligand interactions using a Monte Carlo procedure." Doctoral thesis, Universitat de Barcelona, 2017. http://hdl.handle.net/10803/459297.
Full textAbstract:
Biomolecular simulations have been widely used in the study of protein-ligand interactions; comprehending the mechanisms involved in the prediction of binding affinities would have a significant repercussion in the pharmaceutical industry. Notwithstanding the intrinsic difficulty of sampling the phase space, hardware and methodological developments make computer simulations a promising candidate in the resolution of biophysically relevant problems. In this context, the objective of the thesis is the development of a protocol that permits studying protein-ligand interactions, in view to be applied in drug discovery pipelines.
The author contributed to the rewriting PELE, our Monte Carlo sampling procedure, using good practices of software development. These involved testing, improving the readability, modularity, encapsulation, maintenance and version control, just to name a few. Importantly, the recoding resulted in a competitive cutting-edge software that is able to integrate new algorithms and platforms, such as new force fields or a graphical user interface, while being reliable and efficient. The rest of the thesis is built upon this development.
At this point, we established a protocol of unbiased all-atom simulations using PELE, often combined with Markov (state) Models (MSM) to characterize the energy landscape exploration. In the thesis, we have shown that PELE is a suitable tool to map complex mechanisms in an accurate and efficient manner. For example, we successfully conducted studies of ligand migration in prolyl oligopeptidases and nuclear hormone receptors (NHRs). Using PELE, we could map the ligand migration and binding pathway in such complex systems in less than 48 hours. On the other hand, with this technique we often run batches of 100s of simulations to reduce the wall-clock time. MSM is a useful technique to join these independent simulations in a unique statistical model, as individual trajectories only need to characterize the energy landscape locally, and the global characterization can be extracted from the model. We successfully applied the combination of these two methodologies to quantify binding mechanisms and estimate the binding free energy in systems involving NHRs and tyorsinases. However, this technique represents a significant computational effort.
To reduce the computational load, we developed a new methodology to overcome the sampling limitations caused by the ruggedness of the energy landscape. In particular, we used a procedure of iterative simulations with adaptive spawning points based on reinforcement learning ideas. This permits sampling binding mechanisms at a fraction of the cost, and represents a speedup of an order of magnitude in complex systems. Importantly, we show in a proof-of-concept that it can be used to estimate absolute binding free energies.
Overall, we hope that the methodologies presented herein help streamline the drug design process.Las simulaciones biomoleculares se han usado ampliamente en el estudio de interacciones proteína-ligando. Comprender los mecanismos involucrados en la predicción de afinidades de unión tiene una gran repercusión en la industria farmacéutica. A pesar de las dificultades intrínsecas en el muestreo del espacio de fases, mejoras de hardware y metodológicas hacen de las simulaciones por ordenador un candidato prometedor en la resolución de problemas biofísicos con alta relevancia. En este contexto, el objetivo de la tesis es el desarrollo de un protocolo que introduce un estudio más eficiente de las interacciones proteína-ligando, con vistas a diseminar PELE, un procedimiento de muestreo de Monte Carlo, en el diseño de fármacos. Nuestro principal foco ha sido sobrepasar las limitaciones de muestreo causadas por la rugosidad del paisaje de energías, aplicando nuestro protocolo para hacer analsis detallados a nivel atomístico en receptores nucleares de hormonas, receptores acoplados a proteínas G, tirosinasas y prolil oligopeptidasas, en colaboración con una compañía farmacéutica y de varios laboratorios experimentales. Con todo ello, esperamos que las metodologías presentadas en esta tesis ayuden a mejorar el diseño de fármacos.
5
Prats, Garcia Hèctor. "Monte Carlo based methods applied to heterogeneous catalysis and gas separation." Doctoral thesis, Universitat de Barcelona, 2019. http://hdl.handle.net/10803/666583.
Full textAbstract:
The research work presented in this thesis is divided in two main topics: gas separation and heterogeneous catalysis. Although the systems studied in one part and another are quite different, they share two fundamental features: both topics have a special industrial interest and they have been studied through stochastic Monte Carlo based methods.
The present work on gas separation aims to assess the performance of several faujasite structures, a well-known family of zeolites, in CO2 capture processes. Concretely, ten faujasite structures with different Al content have been evaluated in the separation of post-combustion CO2 mixtures via simulation of swing adsorption processes. Through GCMC simulations performed on a wide range of pressures and temperatures, the pure and mixture adsorption isotherms and isobars for the different structures are obtained. This data is used to calculate several performance criteria such as purity, working capacity, selectivity and energy required per ton of CO2 captured. The results show that high Al content structures are suitable for operating under a TSA unit, while intermediate and low Al content structures show better performance in PSA and VSA units, respectively.
On the other hand, the research work on chemical reactivity focus on the study of the water-gas shift reaction (WGSR) on copper surfaces both from a thermodynamic and from a kinetic point of view. First, a kMC study is performed on the flat Cu(111) surface. The lattice model is quite simple, consisting on an hexagonal periodic grid of points. All sites are considered equivalent, and only repulsive lateral interactions between neighboring CO adsorbed species are included. However, even with this simple model, the kMC results agree quite well to the available experimental data, and demonstrate that the dominant reaction mechanism is the COOH mediated associative mechanism.
The effect of van der Waals interactions is then studied, by performing DFT calculations of the WGSR on Cu(321) using the Grimme D2 correction accounting for the dispersion forces. The results obtained are compared with previous DFT results
published in the literature where no van der Waals corrections were included. The comparison shows big differences on the adsorption energies of some gas species, as well as important differences in some energy barriers, hence demonstrating the importance of including dispersion terms in order to obtain a meaningful description of the energetics of the WGSR.
New kMC simulations are then performed for the WGSR on Cu(321) surface to study the effect of step sites on the WGSR activity. The recently developed graph- theoretical kMC framework is used, coupled with cluster expansion Hamiltonians to account for the lateral interactions between neighboring species. The simulation results show that the activity is much lower on the stepped Cu(321) surface. Analysis of the kMC simulations suggests that the reason in the poisoning of step sites by CO species, as well as the presence of low energy barriers for some key steps on the reverse direction (e.g. water dissociation and COOH formation).
Finally, the thesis ends with a brief tutorial on kMC simulations where several issues are discussed, like the importance of including diffusion processes of the effect of lateral interactions.El treball de recerca presentat en aquesta tesi es divideix en dos temes principals: separació de gasos i catàlisi heterogènia. Tot i que els sistemes estudiats en ambdues parts són molt diferents, comparteixen dues característiques fonamentals: ambdós temes tenen un elevat interès industrial i s'han estudiat mitjançant mètodes estocàstics de Monte Carlo. El treball corresponent a la separació de gasos pretén avaluar el rendiment de diverses estructures de faujasites, una coneguda família de zeolites, en processos de captura de CO2. Concretament, s'han avaluat deu estructures de faujasites amb diferent contingut d’alumini en la separació de mescles post-combustió. Mitjançant simulacions GCMC realitzades en una àmplia gamma de pressions i temperatures, s’han obtingut les isotermes i isòbares d'adsorció pures i de mescla per les diferents estructures. Aquesta informació s'ha emprat per calcular diversos criteris de rendiment com ara la puresa, la capacitat de treball, la selectivitat i l'energia requerida per tona de CO2 capturat. D'altra banda, els treballs de recerca sobre reactivitat química es centren en l'estudi de la reacció water-gas shift (WGSR) sobre superfícies de coure tant des d'un punt de vista termodinàmic com cinètic. En aquest context, s’ha estudiat l’efecte de les superfícies esglaonades i de les forces de van der Waals mitjançant càlculs d’estructura electrònica i simulacions amb el mètode de Monte Carlo cinètic (kMC) en la superfície plana Cu(111) i la superfície esglaonada Cu(321). Els resultats mostren que les superfícies esglaonades no sempre són més actives que les planes, i que la introducció de les interaccions de van der Waals és crucial per a obtenir una descripció correcta dels diferents processos que ocorren en superfície.
