A mathematical model for malaria transmission relating global warming and local socioeconomic conditions

OBJECTIVE: Sensitivity analysis was applied to a mathematical model describing malaria transmission relating global warming and local socioeconomic conditions. METHODS: A previous compartment model was proposed to describe the overall transmission of malaria. This model was built up on several parameters and the prevalence of malaria in a community was characterized by the values assigned to them. To assess the control efforts, the model parameters can vary on broad intervals. RESULTS: By performing the sensitivity analysis on equilibrium points, which represent the level of malaria infection in a community, the different possible scenarios are obtained when the parameters are changed. CONCLUSIONS: Depending on malaria risk, the efforts to control its transmission can be guided by a subset of parameters used in the mathematical model.

Utilização de redes neuronais artificiais na gestão de processos de digestão anaeróbia

Numa Estação de Tratamento de Águas Residuais (ETAR), a otimização do processo de Digestão Anaeróbia (DA) é fundamental para o aumento da produção de biogás, que por sua vez é convertido em energia, essencial para a rentabilidade de exploração de ETAR. No entanto, a complexidade do processo de Digestão Anaeróbia das lamas constitui um obstáculo à sua otimização. Com este trabalho pretende-se efetuar a análise e tratamento de dados de Digestão Anaeróbia, com recurso a Redes Neuronais Artificiais (RNA), contribuindo, desta forma, para a compreensão do processo e do impacto de algumas variáveis na produção de biogás. As Redes Neuronais Artificiais são modelos matemáticos computacionais inspirados no funcionamento do cérebro humano, com capacidade para entender relações complexas num determinado conjunto de dados, motivo por que se optou pela sua utilização na procura de soluções que permitem predizer o comportamento de uma DA. Para o desenvolvimento das RNA utilizou-se o programa NeuralToolsTM da PalisadeTM. Como caso de estudo, a metodologia foi aplicada ao Digestor A da ETAR Sul da SIMRIA, empresa onde teve lugar o estágio curricular que originou o presente trabalho. Nesse contexto, utilizaram-se dados com informação referente aos últimos dois anos de funcionamento do digestor, disponíveis na empresa. Apesar de se terem verificado certas limitações, na predição em alguns casos particulares, de um modo geral, considera-se que os resultados obtidos permitiram concluir que as redes neuronais modeladas apresentam boa capacidade de generalização na imitação do processo anaeróbio. Conclui-se, portanto, que o estudo realizado pode constituir um contributo com interesse para a otimização da produção do biogás na DA de ETAR Sul da SIMRIA e que a utilização de RNA poderá ser uma ferramenta a explorar, quer nessa área, quer noutras áreas de gestão de sistemas de saneamento básico.

Mathematical model for HIV dynamics in HIV-specific helper cells

In this paper we study a delay mathematical model for the dynamics of HIV in HIV-specific CD4 + T helper cells. We modify the model presented by Roy and Wodarz in 2012, where the HIV dynamics is studied, considering a single CD4 + T cell population. Non-specific helper cells are included as alternative target cell population, to account for macrophages and dendritic cells. In this paper, we include two types of delay: (1) a latent period between the time target cells are contacted by the virus particles and the time the virions enter the cells and; (2) virus production period for new virions to be produced within and released from the infected cells. We compute the reproduction number of the model, R0, and the local stability of the disease free equilibrium and of the endemic equilibrium. We find that for values of R0<1, the model approaches asymptotically the disease free equilibrium. For values of R0>1, the model approximates asymptotically the endemic equilibrium. We observe numerically the phenomenon of backward bifurcation for values of R0⪅1. This statement will be proved in future work. We also vary the values of the latent period and the production period of infected cells and free virus. We conclude that increasing these values translates in a decrease of the reproduction number. Thus, a good strategy to control the HIV virus should focus on drugs to prolong the latent period and/or slow down the virus production. These results suggest that the model is mathematically and epidemiologically well-posed.

Compartmentalized Cerebral Metabolism of [1,6-(13)C]Glucose Determined by in vivo (13)C NMR Spectroscopy at 14.1 T.

