Monte Carlo Methods in Parameter Estimation of Nonlinear Models

Yksi keskeisimmistä tehtävistä matemaattisten mallien tilastollisessa analyysissä on mallien tuntemattomien parametrien estimointi. Tässä diplomityössä ollaan kiinnostuneita tuntemattomien parametrien jakaumista ja niiden muodostamiseen sopivista numeerisista menetelmistä, etenkin tapauksissa, joissa malli on epälineaarinen parametrien suhteen. Erilaisten numeeristen menetelmien osalta pääpaino on Markovin ketju Monte Carlo -menetelmissä (MCMC). Nämä laskentaintensiiviset menetelmät ovat viime aikoina kasvattaneet suosiotaan lähinnä kasvaneen laskentatehon vuoksi. Sekä Markovin ketjujen että Monte Carlo -simuloinnin teoriaa on esitelty työssä siinä määrin, että menetelmien toimivuus saadaan perusteltua. Viime aikoina kehitetyistä menetelmistä tarkastellaan etenkin adaptiivisia MCMC menetelmiä. Työn lähestymistapa on käytännönläheinen ja erilaisia MCMC -menetelmien toteutukseen liittyviä asioita korostetaan. Työn empiirisessä osuudessa tarkastellaan viiden esimerkkimallin tuntemattomien parametrien jakaumaa käyttäen hyväksi teoriaosassa esitettyjä menetelmiä. Mallit kuvaavat kemiallisia reaktioita ja kuvataan tavallisina differentiaaliyhtälöryhminä. Mallit on kerätty kemisteiltä Lappeenrannan teknillisestä yliopistosta ja Åbo Akademista, Turusta.

Structural changes induced by daily music listening in the recovering brain after middle cerebral artery stroke: a voxel-based morphometry study

Music is a highly complex and versatile stimulus for the brain that engages many temporal, frontal, parietal, cerebellar, and subcortical areas involved in auditory, cognitive, emotional, and motor processing. Regular musical activities have been shown to effectively enhance the structure and function of many brain areas, making music a potential tool also in neurological rehabilitation. In our previous randomized controlled study, we found that listening to music on a daily basis can improve cognitive recovery and improve mood after an acute middle cerebral artery stroke. Extending this study, a voxel-based morphometry (VBM) analysis utilizing cost function masking was performed on the acute and 6-month post-stroke stage structural magnetic resonance imaging data of the patients (n = 49) who either listened to their favorite music [music group (MG), n = 16] or verbal material [audio book group (ABG), n = 18] or did not receive any listening material [control group (CG), n = 15] during the 6-month recovery period. Although all groups showed significant gray matter volume (GMV) increases from the acute to the 6-month stage, there was a specific network of frontal areas [left and right superior frontal gyrus (SFG), right medial SFG] and limbic areas [left ventral/subgenual anterior cingulate cortex (SACC) and right ventral striatum (VS)] in patients with left hemisphere damage in which the GMV increases were larger in the MG than in the ABG and in the CG. Moreover, the GM reorganization in the frontal areas correlated with enhanced recovery of verbal memory, focused attention, and language skills, whereas the GM reorganization in the SACC correlated with reduced negative mood. This study adds on previous results, showing that music listening after stroke not only enhances behavioral recovery, but also induces fine-grained neuroanatomical changes in the recovering brain.

Local alignment refinement using structural assessment.

Homology modeling is the most commonly used technique to build a three-dimensional model for a protein sequence. It heavily relies on the quality of the sequence alignment between the protein to model and related proteins with a known three dimensional structure. Alignment quality can be assessed according to the physico-chemical properties of the three dimensional models it produces.In this work, we introduce fifteen predictors designed to evaluate the properties of the models obtained for various alignments. They consist of an energy value obtained from different force fields (CHARMM, ProsaII or ANOLEA) computed on residue selected around misaligned regions. These predictors were evaluated on ten challenging test cases. For each target, all possible ungapped alignments are generated and their corresponding models are computed and evaluated.The best predictor, retrieving the structural alignment for 9 out of 10 test cases, is based on the ANOLEA atomistic mean force potential and takes into account residues around misaligned secondary structure elements. The performance of the other predictors is significantly lower. This work shows that substantial improvement in local alignments can be obtained by careful assessment of the local structure of the resulting models.