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Blanco, Pablo Miguel. "Coupling of binding and conformational equilibria in weak polyelectrolytes. Dynamics and charge regulation of biopolymers in crowded media." Doctoral thesis, Universitat de Barcelona, 2020. http://hdl.handle.net/10803/670053.
Full textAbstract:
I have carried out this thesis in the Biophysical Chemistry of Macromolecules and Colloids research group of the University of Barcelona. In the recent years, the research group have made significant contributions to the study of the conformational, binding, diffusion and reactivity properties of weak polyelectrolytes and biopolymers. On the one hand, the group has contributed to the design and development of the Site Binding Rotational Isomeric State (SBRIS) model for weak polyelectrolytes. They have also successfully used the SBRIS model to reproduce the complex experimental titration curves of polyethylenimine. On the other hand, the research group has done significant contributions in the study of biopolymer diffusion and reactivity in crowded media. They tracked the diffusion of α-chymiotrypsin in solutions crowded by different- sized dextran macromolecules. They rationalized the experimental results comparing them with on-lattice Monte Carlo (MC) simulations, observing a qualitative agreement between both sets of data.
The present thesis follows the efforts of the research group in the development of theoretical and computational models for weak polyelectrolytes and biopolymers. I investigate different theoretical aspects of the conformational, ionization, elastic and diffusive properties of weak polyelectrolytes and biopolymers using theoretical and computational simulation techniques. The thesis includes six original peer-reviewed publications, which are distributed in six different chapters. Moreover, a complete description of the fundamental concepts and methodologies relevant for the thesis is also given.
On the one hand, I focus in the complex interplay of the ionization and conformational degrees of freedom of weak polyelectrolytes using the recently developed Site Binding Rotational Isomeric State (SBRIS) model. A new analytical technique, the Local Effective Interaction Parameters (LEIP) method, is presented to solve the SBRIS model including long range intramolecular electrostatic interactions. The model is validated against constant pH Monte Carlo (MC) simulations. The SBRIS model is used to study the elastic response of a model weak polyelectrolyte. A new force regime is found for which (i) the force-extension curves are significantly dependent on the pH and the ionic strength values (ii) the polyelectrolyte charge is modified by the stretching force. The effect of charge fluctuation in the conformational and stretching properties of weak polyelectrolytes is studied comparing the results obtained with SGCMC simulation with those obtained with MC simulation with the same charge but keeping it constant. The conformational and elastic properties of the polyelectrolyte are observed to be significantly affected by the presence of charge regulation.
On the other hand, I study the diffusive and ionization properties of biopolymers in solution with a high concentration of macromolecules. These conditions, known as macromolecular crowding, are characteristic of biological media where up to the 40% of the volume is occupied by macromolecules. The diffusion of two globular proteins, α-chymiotrypsin and streptavidin, is analysed in different crowding conditions with Brownian Dynamics simulations. A new coarse grained model is proposed, named as Chain Entanglement Softened Potential (CESP), which is found to reproduce quantitatively the experimental data. I have investigated the effect of macromolecular crowding in the binding and conformational properties of two Intrinsically Disordered Proteins (IDPs), histatin-5 and β-amyloid 42, which are modelled using a bead and
spring model. The crowders are modelled using the CESP model mimicking Bovin Serum Albumin (BSA). The investigation is motivated by the hypothesis that, in the same way that the conformational and ionization degrees of freedom are coupled in weak polyelectrolytes, the macromolecular crowding should also cause a charge regulation in IDPs whose flexible structure is similar to those of weak polyelectrolytes. Two possible mechanisms through by macromolecular crowding can alter the IDP ionization are proposed: (i) the increase in the effective ionic strength (same ions in a reduced volume) and (ii) the IDP compaction due to macromolecular crowding. The IDPs global charge is found to exhibit significant variations when neutral and charged crowders are added to the system, due to the increase in the effective ionic strength.Els polímers són omnipresents a la nostra vida diària, presents en múltiples aplicacions industrials i involucrats en processos biològics essencials. Per exemple, l’ADN, les proteïnes i els sucres poden ser considerats polímers, normalment denominats biopolímers. Aquells polímers amb un gran nombre de grups carregats són coneguts com a polielectròlits i freqüentment classificats en termes de la seva ionització com a forts (completament ionizats) o febles (parcialment ionizats). En aquesta tesi, investigo diferents aspectes teòrics de les propietats conformacionals, elàstiques, difusives i d'ionització de polielectròlits febles i biopolímers. Per un costat, em centro en la complexa interació entre els graus de llibertat d'ionització i conformacionals dels polielectròlits febles utilitzant el model Site Binding Rotational Isomeric State (SBRIS), desenvolupat recentment. S’introdueix una nova tècnica analítica, el mètode Local Effective Interaction Parameters (LEIP), per resoldre el model SBRIS incloent les interaccions electroestàtiques intramoleculars de llarg abast. El model es valida comparant els resultats amb la solució obtinguda per simulacions Monte Carlo a pH constant. El model SBRIS s’utilitza per estudiar la resposta elàstica d’un polielectròlit model. Es troba un nou règim de força en el que (i) les corbes força-extensió són significativament dependents del valor del pH i la força iònica (ii) la càrrega del polielectròlit es modificada per la acció de la força d’estirament. S’observa que les propietats conformacionals i elàstiques del polielectròlit es veuen significativament i moderadament afectades per la presència de fluctuacions en la càrrega, respectivament. Per l’altre costat, avaluo les propietats difusives i d'ionització de biopolímers en solució amb una elevada concentració de macromolecules. Aquestes condicions, conegudes com crowding macromolecular, son característiques dels medis biologics on fins el 40% del volum es ocupat per macromolecules. S’analitza la difusió de dues proteïnes globulars, α-chimiotripsina i estreptavidina, en diferents condicions de crowding macromolecular amb simulacions de Dinàmica Browniana. Es proposa un nou model de gra gruixut, anomenat Chain Entanglement Softened Potential (CESP), el qual es trobat que reprodueix quantitativament les dades experimentals. S’ha investigat l’efecte del \emph{crowding} macromolecular en les propietats conformacionals i de protonació de dues proteïnes intrínsecament desordenades (IDPs), histidina
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Janzon, Krister. "Monte Carlo Path Simulation and the Multilevel Monte Carlo Method." Thesis, Umeå universitet, Institutionen för fysik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-151975.
