Crystallization of selected anions and cations from mine waters

The aim of this Master’s thesis was to review some methods that are already being utilized in a field of mine water purification and to find and study possible new methods and chemicals for mine water purification by precipitation. The target was also to list the optimal process conditions for these precipitating chemicals. Separation methods were reviewed for several anions and cations, but being a real topical issue, sulphate removal was selected to be in the main focus. Sulphate salts e.g. Na2SO4 are relatively soluble in water, which makes the separation processes difficult. Eutectic freeze crystallization was studied more closely in laboratory tests for sodium sulphate removal. Gravimetric solubility tests were made for three cases of mixed electrolyte solutions: Na2SO4 – NaOH, BaSO4 – NaOH and Na3PO4 – NaOH. The aim of these experiments was to study the effect of NaOH addition on solubility of the studied salt. These phenomena were however noticed to be difficult to see in the used laboratory tests. Thus mathematical modelling was utilized to contribute the laboratory experiments and to bring additional information of the influence of NaOH presence on solubility of selected electrolytes, Na2SO4 and Na3PO4. The results from mathematical modelling of activity coefficients suggest Na2SO4 and Na3PO4 to be precipitated rather with presence and with higher concentrations of NaOH, since the raise of NaOH concentration decreases the solubility of these electrolytes in water.

Applications and modelling in mathematics teaching

The aim of this paper is a comprehensive presentation of some important basic and general aspects of the topic applications and modelling, with emphasis on the secondary school level. Owing to the review character of this paper, some overlap with the survey paper Blum and Niss (1989) for ICME-6 in Budapest is inevitable. The paper will consist of three parts. In part 1, I shall try to clarify some basic concepts and remind the reader of a few application and modelling examples suitable for teaching. In part 2, I shall formulate some general aims for mathematics instruction and, on that basis, summarise the most important arguments for and against applications and modelling in mathematics teaching. Finally, in part 3, I shall discuss some relevant instructional aspects resulting from the considerations in part 2.

Avaliação da função de barreira da pele pela análise Bi-compartimental de medições dinâmincas da PTEA : validação de novas condições analíticas

Neste trabalho é revista uma metodologia baseada na modelação matemática de dados de perda transepidérmica de água (PTEA) após a realização de um plastic occlusion stress test (POST), para avaliar a dinâmica hídrica cutânea através de parâmetros cinéticos. Embora simples de executar, esta metodologia consome muito tempo, uma vez que normalmente envolve a recolha de dados durante, pelo menos, 30 minutos. Esta investigação tem como objectivo optimizar o protocolo, reduzindo o tempo total da experiência através da recolha de mais pontos na fase inicial do estudo.Foi possível reduzir significativamente o tempo de análise, o que se torna vantajoso tanto para os investigadores, como para os voluntários, uma vez que, por um lado, há redução dos custos de investigação, bem como se assegura o conforto dos participantes no estudo.

Robustness and applicability of Markov chain Monte Carlo algorithms for eigenvalue problems

In this paper we analyse applicability and robustness of Markov chain Monte Carlo algorithms for eigenvalue problems. We restrict our consideration to real symmetric matrices. Almost Optimal Monte Carlo (MAO) algorithms for solving eigenvalue problems are formulated. Results for the structure of both - systematic and probability error are presented. It is shown that the values of both errors can be controlled independently by different algorithmic parameters. The results present how the systematic error depends on the matrix spectrum. The analysis of the probability error is presented. It shows that the close (in some sense) the matrix under consideration is to the stochastic matrix the smaller is this error. Sufficient conditions for constructing robust and interpolation Monte Carlo algorithms are obtained. For stochastic matrices an interpolation Monte Carlo algorithm is constructed. A number of numerical tests for large symmetric dense matrices are performed in order to study experimentally the dependence of the systematic error from the structure of matrix spectrum. We also study how the probability error depends on the balancing of the matrix. (c) 2007 Elsevier Inc. All rights reserved.