Cerebral metabolism is compartmentalized between neurons and glia. Although glial glycolysis is thought to largely sustain the energetic requirements of neurotransmission while oxidative metabolism takes place mainly in neurons, this hypothesis is matter of debate. The compartmentalization of cerebral metabolic fluxes can be determined by (13)C nuclear magnetic resonance (NMR) spectroscopy upon infusion of (13)C-enriched compounds, especially glucose. Rats under light α-chloralose anesthesia were infused with [1,6-(13)C]glucose and (13)C enrichment in the brain metabolites was measured by (13)C NMR spectroscopy with high sensitivity and spectral resolution at 14.1 T. This allowed determining (13)C enrichment curves of amino acid carbons with high reproducibility and to reliably estimate cerebral metabolic fluxes (mean error of 8%). We further found that TCA cycle intermediates are not required for flux determination in mathematical models of brain metabolism. Neuronal tricarboxylic acid cycle rate (V(TCA)) and neurotransmission rate (V(NT)) were 0.45 ± 0.01 and 0.11 ± 0.01 μmol/g/min, respectively. Glial V(TCA) was found to be 38 ± 3% of total cerebral oxidative metabolism, accounting for more than half of neuronal oxidative metabolism. Furthermore, glial anaplerotic pyruvate carboxylation rate (V(PC)) was 0.069 ± 0.004 μmol/g/min, i.e., 25 ± 1% of the glial TCA cycle rate. These results support a role of glial cells as active partners of neurons during synaptic transmission beyond glycolytic metabolism.

Stem cell transplantation in brain tumors: a new field for molecular imaging?

Neural stem cells have been proposed as a new and promising treatment modality in various pathologies of the central nervous system, including malignant brain tumors. However, the underlying mechanism by which neural stem cells target tumor areas remains elusive. Monitoring of these cells is currently done by use of various modes of molecular imaging, such as optical imaging, magnetic resonance imaging and positron emission tomography, which is a novel technology for visualizing metabolism and signal transduction to gene expression. In this new context, the microenvironment of (malignant) brain tumors and the blood-brain barrier gains increased interest. The authors of this review give a unique overview of the current molecular-imaging techniques used in different therapeutic experimental brain tumor models in relation to neural stem cells. Such methods for molecular imaging of gene-engineered neural stem/progenitor cells are currently used to trace the location and temporal level of expression of therapeutic and endogenous genes in malignant brain tumors, closing the gap between in vitro and in vivo integrative biology of disease in neural stem cell transplantation.

Study and implementation of some quantitative trading models

Quantitative or algorithmic trading is the automatization of investments decisions obeying a fixed or dynamic sets of rules to determine trading orders. It has increasingly made its way up to 70% of the trading volume of one of the biggest financial markets such as the New York Stock Exchange (NYSE). However, there is not a signi cant amount of academic literature devoted to it due to the private nature of investment banks and hedge funds. This projects aims to review the literature and discuss the models available in a subject that publications are scarce and infrequently. We review the basic and fundamental mathematical concepts needed for modeling financial markets such as: stochastic processes, stochastic integration and basic models for prices and spreads dynamics necessary for building quantitative strategies. We also contrast these models with real market data with minutely sampling frequency from the Dow Jones Industrial Average (DJIA). Quantitative strategies try to exploit two types of behavior: trend following or mean reversion. The former is grouped in the so-called technical models and the later in the so-called pairs trading. Technical models have been discarded by financial theoreticians but we show that they can be properly cast into a well defined scientific predictor if the signal generated by them pass the test of being a Markov time. That is, we can tell if the signal has occurred or not by examining the information up to the current time; or more technically, if the event is F_t-measurable. On the other hand the concept of pairs trading or market neutral strategy is fairly simple. However it can be cast in a variety of mathematical models ranging from a method based on a simple euclidean distance, in a co-integration framework or involving stochastic differential equations such as the well-known Ornstein-Uhlenbeck mean reversal ODE and its variations. A model for forecasting any economic or financial magnitude could be properly defined with scientific rigor but it could also lack of any economical value and be considered useless from a practical point of view. This is why this project could not be complete without a backtesting of the mentioned strategies. Conducting a useful and realistic backtesting is by no means a trivial exercise since the \laws" that govern financial markets are constantly evolving in time. This is the reason because we make emphasis in the calibration process of the strategies' parameters to adapt the given market conditions. We find out that the parameters from technical models are more volatile than their counterpart form market neutral strategies and calibration must be done in a high-frequency sampling manner to constantly track the currently market situation. As a whole, the goal of this project is to provide an overview of a quantitative approach to investment reviewing basic strategies and illustrating them by means of a back-testing with real financial market data. The sources of the data used in this project are Bloomberg for intraday time series and Yahoo! for daily prices. All numeric computations and graphics used and shown in this project were implemented in MATLAB^R scratch from scratch as a part of this thesis. No other mathematical or statistical software was used.

Epidemic models with an infected-infectious period

The introduction of an infective-infectious period on the geographic spread of epidemics is considered in two different models. The classical evolution equations arising in the literature are generalized and the existence of epidemic wave fronts is revised. The asymptotic speed is obtained and improves previous results for the Black Death plague

Exactly solvable phase oscillator models with syncrhonization dynamics

Populations of phase oscillators interacting globally through a general coupling function f(x) have been considered. We analyze the conditions required to ensure the existence of a Lyapunov functional giving close expressions for it in terms of a generating function. We have also proposed a family of exactly solvable models with singular couplings showing that it is possible to map the synchronization phenomenon into other physical problems. In particular, the stationary solutions of the least singular coupling considered, f(x) = sgn(x), have been found analytically in terms of elliptic functions. This last case is one of the few nontrivial models for synchronization dynamics which can be analytically solved.