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A standard problem in the field of computational finance is that of pricing derivative securities. This is often accomplished by estimating an expected value of a functional of a stochastic process, defined by a stochastic differential equation (SDE). In such a setting the random sampling algorithm Monte Carlo (MC) is useful, where paths of the process are sampled. However, MC in its standard form (SMC) is inherently slow. Additionally, if the analytical solution to the underlying SDE is not available, a numerical approximation of the process is necessary, adding another layer of computational complexity to the SMC algorithm. Thus, the computational cost of achieving a certain level of accuracy of the estimation using SMC may be relatively high. In this thesis we introduce and review the theory of the SMC method, with and without the need of numerical approximation for path simulation. Two numerical methods for path approximation are introduced: the Euler–Maruyama method and Milstein's method. Moreover, we also introduce and review the theory of a relatively new (2008) MC method – the multilevel Monte Carlo (MLMC) method – which is only applicable when paths are approximated. This method boldly claims that it can – under certain conditions – eradicate the additional complexity stemming from the approximation of paths. With this in mind, we wish to see whether this claim holds when pricing a European call option, where the underlying stock process is modelled by geometric Brownian motion. We also want to compare the performance of MLMC in this scenario to that of SMC, with and without path approximation. Two numerical experiments are performed. The first to determine the optimal implementation of MLMC, a static or adaptive approach. The second to illustrate the difference in performance of adaptive MLMC and SMC – depending on the used numerical method and whether the analytical solution is available. The results show that SMC is inferior to adaptive MLMC if numerical approximation of paths is needed, and that adaptive MLMC seems to meet the complexity of SMC with an analytical solution. However, while the complexity of adaptive MLMC is impressive, it cannot quite compensate for the additional cost of approximating paths, ending up roughly ten times slower than SMC with an analytical solution.
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Jun, Seong-Hwan. "Entangled Monte Carlo." Thesis, University of British Columbia, 2013. http://hdl.handle.net/2429/44953.
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A recurrent problem in statistics is that of computing an expectation involving intractable integration. In particular, this problem arises in
Bayesian statistics when computing an expectation with respect to a posterior distribution known only up to a normalizing constant. A common solution is to use Monte Carlo simulation to estimate the target expectation. Two of the most
commonly adopted simulation methods are Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) methods. However, these methods fail to scale up with the size of the inference problem. For MCMC, the problem takes the form of simulations that must be ran for a long time in order to obtain an accurate inference. For SMC, one may not be able to store enough particles to exhaustively explore the state space. We propose a novel scalable parallelization of Monte Carlo simulation, Entangled Monte Carlo simulation, that can scale up with the size of the inference problem. Instead of transmitting particles over the network, our proposed algorithm reconstructs the particles from the particle genealogy using the notion of stochastic maps borrowed from perfect simulation literature. We propose bounds on the expected time for particles to coalesce based on the coalescent model. Our empirical results also demonstrate the efficacy of our method on datasets from the field of phylogenetics.
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Carreras, Conill Abel. "Estudi teòric de l’estereodinàmica de rotors i engranatges moleculars." Doctoral thesis, Universitat de Barcelona, 2013. http://hdl.handle.net/10803/133335.
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Els rotors, motors i engranatges moleculars són molècules o sistemes moleculars que tenen com a característica que presenten moviments conformacionals de gran amplitud, majoritàriament associats a rotacions internes al voltant d’un o diversos enllaços senzills entre els seus àtoms. Aquesta propietat permet a aquestes molècules adoptar diferents geometries conformacionals en funció de la rotació al voltant d’aquests enllaços, podent donar comportaments mecànics anàlogs al dʼengranatges macroscòpics, de manera que aquestes molècules puguin ser considerades com a components bàsics per a un futur disseny de màquines nanoscòpiques més complexes. És per aquesta raó que l'anàlisi del comportament dinàmic de rotors i engranatges moleculars ha despertat l’interès d’una gran quantitat de científics que, des de fa temps, treballen en la síntesi i caracterització d’aquest tipus de compostos.
Una manera de poder abordar l’estudi teòric dels rotors moleculars sense haver de renunciar a l’ús d’un mètode de càlcul de les interaccions intermoleculars acurat, és efectuant una dinàmica molecular restringida, on només es tenen en compte un nombre reduït de graus de llibertat mentre que els efectes de la resta modes en el comportament dinàmic es menysprea o s’inclou només de manera aproximada com a pertorbació del moviment que s’estudia en detall. D’aquesta manera és possible reduir el cost computacional del càlcul i poder accedir així, a temps de simulació molt més elevats amb un cost computacional assumible.
En aquesta tesi doctoral s’ha desenvolupat un conjunt de programes informàtics que permeten simular el comportament dinàmic de sistemes formats per un nombre de fragments que es consideren rígids amb una energia potencial total definida a partir d’interaccions a parells entre ells. Això permet tractar sistemes grans reduint el nombre de graus de llibertat, separant així les interaccions més rellevants. D’aquesta manera, al tenir en compte només uns pocs graus de llibertat, es pot realitzar un càlcul més precís de l’energia en un temps assumible.
Per tal de descriure les interaccions entre fragments s’han calculat superfícies de potencial en funció de les variables que descriuen les rotacions internes entre fragments rígids. Aquesta descripció, permet veure més clarament els possibles acoblaments entre els diferents graus de llibertat rotacionals de la molècula. Per fer-ho, s’ha elaborat una metodologia que permet descriure els processos de flexió que tenen lloc a la molècula al mateix temps que és produeix la rotació. Amb aquesta metodologia, s’ha realitzat l’estudi dels tripticil[n]helicens, molècules formades per la unió d’un grup tripticil i un helicè
mitjançant un enllaç senzill, que han estat estudiades per la seva relació amb els anomenats trinquets moleculars, sistemes on hi ha una rotació interna en un entorn asimètric degut a la presència de fragments moleculars quirals.
Utilitzant programes de simulació de Monte Carlo i de dinàmica molecular desenvolupats en el transcurs de la tesi s’ha estudiat també en col•laboració amb el grup experimental del Prof. Miguel A. Garcia-Garibay de la Universitat de California, dos cristalls amfidinàmics, sòlids on fragments de les molècules empaquetades conserven una alta llibertat de rotació, sintetitzats recentment: el rotor de mestranol i l’IDipp-C60.Molecular motors, rotors and gears are complex molecules that undergo wide conformational movements that mimic those of their macroscopic mechanical counterparts. For this reason these molecular systems have recently been the subject of numerous experimental and theoretical studies with the aim to incorporate them as basic building blocks of more complex nanoscopic devices. Due to their intrinsic structural complexity it is difficult to perform accurate dynamical studies using standard molecular dynamics techniques considering all atoms of the system and for this reason in this thesis we have developed programs to simulate the dynamical behavior of such systems !considering only a restricted set of degrees of freedom. The systems are modeled by a collection of rigid fragments that interact through pair potentials that lead to a reduced potential energy surface for the relevant degrees of freedom that is being used in conjunction of molecular dynamics or Monte Carlo simulation techniques to study the dynamic behavior of molecular gears or ensembles of molecular rotors. Using the general purpose molecular dynamics and Monte Carlo programs developed in this thesis have also been adapted to be used in the study of the dynamical behavior of amphidynamic solids, a new class of molecular crystals where some fragments of the constituent molecules exhibit large conformational motions. This part of the work, devoted to the simulation of the dynamic behavior of the mestranol rotor and the crystals of IDipp-C60 has been developed in collaboration with the experimental group of Prof. Miguel Angel García Garibay at UCLA that worked in the synthesis and experimental characterization of these two compounds.
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Dickinson, Andrew Samuel. "On the analysis of Monte Carlo and quasi-Monte Carlo methods." Thesis, University of Oxford, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.409715.
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Göncü, Ahmet. "Monte Carlo and quasi-Monte Carlo methods in pricing financial derivatives." Tallahassee, Florida : Florida State University, 2009. http://etd.lib.fsu.edu/theses/available/etd-06232009-140439/.
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Thesis (Ph. D.)--Florida State University, 2009.Advisor: Giray Ökten, Florida State University, College of Arts and Sciences, Dept. of Mathematics. Title and description from dissertation home page (viewed on Oct. 5, 2009). Document formatted into pages; contains x, 105 pages. Includes bibliographical references.
