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.

A measure of stability as a criterion for the verification and analysis of simulation models

The aim of this study is to define a new statistic, PVL, based on the relative distance between the likelihood associated with the simulation replications and the likelihood of the conceptual model. Our results coming from several simulation experiments of a clinical trial show that the PVL statistic range can be a good measure of stability to establish when a computational model verifies the underlying conceptual model. PVL improves also the analysis of simulation replications because only one statistic is associated with all the simulation replications. As well it presents several verification scenarios, obtained by altering the simulation model, that show the usefulness of PVL. Further simulation experiments suggest that a 0 to 20 % range may define adequate limits for the verification problem, if considered from the viewpoint of an equivalence test.

Front Speed of Language Replacement

We use two coupled equations to analyze the space-time dynamics of two interacting languages. Firstly, we introduce a cohabitation model, which is more appropriate for human populations than classical (non-cohabitation) models. Secondly, using numerical simulations we nd the front speed of a new language spreading into a region where another language was previously used. Thirdly, for a special case we derive an analytical formula that makes it possible to check the validity of our numerical simulations. Finally, as an example, we nd that the observed front speed for the spread of the English language into Wales in the period 1961-1981 is consistent with the model predictions. We also nd that the e¤ects of linguistic parameters are much more important than those of parameters related to population dispersal and reproduction. If the initial population densities of both languages are similar, they have no e¤ect on the front speed. We outline the potential of the new model to analyze relationships between language replacement and genetic replacement

The internal wave field in Sau reservoir : Observation and modeling of a third vertical mode

Water withdrawal from Mediterranean reservoirs in summer is usually very high. Because of this, stratification is often continuous and far from the typical two-layered structure, favoring the excitation of higher vertical modes. The analysis of wind, temperature, and current data from Sau reservoir (Spain) shows that the third vertical mode of the internal seiche (baroclinic mode) dominated the internal wave field at the beginning of September 2003. We used a continuous stratification two-dimensional model to calculate the period and velocity distribution of the various modes of the internal seiche, and we calculated that the period of the third vertical mode is ;24 h, which coincides with the period of the dominating winds. As a result of the resonance between the third mode and the wind, the other oscillation modes were not excited during this period

The seasonal evolution of high vertical–mode internal waves in a deep reservoir

The causal mechanism and seasonal evolution of the internal wave field in a deep, warm, monomictic reservoirare examined through the analysis of field observations and numerical techniques. The study period extends fromthe onset of thermal stratification in the spring until midsummer in 2005. During this time, wind forcing wasperiodic, with a period of 24 h (typical of land–sea breezes), and the thermal structure in the lake wascharacterized by the presence of a shallow surface layer overlying a thick metalimnion, typical of small to mediumsized reservoirs with deep outtakes. Basin-scale internal seiches of high vertical mode (ranging from mode V3 toV5) were observed in the metalimnion. The structure of the dominant modes of oscillation changed asstratification evolved on seasonal timescales, but in all cases, their periods were close to that of the local windforcing (i.e., 24 h), suggesting a resonant response. Nonresonant oscillatory modes of type V1 and V2 becamedominant after large frontal events, which disrupted the diurnal periodicity of the wind forcing

The permanence of the client under uncertain estimations

Marketing has studied the permanence of a client within an enterprise because it is a key element in the study of the value (economic) of the client (CLV). The research that they have developed is based in deterministic or random models, which allowed estimating the permanence of the client, and the CLV. However, when it is not possible to apply these schemes for not having the panel data that this model requires, the period of time of a client with the enterprise is uncertain data. We consider that the value of the current work is to have an alternative way to estimate the period of time with subjective information proper of the theory of uncertainty.