Evaluation of uptake and transport of ultrasmall superparamagnetic iron oxide nanoparticles by human brain-derived endothelial cells.

Aim: Ultrasmall superparamagnetic iron oxide nanoparticles (USPIO-NPs) are under development for imaging and drug delivery; however, their interaction with human blood-brain barrier models is not known. Materials & Methods: The uptake, reactive oxygen species production and transport of USPIO-NPs across human brain-derived endothelial cells as models of the blood-brain tumor barrier were evaluated for either uncoated, oleic acid-coated or polyvinylamine-coated USPIO-NPs. Results: Reactive oxygen species production was observed for oleic acid-coated and polyvinylamine-coated USPIO-NPs. The uptake and intracellular localization of the iron oxide core of the USPIO-NPs was confirmed by transmission electron microscopy. However, while the uptake of these USPIO-NPs by cells was observed, they were neither released by nor transported across these cells even in the presence of an external dynamic magnetic field. Conclusion: USPIO-NP-loaded filopodia were observed to invade the polyester membrane, suggesting that they can be transported by migrating angiogenic brain-derived endothelial cells.

Dynamic models of viral replication and latency.

PURPOSE OF REVIEW: HIV targets primary CD4(+) T cells. The virus depends on the physiological state of its target cells for efficient replication, and, in turn, viral infection perturbs the cellular state significantly. Identifying the virus-host interactions that drive these dynamic changes is important for a better understanding of viral pathogenesis and persistence. The present review focuses on experimental and computational approaches to study the dynamics of viral replication and latency. RECENT FINDINGS: It was recently shown that only a fraction of the inducible latently infected reservoirs are successfully induced upon stimulation in ex-vivo models while additional rounds of stimulation make allowance for reactivation of more latently infected cells. This highlights the potential role of treatment duration and timing as important factors for successful reactivation of latently infected cells. The dynamics of HIV productive infection and latency have been investigated using transcriptome and proteome data. The cellular activation state has shown to be a major determinant of viral reactivation success. Mathematical models of latency have been used to explore the dynamics of the latent viral reservoir decay. SUMMARY: Timing is an important component of biological interactions. Temporal analyses covering aspects of viral life cycle are essential for gathering a comprehensive picture of HIV interaction with the host cell and untangling the complexity of latency. Understanding the dynamic changes tipping the balance between success and failure of HIV particle production might be key to eradicate the viral reservoir.

Application of theoretical models to financial innovation

The present paper is aimed at providing a general strategic overview of the existing theoretical models that have applications in the field of financial innovation. Whereas most financialdevelopments have relied upon traditional economic tools, a new stream of research is defining a novel paradigm in which mathematical models from diverse scientific disciplines are being applied to conceptualize and explain economic and financial behavior. Indeed, terms such as ‘econophysics’ or ‘quantum finance’ have recently appeared to embrace efforts in this direction. As a first contact with such research, the project will present a brief description of some of the main theoretical models that have applications in finance and economics, and will try to present, if possible, potential new applications to particular areas in financial analysis, or new applicable models. As a result, emphasiswill be put on the implications of this research for the financial sector and its future dynamics.

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.

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.

Cyclosporine A kinetics in brain cell cultures and its potential of crossing the blood-brain barrier.

There is an increasing need to develop improved systems for predicting the safety of xenobiotics. However, to move beyond hazard identification the available concentration of the test compounds needs to be incorporated. In this study cyclosporine A (CsA) was used as a model compound to assess the kinetic profiles in two rodent brain cell cultures after single and repeated exposures. CsA induced-cyclophilin B (Cyp-B) secretion was also determined as CsA-specific pharmacodynamic endpoint. Since CsA is a potent p-glycoprotein substrate, the ability of this compound to cross the blood-brain barrier (BBB) was also investigated using an in vitro bovine model with repeated exposures up to 14days. Finally, CsA uptake mechanisms were studied using a parallel artificial membrane assay (PAMPA) in combination with a Caco-2 model. Kinetic results indicate a low intracellular CsA uptake, with no marked bioaccumulation or biotransformation. In addition, only low CsA amounts crossed the BBB. PAMPA and Caco-2 experiments revealed that CsA is mostly trapped to lipophilic compartments and exits the cell apically via active transport. Thus, although CsA is unlikely to enter the brain at cytotoxic concentrations, it may cause alterations in electrical activity and is likely to increase the CNS concentration of other compounds by occupying the BBBs extrusion capacity. Such an integrated testing system, incorporating BBB, brain culture models and kinetics could be applied for assessing neurotoxicity potential of compounds.