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Melo, Martínez Oscar Orlando. "Modelos lineales generalizados geoestadísticos basados en distancias." Doctoral thesis, Universitat de Barcelona, 2013. http://hdl.handle.net/10803/127219.
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En esta tesis se hace una mezcla del método de distancias con los modelos lineales generalizados mixtos tanto en lo espacial como en lo espacio-temporal. Con el empleo de las distancias se logran buenas predicciones y menores variabilidades en el espacio o espacio-tiempo de la región de estudio, provocando todo esto que se tomen mejores decisiones en los diferentes problemas de interés.
Se propone un método alternativo para ajustar una variable respuesta tipo beta con dispersión variable usando distancias euclidianas entre los individuos. Se emplea el método de máxima verosimilitud para estimar los parámetros desconocidos del modelo propuesto y se presentan las principales propiedades de estos estimadores. Además, se realiza la inferencia estadística sobre los parámetros utilizando las aproximaciones obtenidas a partir de la normalidad asintótica del estimador de máxima verosimilitud; se desarrolla el diagnóstico y predicción de una nueva observación, y se estudia el problema de datos faltantes utilizando la metodología propuesta.
Posteriormente, se propone una solución alterna para resolver problemas como el de prevalencia de Loa loa utilizando distancias euclidianas entre individuos; se describe un modelo lineal generalizado espacial mixto incorporando medidas generales de distancia o disimilaridad que se pueden aplicar a variables explicativas. En este caso, los parámetros involucrados en el modelo propuesto se estiman utilizando máxima verosimilitud mediante el método de Monte Carlo vía cadenas de Markov (MCMC).
También se formula un modelo lineal beta espacial mixto con dispersión variable utilizando máxima verosimilitud mediante el método MCMC. El método propuesto se utiliza en situaciones donde la variable respuesta es una razón o proporción que esta relacionada con determinadas variables explicativas. Para este fin, se desarrolla una aproximación utilizando modelos lineales generalizados espaciales mixtos empleando la transformación Box-Cox en el modelo de precisión. Por lo tanto, se realiza el proceso de optimización de los parámetros tanto para modelo espacial de media como para el modelo espacial de dispersión variable. Además, se realiza la inferencia estadística sobre los parámetros utilizando las aproximaciones obtenidas a partir de la normalidad asintótica del estimador de máxima verosimilitud. También se desarrolla el diagnóstico del modelo y la predicción de nuevas observaciones. Por último, el método se ilustra a través de los contenidos de arcilla y magnesio.
Adicionalmente, se describe el modelo basado en distancias para la predicción espacio-temporal usando modelos lineales generalizados. Se realiza el proceso de estimación de los parámetros involucrados en el modelo propuesto, mediante el método de ecuaciones de estimación generalizada y la inferencia estadística sobre los parámetros empleando las aproximaciones obtenidas a partir de la normalidad asintótica del estimador de máxima verosimilitud. Además, se desarrolla el diagnóstico del modelo y la predicción de nuevas observaciones. Se realiza una aplicación de la metodología propuesta para el número de acciones armadas estandarizada por cada 1000 km2 de los grupos irregulares FARC-EP y ELN en los diferentes departamentos de Colombia entre los años 2003 a 2009.
Finalmente, se presenta un modelo autorregresivo espacial lineal generalizado mixto utilizando el método basado en distancias. Este modelo incluye retrasos tanto espaciales como temporales entre vectores de variables de estado estacionarias. Se utiliza la dinámica espacial de los datos econométricos tipo panel para estimar el modelo propuesto; los parámetros involucrados en el modelo se estiman utilizando el método MCMC mediante máxima verosimilitud. Además, se discute en este capítulo la interacción entre estacionariedad temporal y espacial, y se derivan las respuestas al impulso para el modelo propuesto, lo cual naturalmente depende de la dinámica temporal y espacial del modelo.In the context of regression with a beta-type response variable, we propose a new method that links two methodologies: a distance-based model, and a beta regression with variable dispersion. The proposed model is useful for those situations where the response variable is a rate, a proportion or parts per million. This variable is related with a mixture between continuous and categorical explanatory variables. We present its main statistical properties and some measures for selection of the most predictive dimensions in the model. Furthermore, the prediction of a new observation and the problem of missing data are also developed. Using the proposed model, the mutual funds are analyzed employing the Gower distance for both the mean model and the variable dispersion model. Also, we present a new method based on distances, which allows the modeling of continuous and non-continuous random variables through distance-based spatial generalized linear mixed models (SGLMMs). The parameters are estimated using Markov chain Monte Carlo (MCMC) maximum likelihood. The method is illustrated through the analysis of the variation in the prevalence of Loa loa among a sample of village residents in Cameroon, where the explanatory variables included elevation, together with maximum normalized-difference vegetation index (NDVI) and the standard deviation of NDVI calculated from repeated satellite scans over time. Additionally, we propose a beta spatial linear mixed model with variable dispersion using MCMC. An approach to the SGLMMs using the Box-Cox transformation in the precision model is developed. Thus, the parameter optimization process is made for both the spatial mean model as the spatial variable dispersion model. Statistical inference over the parameters is performed using approximations obtained from the asymptotic normality of the maximum likelihood estimator. Diagnosis and prediction of a new observation are also developed. This model is illustrated through of the clay and magnesium contents. On the other hand, we present a solution to problems where the response variable is a count, a rate or a binary (dichotomous) using a refined distance-based generalized linear space-time-autoregressive model with space-time-autoregressive disturbances. This model may also contain additional spatial exogenous variables as well as time exogenous variables. The parameter estimation process is done by the space-time generalized estimating equations (GEE) method, and a measure of goodness-of-fit is presented. Also, the best linear unbiased predictor for prediction purposes is presented. An application for the standardized number of armed actions per 1000 km2 of rebel groups FARC-EP and ELN in different departments of Colombia from 2003 to 2009 is employed to illustrate the proposed methodology. Finally, a spatial generalized linear mixed autoregressive model using distance-based is defined including spatial as well as temporal lags between vectors of stationary state variables. Although the structural parameters are not fully identified in this model, contemporaneous spatial lag coefficients may be identified by exogenous state variables. Dynamic spatial panel data econometrics is used to estimate our proposed model. In this way, the parameters are estimated using MCMC maximum likelihood. We also discuss the interaction between temporal and spatial stationarity, and we derive the impulse responses for our model, which naturally depend upon the temporal and spatial dynamics of the model.
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Berezovska, Ganna [Verfasser], and Alexander [Akademischer Betreuer] Blumen. "Monte Carlo study of semiflexible polymers = Monte Carlo Studie von semiflexiblen Polymeren." Freiburg : Universität, 2011. http://d-nb.info/1125885467/34.
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Drumond, Lorenzo. "Il Metodo Monte Carlo." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/20698/.
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La tesi introduce le tecniche di approssimazione numerica note come Metodo Monte Carlo. Dopo una breve presentazione dell'apparato teorico che giustifica il funzionamento di questo metodo, si procede con uno studio sulla stima dell'errore, focalizzando l'interesse sulla dimostrazione del Teorema di Berry-Esseen. La tesi continua affrontando il tema della generazione di numeri pseudocasuali, fondamentali nel Metodo Monte Carlo, per poi finire con tre esempi di applicazione.
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Chin, Mary Pik Wai. "Monte Carlo portal dosimetry." Thesis, Cardiff University, 2005. http://orca.cf.ac.uk/54085/.
