Mathematical modelling of neural processes within the oculomotor system

It is presented a mathematical model of the oculomotor plant, based on experimental data in cats. The system that generates, from the neuronal processes at the motoneuron, the control signals to the eye muscles that moves the eye. In contrast with previous models, that base the eye movement related motoneuron behavior on a first order linear differential equation, non-linear effects are described: A dependency on the eye angular position of the model parameters.

A INFLUÊNCIA DAS PRÁTICAS PEDAGÓGICAS DOCENTES E DAS BARREIRAS DISCENTES SOBRE O DESENVOLVIMENTO DA CRIATIVIDADE DO FUTURO ADMINISTRADOR

As empresas que almejam garantir e melhorar sua posição dentro de em um mercado cada vez mais competitivo precisam estar sempre atualizadas e em constante evolução. Na busca contínua por essa evolução, investem em projetos de Pesquisa & Desenvolvimento (P&D) e em seu capital humano para promover a criatividade e a inovação organizacional. As pessoas têm papel fundamental no desenvolvimento da inovação, mas para que isso possa florescer de forma constante é preciso comprometimento e criatividade para a geração de ideias. Criatividade é pensar o novo; inovação é fazer acontecer. Porém, encontrar pessoas com essas qualidades nem sempre é tarefa fácil e muitas vezes é preciso estimular essas habilidades e características para que se tornem efetivamente criativas. Os cursos de graduação podem ser uma importante ferramenta para trabalhar esses aspectos, características e habilidades, usando métodos e práticas de ensino que auxiliem no desenvolvimento da criatividade, pois o ambiente ensino-aprendizagem pesa significativamente na formação das pessoas. O objetivo deste estudo é de identificar quais fatores têm maior influência sobre o desenvolvimento da criatividade em um curso de graduação em administração, analisando a influência das práticas pedagógicas dos docentes e as barreiras internas dos discentes. O referencial teórico se baseia principalmente nos trabalhos de Alencar, Fleith, Torrance e Wechsler. A pesquisa transversal de abordagem quantitativa teve como público-alvo os alunos do curso de Administração de uma universidade confessional da Grande São Paulo, que responderam 465 questionários compostos de três escalas. Para as práticas docentes foi adaptada a escala de Práticas Docentes em relação à Criatividade. Para as barreiras internas foi adaptada a escala de Barreiras da Criatividade Pessoal. Para a análise da percepção do desenvolvimento da criatividade foi construída e validada uma escala baseada no referencial de características de uma pessoa criativa. As análises estatísticas descritivas e fatoriais exploratórias foram realizadas no software Statistical Package for the Social Sciences (SPSS), enquanto as análises fatoriais confirmatórias e a mensuração da influência das práticas pedagógicas e das barreiras internas sobre a percepção do desenvolvimento da criatividade foram realizadas por modelagem de equação estrutural utilizando o algoritmo Partial Least Squares (PLS), no software Smart PLS 2.0. Os resultados apontaram que as práticas pedagógicas e as barreiras internas dos discentes explicam 40% da percepção de desenvolvimento da criatividade, sendo as práticas pedagógicas que exercem maior influencia. A pesquisa também apontou que o tipo de temática e o período em que o aluno está cursando não têm influência sobre nenhum dos três construtos, somente o professor influencia as práticas pedagógicas.

Stability threshold approach for complex dynamical systems

Acknowledgments This paper was developed within the scope of the IRTG 1740/TRP 2011/50151-0, funded by the DFG/FAPESP, and supported by the Government of the Russian Federation (Agreement No. 14.Z50.31.0033 with the Institute of Applied Physics RAS). The first author thanks Dr Roman Ovsyannikov for valuable discussions regarding estimation of the mistake probability.

The problem of the spreading of a liquid film along a solid surface: A new mathematical formulation

A new mathematical model is proposed for the spreading of a liquid film on a solid surface. The model is based on the standard lubrication approximation for gently sloping films (with the no-slip condition for the fluid at the solid surface) in the major part of the film where it is not too thin. In the remaining and relatively small regions near the contact lines it is assumed that the so-called autonomy principle holds—i.e., given the material components, the external conditions, and the velocity of the contact lines along the surface, the behavior of the fluid is identical for all films. The resulting mathematical model is formulated as a free boundary problem for the classical fourth-order equation for the film thickness. A class of self-similar solutions to this free boundary problem is considered.

