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.

Stage fright: its experience as a problem and coping with it.

PURPOSE AND METHOD: This questionnaire survey of 190 university music students assessed negative feelings of music performance anxiety (MPA) before performing, the experience of stage fright as a problem, and how closely they are associated with each other. The study further investigated whether the experience of stage fright as a problem and negative feelings of MPA predict the coping behavior of the music students. Rarely addressed coping issues were assessed, i.e., self-perceived effectiveness of different coping strategies, knowledge of possible risks and acceptance of substance-based coping strategies, and need for more support.RESULTS: The results show that one-third of the students experienced stage fright as a problem and that this was only moderately correlated with negative feelings of MPA. The experience of stage fright as a problem significantly predicted the frequency of use and the acceptance of medication as a coping strategy. Breathing exercises and self-control techniques were rated as effective as medication. Finally, students expressed a strong need to receive more support (65%) and more information (84%) concerning stage fright.CONCLUSION: Stage fright was experienced as a problem and perceived as having negative career consequences by a considerable percentage of the surveyed students. In addition to a desire for more help and support, the students expressed an openness and willingness to seriously discuss and address the topic of stage fright. This provides a necessary and promising basis for optimal career preparation and, hence, an opportunity to prevent occupational problems in professional musicians. [Authors]

Bioreporters and biosensors for arsenic detection. Biotechnological solutions for a world-wide pollution problem.

A wide variety of whole cell bioreporter and biosensor assays for arsenic detection has been developed over the past decade. The assays permit flexible detection instrumentation while maintaining excellent method of detection limits in the environmentally relevant range of 10-50 μg arsenite per L and below. New emerging trends focus on genetic rewiring of reporter cells and/or integration into microdevices for more optimal detection. A number of case studies have shown realistic field applicability of bioreporter assays.

Peso problem anddevaluation expectations: Evidence from Latin America

Tämän tutkielman tavoitteena on tutkia peso-ongelmaa sekä devalvaatio-odotuksia seuraavissa Latinalaisen Amerikan maissa: Argentiina, Brasilia, Costa Rica, Uruguay ja Venezuela. Lisäksi tutkitaan, onko peso-ongelmalla mahdollista selittää korkojen epäsäännöllistä käyttäytymistä ennen todellisen devalvaation tapahtumista. Jotta näiden tutkiminen olisi mahdollista, lasketaan markkinoiden odotettu devalvaation todennäköisyys tutkittavissa maissa. Odotettu devalvaation todennäköisyys lasketaan aikavälillä tammikuusta 1996 joulukuuhun 2006 käyttäen kahta erilaista mallia. Korkoero-mallin mukaan maiden välisestä korkoerosta on mahdollista laskea markkinoiden devalvaatio-odotukset. Toiseksi, Probit-mallissa käytetään useita makrotaloudellisia tekijöitä selittävinä muuttujina laskettaessa odotettua devalvaation todennäköisyyttä. Lisäksi tutkitaan, miten yksittäisten makrotaloudellisten muuttujien kehitys vaikuttaa odotettuun devalvaation todennäköisyyteen. Empiiriset tulokset osoittavat, että tutkituissa Latinalaisen Amerikan maissa oli peso-ongelma aikavälillä tammikuusta 1996 joulukuuhun 2006. Korkoero-mallin tulosten mukaan peso-ongelma löytyi kaikista muista tutkituista maista lukuun ottamatta Argentiinaa. Vastaavasti Probit-mallin mukaan peso-ongelma löytyi kaikista tutkituista maista. Tulokset osoittavat myös, että korkojen epäsäännöllinen kehitys ennen varsinaista devalvaatiota on mahdollista selittää peso-ongelmalla. Probit-mallin tulokset osoittavat lisäksi, että makrotaloudellisten muuttujien kehityksellä ei ole mitään tiettyä kaavaa liittyen siihen, kuinka ne vaikuttavat markkinoiden devalvaatio-odotuksiin Latinalaisessa Amerikassa. Pikemmin vaikutukset näyttävät olevan maakohtaisia.