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This project developed a solution for verifying external photon beam radiotherapy. The solution is based on a calibration chain for deriving portal dose maps from acquired portal images, and a calculation framework for predicting portal dose maps. Quantitative comparison between acquired and predicted portal dose maps accomplishes both geometric (patient positioning with respect to the beam) and dosimetric (2D fluence distribution of the beam) verifications. A disagreement would indicate that beam delivery had not been according to plan. The solution addresses the clinical need for verifying radiotherapy both pre-treatment (without patient in the beam) and on-treatment (with patient in the beam). Medical linear accelerators mounted with electronic portal imaging devices (EPIDs) were used to acquire portal images. Two types of EPIDs were investigated: the amorphous silicon (a-Si) and the scanning liquid ion chamber (SLIC). The EGSnrc family of Monte Carlo codes were used to predict portal dose maps by computer simulation of radiation transport in the beam-phantom-EPID configuration. Monte Carlo simulations have been implemented on several levels of High Throughput Computing (HTC), including the Grid, to reduce computation time. The solution has been tested across the entire clinical range of gantry angle, beam size (5 cm x 5 cm to 20 cm x 20 cm), beam-patient and patient-EPID separations (4 cm to 38 cm). In these tests of known beam-phantom-EPID configurations, agreement between acquired and predicted portal dose profiles was consistently within 2% of the central axis value. This Monte Carlo portal dosimetry solution therefore achieved combined versatility, accuracy and speed not readily achievable by other techniques.
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McNeil-Watson, Graham. "Phase switch Monte Carlo." Thesis, University of Bath, 2007. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.486842.
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Computational studies of phase behaviour have always proved difficult, since phase . transitions are inherently slow processes compared to accessible simulation timescales. Despite valiant efforts by researchers there remains a dearth of efficient, robust and scalable methods for determining phase equilibria,· especially in the case of fluid-crystalline solid transitions. This thesis is about such phase coexistence problems, the existing solutions, and more advanced methods that have only recently come into their own. ... Extended sampling methods are examined in detail, and applied to a testbed system, the critical point Lennard-Jones fluid, leading to an estimate of the system free energy in the thermodynamic limit. Then a comparatively new technique, phase switch Monte Carlo (Phys. Rev. Lett. 85, 5138) is applied initially to the venerable hard sphere system. The method overcomes many of the shortcomings present in other works by directly connecting the coexisting phases in a single simulation, and doing so without creating an artificial inter-phase route but rather affecting a direct 'phase leap' from one phase to the other. Finally, phase switch is generalised to soft potentials and applied to the Lennard-Jones freezing transition, resulting in an extensive mapping of the phase boundary for a variety of system sizes (J. Chern. Phys 124, 064504).
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Bakra, Eleni. "Aspects of population Markov chain Monte Carlo and reversible jump Markov chain Monte Carlo." Thesis, University of Glasgow, 2009. http://theses.gla.ac.uk/1247/.
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Bryskhe, Henrik. "Optimization of Monte Carlo simulations." Thesis, Uppsala University, Department of Information Technology, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-121843.
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This thesis considers several different techniques for optimizing Monte Carlo simulations. The Monte Carlo system used is Penelope but most of the techniques are applicable to other systems. The two mayor techniques are the usage of the graphics card to do geometry calculations, and raytracing. Using graphics card provides a very efficient way to do fast ray and triangle intersections. Raytracing provides an approximation of Monte Carlo simulation but is much faster to perform. A program was also written in order to have a platform for Monte Carlo simulations where the different techniques were implemented and tested. The program also provides an overview of the simulation setup, were the user can easily verify that everything has been setup correctly. The thesis also covers an attempt to rewrite Penelope from FORTAN to C. The new version is significantly faster and can be used on more systems. A distribution package was also added to the new Penelope version. Since Monte Carlo simulations are easily distributed, running this type of simulations on ten computers yields ten times the speedup. Combining the different techniques in the platform provides an easy to use and at the same time efficient way of performing Monte Carlo simulations.
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Holenstein, Roman. "Particle Markov chain Monte Carlo." Thesis, University of British Columbia, 2009. http://hdl.handle.net/2429/7319.
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Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) methods have emerged as the two main tools to sample from high-dimensional probability distributions. Although asymptotic convergence of MCMC algorithms is ensured under weak assumptions, the performance of these latters is unreliable when the proposal distributions used to explore the space are poorly chosen and/or if highly correlated variables are updated independently. In this thesis we propose a new Monte Carlo framework in which we build efficient high-dimensional proposal distributions using SMC methods. This allows us to design effective MCMC algorithms in complex scenarios where standard strategies fail. We demonstrate these algorithms on a number of example problems, including simulated tempering, nonlinear non-Gaussian state-space model, and protein folding.
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Zeineh, Rami. "Adaptive threshold Monte Carlo localization." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/MQ61962.pdf.
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Byrd, Jonathan Michael Robert. "Parallel Markov Chain Monte Carlo." Thesis, University of Warwick, 2010. http://wrap.warwick.ac.uk/3634/.
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The increasing availability of multi-core and multi-processor architectures provides new opportunities for improving the performance of many computer simulations. Markov Chain Monte Carlo (MCMC) simulations are widely used for approximate counting problems, Bayesian inference and as a means for estimating very highdimensional integrals. As such MCMC has found a wide variety of applications in fields including computational biology and physics,financial econometrics, machine learning and image processing. This thesis presents a number of new method for reducing the runtime of Markov Chain Monte Carlo simulations by using SMP machines and/or clusters. Two of the methods speculatively perform iterations in parallel, reducing the runtime of MCMC programs whilst producing statistically identical results to conventional sequential implementations. The other methods apply only to problem domains that can be presented as an image, and involve using various means of dividing the image into subimages that can be proceed with some degree of independence. Where possible the thesis includes a theoretical analysis of the reduction in runtime that may be achieved using our technique under perfect conditions, and in all cases the methods are tested and compared on selection of multi-core and multi-processor architectures. A framework is provided to allow easy construction of MCMC application that implement these parallelisation methods.
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Lewis, R. D. "Monte Carlo modelling for radiotherapy." Thesis, Swansea University, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.637892.
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The Monte Carlo code MCNP-4B has been utilised to investigate the origins of radiation dose perturbation in the head and neck region, arising from natural heterogeneities, the changing external contours of the patient, boundaries between materials of different atomic number and prosthetic implants. MCNP-4B was used to develop a simple model of a linear accelerator treatment head which incorporated the electron target, primary collimator, beam flattening filter and the secondary collimators. The model was used to calculate the energy spectra and angular distribution of the x-ray beam from a 4 MV Philips SL 75/5 and a 10 MV SL 15, and then tested by using these data to compute the central and off-axis x-ray beam profiles for various field sizes in water. Monte Carlo simulations using the calculated spectra were used to assess the dose distribution of treatment plans obtained in a simple heterogeneous phantom by several commercially available treatment planning systems. Practical measurements were undertaken using film dosimetry. The dose distributions were calculated for a variety of irradiation conditions designed to show the effects of surface obliquity, inhomogeneities and missing tissue above tangential beams. The results show maximum differences of 47% between some planning algorithm and film. Overall, the dose distribution obtained from film was most faithfully reproduced by the MCNP. The dose due to backscatter and lack of forward scatter from a metal implant within a head and neck phantom has been shown vary with atomic number, field size, surface obliquity, implant thickness, variations in secondary electron transport and the presence of teeth.
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Taft, Keith. "Monte Carlo methods for radiosity." Thesis, University of Liverpool, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.272796.
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Whiteley, Nicholas Paul. "Advances in Monte Carlo filtering." Thesis, University of Cambridge, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.611476.