Predicting human resting-state functional connectivity from structural connectivity

In the cerebral cortex, the activity levels of neuronal populations are continuously fluctuating. When neuronal activity, as measured using functional MRI (fMRI), is temporally coherent across 2 populations, those populations are said to be functionally connected. Functional connectivity has previously been shown to correlate with structural (anatomical) connectivity patterns at an aggregate level. In the present study we investigate, with the aid of computational modeling, whether systems-level properties of functional networks-including their spatial statistics and their persistence across time-can be accounted for by properties of the underlying anatomical network. We measured resting state functional connectivity (using fMRI) and structural connectivity (using diffusion spectrum imaging tractography) in the same individuals at high resolution. Structural connectivity then provided the couplings for a model of macroscopic cortical dynamics. In both model and data, we observed (i) that strong functional connections commonly exist between regions with no direct structural connection, rendering the inference of structural connectivity from functional connectivity impractical; (ii) that indirect connections and interregional distance accounted for some of the variance in functional connectivity that was unexplained by direct structural connectivity; and (iii) that resting-state functional connectivity exhibits variability within and across both scanning sessions and model runs. These empirical and modeling results demonstrate that although resting state functional connectivity is variable and is frequently present between regions without direct structural linkage, its strength, persistence, and spatial statistics are nevertheless constrained by the large-scale anatomical structure of the human cerebral cortex.

Multimodal MRI analysis of structural and functional networks in the human brain : application to two clinical studies : driving abilities under THC intoxication and early white matter changes in FXTAS

Les approches multimodales dans l'imagerie cérébrale non invasive sont de plus en plus considérées comme un outil indispensable pour la compréhension des différents aspects de la structure et de la fonction cérébrale. Grâce aux progrès des techniques d'acquisition des images de Resonance Magnetique et aux nouveaux outils pour le traitement des données, il est désormais possible de mesurer plusieurs paramètres sensibles aux différentes caractéristiques des tissues cérébraux. Ces progrès permettent, par exemple, d'étudier les substrats anatomiques qui sont à la base des processus cognitifs ou de discerner au niveau purement structurel les phénomènes dégénératifs et développementaux. Cette thèse met en évidence l'importance de l'utilisation d'une approche multimodale pour étudier les différents aspects de la dynamique cérébrale grâce à l'application de cette approche à deux études cliniques: l'évaluation structurelle et fonctionnelle des effets aigus du cannabis fumé chez des consommateurs réguliers et occasionnels, et l'évaluation de l'intégrité de la substance grise et blanche chez des jeunes porteurs de la prémutations du gène FMR1 à risque de développer le FXTAS (Fragile-X Tremor Ataxia Syndrome). Nous avons montré que chez les fumeurs occasionnels de cannabis, même à faible concentration du principal composant psychoactif (THC) dans le sang, la performance lors d'une tâche visuo-motrice est fortement diminuée, et qu'il y a des changements dans l'activité des trois réseaux cérébraux impliqués dans les processus cognitifs: le réseau de saillance, le réseau du contrôle exécutif, et le réseau actif par défaut (Default Mode). Les sujets ne sont pas en mesure de saisir les saillances dans l'environnement et de focaliser leur attention sur la tâche. L'augmentation de la réponse hémodynamique dans le cortex cingulaire antérieur suggère une augmentation de l'activité introspective. Une investigation des ef¬fets au niveau cérébral d'une exposition prolongée au cannabis, montre des changements persistants de la substance grise dans les régions associées à la mémoire et au traitement des émotions. Le niveau d'atrophie dans ces structures corrèle avec la consommation de cannabis au cours des trois mois précédant l'étude. Dans la deuxième étude, nous démontrons des altérations structurelles des décennies avant l'apparition du syndrome FXTAS chez des sujets jeunes, asymptomatiques, et porteurs de la prémutation du gène FMR1. Les modifications trouvées peuvent être liées à deux mécanismes différents. Les altérations dans le réseau moteur du cervelet et dans la fimbria de l'hippocampe, suggèrent un effet développemental de la prémutation. Elles incluent aussi une atrophie de la substance grise du lobule VI du cervelet et l'altération des propriétés tissulaires de la substance blanche des projections afférentes correspondantes aux pédoncules cérébelleux moyens. Les lésions diffuses de la substance blanche cérébrale peu¬vent être un marquer précoce du développement de la maladie, car elles sont liées à un phénomène dégénératif qui précède l'apparition des symptômes du FXTAS. - Multimodal brain imaging is becoming a leading tool for understanding different aspects of brain structure and function. Thanks to the advances in Magnetic Resonance imaging (MRI) acquisition schemes and data processing techniques, it is now possible to measure different parameters sensitive to different tissue characteristics. This allows for example to investigate anatomical substrates underlying cognitive processing, or to disentangle, at a pure structural level degeneration and developmental processes. This thesis highlights the importance of using a multimodal approach for investigating different aspects of brain dynamics by applying this approach to two clinical studies: functional and structural assessment of the acute effects of cannabis smoking in regular and occasional users, and grey and white matter assessment in young FMR1 premutation carriers at risk of developing FXTAS. We demonstrate that in occasional smokers cannabis smoking, even at low concentration of the main psychoactive component (THC) in the blood, strongly decrease subjects' performance on a visuo-motor tracking task, and globally alters the activity of the three brain networks involved in cognitive processing: the Salience, the Control Executive, and the Default Mode networks. Subjects are unable to capture saliences in the environment and to orient attention to the task; the increase in Hemodynamic Response in the Anterior Cingulate Cortex suggests an increase in self-oriented mental activity. A further investigation on long term exposure to cannabis, shows a persistent grey matter modification in brain regions associated with memory and affective processing. The degree of atrophy in these structures also correlates with the estimation of drug use in the three months prior the participation to the study. In the second study we demonstrate structural changes in young asymptomatic premutation carriers decades before the onset of FXTAS that might be related to two different mechanisms. Alteration of the cerebellar motor network and of the hippocampal fimbria/ fornix, may reflect a potential neurodevelopmental effect of the premutation. These include grey matter atrophy in lobule VI and modification of white matter tissue property in the corresponding afferent projections through the Middle Cerebellar Peduncles. Diffuse hemispheric white matter lesions that seem to appear closer to the onset of FXTAS and be related to a neurodegenerative phenomenon may mark the imminent onset of FXTAS.