A Monte Carlo approach to the inverse problem of diffuse pollution risk in agricultural catchments

The hydrological and biogeochemical processes that operate in catchments influence the ecological quality of freshwater systems through delivery of fine sediment, nutrients and organic matter. Most models that seek to characterise the delivery of diffuse pollutants from land to water are reductionist. The multitude of processes that are parameterised in such models to ensure generic applicability make them complex and difficult to test on available data. Here, we outline an alternative - data-driven - inverse approach. We apply SCIMAP, a parsimonious risk based model that has an explicit treatment of hydrological connectivity. we take a Bayesian approach to the inverse problem of determining the risk that must be assigned to different land uses in a catchment in order to explain the spatial patterns of measured in-stream nutrient concentrations. We apply the model to identify the key sources of nitrogen (N) and phosphorus (P) diffuse pollution risk in eleven UK catchments covering a range of landscapes. The model results show that: 1) some land use generates a consistently high or low risk of diffuse nutrient pollution; but 2) the risks associated with different land uses vary both between catchments and between nutrients; and 3) that the dominant sources of P and N risk in the catchment are often a function of the spatial configuration of land uses. Taken on a case-by-case basis, this type of inverse approach may be used to help prioritise the focus of interventions to reduce diffuse pollution risk for freshwater ecosystems. (C) 2012 Elsevier B.V. All rights reserved.

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.

On Modelling, System Identification and Control of Servo-Systems with a Flexible Load

The present study was done with two different servo-systems. In the first system, a servo-hydraulic system was identified and then controlled by a fuzzy gainscheduling controller. The second servo-system, an electro-magnetic linear motor in suppressing the mechanical vibration and position tracking of a reference model are studied by using a neural network and an adaptive backstepping controller respectively. Followings are some descriptions of research methods. Electro Hydraulic Servo Systems (EHSS) are commonly used in industry. These kinds of systems are nonlinearin nature and their dynamic equations have several unknown parameters.System identification is a prerequisite to analysis of a dynamic system. One of the most promising novel evolutionary algorithms is the Differential Evolution (DE) for solving global optimization problems. In the study, the DE algorithm is proposed for handling nonlinear constraint functionswith boundary limits of variables to find the best parameters of a servo-hydraulic system with flexible load. The DE guarantees fast speed convergence and accurate solutions regardless the initial conditions of parameters. The control of hydraulic servo-systems has been the focus ofintense research over the past decades. These kinds of systems are nonlinear in nature and generally difficult to control. Since changing system parameters using the same gains will cause overshoot or even loss of system stability. The highly non-linear behaviour of these devices makes them ideal subjects for applying different types of sophisticated controllers. The study is concerned with a second order model reference to positioning control of a flexible load servo-hydraulic system using fuzzy gainscheduling. In the present research, to compensate the lack of dampingin a hydraulic system, an acceleration feedback was used. To compare the results, a pcontroller with feed-forward acceleration and different gains in extension and retraction is used. The design procedure for the controller and experimental results are discussed. The results suggest that using the fuzzy gain-scheduling controller decrease the error of position reference tracking. The second part of research was done on a PermanentMagnet Linear Synchronous Motor (PMLSM). In this study, a recurrent neural network compensator for suppressing mechanical vibration in PMLSM with a flexible load is studied. The linear motor is controlled by a conventional PI velocity controller, and the vibration of the flexible mechanism is suppressed by using a hybrid recurrent neural network. The differential evolution strategy and Kalman filter method are used to avoid the local minimum problem, and estimate the states of system respectively. The proposed control method is firstly designed by using non-linear simulation model built in Matlab Simulink and then implemented in practical test rig. The proposed method works satisfactorily and suppresses the vibration successfully. In the last part of research, a nonlinear load control method is developed and implemented for a PMLSM with a flexible load. The purpose of the controller is to track a flexible load to the desired position reference as fast as possible and without awkward oscillation. The control method is based on an adaptive backstepping algorithm whose stability is ensured by the Lyapunov stability theorem. The states of the system needed in the controller are estimated by using the Kalman filter. The proposed controller is implemented and tested in a linear motor test drive and responses are presented.

