Basic ingredients for mathematical modeling of tumor growth in vitro: Cooperative effects and search for space

Based on the literature data from HT-29 cell monolayers, we develop a model for its growth, analogous to an epidemic model, mixing local and global interactions. First, we propose and solve a deterministic equation for the progress of these colonies. Thus, we add a stochastic (local) interaction and simulate the evolution of an Eden-like aggregate by using dynamical Monte Carlo methods. The growth curves of both deterministic and stochastic models are in excellent agreement with the experimental observations. The waiting times distributions, generated via our stochastic model, allowed us to analyze the role of mesoscopic events. We obtain log-normal distributions in the initial stages of the growth and Gaussians at long times. We interpret these outcomes in the light of cellular division events: in the early stages, the phenomena are dependent each other in a multiplicative geometric-based process, and they are independent at long times. We conclude that the main ingredients for a good minimalist model of tumor growth, at mesoscopic level, are intrinsic cooperative mechanisms and competitive search for space. © 2013 Elsevier Ltd.

Effectiveness of an Online Social Constructivist Mathematical Problem Solving Course for Malaysian Pre-Service Teachers

This study assessed the effectiveness of an online mathematical problem solving course designed using a social constructivist approach for pre-service teachers. Thirty-seven pre-service teachers at the Batu Lintang Teacher Institute, Sarawak, Malaysia were randomly selected to participate in the study. The participants were required to complete the course online without the typical face-to-face classes and they were also required to solve authentic mathematical problems in small groups of 4-5 participants based on the Polya’s Problem Solving Model via asynchronous online discussions. Quantitative and qualitative methods such as questionnaires and interviews were used to evaluate the effects of the online learning course. Findings showed that a majority of the participants were satisfied with their learning experiences in the course. There were no significant changes in the participants’ attitudes toward mathematics, while the participants’ skills in problem solving for “understand the problem” and “devise a plan” steps based on the Polya’s Model were significantly enhanced, though no improvement was apparent for “carry out the plan” and “review”. The results also showed that there were significant improvements in the participants’ critical thinking skills. Furthermore, participants with higher initial computer skills were also found to show higher performance in mathematical problem solving as compared to those with lower computer skills. However, there were no significant differences in the participants’ achievements in the course based on gender. Generally, the online social constructivist mathematical problem solving course is beneficial to the participants and ought to be given the attention it deserves as an alternative to traditional classes. Nonetheless, careful considerations need to be made in the designing and implementing of online courses to minimize problems that participants might encounter while participating in such courses.

Process considerations related to the microencapsulation of plasmid DNA via ultrasonic atomization

An effective means of facilitating DNA vaccine delivery to antigen presenting cells is through biodegradable microspheres. Microspheres offer distinct advantages over other delivery technologies by providing release of DNA vaccine in its bioactive form in a controlled fashion. In this study, biodegradable poly(D,L-lactide-coglycolide) (PLGA) microspheres containing polyethylenimine (PEI) condensed plasmid DNA (pDNA) were prepared using a 40 kHz ultrasonic atomization system. Process synthesis parameters, which are important to the scale-up of microspheres that are suitable for nasal delivery (i.e., less than 20 μm), were studied. These parameters include polymer concentration; feed flowrate; volumetric ratio of polymer and pDNA-PEI (plasmid DNA-polyethylenimine) complexes; and nitrogen to phosphorous (N/P) ratio. PDNA encapsulation efficiencies were predominantly in the range 82-96%, and the mean sizes of the particle were between 6 and 15 μm. The ultrasonic synthesis method was shown to have excellent reproducibility. PEI affected morphology of the microspheres, as it induced the formation of porous particles that accelerate the release rate of pDNA. The PLGA microspheres displayed an in vitro release of pDNA of 95-99% within 30 days and demonstrated zero order release kinetics without an initial spike of pDNA. Agarose electrophoresis confirmed conservation of the supercoiled form of pDNA throughout the synthesis and in vitro release stages. It was concluded that ultrasonic atomization is an efficient technique to overcome the key obstacles in scaling-up the manufacture of encapsulated vaccine for clinical trials and ultimately, commercial applications.