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Badinski, Alexander Nikolai. "Forces in quantum Monte Carlo." Thesis, University of Cambridge, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.612494.
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Strathmann, Heiko. "Kernel methods for Monte Carlo." Thesis, University College London (University of London), 2018. http://discovery.ucl.ac.uk/10040707/.
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This thesis investigates the use of reproducing kernel Hilbert spaces (RKHS) in the context of Monte Carlo algorithms. The work proceeds in three main themes. Adaptive Monte Carlo proposals: We introduce and study two adaptive Markov chain Monte Carlo (MCMC) algorithms to sample from target distributions with non-linear support and intractable gradients. Our algorithms, generalisations of random walk Metropolis and Hamiltonian Monte Carlo, adaptively learn local covariance and gradient structure respectively, by modelling past samples in an RKHS. We further show how to embed these methods into the sequential Monte Carlo framework. Efficient and principled score estimation: We propose methods for fitting an RKHS exponential family model that work by fitting the gradient of the log density, the score, thus avoiding the need to compute a normalization constant. While the problem is of general interest, here we focus on its embedding into the adaptive MCMC context from above. We improve the computational efficiency of an earlier solution with two novel fast approximation schemes without guarantees, and a low-rank, Nyström-like solution. The latter retains the consistency and convergence rates of the exact solution, at lower computational cost. Goodness-of-fit testing: We propose a non-parametric statistical test for goodness-of-fit. The measure is a divergence constructed via Stein's method using functions from an RKHS. We derive a statistical test, both for i.i.d. and non-i.i.d. samples, and apply the test to quantifying convergence of approximate MCMC methods, statistical model criticism, and evaluating accuracy in non-parametric score estimation.
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Silva, Ivair Ramos. "Otimalidade de Testes Monte Carlo." Universidade Federal de Minas Gerais, 2011. http://hdl.handle.net/1843/ICED-8H2HFS.
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A operacionalização de um teste de hipóteses é condicionada ao conhecimento da distribuição de probabilidade da estatística de teste sob a hipótese nula H0. Caso não se conheça a distribuição da estatística de teste sob H0, sua distribuição assintótica pode ser usada para que a decisão sobre a rejeição ou não de H0 possa ser feita, o que exige o estudo dos tamanhos amostrais para os quais tal distribuição assintótica se verifica. Quando a distribuição assintótica também não pode ser deduzida analiticamente, métodos de reamostragem podem ser aplicados para a construção de um critério alternativo de decisão, tais como reamostragem Bootstrap, testes de permutação e simulação Monte Carlo (MC), sendo este último o objeto de estudo deste trabalho. Os testes de hipóteses montados pela utilização de simulações Monte Carlo podem ser divididos em dois tipos: os que se baseiam em um número m fixo de simulações, que é a estratégia convencional; e os procedimentos sequenciais, com os quais o número de simulações a serem geradas não é previamente fxado. Apesar de atualmente contarmos com recursos computacionais que favorecem o processamento de grandes bases de dados de forma extremamente veloz, ainda existem situações em que o tempo de processamento de uma estatística de teste é longo, o que motiva o desenvolvimento e utilização dos procedimentos sequenciais. Os aspectos que recebem forte atenção na literatura sobre testes MC são: a busca por procedimentos que apresentem reduzido tempo médio de simulação até que a decisão sobre H0 seja efetuada; a estipulação de cotas para a probabilidade da decisão quanto à rejeição de H0 ser diferente da que se tomaria com o teste exato (risco de reamostragem); a estimação do
valor-p; e a estipulação de cotas para as possíveis perdas de poder do teste MC sequencial em relação ao teste MC convencional ou em relação ao respectivo teste exato. Usando certas suposições sobre a distribuição de probabilidade e a função poder associadas à estatística de teste, a literatura mostra que o poder do teste MC convencional é
praticamente igual ao poder do teste exato. Um dos objetivos desta tese é demonstrar que é possível obter cotas para a diferença de poder entre o teste MC convencional e o teste exato que valem para qualquer estatística de teste, ou seja, a validade de tais cotas não depende de
suposições além das necessárias à existência de um teste exato.
Besag and Clifford (1991) propuseram um procedimento de teste MC sequencial que, sob H0, apresenta baixo tempo de execução. bjetivamos mostrar aqui como deve ser feita a escolha dos parâmetros de operacionalização deste procedimento sequencial. Primeiramente, mostramos como otimizar a escolha do número máximo de simulações sem afetar seu poder e, em seguida, demonstramos a forma de aplicar a regra de interrupção das simulações de modo a garantir um mesmo poder que o teste convencional. O procedimento sequencial de Besag and Clifford (1991) só apresenta redução no tempo de execução nos casos em que H0 é verdadeira. Com a principal finalidade de tornar o teste MC sequencial mais veloz que o MC convencional também quando a hipótese nula é falsa, procedimentos sequenciais alternativos tem sido propostos na literatura. O cálculo analítico exato do poder de tais procedimentos sequenciais, bem como do valor esperado do número
de simulações, são intratáveis para o caso geral, pois envolve o conhecimento da distribuição de probabilidade do valor-p, que por sua vez depende de cada aplicação específica. Pelo uso de algumas restrições ao comportamento da distribuição de probabilidade do valor-p, alguns autores obtiveram cotas para o risco de reamostragem e para a esperança do número de simulações para procedimentos sequenciais para os quais, em cada tempo t de simulação, a regra de iinterrupção das simulações é dada por uma função linear em t. Nesta tese, construimos um procedimento sequencial que permite um formato geral para a regra de interrupção das simulações, o qual chamaremos de teste MC sequencial generalizado. Esta construção absorve as principais propostas apresentadas na literatura e permite um tratamento analítico do poder e do número esperado de simulações para uma estatística de teste qualquer. Isto é feito pela elaboração de cotas superiores para a perda de poder e para a esperança do número de simulações. Com base em conceitos desenvolvidos nesta tese, apresentamos a construção do procedimento ótimo em termos do número esperado de simulações. Nós também cotamos o risco de reamostragem dentro de uma extensa classe de distribuições de probabilidade para o valor-p.
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Lin, Xichen. "Monte Carlo Simulation and Integration." Scholarship @ Claremont, 2018. https://scholarship.claremont.edu/cmc_theses/2009.
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In this paper, we introduce the Tootsie Pop Algorithm and explore its use in different contexts. It can be used to estimate more general problems where a measure is defined, or in the context of statistics application, integration involving high dimensions. The Tootsie Pop Algorithm was introduced by Huber and Schott[2] The general process of Tootsie Pop Algorithm, just like what its name suggests, is a process of peeling down the outer shell, which is the larger enclosing set, to the center, which is the smaller enclosed. We obtain the average number of peels, which gives us an understanding of the ratio between the size of the shell and the size of the center. Each peel is generated by a random draw within the outer shell: if the drawn point is located in the center, we are done, else we update the outer shell such that the drawn point is right on its edge.
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Hoffmann, Jochen. "Monte-Carlo- und Pfad-Integral-Monte-Carlo-Simulationen zu Strukturen und Phasenübergängen in Nano-Porenkondensaten." [S.l. : s.n.], 2002. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB9910270.
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Tuffin, Bruno. "Simulation acceleree par les methodes de monte carlo et quasi-monte carlo : theorie et applications." Rennes 1, 1997. http://www.theses.fr/1997REN10181.