Structural connectomics in brain diseases.

Imaging the connectome in vivo has become feasible through the integration of several rapidly developing fields of science and engineering, namely magnetic resonance imaging and in particular diffusion MRI on one side, image processing and network theory on the other side. This framework brings in vivo brain imaging closer to the real topology of the brain, contributing to narrow the existing gap between our understanding of brain structural organization on one side and of human behavior and cognition on the other side. Given the seminal technical progresses achieved in the last few years, it may be ready to tackle even greater challenges, namely exploring disease mechanisms. In this review we analyze the current situation from the technical and biological perspectives. First, we critically review the technical solutions proposed in the literature to perform clinical studies. We analyze for each step (i.e. MRI acquisition, network building and network statistical analysis) the advantages and potential limitations. In the second part we review the current literature available on a selected subset of diseases, namely, dementia, schizophrenia, multiple sclerosis and others, and try to extract for each disease the common findings and main differences between reports.

Isolation, structural assignment and total synthesis of Barmumycin

Barmumycin was isolated from an extract of the marine actinomycete Streptomyces sp. BOSC-022A and found to be cytotoxic against various human tumor cell lines. Based on preliminary one- and two-dimensional 1H- and 13C-NMR spectra, the natural compound was initially assigned the structure of macrolactone-type compound 1, which was later prepared by two different routes. However, major spectroscopic differences between isolated barmumycin and 1 led to revision of the proposed structure as E-16. Based on synthesis of this new compound, and subsequent spectroscopic comparison of it to an authentic sample of barmumycin, the structure of the natural compound was indeed confirmed as that of E-16.

Studies on integrating kinematic design method with mechanical systems simulation techniques