Response kinetics in the complex chemotaxis signalling pathway of Rhodobacter sphaeroides

Chemotaxis is one of the best characterised signalling systems in biology. It is the mechanism by which bacteria move towards optimal environments and is implicated in biofilm formation, pathogenesis and symbiosis. The properties of the bacterial chemosensory response have been described in detail for the single chemosensory pathway of Escherichia coli. We have characterised the properties of the chemosensory response of Rhodobacter sphaeroides, an -proteobacterium with multiple chemotaxis pathways, under two growth conditions allowing the effects of protein expression levels and cell architecture to be investigated. Using tethered cell assays we measured the responses of the system to step changes in concentration of the attractant propionate and show that, independently of the growth conditions, R. sphaeroides is chemotactic over at least five orders of magnitude and has a sensing profile following Weber’s law. Mathematical modelling also shows that, like E. coli, R. sphaeroides is capable of showing Fold-Change Detection (FCD). Our results indicate that general features of bacterial chemotaxis such as the range and sensitivity of detection, adaptation times, adherence to Weber’s law and the presence of FCD may be integral features of chemotaxis systems in general, regardless of network complexity, protein expression levels and cellular architecture across different species.

Modelling negative feedback networks for activating transcription factor 3 predicts a dominant role for miRNAs in immediate early gene regulation

Activating transcription factor 3 (Atf3) is rapidly and transiently upregulated in numerous systems, and is associated with various disease states. Atf3 is required for negative feedback regulation of other genes, but is itself subject to negative feedback regulation possibly by autorepression. In cardiomyocytes, Atf3 and Egr1 mRNAs are upregulated via ERK1/2 signalling and Atf3 suppresses Egr1 expression. We previously developed a mathematical model for the Atf3-Egr1 system. Here, we adjusted and extended the model to explore mechanisms of Atf3 feedback regulation. Introduction of an autorepressive loop for Atf3 tuned down its expression and inhibition of Egr1 was lost, demonstrating that negative feedback regulation of Atf3 by Atf3 itself is implausible in this context. Experimentally, signals downstream from ERK1/2 suppress Atf3 expression. Mathematical modelling indicated that this cannot occur by phosphorylation of pre-existing inhibitory transcriptional regulators because the time delay is too short. De novo synthesis of an inhibitory transcription factor (ITF) with a high affinity for the Atf3 promoter could suppress Atf3 expression, but (as with the Atf3 autorepression loop) inhibition of Egr1 was lost. Developing the model to include newly-synthesised miRNAs very efficiently terminated Atf3 protein expression and, with a 4-fold increase in the rate of degradation of mRNA from the mRNA/miRNA complex, profiles for Atf3 mRNA, Atf3 protein and Egr1 mRNA approximated to the experimental data. Combining the ITF model with that of the miRNA did not improve the profiles suggesting that miRNAs are likely to play a dominant role in switching off Atf3 expression post-induction.

Eutrofização do Reservatório Cruzeta na bacia representativa do rio Seridó RN

Eutrophication has been listed as one of the main problems of water pollution on a global level. In the Brazilian semi-arid areas this problem takes even greater proportions due to characteristical water scarcity of the region. It is extremely important to the predictive eutrophication models development and to the reservoirs management in the semi-arid region, studies that promotes understanding of the mechanisms responsible for the expansion and control of algae blooms, essential for improving the water quality of these environments. The present study had as its main aims, evaluate the temporal pattern of trophic state, considering the influence of nutrients (N and P) and the light availability in the water column in the development of phytoplankton biomass, and perform the mathematical modelling of changes in phosphorus and chlorophyll a concentrations in the Cruzeta man-made lake located on Seridó, a typical semi-arid region of Rio Grande do Norte. To this, a fortnightly monitoring was performed in the reservoir in 05 stations over the months of March 2007 to May 2008. Were measured the concentrations of total phosphorus, total organic nitrogen, chlorophyll a, total, fixed and volatile suspended solids, as well as the measure of transparency (Secchi) and the profiles of photosynthetic active radiation (PAR), temperature, pH, dissolved oxygen and electrical conductivity in the water column. Measurements of vertical profiles have shown some periods of chemical and thermal stratification, especially in the rainy season, due to increased water column depth, however, the reservoir can be classified as warm polimitic. During the study period the reservoir was characterized as eutrophic considering the concentrations of phosphorus and most of the time as mesotrophic, based on the concentrations of chlorophyll a, according to the Thornton & Rast (1993) classification. The N:P relations suggest N limitation, conversely, significant linear relationship between the algae biomass and nutrients (N and P) were not observed in our study. However, a relevant event was the negative and significant correlation presented by Kt and chlorophyll a (r ² = 0.83) at the end of the drought of 2007 and the rainy season of 2008, and the algal biomass collapse observed at the end of the drought season (Dec/07). The equation used to simulate the change in the total phosphorus was not satisfactory, being necessary inclusion of parameters able to increase the power of the model prediction. The chlorophyll a simulation presented a good adjustment trend, however there is a need to check the calibrated model parameters and subsequent equation validation