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Dans cette these nous etudions et appliquons les methodes de monte carlo et quasi-monte carlo. Nous nous interessons premierement a la theorie. Les methodes de quasi-monte carlo sont basees sur deux notions : la variation et la discrepance. Comme premiere contribution, nous ameliorons la repartition d'une famille importante de suites a discrepance faible, les suites de halton. Nous realisons ensuite une technique analogue a la reduction de la variance dans les methodes de monte carlo, la reduction de la variation. La borne de l'erreur n'etant que rarement utilisable en pratique, nous proposons une approche pour l'utilisation des suites a discrepance faible comme technique de reduction de la variance dans les methodes de monte carlo. Nous analysons l'efficacite de cette reduction et comparons les differentes suites afin de choisir la mieux adaptee. La deuxieme partie de la these est consacree a des applications concretes et efficaces de ces methodes. Nous considerons d'abord les reseaux de files d'attente multi-classes a forme produit et ameliorons leur simulation par deux techniques differentes de reduction de la variance : les variables antagonistes et les suites a discrepance faible. Cette derniere methode est ensuite appliquee a la simulation d'un systeme cellulaire avec partage dynamique des ressources. Finalement, nous etudions la simulation des systemes markoviens hautement fiables et approfondissons les methodes existantes. Nous introduisons un nouveau concept, l'approximation normale bornee, qui permet d'obtenir une approximation de la loi normale satisfaisante dans le theoreme de la limite centrale, quelle que soit la fiabilite du systeme etudie, et donnons une condition necessaire et suffisante sur la mesure d'echantillonnage preferentiel pour obtenir cette propriete.
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Masella, Guido. "Exotic quantum phenomena in cold atomic gases : numerical approaches." Thesis, Strasbourg, 2019. http://www.theses.fr/2019STRAF061.
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L'objectif principal de cette thèse est l'étude des propriétés à basse énergie et température de systèmes fortement corrélés de bosons interagissant via des potentiels à portée longue et étendue, et pertinentes pour la réalisation expérimentale avec des gaz atomiques froids. Cette étude est réalisée à l'aide d'une combinaison de techniques numériques, comme le Path Integral Montecarlo et de techniques analytiques. Le principal résultat de mon travail est la démonstration de l’existence d’une phase supersolide à bandes et d’une rare transition entre différents supersolides dans un modèle à interaction finie de bosons de coer dur sur un réseau carré. J'étudie également les scénarios hors d'équilibre de tels modèles via des quenches de température simulées. Enfin, j'étudie comment la restauration de l'extensibilité énergétique dans des systèmes en interaction à longue portée peut avoir une incidence profonde sur les propriétés de basse énergie dans la limite thermodynamiqueThe central aim of this thesis is the study of the low-energy and low-temperature properties of strongly correlated systems of bosonic particles interacting via finite- and long-range potentials, and relevant to experimental realization with cold atomic gases. This study is carried out with a combination of state-of-the-art numerical techniques such as Path Integral Monte Carlo and analytical techniques. The main result of my work is the demonstration of the existence of a stripe supersolid phase and of a rare transition between isotropic and anisotropic supersolids in a finite-range interacting model of hard-bosons on a square lattice. I also investigate the out-of-equilibrium scenarios of such models via simulated temperature quenches. Finally, I investigate how restoring energy extensivity in long-range interacting systems can have a profound incidence on the low-energy properties in the thermodynamic limit
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Ounaissi, Daoud. "Méthodes quasi-Monte Carlo et Monte Carlo : application aux calculs des estimateurs Lasso et Lasso bayésien." Thesis, Lille 1, 2016. http://www.theses.fr/2016LIL10043/document.
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La thèse contient 6 chapitres. Le premier chapitre contient une introduction à la régression linéaire et aux problèmes Lasso et Lasso bayésien. Le chapitre 2 rappelle les algorithmes d’optimisation convexe et présente l’algorithme FISTA pour calculer l’estimateur Lasso. La statistique de la convergence de cet algorithme est aussi donnée dans ce chapitre en utilisant l’entropie et l’estimateur de Pitman-Yor. Le chapitre 3 est consacré à la comparaison des méthodes quasi-Monte Carlo et Monte Carlo dans les calculs numériques du Lasso bayésien. Il sort de cette comparaison que les points de Hammersely donne les meilleurs résultats. Le chapitre 4 donne une interprétation géométrique de la fonction de partition du Lasso bayésien et l’exprime en fonction de la fonction Gamma incomplète. Ceci nous a permis de donner un critère de convergence pour l’algorithme de Metropolis Hastings. Le chapitre 5 présente l’estimateur bayésien comme la loi limite d’une équation différentielle stochastique multivariée. Ceci nous a permis de calculer le Lasso bayésien en utilisant les schémas numériques semi implicite et explicite d’Euler et les méthodes de Monte Carlo, Monte Carlo à plusieurs couches (MLMC) et l’algorithme de Metropolis Hastings. La comparaison des coûts de calcul montre que le couple (schéma semi-implicite d’Euler, MLMC) gagne contre les autres couples (schéma, méthode). Finalement dans le chapitre 6 nous avons trouvé la vitesse de convergence du Lasso bayésien vers le Lasso lorsque le rapport signal/bruit est constant et le bruit tend vers 0. Ceci nous a permis de donner de nouveaux critères pour la convergence de l’algorithme de Metropolis HastingsThe thesis contains 6 chapters. The first chapter contains an introduction to linear regression, the Lasso and the Bayesian Lasso problems. Chapter 2 recalls the convex optimization algorithms and presents the Fista algorithm for calculating the Lasso estimator. The properties of the convergence of this algorithm is also given in this chapter using the entropy estimator and Pitman-Yor estimator. Chapter 3 is devoted to comparison of Monte Carlo and quasi-Monte Carlo methods in numerical calculations of Bayesian Lasso. It comes out of this comparison that the Hammersely points give the best results. Chapter 4 gives a geometric interpretation of the partition function of the Bayesian lasso expressed as a function of the incomplete Gamma function. This allowed us to give a convergence criterion for the Metropolis Hastings algorithm. Chapter 5 presents the Bayesian estimator as the law limit a multivariate stochastic differential equation. This allowed us to calculate the Bayesian Lasso using numerical schemes semi-implicit and explicit Euler and methods of Monte Carlo, Monte Carlo multilevel (MLMC) and Metropolis Hastings algorithm. Comparing the calculation costs shows the couple (semi-implicit Euler scheme, MLMC) wins against the other couples (scheme method). Finally in chapter 6 we found the Lasso convergence rate of the Bayesian Lasso when the signal / noise ratio is constant and when the noise tends to 0. This allowed us to provide a new criteria for the convergence of the Metropolis algorithm Hastings
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Schyberg, Oskar. "Monte Carlo Study of Reinsurance Contracts." Licentiate thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-18374.
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This thesis is based on three articles concerning to experimental softwarefor evaluation of reinsurance contracts. In paper A we describe and usethe reinsurance analyser (ReAn), an open-source software for analysis ofreinsurance contacts. Moreover, we discuss experimental results, especiallythe risk comparison of excess-of-loss and largest claims reinsurance treaties.In paper B we expand the software including a new excess-of-loss treaty withupper limit. We perform experimental studies comparing extreme value andexcess-of-loss reinsurance treaties. In paper C, we perform a more in depthpresentation of the software. We introduce new treaties as combinations ofstandard treaties. Experimental comparisons are made between these treatiesand other extreme value treaties.
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Mandreoli, Lorenzo. "Density based Kinetic Monte Carlo Methods." [S.l.] : [s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=975329111.
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Brangian, Claudio. "Monte Carlo simulations of Potts glasses." [S.l.] : [s.n.], 2002. http://ArchiMeD.uni-mainz.de/pub/2002/0115/diss.pdf.
