Riesz potential versus fractional Laplacian

This paper starts by introducing the Grünwald–Letnikov derivative, the Riesz potential and the problem of generalizing the Laplacian. Based on these ideas, the generalizations of the Laplacian for 1D and 2D cases are studied. It is presented as a fractional version of the Cauchy–Riemann conditions and, finally, it is discussed with the n-dimensional Laplacian.

On the requirements of interpolating polynomials for path motion constraints

In the framework of multibody dynamics, the path motion constraint enforces that a body follows a predefined curve being its rotations with respect to the curve moving frame also prescribed. The kinematic constraint formulation requires the evaluation of the fourth derivative of the curve with respect to its arc length. Regardless of the fact that higher order polynomials lead to unwanted curve oscillations, at least a fifth order polynomials is required to formulate this constraint. From the point of view of geometric control lower order polynomials are preferred. This work shows that for multibody dynamic formulations with dependent coordinates the use of cubic polynomials is possible, being the dynamic response similar to that obtained with higher order polynomials. The stabilization of the equations of motion, always required to control the constraint violations during long analysis periods due to the inherent numerical errors of the integration process, is enough to correct the error introduced by using a lower order polynomial interpolation and thus forfeiting the analytical requirement for higher order polynomials.

Molecular details of INH-C-10 binding to wt KatG and Its S315T mutant

Isoniazid (INH) is still one of the two most effective antitubercular drugs and is included in all recommended multitherapeutic regimens. Because of the increasing resistance of Mycobacterium tuberculosis to INH, mainly associated with mutations in the katG gene, new INH-based compounds have been proposed to circumvent this problem. In this work, we present a detailed comparative study of the molecular determinants of the interactions between wt KatG or its S315T mutant form and either INH or INH-C10, a new acylated INH derivative. MD simulations were used to explore the conformational space of both proteins, and results indicate that the S315T mutation did not have a significant impact on the average size of the access tunnel in the vicinity of these residues. Our simulations also indicate that the steric hindrance role assigned to Asp137 is transient and that electrostatic changes can be important in understanding the enzyme activity data of mutations in KatG. Additionally, molecular docking studies were used to determine the preferred modes of binding of the two substrates. Upon mutation, the apparently less favored docking solution for reaction became the most abundant, suggesting that S315T mutation favors less optimal binding modes. Moreover, the aliphatic tail in INH-C10 seems to bring the hydrazine group closer to the heme, thus favoring the apparent most reactive binding mode, regardless of the enzyme form. The ITC data is in agreement with our interpretation of the C10 alkyl chain role and helped to rationalize the significantly lower experimental MIC value observed for INH-C10. This compound seems to be able to counterbalance most of the conformational restrictions introduced by the mutation, which are thought to be responsible for the decrease in INH activity in the mutated strain. Therefore, INH-C10 appears to be a very promising lead compound for drug development.

Light controlled synthesis of nucleic acids

Dissertação apresentada para obtenção do grau de Doutor em Bioquímica - especialidade Biotecnologia, pela Universidade Nova de Lisboa,Faculdade de Ciências e Tecnologia

New and low cost plastic membrane electrode with low detection limits for sulfadimethoxine determination in aquaculture waters

Sulfadimethoxine (SDM) is one of the drugs, often used in the aquaculture sector to prevent the spread of disease in freshwater fish aquaculture. Its spread through the soil and surface water can contribute to an increase in bacterial resistance. It is therefore important to control this product in the environment. This work proposes a simple and low-cost potentiometric device to monitor the levels of SDM in aquaculture waters, thus avoiding its unnecessary release throughout the environment. The device combines a micropipette tip with a PVC membrane selective to SDM, prepared from an appropriate cocktail, and an inner reference solution. The membrane includes 1% of a porphyrin derivative acting as ionophore and a small amount of a lipophilic cationic additive (corresponding to 0.2% in molar ratio). The composition of the inner solution was optimized with regard to the kind and/or concentration of primary ion, chelating agent and/or a specific interfering charged species, in different concentration ranges. Electrodes constructed with inner reference solutions of 1 × 10−8 mol/L SDM and 1 × 10−4 mol/L chromate ion showed the best analytical features. Near-Nernstian response was obtained with slopes of −54.1 mV/decade, an extraordinary detection limit of 7.5 ng/mL (2.4 × 10−8 mol/L) when compared with other electrodes of the same type. The reproducibility, stability and response time are good and even better than those obtained by liquid contact ISEs. Recovery values of 98.9% were obtained from the analysis of aquaculture water samples.

Fractional Dynamics of Computer Virus Propagation

We propose a fractional model for computer virus propagation. The model includes the interaction between computers and removable devices. We simulate numerically the model for distinct values of the order of the fractional derivative and for two sets of initial conditions adopted in the literature. We conclude that fractional order systems reveal richer dynamics than the classical integer order counterpart. Therefore, fractional dynamics leads to time responses with super-fast transients and super-slow evolutions towards the steady-state, effects not easily captured by the integer order models.