A novel approach based on recurrent neural networks applied to nonlinear systems optimization

This paper presents an efficient approach based on recurrent neural network for solving nonlinear optimization. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid subspace technique. These parameters guarantee the convergence of the network to the equilibrium points that represent an optimal feasible solution. The main advantage of the developed network is that it treats optimization and constraint terms in different stages with no interference with each other. Moreover, the proposed approach does not require specification of penalty and weighting parameters for its initialization. A study of the modified Hopfield model is also developed to analyze its stability and convergence. Simulation results are provided to demonstrate the performance of the proposed neural network. (c) 2005 Elsevier B.V. All rights reserved.

Mathematical analysis and simulations involving chemotherapy and surgery on large human tumours under a suitable cell-kill functional response

Dosage and frequency of treatment schedules are important for successful chemotherapy. However, in this work we argue that cell-kill response and tumoral growth should not be seen as separate and therefore are essential in a mathematical cancer model. This paper presents a mathematical model for sequencing of cancer chemotherapy and surgery. Our purpose is to investigate treatments for large human tumours considering a suitable cell-kill dynamics. We use some biological and pharmacological data in a numerical approach, where drug administration occurs in cycles (periodic infusion) and surgery is performed instantaneously. Moreover, we also present an analysis of stability for a chemotherapeutic model with continuous drug administration. According to Norton & Simon [22], our results indicate that chemotherapy is less eficient in treating tumours that have reached a plateau level of growing and that a combination with surgical treatment can provide better outcomes.

Platelet-Rich Plasma And Chronic Wounds: Remaining Fibronectin May Influence Matrix Remodeling And Regeneration Success

Background: Platelet-rich plasma has been largely used as a therapeutic option for the treatment of chronic wounds of different etiologies. The enhanced regeneration observed after the use of platelet-rich plasma has been systematically attributed to the growth factors that are present inside platelets' granules. Aim: We hypothesize that the remaining plasma and platelet-bound fibronectin may act as a further bioactive protein in platelet-rich plasma preparations. Methods: Recent reports were analyzed and presented as direct evidences of this hypotheses. Results: Fibronectin may directly influence the extracellular matrix remodeling during wound repair. This effect is probably through matrix metalloproteinase expression, thus exerting an extra effect on chronic wound regeneration. Conclusions: Physicians should be well aware of the possible fibronectin-induced effects in their future endeavors with PRP in chronic wound treatment. © 2013 International Society for Cellular Therapy.

Ecological optimization of an irreversible Brayton cycle with regeneration, inter-cooling and reheating

A mathematical model is developed for an irreversible Brayton cycle with regeneration, inter-cooling and reheating. The irreversibility are from the thermal resistance in the heat exchangers, the pressure drops in pipes, the non-isentropic behavior in the adiabatic expansions and compressions and the heat leakage to the cold source. The cycle is optimized by maximizing the ecological function, which is achieved by the search for optimal values for the temperatures of the cycle and for the pressure ratios of the first stage compression and the first stage expansion. The advantages of using the regenerator, intercooler and reheater are presented by comparison with cycles that do not incorporate one or more of these processes. Optimization results are compared with those obtained by maximizing the power output and it is concluded that the point of maximum ecological function has major advantages with respect to the entropy generation rate and the thermal efficiency, at the cost of a small loss in power.

Metaheuristics for a crop rotation problem

This paper presents a mathematical model adapted from literature for the crop rotation problem with demand constraints (CRP-D). The main aim of the present work is to study metaheuristics and their performance in a real context. The proposed algorithms for solution of the CRP-D are a genetic algorithm, a simulated annealing and hybrid approaches: a genetic algorithm with simulated annealing and a genetic algorithm with local search algorithm. A new constructive heuristic was also developed to provide initial solutions for the metaheuristics. Computational experiments were performed using a real planting area and semi-randomly generated instances created by varying the number, positions and dimensions of the lots. The computational results showed that these algorithms determined good feasible solutions in a short computing time as compared with the time spent to get optimal solutions, thus proving their efficacy for dealing with this practical application of the CRP-D.