Patents in the Information and Communications Technology Sector - Development Trends, Problem Areas and Pressures for Change

The patent system was created for the purpose of promoting innovation by granting the inventors a legally defined right to exclude others in return for public disclosure. Today, patents are being applied and granted in greater numbers than ever, particularly in new areas such as biotechnology and information andcommunications technology (ICT), in which research and development (R&D) investments are also high. At the same time, the patent system has been heavily criticized. It has been claimed that it discourages rather than encourages the introduction of new products and processes, particularly in areas that develop quickly, lack one-product-one-patent correlation, and in which theemergence of patent thickets is characteristic. A further concern, which is particularly acute in the U.S., is the granting of so-called 'bad patents', i.e. patents that do not factually fulfil the patentability criteria. From the perspective of technology-intensive companies, patents could,irrespective of the above, be described as the most significant intellectual property right (IPR), having the potential of being used to protect products and processes from imitation, to limit competitors' freedom-to-operate, to provide such freedom to the company in question, and to exchange ideas with others. In fact, patents define the boundaries of ownership in relation to certain technologies. They may be sold or licensed on their ownor they may be components of all sorts of technology acquisition and licensing arrangements. Moreover, with the possibility of patenting business-method inventions in the U.S., patents are becoming increasingly important for companies basing their businesses on services. The value of patents is dependent on the value of the invention it claims, and how it is commercialized. Thus, most of them are worth very little, and most inventions are not worth patenting: it may be possible to protect them in other ways, and the costs of protection may exceed the benefits. Moreover, instead of making all inventions proprietary and seeking to appropriate as highreturns on investments as possible through patent enforcement, it is sometimes better to allow some of them to be disseminated freely in order to maximize market penetration. In fact, the ideology of openness is well established in the software sector, which has been the breeding ground for the open-source movement, for instance. Furthermore, industries, such as ICT, that benefit from network effects do not shun the idea of setting open standards or opening up their proprietary interfaces to allow everyone todesign products and services that are interoperable with theirs. The problem is that even though patents do not, strictly speaking, prevent access to protected technologies, they have the potential of doing so, and conflicts of interest are not rare. The primary aim of this dissertation is to increase understanding of the dynamics and controversies of the U.S. and European patent systems, with the focus on the ICT sector. The study consists of three parts. The first part introduces the research topic and the overall results of the dissertation. The second part comprises a publication in which academic, political, legal and business developments that concern software and business-method patents are investigated, and contentiousareas are identified. The third part examines the problems with patents and open standards both of which carry significant economic weight inthe ICT sector. Here, the focus is on so-called submarine patents, i.e. patentsthat remain unnoticed during the standardization process and then emerge after the standard has been set. The factors that contribute to the problems are documented and the practical and juridical options for alleviating them are assessed. In total, the dissertation provides a good overview of the challenges and pressures for change the patent system is facing,and of how these challenges are reflected in standard setting.

A Sequential Allocation Problem: The Asymptotic Distribution of Resources

In this paper we consider a sequential allocation problem with n individuals. The first individual can consume any amount of some endowment leaving the remaining for the second individual, and so on. Motivated by the limitations associated with the cooperative or non-cooperative solutions we propose a new approach. We establish some axioms that should be satisfied, representativeness, impartiality, etc. The result is a unique asymptotic allocation rule. It is shown for n = 2; 3; 4; and a claim is made for general n. We show that it satisfies a set of desirable properties. Key words: Sequential allocation rule, River sharing problem, Cooperative and non-cooperative games, Dictator and ultimatum games. JEL classification: C79, D63, D74.

The global carbon budget:a conflicting claims problem

Despite global environmental governance has traditionally couched global warming in terms of annual CO2 emissions (a flow), global mean temperature is actually determined by cumulative CO2 emissions in the atmosphere (a stock). Thanks to advances of scientific community, nowadays it is possible to quantify the \global carbon budget", that is, the amount of available cumulative CO2 emissions before crossing the 2oC threshold (Meinshausen et al., 2009). The current approach proposes to analyze the allocation of such global carbon budget among countries as a classical conflicting claims problem (O'Neill, 1982). Based on some appealing principles, it is proposed an efficient and sustainable allocation of the available carbon budget from 2000 to 2050 taking into account different environmental risk scenarios. Keywords: Carbon budget, Conflicting claims problem, Distribution, Climate change. JEL classification: C79, D71, D74, H41, H87, Q50, Q54, Q58.