Riesz potential versus fractional Laplacian

This paper starts by introducing the Grünwald–Letnikov derivative, the Riesz potential and the problem of generalizing the Laplacian. Based on these ideas, the generalizations of the Laplacian for 1D and 2D cases are studied. It is presented as a fractional version of the Cauchy–Riemann conditions and, finally, it is discussed with the n-dimensional Laplacian.

Efficient Legendre spectral tau algorithm for solving two-sided space-time Caputo fractional advection-dispersion equation

In this paper we present the operational matrices of the left Caputo fractional derivative, right Caputo fractional derivative and Riemann–Liouville fractional integral for shifted Legendre polynomials. We develop an accurate numerical algorithm to solve the two-sided space–time fractional advection–dispersion equation (FADE) based on a spectral shifted Legendre tau (SLT) method in combination with the derived shifted Legendre operational matrices. The fractional derivatives are described in the Caputo sense. We propose a spectral SLT method, both in temporal and spatial discretizations for the two-sided space–time FADE. This technique reduces the two-sided space–time FADE to a system of algebraic equations that simplifies the problem. Numerical results carried out to confirm the spectral accuracy and efficiency of the proposed algorithm. By selecting relatively few Legendre polynomial degrees, we are able to get very accurate approximations, demonstrating the utility of the new approach over other numerical methods.

Nonlinear Dynamics for Local Fractional Burgers Equation Arising in Fractal Flow

The local fractional Burgers’ equation (LFBE) is investigated from the point of view of local fractional conservation laws envisaging a nonlinear local fractional transport equation with a linear non-differentiable diffusion term. The local fractional derivative transformations and the LFBE conversion to a linear local fractional diffusion equation are analyzed.

Introducing numerical analysis tools in engineering: a Scilab user case in electronics course

Software tools in education became popular since the widespread of personal computers. Engineering courses lead the way in this development and these tools became almost a standard. Engineering graduates are familiar with numerical analysis tools but also with simulators (e.g. electronic circuits), computer assisted design tools and others, depending on the degree. One of the main problems with these tools is when and how to start use them so that they can be beneficial to students and not mere substitutes for potentially difficult calculations or design. In this paper a software tool to be used by first year students in electronics/electricity courses is presented. The growing acknowledgement and acceptance of open source software lead to the choice of an open source software tool – Scilab, which is a numerical analysis tool – to develop a toolbox. The toolbox was developed to be used as standalone or integrated in an e-learning platform. The e-learning platform used was Moodle. The first approach was to assess the mathematical skills necessary to solve all the problems related to electronics and electricity courses. Analysing the existing circuit simulators software tools, it is clear that even though they are very helpful by showing the end result they are not so effective in the process of the students studying and self learning since they show results but not intermediate steps which are crucial in problems that involve derivatives or integrals. Also, they are not very effective in obtaining graphical results that could be used to elaborate reports and for an overall better comprehension of the results. The developed tool was based on the numerical analysis software Scilab and is a toolbox that gives their users the opportunity to obtain the end results of a circuit analysis but also the expressions obtained when derivative and integrals calculations, plot signals, obtain vector diagrams, etc. The toolbox runs entirely in the Moodle web platform and provides the same results as the standalone application. The students can use the toolbox through the web platform (in computers where they don't have installation privileges) or in their personal computers by installing both the Scilab software and the toolbox. This approach was designed for first year students from all engineering degrees that have electronics/electricity courses in their curricula.

Bipedal Locomotion: A Fractional CPG for Generating Patterns

Proceedings of the 10th Conference on Dynamical Systems Theory and Applications

Simple Kinematic Design for Evading the Forced Oscillation of a Car-Wheel Suspension System

An adaptive control damping the forced vibration of a car while passing along a bumpy road is investigated. It is based on a simple kinematic description of the desired behavior of the damped system. A modified PID controller containing an approximation of Caputo’s fractional derivative suppresses the high-frequency components related to the bumps and dips, while the low frequency part of passing hills/valleys are strictly traced. Neither a complete dynamic model of the car nor ’a priori’ information on the surface of the road is needed. The adaptive control realizes this kinematic design in spite of the existence of dynamically coupled, excitable internal degrees of freedom. The method is investigated via Scicos-based simulation in the case of a paradigm. It was found that both adaptivity and fractional order derivatives are essential parts of the control that can keep the vibration of the load at bay without directly controlling its motion.

Paracoccidioidomycosis: infiltrated, sarcoid-like cutaneous lesions misinterpreted as tuberculoid leprosy

The authors report a case of paracoccidioidomycosis misinterpreted as tuberculoid leprosy, both on clinical and histological examination. Sarcoid-like cutaneous lesion as the initial presentation is rare in young patient with paracoccidioidomycosis and can simulate other infectious or inflammatory diseases. On histology, tuberculoid granuloma presented similar difficulties. Treatment with dapsone, a sulfonamide derivative, could have delayed the presumed natural clinical course to the classical juvenile type of paracoccidioidomycosis, observed only 24 months after the patient had been treated for leprosy.