A general framework for multi-compartmental analysis of drug chemotherapy dynamics in human immunodeficiency virus type-1 infected individuals

An optimal control strategy for the highly active antiretroviral therapy associated to the acquired immunodeficiency syndrome should be designed regarding a comprehensive analysis of the drug chemotherapy behavior in the host tissues, from major viral replication sites to viral sanctuary compartments. Such approach is critical in order to efficiently explore synergistic, competitive and prohibitive relationships among drugs and, hence, therapy costs and side-effect minimization. In this paper, a novel mathematical model for HIV-1 drug chemotherapy dynamics in distinct host anatomic compartments is proposed and theoretically evaluated on fifteen conventional anti-retroviral drugs. Rather than interdependence between drug type and its concentration profile in a host tissue, simulated results suggest that such profile is importantly correlated with the host tissue under consideration. Furthermore, the drug accumulative dynamics are drastically affected by low patient compliance with pharmacotherapy, even when a single dose lacks. (C) 2012 Elsevier Inc. All rights reserved.

Reconstruction of the aquifer history of Gran Canaria

[EN]A study on the recent history and current state of the aquifer in the Island of Gran Canaria (Canary Is., 28oN, 15oW) is performed. Though rainfall is scarce on the island, traditional agricultural practices and small population were able to keep the aquifer in a constant state for centuries. Nevertheless, at the beginning of the 20th Century, culture of several water-consuming species was introduced on a commercial basis due to the relative proximity of the Canaries to continental Europe and to the possibility of more than one yearly harvest. This led to generalised well digging (more than 300m deep in many cases) and to the appearance of a chronic hydraulic deficit, as well as to spoiling vastcoastal areas of the aquifer through intrusion of brackish water. In the mid 1960’s, coincident with the apex of agricultural exploitation, massive tourism appeared in the scene. This new activity soon became a susbstitute for Agriculture, but it attracted more new labour force to the island, and a fast growth of population was the main result. Moreover, new water use practices entered the scene. As a consequence, the main causes for the aquifer decline are population growth and extensive Agriculture practices in use during the last half of the 20th Century. Some remarks on sustainability issues in order to cope with Climate Change are also offered.

