Analysis of a finite volume method for a cross-diffusion model in population dynamics

The main goal of this paper is to propose a convergent finite volume method for a reactionâeuro"diffusion system with cross-diffusion. First, we sketch an existence proof for a class of cross-diffusion systems. Then the standard two-point finite volume fluxes are used in combination with a nonlinear positivity-preserving approximation of the cross-diffusion coefficients. Existence and uniqueness of the approximate solution are addressed, and it is also shown that the scheme converges to the corresponding weak solution for the studied model. Furthermore, we provide a stability analysis to study pattern-formation phenomena, and we perform two-dimensional numerical examples which exhibit formation of nonuniform spatial patterns. From the simulations it is also found that experimental rates of convergence are slightly below second order. The convergence proof uses two ingredients of interest for various applications, namely the discrete Sobolev embedding inequalities with general boundary conditions and a space-time $L^1$ compactness argument that mimics the compactness lemma due to Kruzhkov. The proofs of these results are given in the Appendix.

Low-frequency transcranial magnetic stimulation over left dorsal premotor cortex improves the dynamic control of visuospatially cued actions.

Left rostral dorsal premotor cortex (rPMd) and supramarginal gyrus (SMG) have been implicated in the dynamic control of actions. In 12 right-handed healthy individuals, we applied 30 min of low-frequency (1 Hz) repetitive transcranial magnetic stimulation (rTMS) over left rPMd to investigate the involvement of left rPMd and SMG in the rapid adjustment of actions guided by visuospatial cues. After rTMS, subjects underwent functional magnetic resonance imaging while making spatially congruent button presses with the right or left index finger in response to a left- or right-sided target. Subjects were asked to covertly prepare motor responses as indicated by a directional cue presented 1 s before the target. On 20% of trials, the cue was invalid, requiring subjects to readjust their motor plan according to the target location. Compared with sham rTMS, real rTMS increased the number of correct responses in invalidly cued trials. After real rTMS, task-related activity of the stimulated left rPMd showed increased task-related coupling with activity in ipsilateral SMG and the adjacent anterior intraparietal area (AIP). Individuals who showed a stronger increase in left-hemispheric premotor-parietal connectivity also made fewer errors on invalidly cued trials after rTMS. The results suggest that rTMS over left rPMd improved the ability to dynamically adjust visuospatial response mapping by strengthening left-hemispheric connectivity between rPMd and the SMG-AIP region. These results support the notion that left rPMd and SMG-AIP contribute toward dynamic control of actions and demonstrate that low-frequency rTMS can enhance functional coupling between task-relevant brain regions and improve some aspects of motor performance.

Analyzing dynamic intellectual capital: System-based theory and application

This research report presents an application of systems theory to evaluating intellectual capital (IC) as organization's ability for self-renewal. As renewal ability is a dynamic capability of an organization as a whole, rather than a static asset or an atomistic competence of separate individuals within the organization, it needs to be understood systemically. Consequently, renewal ability has to be measured with systemic methods that are based on a thorough conceptual analysis of systemic characteristics of organizations. The aim of this report is to demonstrate the theory and analysis methodology for grasping companies' systemic efficiency and renewal ability. The volume is divided into three parts. The first deals with the theory of organizations as self-renewing systems. In the second part, the principles of quantitative analysis of organizations are laid down. Finally, the detailed mathematics of the renewal indices are presented. We also assert that the indices produced by the analysis are an effective tool for the management and valuation of knowledge-intensive companies.

Analysis of thermal properties of phase change materials (PCM) using differential scanning calorimeter (DSC)

Commercially available PCM RT 20, RT 27, SP 22, A17 and SP 25 A8. Were analyzed using dynamic and step method of heat flux DSC. The results of the dinamic and step method were compared with commercial valures. It was found that RT 20 & RT 27 showed good conforming of results with commercial values while SP 22 A17 & SP 25 A8 did not show conformity.