Identifying quantitative operation principles in metabolic pathways: a systematic method for searching feasible enzyme activity patterns leading to cellular adaptive responses

Background: Optimization methods allow designing changes in a system so that specific goals are attained. These techniques are fundamental for metabolic engineering. However, they are not directly applicable for investigating the evolution of metabolic adaptation to environmental changes. Although biological systems have evolved by natural selection and result in well-adapted systems, we can hardly expect that actual metabolic processes are at the theoretical optimum that could result from an optimization analysis. More likely, natural systems are to be found in a feasible region compatible with global physiological requirements. Results: We first present a new method for globally optimizing nonlinear models of metabolic pathways that are based on the Generalized Mass Action (GMA) representation. The optimization task is posed as a nonconvex nonlinear programming (NLP) problem that is solved by an outer- approximation algorithm. This method relies on solving iteratively reduced NLP slave subproblems and mixed-integer linear programming (MILP) master problems that provide valid upper and lower bounds, respectively, on the global solution to the original NLP. The capabilities of this method are illustrated through its application to the anaerobic fermentation pathway in Saccharomyces cerevisiae. We next introduce a method to identify the feasibility parametric regions that allow a system to meet a set of physiological constraints that can be represented in mathematical terms through algebraic equations. This technique is based on applying the outer-approximation based algorithm iteratively over a reduced search space in order to identify regions that contain feasible solutions to the problem and discard others in which no feasible solution exists. As an example, we characterize the feasible enzyme activity changes that are compatible with an appropriate adaptive response of yeast Saccharomyces cerevisiae to heat shock Conclusion: Our results show the utility of the suggested approach for investigating the evolution of adaptive responses to environmental changes. The proposed method can be used in other important applications such as the evaluation of parameter changes that are compatible with health and disease states.

Weierstrass integrability of differential equations

The integrability problem consists in finding the class of functions a first integral of a given planar polynomial differential system must belong to. We recall the characterization of systems which admit an elementary or Liouvillian first integral. We define {\it Weierstrass integrability} and we determine which Weierstrass integrable systems are Liouvillian integrable. Inside this new class of integrable systems there are non--Liouvillian integrable systems.

Cyclicity versus center problem

We prove that there are one-parameter families of planar differential equations for which the center problem has a trivial solution and on the other hand the cyclicity of the weak focus is arbitrarily high. We illustrate this phenomenon in several examples for which this cyclicity is computed.

Identifying the preferred subset of enzymatic profiles in nonlinear kinetic metabolic models via multiobjective global optimization and pareto filters

Optimization models in metabolic engineering and systems biology focus typically on optimizing a unique criterion, usually the synthesis rate of a metabolite of interest or the rate of growth. Connectivity and non-linear regulatory effects, however, make it necessary to consider multiple objectives in order to identify useful strategies that balance out different metabolic issues. This is a fundamental aspect, as optimization of maximum yield in a given condition may involve unrealistic values in other key processes. Due to the difficulties associated with detailed non-linear models, analysis using stoichiometric descriptions and linear optimization methods have become rather popular in systems biology. However, despite being useful, these approaches fail in capturing the intrinsic nonlinear nature of the underlying metabolic systems and the regulatory signals involved. Targeting more complex biological systems requires the application of global optimization methods to non-linear representations. In this work we address the multi-objective global optimization of metabolic networks that are described by a special class of models based on the power-law formalism: the generalized mass action (GMA) representation. Our goal is to develop global optimization methods capable of efficiently dealing with several biological criteria simultaneously. In order to overcome the numerical difficulties of dealing with multiple criteria in the optimization, we propose a heuristic approach based on the epsilon constraint method that reduces the computational burden of generating a set of Pareto optimal alternatives, each achieving a unique combination of objectives values. To facilitate the post-optimal analysis of these solutions and narrow down their number prior to being tested in the laboratory, we explore the use of Pareto filters that identify the preferred subset of enzymatic profiles. We demonstrate the usefulness of our approach by means of a case study that optimizes the ethanol production in the fermentation of Saccharomyces cerevisiae.