Fractional State Space Analysis of Temperature Time Series

Atmospheric temperatures characterize Earth as a slow dynamics spatiotemporal system, revealing long-memory and complex behavior. Temperature time series of 54 worldwide geographic locations are considered as representative of the Earth weather dynamics. These data are then interpreted as the time evolution of a set of state space variables describing a complex system. The data are analyzed by means of multidimensional scaling (MDS), and the fractional state space portrait (fSSP). A centennial perspective covering the period from 1910 to 2012 allows MDS to identify similarities among different Earth’s locations. The multivariate mutual information is proposed to determine the “optimal” order of the time derivative for the fSSP representation. The fSSP emerges as a valuable alternative for visualizing system dynamics.

The inhibitory activity of synthetic compounds and ions against transporters of multi-drug resistant bacteria

RESUMO: Sessenta e três derivados de hidantoína foram utilizados para avaliar possíveis efeitos de modulação na actividade das bombas de efluxo (BE) na Salmonella NCTC 13349 utilizando um método fluorimétrico semi-automático. Nenhum dos compostos apresentaram actividade anti-bacteriana até concentrações de 240 mg/L. Entre todos os compostos, SZ-7 demonstrou possuir propriedades de modulação de effluxo na presença de glucose. Para testar esta actividade, estirpes de Salmonella resistentes à ciprofloxacina, induzidas a elevados níveis de resistência com sobre-expressão de BE, foram expostas ao SZ-7. Este derivado afectou a susceptibilidade das estirpes à ciprofloxacina. Uma vez que os 63 compostos estudados apresentaram pouco efeito inibitório /cumulativo, apesar de serem conhecidos pelos seus efeitos moduladores de BE-dependentes de iões em eucariotas, foi questionado o papel dos iões na regulação de BE bacterianas, que poderão influenciar a eficácia de novos compostos. Para este estudo, utilizamos a Escherichia coli AG100 como modelo, devido ao extenso conhecimento no que respeita a estrutura e actividade das BE. Devido à importância de iões de cálcio (Ca2+) nos canais de transporte membranar e na actividade de ATPases, a sua actividade na modulação do efluxo foi investigada. De resultados anteriormente obtidos concluiu-se que a pH 5 o efluxo é independente de energia metabólica; contudo, a pH 8 é absolutamente dependente, sendo que o Ca2+ é indispensável para manter a actividade das ATPases bacterianas. A acumulação/effluxo de EtBr pela E. coli AG100 foi determinada na presença/ausência de Ca2+, clorpromazina (inibidor de ligação de Ca2+ a proteínas), e ácido etilenodiamino tetra-acético (quelante de Ca2+). Acumulação/effluxo aumentou a pH 8, contudo o Ca2+ reverte estes efeitos evidenciando a sua importância no funcionamento das BE bacterianas. Em resumo este trabalho colocou em evidência que muitos aspectos bioquímicos e bioenergéticos devem ser tomados em consideração no estudo da resistência bacteriana mediada por BE.------- ABSTRACT: Sixty-three hydantoin derivatives were evaluated for their modulating effects on efflux pump (EP) activity of Salmonella NCTC 13349 utilizing a semi-automatic fluorometric method. None of the compounds presented antibacterial activities at concentrations as high as 240 mg/L. Among all compounds, SZ-7 showed possible efflux modulating activity in the presence of glucose, indicative of a potential EP inhibitor. To verify its potential effects, ciprofloxacin-resistant Salmonella strains, induced to high level resistance with over-expressing EPs, were exposed to SZ-7. This derivative affected the susceptibility of the ciprofloxacin-resistant strains. Since the 63 compounds studied had very low inhibitory/accumulative effects, even though their known for being efficient in modulating ion-driven eukaryotic EPs, we questioned whether ions had a leading role in regulating bacterial EPs, influencing the effectiveness of new compounds. For this study we used Escherichia coli AG100 as a model, due to the extensive knowledge on its EPs structure and activity. Owing the importance of calcium ions (Ca2+) for membrane transport channels and activity of ATPases, the role of Ca2+ was investigated. From previous results we concluded that at pH 5 efflux is independent of metabolic energy; however, at pH 8 it is entirely dependent of metabolic energy and the Ca2+ ions are essential to maintain the activity of bacterial ATPases. Accumulation and efflux of ethidium bromide (EtBr) by E. coli AG100 was determined in the presence and absence of Ca2+, chlorpromazine (inhibitor of Ca2+-binding to proteins), and ethylenediaminetetraacetic acid (Ca2+ chelator). Accumulation of EtBr increased at pH 8; however Ca2+ reversed these effects providing information as to the importance of this ion in the regulation of bacterial EP systems. Overall this work puts in evidence that many biochemical and bioenergetic aspects related to the strains physiology need to be taken into consideration in bacterial drug resistance mediated by EPs.