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Radev, Rossen. "Monte Carlo Group - Atomic Physics Department." Phd thesis, Monte Carlo Group, Atomic Physics Department, University of Sofia, 1997. http://cluster.phys.uni-sofia.bg:8080/.
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Sebastian, Shalin. "Empirical evaluation of Monte Carlo sampling /." Available to subscribers only, 2005. http://proquest.umi.com/pqdweb?did=1075709431&sid=9&Fmt=2&clientId=1509&RQT=309&VName=PQD.
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Hine, Nicholas. "New applications of quantum Monte Carlo." Thesis, Imperial College London, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.446023.
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Zhang, Kai. "Monte Carlo methods in derivative modelling." Thesis, University of Warwick, 2011. http://wrap.warwick.ac.uk/35689/.
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This thesis addresses issues in discretization and variance reduction methods for Monte Carlo simulation. For the discretization methods, we investigate the convergence properties of various Itˆo-Taylor schemes and the strong Taylor expansion (Siopacha and Teichmann [77]) for the LIBOR market model. We also provide an improvement on the strong Taylor expansion method which produces lower pricing bias. For the variance reduction methods, we have four contributions. Firstly, we formulate a general stochastic volatility model nesting many existing models in the literature. Secondly, we construct a correlation control variate for this model. Thirdly, we apply the model as well as the new control variate to pricing average rate and barrier options. Numerical results demonstrate the improvement over using old control variates alone. Last but not least, with the help of our model and control variate, we explore the variations in barrier option pricing consistent with the implied volatility surface.
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Maggio, Emilio. "Monte Carlo methods for visual tracking." Thesis, Queen Mary, University of London, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.497791.
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Lee, Ming Ripman, and 李明. "Monte Carlo simulation for confined electrolytes." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31240513.
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Swetnam, Adam D. "Monte Carlo simulation of lattice polymers." Thesis, University of Warwick, 2011. http://wrap.warwick.ac.uk/49196/.
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The phase behaviour of lattice polymers and peptides, under various conditions, is investigated using Monte Carlo simulation. Wang-Landau sampling is used so that, in principle, phase diagrams can be determined from a single simulation. It is demonstrated that the pseudophase diagram for polymer molecules, in several environments, can be plotted when sampling only from the internal degrees of freedom, by determining an appropriate density of states. Several improvements to the simulation methods used are detailed. A new prescription for setting the modification factor in the Wang-Landau algorithm is described, tested and found, for homopolymers, to result in near optimum convergence throughout the simulation. Different methods of selecting moves from the pull move set are detailed, and their relative efficiencies determined. Finally, it is shown that results for a polymer in a slit with one attractive surface can be determined by sampling only from the internal degrees of freedom of a lattice polymer. Adsorption of lattice polymers and peptides is investigated by determining pseudophase diagrams for individual molecules. The phase diagram for a homopolymer molecule, near a surface with a pattern of interaction, is determined, with a pseudophase identified where the polymer is commensurate with the pattern. For an example lattice peptide, the existence of the new pseudophase is found to depend on whether both hydrophobic and polar beads are attracted to the surface. The phase diagram for a ring polymer under applied force, with variable solvent quality, is determined for the first time. The effect, on the phase diagram, of topological knots in the ring polymer is investigated. In addition to eliminating pseudophases where the polymer is flattened into a single layer, it is found that non-trivial knots result in additional pseudophases for tensile force.
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Phillips, Richard J. "Monte Carlo generation of Cerenkov radiation." Thesis, Monterey, California. Naval Postgraduate School, 1989. http://hdl.handle.net/10945/26090.
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Anderson, Jeppe Rosenkrantz. "Monte Carlo studies of BFKL physics." Thesis, Durham University, 2002. http://etheses.dur.ac.uk/4118/.
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We study the properties of the BFKL evolution of a (-channel gluon exchange in the high-energy limit. In particular we formulate a solution to the BFKL evolution equation in terms of an explicit sum over emitted gluons, which allows for a Monte Carlo integration of the resulting rapidity ordered multi-gluon phase space. This formulation allows for an introduction of the running of the coupling to the BFKL evolution. More importantly, the Monte Carlo implementation of the solution to the BFKL evolution equation allows for studies of the exclusive final states resulting from the exchange. The full control over the gluon radiation allows for energy and momentum conservation to be observed when calculating the hadronic cross sections. This is in contrast to the standard analytic approach to BFKL physics, which solves the BFKL equation by effectively summing over any number of gluons emitted and integrating over the full rapidity ordered allowed phase space. It is therefore impossible to reconstruct the parton momentum fractions exactly, and thus energy and longitudinal momentum conservation is violated. Although the effect is indeed formally subleading, we show that the numerical impact at present and planned collider energies is very significant. The reduction in parton flux due to the increased energy consumption by the BFKL evolution is sufficient to change the parton level result of an exponential rise of the dijet cross section as a function of the rapidity separation of the leading dijets to a situation much like the LO case. However, we identify the azimuthal correlation between the dijets as an observable sensitive to BFKL effects but more stable under the observation of energy and momentum conservation. We also apply the BFKL MC to a study of dijets at the Tevatron. Finally we consider W + 2-jet production, a process which in the limit of large rapidity separation between the two jets exhibit the same factorisation into two impact factors and a (-channel gluon exchange as dijet production. We identify observables in this setup, for which BFKL effects could be important.
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Veld, Pieter Jacob in 't. "Monte Carlo studies of liquid structure /." Digital version:, 2000. http://wwwlib.umi.com/cr/utexas/fullcit?p9992826.
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Lee, Ming Ripman. "Monte Carlo simulation for confined electrolytes /." Hong Kong : University of Hong Kong, 2000. http://sunzi.lib.hku.hk/hkuto/record.jsp?B22055009.
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Zeppilli, Giulia. "Alcune applicazioni del Metodo Monte Carlo." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2012. http://amslaurea.unibo.it/3091/.
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Dürr, Oliver. "Monte-Carlo-Simulationen zu polymeren Ionenleitern." [S.l. : s.n.], 1998. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB7278696.
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Ekwegh, Ijeoma W. "Newsvendor Models With Monte Carlo Sampling." Digital Commons @ East Tennessee State University, 2016. https://dc.etsu.edu/etd/3125.
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Newsvendor Models with Monte Carlo Sampling by Ijeoma Winifred Ekwegh The newsvendor model is used in solving inventory problems in which demand is random. In this thesis, we will focus on a method of using Monte Carlo sampling to estimate the order quantity that will either maximizes revenue or minimizes cost given that demand is uncertain. Given data, the Monte Carlo approach will be used in sampling data over scenarios and also estimating the probability density function. A bootstrapping process yields an empirical distribution for the order quantity that will maximize the expected profit. Finally, this method will be used on a newsvendor example to show that it works in maximizing profit.
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Neuhoff, Daniel. "Reversible Jump Markov Chain Monte Carlo." Doctoral thesis, Humboldt-Universität zu Berlin, Wirtschaftswissenschaftliche Fakultät, 2016. http://dx.doi.org/10.18452/17461.
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Die vier in der vorliegenden Dissertation enthaltenen Studien beschäftigen sich vorwiegend mit dem dynamischen Verhalten makroökonomischer Zeitreihen. Diese Dynamiken werden sowohl im Kontext eines einfachen DSGE Modells, als auch aus der Sichtweise reiner Zeitreihenmodelle untersucht.The four studies of this thesis are concerned predominantly with the dynamics of macroeconomic time series, both in the context of a simple DSGE model, as well as from a pure time series modeling perspective.