A model-based approach for assessing in vivo combination therapy interactions

We present an approach for evaluating the efficacy of combination antitumor agent schedules that accounts for order and timing of drug administration. Our model-based approach compares in vivo tumor volume data over a time course and offers a quantitative definition for additivity of drug effects, relative to which synergism and antagonism are interpreted. We begin by fitting data from individual mice receiving at most one drug to a differential equation tumor growth/drug effect model and combine individual parameter estimates to obtain population statistics. Using two null hypotheses: (i) combination therapy is consistent with additivity or (ii) combination therapy is equivalent to treating with the more effective single agent alone, we compute predicted tumor growth trajectories and their distribution for combination treated animals. We illustrate this approach by comparing entire observed and expected tumor volume trajectories for a data set in which HER-2/neu-overexpressing MCF-7 human breast cancer xenografts are treated with a humanized, anti-HER-2 monoclonal antibody (rhuMAb HER-2), doxorubicin, or one of five proposed combination therapy schedules.

Neonatal gene transfer leads to widespread correction of pathology in a murine model of lysosomal storage disease

For many inborn errors of metabolism, early treatment is critical to prevent long-term developmental sequelae. We have used a gene-therapy approach to demonstrate this concept in a murine model of mucopolysaccharidosis type VII (MPS VII). Newborn MPS VII mice received a single intravenous injection with 5.4 × 106 infectious units of recombinant adeno-associated virus encoding the human β-glucuronidase (GUSB) cDNA. Therapeutic levels of GUSB expression were achieved by 1 week of age in liver, heart, lung, spleen, kidney, brain, and retina. GUSB expression persisted in most organs for the 16-week duration of the study at levels sufficient to either reduce or prevent completely lysosomal storage. Of particular significance, neurons, microglia, and meninges of the central nervous system were virtually cleared of disease. In addition, neonatal treatment of MPS VII mice provided access to the central nervous system via an intravenous route, avoiding a more invasive procedure later in life. These data suggest that gene transfer mediated by adeno-associated virus can achieve therapeutically relevant levels of enzyme very early in life and that the rapid growth and differentiation of tissues does not limit long-term expression.

Self-similar intermediate asymptotics for a degenerate parabolic filtration-absorption equation

The equation ∂tu = u∂xx2u − (c − 1)(∂xu)2 is known in literature as a qualitative mathematical model of some biological phenomena. Here this equation is derived as a model of the groundwater flow in a water-absorbing fissurized porous rock; therefore, we refer to this equation as a filtration-absorption equation. A family of self-similar solutions to this equation is constructed. Numerical investigation of the evolution of non-self-similar solutions to the Cauchy problems having compactly supported initial conditions is performed. Numerical experiments indicate that the self-similar solutions obtained represent intermediate asymptotics of a wider class of solutions when the influence of details of the initial conditions disappears but the solution is still far from the ultimate state: identical zero. An open problem caused by the nonuniqueness of the solution of the Cauchy problem is discussed.

The operator algebra approach to quantum groups

A relatively simple definition of a locally compact quantum group in the C*-algebra setting will be explained as it was recently obtained by the authors. At the same time, we put this definition in the historical and mathematical context of locally compact groups, compact quantum groups, Kac algebras, multiplicative unitaries, and duality theory.

Correction in trans for Fabry disease: expression, secretion and uptake of alpha-galactosidase A in patient-derived cells driven by a high-titer recombinant retroviral vector.

Fabry disease is an X-linked metabolic disorder due to a deficiency of alpha-galactosidase A (alpha-gal A; EC 3.2.1.22). Patients accumulate glycosphingolipids with terminal alpha-galactosyl residues that come from intracellular synthesis, circulating metabolites, or from the biodegradation Of senescent cells. Patients eventually succumb to renal, cardio-, or cerebrovascular disease. No specific therapy exists. One possible approach to ameliorating this disorder is to target corrective gene transfer therapy to circulating hematopoietic cells. Toward this end, an amphotropic virus-producer cell line has been developed that produces a high titer (>10(6) i.p. per ml) recombinant retrovirus constructed to transduce and correct target cells. Virus-producer cells also demonstrate expression of large amounts of both intracellular and secreted alpha-gal A. To examine the utility of this therapeutic vector, skin fibroblasts from Fabry patients were corrected for the metabolic defect by infection with this recombinant virus and secreted enzyme was observed. Furthermore, the secreted enzyme was found to be taken up by uncorrected cells in a mannose-6-phosphate receptor-dependent manner. In related experiments, immortalized B cell lines from Fabry patients, created as a hematologic delivery test system, were transduced. As with the fibroblasts, transduced patient B cell lines demonstrated both endogenous enzyme correction and a small amount of secretion together with uptake by uncorrected cells. These studies demonstrate that endogenous metabolic correction in transduced cells, combined with secretion, may provide a continuous source of corrective material in trans to unmodified patient bystander cells (metabolic cooperativity).