Estimation of age- and stage-specific Catalan breast cancer survival functions using US and Catalan survival data

During the last part of the 1990s the chance of surviving breast cancer increased. Changes in survival functions reflect a mixture of effects. Both, the introduction of adjuvant treatments and early screening with mammography played a role in the decline in mortality. Evaluating the contribution of these interventions using mathematical models requires survival functions before and after their introduction. Furthermore, required survival functions may be different by age groups and are related to disease stage at diagnosis. Sometimes detailed information is not available, as was the case for the region of Catalonia (Spain). Then one may derive the functions using information from other geographical areas. This work presents the methodology used to estimate age- and stage-specific Catalan breast cancer survival functions from scarce Catalan survival data by adapting the age- and stage-specific US functions. Methods: Cubic splines were used to smooth data and obtain continuous hazard rate functions. After, we fitted a Poisson model to derive hazard ratios. The model included time as a covariate. Then the hazard ratios were applied to US survival functions detailed by age and stage to obtain Catalan estimations. Results: We started estimating the hazard ratios for Catalonia versus the USA before and after the introduction of screening. The hazard ratios were then multiplied by the age- and stage-specific breast cancer hazard rates from the USA to obtain the Catalan hazard rates. We also compared breast cancer survival in Catalonia and the USA in two time periods, before cancer control interventions (USA 1975–79, Catalonia 1980–89) and after (USA and Catalonia 1990–2001). Survival in Catalonia in the 1980–89 period was worse than in the USA during 1975–79, but the differences disappeared in 1990–2001. Conclusion: Our results suggest that access to better treatments and quality of care contributed to large improvements in survival in Catalonia. On the other hand, we obtained detailed breast cancer survival functions that will be used for modeling the effect of screening and adjuvant treatments in Catalonia

A comparison of electricity spot prices simulation using ARMA-GARCH and mean-reverting models

The aim of this work is to compare two families of mathematical models for their respective capability to capture the statistical properties of real electricity spot market time series. The first model family is ARMA-GARCH models and the second model family is mean-reverting Ornstein-Uhlenbeck models. These two models have been applied to two price series of Nordic Nord Pool spot market for electricity namely to the System prices and to the DenmarkW prices. The parameters of both models were calibrated from the real time series. After carrying out simulation with optimal models from both families we conclude that neither ARMA-GARCH models, nor conventional mean-reverting Ornstein-Uhlenbeck models, even when calibrated optimally with real electricity spot market price or return series, capture the statistical characteristics of the real series. But in the case of less spiky behavior (System prices), the mean-reverting Ornstein-Uhlenbeck model could be seen to partially succeeded in this task.

Models and applications for risk assessment and prediction of Asian soybean rust epidemics

Asian rust of soybean [Glycine max (L.) Merril] is one of the most important fungal diseases of this crop worldwide. The recent introduction of Phakopsora pachyrhizi Syd. & P. Syd in the Americas represents a major threat to soybean production in the main growing regions, and significant losses have already been reported. P. pachyrhizi is extremely aggressive under favorable weather conditions, causing rapid plant defoliation. Epidemiological studies, under both controlled and natural environmental conditions, have been done for several decades with the aim of elucidating factors that affect the disease cycle as a basis for disease modeling. The recent spread of Asian soybean rust to major production regions in the world has promoted new development, testing and application of mathematical models to assess the risk and predict the disease. These efforts have included the integration of new data, epidemiological knowledge, statistical methods, and advances in computer simulation to develop models and systems with different spatial and temporal scales, objectives and audience. In this review, we present a comprehensive discussion on the models and systems that have been tested to predict and assess the risk of Asian soybean rust. Limitations, uncertainties and challenges for modelers are also discussed.

Mathematical model to estimate of the deterioration of wooden poles in contact with soil used in rural areas

In São Paulo State, mainly in rural areas, the utilization of wooden poles is observed for different purposes. In this context, wood in contact with the ground presents faster deterioration, which is generally associated to environmental factors and, especially to the presence of fungi and insects. With the use of mathematical models, the useful life of wooden structures can be predicted by obtaining "climatic indexes" to indicate, comparatively among the areas studied, which have more or less tendency to fungi and insects attacks. In this work, by using climatological data of several cities at São Paulo State, a simplified mathematical model was obtained to measure the aggressiveness of the wood in contact with the soil.