Theultimate goal of any research in the mechanism/kinematic/design area may be called predictive design, ie the optimisation of mechanism proportions in the design stage without requiring extensive life and wear testing. This is an ambitious goal and can be realised through development and refinement of numerical (computational) technology in order to facilitate the design analysis and optimisation of complex mechanisms, mechanical components and systems. As a part of the systematic design methodology this thesis concentrates on kinematic synthesis (kinematic design and analysis) methods in the mechanism synthesis process. The main task of kinematic design is to find all possible solutions in the form of structural parameters to accomplish the desired requirements of motion. Main formulations of kinematic design can be broadly divided to exact synthesis and approximate synthesis formulations. The exact synthesis formulation is based in solving n linear or nonlinear equations in n variables and the solutions for the problem areget by adopting closed form classical or modern algebraic solution methods or using numerical solution methods based on the polynomial continuation or homotopy. The approximate synthesis formulations is based on minimising the approximation error by direct optimisation The main drawbacks of exact synthesis formulationare: (ia) limitations of number of design specifications and (iia) failure in handling design constraints- especially inequality constraints. The main drawbacks of approximate synthesis formulations are: (ib) it is difficult to choose a proper initial linkage and (iib) it is hard to find more than one solution. Recentformulations in solving the approximate synthesis problem adopts polynomial continuation providing several solutions, but it can not handle inequality const-raints. Based on the practical design needs the mixed exact-approximate position synthesis with two exact and an unlimited number of approximate positions has also been developed. The solutions space is presented as a ground pivot map but thepole between the exact positions cannot be selected as a ground pivot. In this thesis the exact synthesis problem of planar mechanism is solved by generating all possible solutions for the optimisation process ¿ including solutions in positive dimensional solution sets - within inequality constraints of structural parameters. Through the literature research it is first shown that the algebraic and numerical solution methods ¿ used in the research area of computational kinematics ¿ are capable of solving non-parametric algebraic systems of n equations inn variables and cannot handle the singularities associated with positive-dimensional solution sets. In this thesis the problem of positive-dimensional solutionsets is solved adopting the main principles from mathematical research area of algebraic geometry in solving parametric ( in the mathematical sense that all parameter values are considered ¿ including the degenerate cases ¿ for which the system is solvable ) algebraic systems of n equations and at least n+1 variables.Adopting the developed solution method in solving the dyadic equations in direct polynomial form in two- to three-precision-points it has been algebraically proved and numerically demonstrated that the map of the ground pivots is ambiguousand that the singularities associated with positive-dimensional solution sets can be solved. The positive-dimensional solution sets associated with the poles might contain physically meaningful solutions in the form of optimal defectfree mechanisms. Traditionally the mechanism optimisation of hydraulically driven boommechanisms is done at early state of the design process. This will result in optimal component design rather than optimal system level design. Modern mechanismoptimisation at system level demands integration of kinematic design methods with mechanical system simulation techniques. In this thesis a new kinematic design method for hydraulically driven boom mechanism is developed and integrated in mechanical system simulation techniques. The developed kinematic design method is based on the combinations of two-precision-point formulation and on optimisation ( with mathematical programming techniques or adopting optimisation methods based on probability and statistics ) of substructures using calculated criteria from the system level response of multidegree-of-freedom mechanisms. Eg. by adopting the mixed exact-approximate position synthesis in direct optimisation (using mathematical programming techniques) with two exact positions and an unlimitednumber of approximate positions the drawbacks of (ia)-(iib) has been cancelled.The design principles of the developed method are based on the design-tree -approach of the mechanical systems and the design method ¿ in principle ¿ is capable of capturing the interrelationship between kinematic and dynamic synthesis simultaneously when the developed kinematic design method is integrated with the mechanical system simulation techniques.

Automated formulation of optimisation models for steel beam structures

Over 70% of the total costs of an end product are consequences of decisions that are made during the design process. A search for optimal cross-sections will often have only a marginal effect on the amount of material used if the geometry of a structure is fixed and if the cross-sectional characteristics of its elements are property designed by conventional methods. In recent years, optimalgeometry has become a central area of research in the automated design of structures. It is generally accepted that no single optimisation algorithm is suitable for all engineering design problems. An appropriate algorithm, therefore, mustbe selected individually for each optimisation situation. Modelling is the mosttime consuming phase in the optimisation of steel and metal structures. In thisresearch, the goal was to develop a method and computer program, which reduces the modelling and optimisation time for structural design. The program needed anoptimisation algorithm that is suitable for various engineering design problems. Because Finite Element modelling is commonly used in the design of steel and metal structures, the interaction between a finite element tool and optimisation tool needed a practical solution. The developed method and computer programs were tested with standard optimisation tests and practical design optimisation cases. Three generations of computer programs are developed. The programs combine anoptimisation problem modelling tool and FE-modelling program using three alternate methdos. The modelling and optimisation was demonstrated in the design of a new boom construction and steel structures of flat and ridge roofs. This thesis demonstrates that the most time consuming modelling time is significantly reduced. Modelling errors are reduced and the results are more reliable. A new selection rule for the evolution algorithm, which eliminates the need for constraint weight factors is tested with optimisation cases of the steel structures that include hundreds of constraints. It is seen that the tested algorithm can be used nearly as a black box without parameter settings and penalty factors of the constraints.