Three essays in dynamic corporate finance

The three essays constituting this thesis focus on financing and cash management policy. The first essay aims to shed light on why firms issue debt so conservatively. In particular, it examines the effects of shareholder and creditor protection on capital structure choices. It starts by building a contingent claims model where financing policy results from a trade-off between tax benefits, contracting costs and agency costs. In this setup, controlling shareholders can divert part of the firms' cash ows as private benefits at the expense of minority share- holders. In addition, shareholders as a class can behave strategically at the time of default leading to deviations from the absolute priority rule. The analysis demonstrates that investor protection is a first order determinant of firms' financing choices and that conflicts of interests between firm claimholders may help explain the level and cross-sectional variation of observed leverage ratios. The second essay focuses on the practical relevance of agency conflicts. De- spite the theoretical development of the literature on agency conflicts and firm policy choices, the magnitude of manager-shareholder conflicts is still an open question. This essay proposes a methodology for quantifying these agency conflicts. To do so, it examines the impact of managerial entrenchment on corporate financing decisions. It builds a dynamic contingent claims model in which managers do not act in the best interest of shareholders, but rather pursue private benefits at the expense of shareholders. Managers have discretion over financing and dividend policies. However, shareholders can remove the manager at a cost. The analysis demonstrates that entrenched managers restructure less frequently and issue less debt than optimal for shareholders. I take the model to the data and use observed financing choices to provide firm-specific estimates of the degree of managerial entrenchment. Using structural econometrics, I find costs of control challenges of 2-7% on average (.8-5% at median). The estimates of the agency costs vary with variables that one expects to determine managerial incentives. In addition, these costs are sufficient to resolve the low- and zero-leverage puzzles and explain the time series of observed leverage ratios. Finally, the analysis shows that governance mechanisms significantly affect the value of control and firms' financing decisions. The third essay is concerned with the documented time trend in corporate cash holdings by Bates, Kahle and Stulz (BKS,2003). BKS find that firms' cash holdings double from 10% to 20% over the 1980 to 2005 period. This essay provides an explanation of this phenomenon by examining the effects of product market competition on firms' cash holdings in the presence of financial constraints. It develops a real options model in which cash holdings may be used to cover unexpected operating losses and avoid inefficient closure. The model generates new predictions relating cash holdings to firm and industry characteristics such as the intensity of competition, cash flow volatility, or financing constraints. The empirical examination of the model shows strong support of model's predictions. In addition, it shows that the time trend in cash holdings documented by BKS can be at least partly attributed to a competition effect.

Direct-on-line axial flux permanent magnet synchronous generator static and dynamic performance

In distributed energy production, permanent magnet synchronous generators (PMSG) are often connected to the grid via frequency converters, such as voltage source line converters. The price of the converter may constitute a large part of the costs of a generating set. Some of the permanent magnet synchronous generators with converters and traditional separately excited synchronous generators couldbe replaced by direct-on-line (DOL) non-controlled PMSGs. Small directly networkconnected generators are likely to have large markets in the area of distributed electric energy generation. Typical prime movers could be windmills, watermills and internal combustion engines. DOL PMSGs could also be applied in island networks, such as ships and oil platforms. Also various back-up power generating systems could be carried out with DOL PMSGs. The benefits would be a lower priceof the generating set and the robustness and easy use of the system. The performance of DOL PMSGs is analyzed. The electricity distribution companies have regulations that constrain the design of the generators being connected to the grid. The general guidelines and recommendations are applied in the analysis. By analyzing the results produced by the simulation model for the permanent magnet machine, the guidelines for efficient damper winding parameters for DOL PMSGs are presented. The simulation model is used to simulate grid connections and load transients. The damper winding parameters are calculated by the finite element method (FEM) and determined from experimental measurements. Three-dimensional finite element analysis (3D FEA) is carried out. The results from the simulation model and 3D FEA are compared with practical measurements from two prototype axial flux permanent magnet generators provided with damper windings. The dimensioning of the damper winding parameters is case specific. The damper winding should be dimensioned based on the moment of inertia of the generating set. It is shown that the damper winding has optimal values to reach synchronous operation in the shortest period of time after transient operation. With optimal dimensioning, interferenceon the grid is minimized.

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.

R&D Performance Analysis: Case Studies on the Challenges and Promotion of the Evaluation and Measurement of R&D