Adjust of regression models to estimate the rectal temperature of broilers for the first 14 days of life

The broiler rectal temperature (t rectal) is one of the most important physiological responses to classify the animal thermal comfort. Therefore, the aim of this study was to adjust regression models in order to predict the rectal temperature (t rectal) of broiler chickens under different thermal conditions based on age (A) and a meteorological variable (air temperature - t air) or a thermal comfort index (temperature and humidity index -THI or black globe humidity index - BGHI) or a physical quantity enthalpy (H). In addition, through the inversion of these models and the expected t rectal intervals for each age, the comfort limits of t air, THI, BGHI and H for the chicks in the heating phase were determined, aiding in the validation of the equations and the preliminary limits for H. The experimental data used to adjust the mathematical models were collected in two commercial poultry farms, with Cobb chicks, from 1 to 14 days of age. It was possible to predict the t rectal of conditions from the expected t rectal and determine the lower and superior comfort thresholds of broilers satisfactorily by applying the four models adjusted; as well as to invert the models for prediction of the environmental H for the chicks first 14 days of life.

Draft prediction models for soil engaging tines in two soils of Rio Grande do Sul, Brazil

The draft forces of soil engaging tines and theoretical analysis compared to existing mathematical models, have yet not been studied in Rio Grande do Sul soils. From the existing models, those which can get the closest fitting draft forces to real measure on field have been established for two of Rio Grande do Sul soils. An Albaqualf and a Paleudult were evaluated. From the studied models, those suggested by Reece, so called "Universal Earthmoving Equation", Hettiaratchi and Reece, and Godwin and Spoor were the best fitting ones, comparing the calculated results with those measured "in situ". Allowing for the less complexity of Reece's model, it is suggested that this model should be used for modeling draft forces prediction for narrow tines in Albaqualf and Paleudut.

Mathematical modeling applied to the growth of tilapia in net cages in the sub middle of the São Francisco river

This study aimed to apply mathematical models to the growth of Nile tilapia (Oreochromis niloticus) reared in net cages in the lower São Francisco basin and choose the model(s) that best represents the conditions of rearing for the region. Nonlinear models of Brody, Bertalanffy, Logistic, Gompertz, and Richards were tested. The models were adjusted to the series of weight for age according to the methods of Gauss, Newton, Gradiente and Marquardt. It was used the procedure "NLIN" of the System SAS® (2003) to obtain estimates of the parameters from the available data. The best adjustment of the data were performed by the Bertalanffy, Gompertz and Logistic models which are equivalent to explain the growth of the animals up to 270 days of rearing. From the commercial point of view, it is recommended that commercialization of tilapia from at least 600 g, which is estimated in the Bertalanffy, Gompertz and Logistic models for creating over 183, 181 and 184 days, and up to 1 Kg of mass , it is suggested the suspension of the rearing up to 244, 244 and 243 days, respectively.

Linguistic models for decision support

Linguistic modelling is a rather new branch of mathematics that is still undergoing rapid development. It is closely related to fuzzy set theory and fuzzy logic, but knowledge and experience from other fields of mathematics, as well as other fields of science including linguistics and behavioral sciences, is also necessary to build appropriate mathematical models. This topic has received considerable attention as it provides tools for mathematical representation of the most common means of human communication - natural language. Adding a natural language level to mathematical models can provide an interface between the mathematical representation of the modelled system and the user of the model - one that is sufficiently easy to use and understand, but yet conveys all the information necessary to avoid misinterpretations. It is, however, not a trivial task and the link between the linguistic and computational level of such models has to be established and maintained properly during the whole modelling process. In this thesis, we focus on the relationship between the linguistic and the mathematical level of decision support models. We discuss several important issues concerning the mathematical representation of meaning of linguistic expressions, their transformation into the language of mathematics and the retranslation of mathematical outputs back into natural language. In the first part of the thesis, our view of the linguistic modelling for decision support is presented and the main guidelines for building linguistic models for real-life decision support that are the basis of our modeling methodology are outlined. From the theoretical point of view, the issues of representation of meaning of linguistic terms, computations with these representations and the retranslation process back into the linguistic level (linguistic approximation) are studied in this part of the thesis. We focus on the reasonability of operations with the meanings of linguistic terms, the correspondence of the linguistic and mathematical level of the models and on proper presentation of appropriate outputs. We also discuss several issues concerning the ethical aspects of decision support - particularly the loss of meaning due to the transformation of mathematical outputs into natural language and the issue or responsibility for the final decisions. In the second part several case studies of real-life problems are presented. These provide background and necessary context and motivation for the mathematical results and models presented in this part. A linguistic decision support model for disaster management is presented here – formulated as a fuzzy linear programming problem and a heuristic solution to it is proposed. Uncertainty of outputs, expert knowledge concerning disaster response practice and the necessity of obtaining outputs that are easy to interpret (and available in very short time) are reflected in the design of the model. Saaty’s analytic hierarchy process (AHP) is considered in two case studies - first in the context of the evaluation of works of art, where a weak consistency condition is introduced and an adaptation of AHP for large matrices of preference intensities is presented. The second AHP case-study deals with the fuzzified version of AHP and its use for evaluation purposes – particularly the integration of peer-review into the evaluation of R&D outputs is considered. In the context of HR management, we present a fuzzy rule based evaluation model (academic faculty evaluation is considered) constructed to provide outputs that do not require linguistic approximation and are easily transformed into graphical information. This is achieved by designing a specific form of fuzzy inference. Finally the last case study is from the area of humanities - psychological diagnostics is considered and a linguistic fuzzy model for the interpretation of outputs of multidimensional questionnaires is suggested. The issue of the quality of data in mathematical classification models is also studied here. A modification of the receiver operating characteristics (ROC) method is presented to reflect variable quality of data instances in the validation set during classifier performance assessment. Twelve publications on which the author participated are appended as a third part of this thesis. These summarize the mathematical results and provide a closer insight into the issues of the practicalapplications that are considered in the second part of the thesis.