A modified structural stress method for fatigue assessment of welded structures

Fatigue life assessment of weldedstructures is commonly based on the nominal stress method, but more flexible and accurate methods have been introduced. In general, the assessment accuracy is improved as more localized information about the weld is incorporated. The structural hot spot stress method includes the influence of macro geometric effects and structural discontinuities on the design stress but excludes the local features of the weld. In this thesis, the limitations of the structural hot spot stress method are discussed and a modified structural stress method with improved accuracy is developed and verified for selected welded details. The fatigue life of structures in the as-welded state consists mainly of crack growth from pre-existing cracks or defects. Crack growth rate depends on crack geometry and the stress state on the crack face plane. This means that the stress level and shape of the stress distribution in the assumed crack path governs thetotal fatigue life. In many structural details the stress distribution is similar and adequate fatigue life estimates can be obtained just by adjusting the stress level based on a single stress value, i.e., the structural hot spot stress. There are, however, cases for which the structural stress approach is less appropriate because the stress distribution differs significantly from the more common cases. Plate edge attachments and plates on elastic foundations are some examples of structures with this type of stress distribution. The importance of fillet weld size and weld load variation on the stress distribution is another central topic in this thesis. Structural hot spot stress determination is generally based on a procedure that involves extrapolation of plate surface stresses. Other possibilities for determining the structural hot spot stress is to extrapolate stresses through the thickness at the weld toe or to use Dong's method which includes through-thickness extrapolation at some distance from the weld toe. Both of these latter methods are less sensitive to the FE mesh used. Structural stress based on surface extrapolation is sensitive to the extrapolation points selected and to the FE mesh used near these points. Rules for proper meshing, however, are well defined and not difficult to apply. To improve the accuracy of the traditional structural hot spot stress, a multi-linear stress distribution is introduced. The magnitude of the weld toe stress after linearization is dependent on the weld size, weld load and plate thickness. Simple equations have been derived by comparing assessment results based on the local linear stress distribution and LEFM based calculations. The proposed method is called the modified structural stress method (MSHS) since the structural hot spot stress (SHS) value is corrected using information on weld size andweld load. The correction procedure is verified using fatigue test results found in the literature. Also, a test case was conducted comparing the proposed method with other local fatigue assessment methods.

Identifying the Role of Final Consumption in Structural Path Analysis: An Application to Water Uses

The complexity of the connexions within an economic system can only be reliably reflected in academic research if powerful methods are used. Researchers have used Structural Path Analysis (SPA) to capture not only the linkages within the production system but also the propagation of the effects into different channels of impacts. However, the SPA literature has restricted itself to showing the relations among sectors of production, while the connections between these sectors and final consumption have attracted little attention. In order to consider the complete set of channels involved, in this paper we propose a structural path method that endogenously incorporates not only sectors of production but also the final consumption of the economy. The empirical application comprises water usages, and analyses the dissemination of exogenous impacts into various channels of water consumption. The results show that the responsibility for water stress is imputed to different sectors and depends on the hypothesis used for the role played by final consumption in the model. This highlights the importance of consumers’ decisions in the determination of ecological impacts. Keywords: Input-Output Analysis, Structural Path Analysis, Final Consumption, Water uses.

T-Coffee: a web server for the multiple sequence alignment of protein and RNA sequences using structural information and homology extension

This article introduces a new interface for T-Coffee, a consistency-based multiple sequence alignment program. This interface provides an easy and intuitive access to the most popular functionality of the package. These include the default T-Coffee mode for protein and nucleic acid sequences, the M-Coffee mode that allows combining the output of any other aligners, and template-based modes of T-Coffee that deliver high accuracy alignments while using structural or homology derived templates. These three available template modes are Expresso for the alignment of protein with a known 3D-Structure, R-Coffee to align RNA sequences with conserved secondary structures and PSI-Coffee to accurately align distantly related sequences using homology extension. The new server benefits from recent improvements of the T-Coffee algorithm and can align up to 150 sequences as long as 10 000 residues and is available from both http://www.tcoffee.org and its main mirror http://tcoffee.crg.cat.