Correction of diabetic alterations by glucokinase.

Hyperglycemia is a common feature of diabetes mellitus. It results from a decrease in glucose utilization by the liver and peripheral tissues and an increase in hepatic glucose production. Glucose phosphorylation by glucokinase is an initial event in glucose metabolism by the liver. However, glucokinase gene expression is very low in diabetic animals. Transgenic mice expressing the P-enolpyruvate carboxykinase/glucokinase chimeric gene were generated to study whether the return of the expression of glucokinase in the liver of diabetic mice might prevent metabolic alterations. In contrast to nontransgenic mice treated with streptozotocin, mice with the transgene previously treated with streptozotocin showed high levels of both glucokinase mRNA and its enzyme activity in the liver, which were associated with an increase in intracellular levels of glucose 6-phosphate and glycogen. The liver of these mice also showed an increase in pyruvate kinase activity and lactate production. Furthermore, normalization of both the expression of genes involved in gluconeogenesis and ketogenesis in the liver and the production of glucose and ketone body by hepatocytes in primary culture were observed in streptozotocin-treated transgenic mice. Thus, glycolysis was induced while gluconeogenesis and ketogenesis were blocked in the liver of diabetic mice expressing glucokinase. This was associated with normalization of blood glucose, ketone bodies, triglycerides, and free fatty acids even in the absence of insulin. These results suggest that the expression of glucokinase during diabetes might be a new approach to the normalization of hyperglycemia.

Long-term in vitro correction of alpha-L-iduronidase deficiency (Hurler syndrome) in human bone marrow.

Allogeneic bone marrow transplantation is the most effective treatment for Hurler syndrome but, since this therapy is not available to all patients, we have considered an alternative approach based on transfer and expression of the normal gene in autologous bone marrow. A retroviral vector carrying the full-length cDNA for alpha-L-iduronidase has been constructed and used to transduce bone marrow from patients with this disorder. Various gene-transfer protocols have been assessed including the effect of intensive schedules of exposure of bone marrow to viral supernatant and the influence of growth factors. With these protocols, we have demonstrated successful gene transfer into primitive CD34+ cells and subsequent enzyme expression in their maturing progeny. Also, by using long-term bone marrow cultures, we have demonstrated high levels of enzyme expression sustained for several months. The efficiency of gene transfer has been assessed by PCR analysis of hemopoietic colonies as 25-56%. No advantage has been demonstrated for the addition of growth factors or intensive viral exposure schedules. The enzyme is secreted into the medium and functional localization has been demonstrated by reversal of the phenotypic effects of lysosomal storage in macrophages. This work suggests that retroviral gene transfer into human bone marrow may offer the prospect for gene therapy of Hurler syndrome in young patients without a matched sibling donor.

Impact of artifact correction methods on R-R interbeat signals to quantifying heart rate variability (HRV) according to linear and nonlinear methods.