Mathematical models of cognitive processes

The research activity carried out during the PhD course was focused on the development of mathematical models of some cognitive processes and their validation by means of data present in literature, with a double aim: i) to achieve a better interpretation and explanation of the great amount of data obtained on these processes from different methodologies (electrophysiological recordings on animals, neuropsychological, psychophysical and neuroimaging studies in humans), ii) to exploit model predictions and results to guide future research and experiments. In particular, the research activity has been focused on two different projects: 1) the first one concerns the development of neural oscillators networks, in order to investigate the mechanisms of synchronization of the neural oscillatory activity during cognitive processes, such as object recognition, memory, language, attention; 2) the second one concerns the mathematical modelling of multisensory integration processes (e.g. visual-acoustic), which occur in several cortical and subcortical regions (in particular in a subcortical structure named Superior Colliculus (SC)), and which are fundamental for orienting motor and attentive responses to external world stimuli. This activity has been realized in collaboration with the Center for Studies and Researches in Cognitive Neuroscience of the University of Bologna (in Cesena) and the Department of Neurobiology and Anatomy of the Wake Forest University School of Medicine (NC, USA). PART 1. Objects representation in a number of cognitive functions, like perception and recognition, foresees distribute processes in different cortical areas. One of the main neurophysiological question concerns how the correlation between these disparate areas is realized, in order to succeed in grouping together the characteristics of the same object (binding problem) and in maintaining segregated the properties belonging to different objects simultaneously present (segmentation problem). Different theories have been proposed to address these questions (Barlow, 1972). One of the most influential theory is the so called “assembly coding”, postulated by Singer (2003), according to which 1) an object is well described by a few fundamental properties, processing in different and distributed cortical areas; 2) the recognition of the object would be realized by means of the simultaneously activation of the cortical areas representing its different features; 3) groups of properties belonging to different objects would be kept separated in the time domain. In Chapter 1.1 and in Chapter 1.2 we present two neural network models for object recognition, based on the “assembly coding” hypothesis. These models are networks of Wilson-Cowan oscillators which exploit: i) two high-level “Gestalt Rules” (the similarity and previous knowledge rules), to realize the functional link between elements of different cortical areas representing properties of the same object (binding problem); 2) the synchronization of the neural oscillatory activity in the γ-band (30-100Hz), to segregate in time the representations of different objects simultaneously present (segmentation problem). These models are able to recognize and reconstruct multiple simultaneous external objects, even in difficult case (some wrong or lacking features, shared features, superimposed noise). In Chapter 1.3 the previous models are extended to realize a semantic memory, in which sensory-motor representations of objects are linked with words. To this aim, the network, previously developed, devoted to the representation of objects as a collection of sensory-motor features, is reciprocally linked with a second network devoted to the representation of words (lexical network) Synapses linking the two networks are trained via a time-dependent Hebbian rule, during a training period in which individual objects are presented together with the corresponding words. Simulation results demonstrate that, during the retrieval phase, the network can deal with the simultaneous presence of objects (from sensory-motor inputs) and words (from linguistic inputs), can correctly associate objects with words and segment objects even in the presence of incomplete information. Moreover, the network can realize some semantic links among words representing objects with some shared features. These results support the idea that semantic memory can be described as an integrated process, whose content is retrieved by the co-activation of different multimodal regions. In perspective, extended versions of this model may be used to test conceptual theories, and to provide a quantitative assessment of existing data (for instance concerning patients with neural deficits). PART 2. The ability of the brain to integrate information from different sensory channels is fundamental to perception of the external world (Stein et al, 1993). It is well documented that a number of extraprimary areas have neurons capable of such a task; one of the best known of these is the superior colliculus (SC). This midbrain structure receives auditory, visual and somatosensory inputs from different subcortical and cortical areas, and is involved in the control of orientation to external events (Wallace et al, 1993). SC neurons respond to each of these sensory inputs separately, but is also capable of integrating them (Stein et al, 1993) so that the response to the combined multisensory stimuli is greater than that to the individual component stimuli (enhancement). This enhancement is proportionately greater if the modality-specific paired stimuli are weaker (the principle of inverse effectiveness). Several studies have shown that the capability of SC neurons to engage in multisensory integration requires inputs from cortex; primarily the anterior ectosylvian sulcus (AES), but also the rostral lateral suprasylvian sulcus (rLS). If these cortical inputs are deactivated the response of SC neurons to cross-modal stimulation is no different from that evoked by the most effective of its individual component stimuli (Jiang et al 2001). This phenomenon can be better understood through mathematical models. The use of mathematical models and neural networks can place the mass of data that has been accumulated about this phenomenon and its underlying circuitry into a coherent theoretical structure. In Chapter 2.1 a simple neural network model of this structure is presented; this model is able to reproduce a large number of SC behaviours like multisensory enhancement, multisensory and unisensory depression, inverse effectiveness. In Chapter 2.2 this model was improved by incorporating more neurophysiological knowledge about the neural circuitry underlying SC multisensory integration, in order to suggest possible physiological mechanisms through which it is effected. This endeavour was realized in collaboration with Professor B.E. Stein and Doctor B. Rowland during the 6 months-period spent at the Department of Neurobiology and Anatomy of the Wake Forest University School of Medicine (NC, USA), within the Marco Polo Project. The model includes four distinct unisensory areas that are devoted to a topological representation of external stimuli. Two of them represent subregions of the AES (i.e., FAES, an auditory area, and AEV, a visual area) and send descending inputs to the ipsilateral SC; the other two represent subcortical areas (one auditory and one visual) projecting ascending inputs to the same SC. Different competitive mechanisms, realized by means of population of interneurons, are used in the model to reproduce the different behaviour of SC neurons in conditions of cortical activation and deactivation. The model, with a single set of parameters, is able to mimic the behaviour of SC multisensory neurons in response to very different stimulus conditions (multisensory enhancement, inverse effectiveness, within- and cross-modal suppression of spatially disparate stimuli), with cortex functional and cortex deactivated, and with a particular type of membrane receptors (NMDA receptors) active or inhibited. All these results agree with the data reported in Jiang et al. (2001) and in Binns and Salt (1996). The model suggests that non-linearities in neural responses and synaptic (excitatory and inhibitory) connections can explain the fundamental aspects of multisensory integration, and provides a biologically plausible hypothesis about the underlying circuitry.