Development of a pilot-scale bacterial fermentation for plasmid-based biopharmaceutical production using a stoichiometric medium

The recognition of the potential efficacy of plasmid DNA (pDNA) molecules as vectors in the treatment and prevention of emerging diseases has birthed the confidence to combat global pandemics. This is due to the close-to-zero safety concern associated with pDNA vectors compared to viral vectors in cell transfection and targeting. Considerable attention has been paid to the potential of pDNA vectors but comparatively less thought has been given to the practical challenges in producing large quantities to meet current rising demands. A pilot-scale fermentation scheme was developed by employing a stoichiometrically-designed growth medium whose exceptional plasmid yield performance was attested in a shake flask environment for pUC19 and pEGFP-N1 transformed into E. coliDH5α and E. coliJM109, respectively. Batch fermentation of E. coliDH5α-pUC19 employing the stoichiometric medium displayed a maximum plasmid volumetric and specific yield of 62.6 mg/L and 17.1 mg/g (mg plasmid/g dry cell weight), respectively. Fed-batch fermentation of E. coliDH5α-pUC19 on a glycerol substrate demonstrated one of the highest ever reported pilot-scale plasmid specific yield of 48.98 mg/g and a volumetric yield of 0.53 g/L. The attainment of high plasmid specific yields constitutes a decrease in plasmid manufacturing cost and enhances the effectiveness of downstream processes by reducing the proportion of intracellular impurities. The effect of step-rise temperature induction was also considered to maximize ColE1-origin plasmid replication.

Programmes informatiques permettant l'adaptation des DRG aux statistiques médicales VESKA

Le présent cahier documente les différents programmes informatiques nécessaires à l'adaptation suisse des DRG.

Theoretical Dynamics of Experimental Populations of Introduced and Native Blowflies (Diptera: Calliphoridae)

Equilibrium dynamics in experimental populations of Chrysomya megacephala (F.) and C. putoria (Wiedemann), which have recently invaded the Americas, and the native species Cochliomyia macellaria (F.), were investigated using nonlinear difference equations. A theoretical analysis of the mathematical model using bifurcation theory established the combination of demographic parameters responsible for producing shifts in blowfly population dynamics from stable equilibria to bounded cycles and aperiodic behavior. Mathematical modeling shows that the populations of the 2 introduced Chrysomya species will form stable oscillations with numbers fluctuating 3-4 times in successive generations. However, in the native species C. macellaria, the dynamics is characterized by damping oscillations in population size, leading to a stable population level.

Relativistic quark spin coupling effects in the nucleon electromagnetic form factors

We investigate the effect of different forms of relativistic spin coupling of constituent quarks in the nucleon electromagnetic form factors. The four-dimensional integrations in the two-loop Feynman diagram are reduced to the null-plane, such that the light-front wave function is introduced in the computation of the form factors. The neutron charge form factor is very sensitive to different choices of spin coupling schemes, once its magnetic moment is fitted to the experimental value. The scalar coupling between two quarks is preferred by the neutron data, when a reasonable fit of the proton magnetic momentum is found. (C) 2000 Elsevier Science B.V.

Exact solutions of the dirac equation for modified coulombic potentials

Exact solutions are found for the Dirac equation for a combination of Lorentz scalar and vector Coulombic potentials with additional non-Coulombic parts. An appropriate linear combination of Lorentz scalar and vector non-Coulombic potentials, with the scalar part dominating, can be chosen to give exact analytic Dirac wave functions. The method works for the ground state or for the lowest orbital state with l = j - 1/2 , for any j.

Influência da concentração de antioxidante na estabilidade do ácido retinóico

Retinoic acid, which has been prescribed for some forms of acne since 1962, is subject to isomerization provoked by atmospheric oxygen and ambient light. Therefore it is very important to keep this material intact through the use of antioxidants. We tested two antioxidants: various concentrations of butylhydroxytoluene or BHT, widely used in cosmetic and dermatological preparations, and vitamin E, found in grape oil, an ingredient of skin lotion. Recently prepared lotions were subject to heat stress and the residual concentrations of retinoic acid determined at predetermined intervals through UV spectrophotometry. The shelf life of the various preparations were determined by the Arrhenius equation. The antioxidants helped conserve the retinoic acid, however, there was no synergism in antioxidant activity between the vitamin E in the grape seed oil and BHT.