Due to the intense international competition, demanding, and sophisticated customers, and diverse transforming technological change, organizations need to renew their products and services by allocating resources on research and development (R&D). Managing R&D is complex, but vital for many organizations to survive in the dynamic, turbulent environment. Thus, the increased interest among decision-makers towards finding the right performance measures for R&D is understandable. The measures or evaluation methods of R&D performance can be utilized for multiple purposes; for strategic control, for justifying the existence of R&D, for providing information and improving activities, as well as for the purposes of motivating and benchmarking. The earlier research in the field of R&D performance analysis has generally focused on either the activities and considerable factors and dimensions - e.g. strategic perspectives, purposes of measurement, levels of analysis, types of R&D or phases of R&D process - prior to the selection of R&Dperformance measures, or on proposed principles or actual implementation of theselection or design processes of R&D performance measures or measurement systems. This study aims at integrating the consideration of essential factors anddimensions of R&D performance analysis to developed selection processes of R&D measures, which have been applied in real-world organizations. The earlier models for corporate performance measurement that can be found in the literature, are to some extent adaptable also to the development of measurement systemsand selecting the measures in R&D activities. However, it is necessary to emphasize the special aspects related to the measurement of R&D performance in a way that make the development of new approaches for especially R&D performance measure selection necessary: First, the special characteristics of R&D - such as the long time lag between the inputs and outcomes, as well as the overall complexity and difficult coordination of activities - influence the R&D performance analysis problems, such as the need for more systematic, objective, balanced and multi-dimensional approaches for R&D measure selection, as well as the incompatibility of R&D measurement systems to other corporate measurement systems and vice versa. Secondly, the above-mentioned characteristics and challenges bring forth the significance of the influencing factors and dimensions that need to be recognized in order to derive the selection criteria for measures and choose the right R&D metrics, which is the most crucial step in the measurement system development process. The main purpose of this study is to support the management and control of the research and development activities of organizations by increasing the understanding of R&D performance analysis, clarifying the main factors related to the selection of R&D measures and by providing novel types of approaches and methods for systematizing the whole strategy- and business-based selection and development process of R&D indicators.The final aim of the research is to support the management in their decision making of R&D with suitable, systematically chosen measures or evaluation methods of R&D performance. Thus, the emphasis in most sub-areas of the present research has been on the promotion of the selection and development process of R&D indicators with the help of the different tools and decision support systems, i.e. the research has normative features through providing guidelines by novel types of approaches. The gathering of data and conducting case studies in metal and electronic industry companies, in the information and communications technology (ICT) sector, and in non-profit organizations helped us to formulate a comprehensive picture of the main challenges of R&D performance analysis in different organizations, which is essential, as recognition of the most importantproblem areas is a very crucial element in the constructive research approach utilized in this study. Multiple practical benefits regarding the defined problemareas could be found in the various constructed approaches presented in this dissertation: 1) the selection of R&D measures became more systematic when compared to the empirical analysis, as it was common that there were no systematic approaches utilized in the studied organizations earlier; 2) the evaluation methods or measures of R&D chosen with the help of the developed approaches can be more directly utilized in the decision-making, because of the thorough consideration of the purpose of measurement, as well as other dimensions of measurement; 3) more balance to the set of R&D measures was desired and gained throughthe holistic approaches to the selection processes; and 4) more objectivity wasgained through organizing the selection processes, as the earlier systems were considered subjective in many organizations. Scientifically, this dissertation aims to make a contribution to the present body of knowledge of R&D performance analysis by facilitating dealing with the versatility and challenges of R&D performance analysis, as well as the factors and dimensions influencing the selection of R&D performance measures, and by integrating these aspects to the developed novel types of approaches, methods and tools in the selection processes of R&D measures, applied in real-world organizations. In the whole research, facilitation of dealing with the versatility and challenges in R&D performance analysis, as well as the factors and dimensions influencing the R&D performance measure selection are strongly integrated with the constructed approaches. Thus, the research meets the above-mentioned purposes and objectives of the dissertation from the scientific as well as from the practical point of view.

Converter-flux-based current control of voltage source PWM rectifiers - analysis and implementation

Pulsewidth-modulated (PWM) rectifier technology is increasingly used in industrial applications like variable-speed motor drives, since it offers several desired features such as sinusoidal input currents, controllable power factor, bidirectional power flow and high quality DC output voltage. To achieve these features,however, an effective control system with fast and accurate current and DC voltage responses is required. From various control strategies proposed to meet these control objectives, in most cases the commonly known principle of the synchronous-frame current vector control along with some space-vector PWM scheme have been applied. Recently, however, new control approaches analogous to the well-established direct torque control (DTC) method for electrical machines have also emerged to implement a high-performance PWM rectifier. In this thesis the concepts of classical synchronous-frame current control and DTC-based PWM rectifier control are combined and a new converter-flux-based current control (CFCC) scheme is introduced. To achieve sufficient dynamic performance and to ensure a stable operation, the proposed control system is thoroughly analysed and simple rules for the controller design are suggested. Special attention is paid to the estimationof the converter flux, which is the key element of converter-flux-based control. Discrete-time implementation is also discussed. Line-voltage-sensorless reactive reactive power control methods for the L- and LCL-type line filters are presented. For the L-filter an open-loop control law for the d-axis current referenceis proposed. In the case of the LCL-filter the combined open-loop control and feedback control is proposed. The influence of the erroneous filter parameter estimates on the accuracy of the developed control schemes is also discussed. A newzero vector selection rule for suppressing the zero-sequence current in parallel-connected PWM rectifiers is proposed. With this method a truly standalone and independent control of the converter units is allowed and traditional transformer isolation and synchronised-control-based solutions are avoided. The implementation requires only one additional current sensor. The proposed schemes are evaluated by the simulations and laboratory experiments. A satisfactory performance and good agreement between the theory and practice are demonstrated.

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.