Mathematical modeling and optimal control of malaria

Malaria continues to infect millions and kill hundreds of thousands of people worldwide each year, despite over a century of research and attempts to control and eliminate this infectious disease. Challenges such as the development and spread of drug resistant malaria parasites, insecticide resistance to mosquitoes, climate change, the presence of individuals with subpatent malaria infections which normally are asymptomatic and behavioral plasticity in the mosquito hinder the prospects of malaria control and elimination. In this thesis, mathematical models of malaria transmission and control that address the role of drug resistance, immunity, iron supplementation and anemia, immigration and visitation, and the presence of asymptomatic carriers in malaria transmission are developed. A within-host mathematical model of severe Plasmodium falciparum malaria is also developed. First, a deterministic mathematical model for transmission of antimalarial drug resistance parasites with superinfection is developed and analyzed. The possibility of increase in the risk of superinfection due to iron supplementation and fortification in malaria endemic areas is discussed. The model results calls upon stakeholders to weigh the pros and cons of iron supplementation to individuals living in malaria endemic regions. Second, a deterministic model of transmission of drug resistant malaria parasites, including the inflow of infective immigrants, is presented and analyzed. The optimal control theory is applied to this model to study the impact of various malaria and vector control strategies, such as screening of immigrants, treatment of drug-sensitive infections, treatment of drug-resistant infections, and the use of insecticide-treated bed nets and indoor spraying of mosquitoes. The results of the model emphasize the importance of using a combination of all four controls tools for effective malaria intervention. Next, a two-age-class mathematical model for malaria transmission with asymptomatic carriers is developed and analyzed. In development of this model, four possible control measures are analyzed: the use of long-lasting treated mosquito nets, indoor residual spraying, screening and treatment of symptomatic, and screening and treatment of asymptomatic individuals. The numerical results show that a disease-free equilibrium can be attained if all four control measures are used. A common pitfall for most epidemiological models is the absence of real data; model-based conclusions have to be drawn based on uncertain parameter values. In this thesis, an approach to study the robustness of optimal control solutions under such parameter uncertainty is presented. Numerical analysis of the optimal control problem in the presence of parameter uncertainty demonstrate the robustness of the optimal control approach that: when a comprehensive control strategy is used the main conclusions of the optimal control remain unchanged, even if inevitable variability remains in the control profiles. The results provide a promising framework for the design of cost-effective strategies for disease control with multiple interventions, even under considerable uncertainty of model parameters. Finally, a separate work modeling the within-host Plasmodium falciparum infection in humans is presented. The developed model allows re-infection of already-infected red blood cells. The model hypothesizes that in severe malaria due to parasite quest for survival and rapid multiplication, the Plasmodium falciparum can be absorbed in the already-infected red blood cells which accelerates the rupture rate and consequently cause anemia. Analysis of the model and parameter identifiability using Markov chain Monte Carlo methods is presented.