Evaluation of the mixtures ammonium phosphate/magnesium nitrate and palladium nitrate/magnesium nitrate as modifiers for simultaneous determination of Cd, Cr, Ni and Pb in mineral water by GFAAS

A method is described for the simultaneous determination of Cd, Cr, Ni and Pb in mineral water samples by graphite furnace atomic absorption spectrometry with a transversely heated graphite atomizer (THGA) and a longitudinal Zeeman-effect background correction system. The electrothermal behavior of analytes during pyrolysis and atomization steps was studied without modifier, in presence of 5 μg Pd and 3 μg Mg(NO3)2 and in presence of 50 μg NH4H2PO4 and 3 μg Mg(NO3)2. A volume of 20 μL of a 0.028 mol L -1 HNO3 solution containing 50 μg L-1 Ni and Pb, 10 μg L-1 Cr and 5 μg L-1 Cd was dispensed into the graphite tube at 20°C. The mixture palladium/magnesium was selected as the optimum modifier. The pyrolysis and atomization temperatures were fixed at 1000°C and 2300°C, respectively. The characteristic masses were calculated as 2.2 pg Cd, 10 pg Cr, 42 pg Ni and 66 pg Pb and the lifetime of the graphite tube was around 600 firings. Limits of detection based on integrated absorbance were 0.02 μg L-1Cd, 0.94 μg L-1 Cr, 0.45 μg L-1 Ni and 0.75 μg L-1 Pb, which exceeded the requirements of Brazilian Food Regulation that establish the maximum permissible level for Cd, Cr, Ni and Pb at 3 μg L-1, 50 μg L-1, 20 μg L-1 and 10 μg L-1, respectively. The recoveries of Cd, Cr, Ni and Pb added to mineral water samples varied within the 93-108%, 96-104%, 87-101% and 98-108% ranges, respectively. Results of analysis of standard reference materials (National Institute of Standards and Technology: 1640-Trace Elements in Natural Water; 1643d-Trace Elements in Water) were in agreement with certified values at the 95% confidence level.

Mapping deformed hyperbolic potentials into nondeformed ones

In this work we introduce a mapping between the so-called deformed hyperbolic potentials, which are presenting a continuous interest in the last few years, and the corresponding nondeformed ones. As a consequence, we conclude that these deformed potentials do not pertain to a new class of exactly solvable potentials, but to the same one of the corresponding nondeformed ones. Notwithstanding, we can reinterpret this type of deformation as a kind of symmetry of the nondeformed potentials. © 2005 Elsevier B.V. All rights reserved.

Consistency between light-front quantization and covariantization for zero modes

In the light-cone gauge choice for Abelian and non-Abelian gauge fields, the vector boson propagator carries in it an additional spurious or unphysical pole intrinsic to the choice requiring a careful mathematical treatment. Research in this field over the years has shown us that mathematical consistency only is not enough to guarantee physically meaningful results. Whatever the prescription invoked to handle such an object, it has to preserve causality in the process. On the other hand, the covariantization technique is a well-suited one to tackle gauge-dependent poles in the Feynman integrals, dispensing the use of ad hoc prescriptions. In this work we show that the covariantization technique in the light-cone gauge is a direct consequence of the canonical quantization of the theory. © World Scientific Publishing Company.

Efeitos dos erros de projeção sobre as grandezas cefalométricas das análises de Steiner e McNamara

Pós-graduação em Odontologia - FOAR

MultiStaR

Multivariate Methoden stellen ein wesentliches Instrumentarium zur Datenanalyse in der Ökologie dar. Sie werden in der Ökologie häufig eingesetzt und sind seit langem Gegenstand der Lehre in der Abteilung Geobotanik der Universität Freiburg. In den letzten Jahren wurde als Werkzeug das Programm R eingeführt. R ist ein frei verfügbares, kommandozeilenorientiertes Statistikprogramm, das für eine Reihe von Betriebssystemen angeboten wird (R-Development Core-Team 2007). Das Programm befindet sich in rascher Entwicklung (derzeit Version 2.10) und wird zunehmend auch von Ökologen eingesetzt. Bislang existiert kein deutschsprachiges Lehrbuch zur Anwendung multivariater Methoden mit R. Mit MultiStaR wird versucht, diese Lücke zu schließen und den Studierenden Lernmaterialien an die Hand zu geben, die Übungen mit dem eigentlichen Analysewerkzeug mit einschließen.

Letters & Numbers : a vehicle to illustrate mathematical and computing fundamentals

The television quiz program Letters and Numbers, broadcast on the SBS network, has recently become quite popular in Australia. This paper explores the potential of this game to illustrate and engage student interest in a range of fundamental concepts of computer science and mathematics. The Numbers Game in particular has a rich mathematical structure whose analysis and solution involves concepts of counting and problem size, discrete (tree) structures, language theory, recurrences, computational complexity, and even advanced memory management. This paper presents an analysis of these games and their teaching applications, and presents some initial results of use in student assignments.