Permanent magnet synchronous motor for industrial inverter applications - analysis and design

During the latest few years the need for new motor types has grown, since both high efficiency and an accurate dynamic performance are demanded in industrial applications. For this reason, new effective control systems such as direct torque control (DTC) have been developed. Permanent magnet synchronous motors (PMSM) are well suitable for new adjustable speed AC inverter drives, because their efficiency and power factor are not depending on the pole pair number and speed to the same extent as it is the case in induction motors. Therefore, an induction motor (IM) with a mechanical gearbox can often be replaced with a direct PM motor drive. Space as well as costs will be saved, because the efficiency increases and the cost of maintenance decreases as well. This thesis deals with design criterion, analytical calculation and analysis of the permanent magnet synchronous motor for both sinusoidal air-gap flux density and rectangular air-gapflux density. It is examined how the air-gap flux, flux densities, inductances and torque can be estimated analytically for salient pole and non-salient pole motors. It has been sought by means of analytical calculations for the ultimate construction for machines rotating at relative low 300 rpm to 600 rpm speeds, which are suitable speeds e.g. in Pulp&Paper industry. The calculations are verified by using Finite Element calculations and by measuring of prototype motor. The prototype motor is a 45 kW, 600 rpm PMSM with buried V-magnets, which is a very appropriate construction for high torque motors with a high performance. With the purposebuilt prototype machine it is possible not only to verify the analytical calculations but also to show whether the 600 rpm PMSM can replace the 1500 rpm IM with a gear. It can also be tested if the outer dimensions of the PMSM may be the same as for the IM and if the PMSM in this case can produce a 2.5 fold torque, in consequence of which it may be possible to achieve the same power. The thesis also considers the question how to design a permanent magnet synchronous motor for relatively low speed applications that require a high motor torqueand efficiency as well as bearable costs of permanent magnet materials. It is shown how a selection of different parameters affects the motor properties. Key words: Permanent magnet synchronous motor, PMSM, surface magnets, buried magnets

Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models

Background: Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Results: Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity. Conclusions: Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task.

Research resource: the dynamic transcriptional profile of sertoli cells during the progression of spermatogenesis.

Sertoli cells (SCs), the only somatic cells within seminiferous tubules, associate intimately with developing germ cells. They not only provide physical and nutritional support but also secrete factors essential to the complex developmental processes of germ cell proliferation and differentiation. The SC transcriptome must therefore adapt rapidly during the different stages of spermatogenesis. We report comprehensive genome-wide expression profiles of pure populations of SCs isolated at 5 distinct stages of the first wave of mouse spermatogenesis, using RNA sequencing technology. We were able to reconstruct about 13 901 high-confidence, nonredundant coding and noncoding transcripts, characterized by complex alternative splicing patterns with more than 45% comprising novel isoforms of known genes. Interestingly, roughly one-fifth (2939) of these genes exhibited a dynamic expression profile reflecting the evolving role of SCs during the progression of spermatogenesis, with stage-specific expression of genes involved in biological processes such as cell cycle regulation, metabolism and energy production, retinoic acid synthesis, and blood-testis barrier biogenesis. Finally, regulatory network analysis identified the transcription factors endothelial PAS domain-containing protein 1 (EPAS1/Hif2α), aryl hydrocarbon receptor nuclear translocator (ARNT/Hif1β), and signal transducer and activator of transcription 1 (STAT1) as potential master regulators driving the SC transcriptional program. Our results highlight the plastic transcriptional landscape of SCs during the progression of spermatogenesis and provide valuable resources to better understand SC function and spermatogenesis and its related disorders, such as male infertility.

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.

Family Size Evolution in Drosophila Chemosensory Gene Families: A Comparative Analysis with a Critical Appraisal of Methods

Gene turnover rates and the evolution of gene family sizes are important aspects of genome evolution. Here, we use curated sequence data of the major chemosensory gene families from Drosophila-the gustatory receptor, odorant receptor, ionotropic receptor, and odorant-binding protein families-to conduct a comparative analysis among families, exploring different methods to estimate gene birth and death rates, including an ad hoc simulation study. Remarkably, we found that the state-of-the-art methods may produce very different rate estimates, which may lead to disparate conclusions regarding the evolution of chemosensory gene family sizes in Drosophila. Among biological factors, we found that a peculiarity of D. sechellia's gene turnover rates was a major source of bias in global estimates, whereas gene conversion had negligible effects for the families analyzed herein. Turnover rates vary considerably among families, subfamilies, and ortholog groups although all analyzed families were quite dynamic in terms of gene turnover. Computer simulations showed that the methods that use ortholog group information appear to be the most accurate for the Drosophila chemosensory families. Most importantly, these results reveal the potential of rate heterogeneity among lineages to severely bias some turnover rate estimation methods and the need of further evaluating the performance of these methods in a more diverse sampling of gene families and phylogenetic contexts. Using branch-specific codon substitution models, we find further evidence of positive selection in recently duplicated genes, which attests to a nonneutral aspect of the gene birth-and-death process.