In the analysis of heart rate variability (HRV) are used temporal series that contains the distances between successive heartbeats in order to assess autonomic regulation of the cardiovascular system. These series are obtained from the electrocardiogram (ECG) signal analysis, which can be affected by different types of artifacts leading to incorrect interpretations in the analysis of the HRV signals. Classic approach to deal with these artifacts implies the use of correction methods, some of them based on interpolation, substitution or statistical techniques. However, there are few studies that shows the accuracy and performance of these correction methods on real HRV signals. This study aims to determine the performance of some linear and non-linear correction methods on HRV signals with induced artefacts by quantification of its linear and nonlinear HRV parameters. As part of the methodology, ECG signals of rats measured using the technique of telemetry were used to generate real heart rate variability signals without any error. In these series were simulated missing points (beats) in different quantities in order to emulate a real experimental situation as accurately as possible. In order to compare recovering efficiency, deletion (DEL), linear interpolation (LI), cubic spline interpolation (CI), moving average window (MAW) and nonlinear predictive interpolation (NPI) were used as correction methods for the series with induced artifacts. The accuracy of each correction method was known through the results obtained after the measurement of the mean value of the series (AVNN), standard deviation (SDNN), root mean square error of the differences between successive heartbeats (RMSSD), Lomb\'s periodogram (LSP), Detrended Fluctuation Analysis (DFA), multiscale entropy (MSE) and symbolic dynamics (SD) on each HRV signal with and without artifacts. The results show that, at low levels of missing points the performance of all correction techniques are very similar with very close values for each HRV parameter. However, at higher levels of losses only the NPI method allows to obtain HRV parameters with low error values and low quantity of significant differences in comparison to the values calculated for the same signals without the presence of missing points.

On the well-posedness of a mathematical model for lithium-ion batteries.

We discuss the well-posedness of a mathematical model that is used in the literature for the simulation of lithium-ion batteries. First, a mathematical model based on a macrohomogeneous approach is presented, following previous work. Then it is shown, from a physical and a mathematical point of view, that a boundary condition widely used in the literature is not correct. Although the errors could be just sign typos (which can be explained as carelessness in the use of d/dx versus d/dn, with n the outward unit vector) and authors using this model probably use the correct boundary condition when they solve it in order to do simulations, readers should be aware of the right choice. Therefore, the deduction of the correct boundary condition is done here, and a mathematical study of the well-posedness of the corresponding problem is presented.

Migração de solutos em basalto fraturado: quantificação experimental em laboratório e validação matemática

A avaliação do risco a contaminação e a escolha de técnicas de remediação de poluentes em aquíferos fraturados depende da quantificação dos fenômenos envolvidos no transporte de solutos. A geometria da fratura, usualmente caracterizada pela abertura, é o principal parâmetro que indiretamente controla o transporte nos aquíferos fraturados. A simplificação mais comum desse problema é assumir que as fraturas são um par de placas planas e paralelas, isto é, com uma abertura constante. No entanto, por causa do limitado número de trabalhos experimentais, não está esclarecida a adequabilidade do uso de uma abertura constante para simular o transporte conservativo em fraturas do Aquífero Serra Geral (ASG), Brasil. O objetivo deste trabalho é avaliar a influência da abertura de uma fratura natural do Aquífero Serra Geral sob o transporte conservativo de solutos. Uma amostra natural de basalto fraturado foi usada em um experimento hidráulico e de transporte de um traçador conservativo (escala de laboratório). O campo de abertura foi medido usando a técnica avançada, de alta resolução e tridimensional, chamada microtomografia computadorizada de raios-X. A concentração de traçador medida foi utilizada para validar uma solução analítica unidimensional da Equação de Advecção-dispersão (ADE). O desemprenho do ajuste da ADE às curvas de passagem experimentais foi avaliado para quatro diferentes tipos de aberturas constantes. Os resultados mostraram que o escoamento de água e o transporte de contaminantes pode ocorrer através de fraturas micrométricas, ocasionando, eventualmente, a contaminação do ASG. A abertura de balanço de massa é a única que pode ser chamada propriamente de \"abertura equivalente\". O uso de aberturas constantes na ADE não permitiu representar completamente o formato das curvas de passagem porque o campo de velocidade não é uniforme e intrinsicamente bidimensional. Portanto, na simulação do transporte deve-se incorporar a heterogeneidade da abertura da fratura.

On some solutions of a functional equation related to the partial sums of the Riemann zeta function

In this paper, we prove that infinite-dimensional vector spaces of α-dense curves are generated by means of the functional equations f(x)+f(2x)+⋯+f(nx)=0, with n≥2, which are related to the partial sums of the Riemann zeta function. These curves α-densify a large class of compact sets of the plane for arbitrary small α, extending the known result that this holds for the cases n=2,3. Finally, we prove the existence of a family of solutions of such functional equation which has the property of quadrature in the compact that densifies, that is, the product of the length of the curve by the nth power of the density approaches the Jordan content of the compact set which the curve densifies.