Applications of a Collaborative Open Object Oriented Learning Environment to Electronics, Computing and Mathematics Education

A lightweight Java application suite has been developed and deployed allowing collaborative learning between students and tutors at remote locations. Students can engage in group activities online and also collaborate with tutors. A generic Java framework has been developed and applied to electronics, computing and mathematics education. The applications are respectively: (a) a digital circuit simulator, which allows students to collaborate in building simple or complex electronic circuits; (b) a Java programming environment where the paradigm is behavioural-based robotics, and (c) a differential equation solver useful in modelling of any complex and nonlinear dynamic system. Each student sees a common shared window on which may be added text or graphical objects and which can then be shared online. A built-in chat room supports collaborative dialogue. Students can work either in collaborative groups or else in teams as directed by the tutor. This paper summarises the technical architecture of the system as well as the pedagogical implications of the suite. A report of student evaluation is also presented distilled from use over a period of twelve months. We intend this suite to facilitate learning between groups at one or many institutions and to facilitate international collaboration. We also intend to use the suite as a tool to research the establishment and behaviour of collaborative learning groups. We shall make our software freely available to interested researchers.

A Discretization of the Hadamard fractional derivative

We present a new discretization for the Hadamard fractional derivative, that simplifies the computations. We then apply the method to solve a fractional differential equation and a fractional variational problem with dependence on the Hadamard fractional derivative.

Repeated evolution of heat responsiveness among Brassicaceae COPIA transposable elements

Eukaryotic genomes contain repetitive DNA sequences. This includes simple repeats and more complex transposable elements (TEs). Many TEs reach high copy numbers in the host genome, owing to their amplification abilities by specific mechanisms. There is growing evidence that TEs contribute to gene transcriptional regulation. However, excess of TE activity may lead to reduced genome stability. Therefore, TEs are suppressed by the transcriptional gene silencing machinery via specific chromatin modifications. In contrary, effectiveness of the epigenetic silencing mechanisms imposes risk for TE survival in the host genome. Therefore, TEs may have evolved specific strategies for bypassing epigenetic control and allowing the emergence of new TE copies. Recent studies suggested that the epigenetic silencing can be, at least transiently, attenuated by heat stress in A. thaliana. Heat stress induced strong transcriptional activation of COPIA78 family LTR-retrotransposons named ONSEN, and even their transposition in mutants deficient in siRNA-biogenesis. ONSEN transcriptional activation was facilitated by the presence of heat responsive elements (HREs) within the long terminal repeats, which serve as a binding platform for the HEAT SHOCK FACTORs (HSFs). This thesis focused on the evolution of ONSEN heat responsiveness in Brassicaceae. By using whole-transcriptome sequencing approach, multiple Arabidopsis lyrata ONSENs with conserved heat response were found and together with ONSENs from other Brassicaceae were used to reconstruct the evolution of ONSEN HREs. This indicated ancestral situation with two, in palindrome organized, HSF binding motifs. In the genera Arabidopsis and Ballantinia, a local duplication of this locus increased number of HSF binding motifs to four, forming a high-efficiency HRE. In addition, whole transcriptome analysis revealed novel heat-responsive TE families COPIA20, COPIA37 and HATE. Notably, HATE represents so far unknown COPIA family which occurs in several Brassicaceae species but is absent in A. thaliana. Putative HREs were identified within the LTRs of COPIA20, COPIA37 and HATE of A. lyrata, and could be preliminarily validated by transcriptional analysis upon heat induction in subsequent survey of Brassicaeae species. Subsequent phylogenetic analysis indicated a repeated evolution of heat responsiveness within Brassicaceae COPIA LTR-retrotransposons. This indicates that acquisition of heat responsiveness may represent a successful strategy for survival of TEs within the host genome.

CpxR activates MexAB-OprM efflux pump expression and enhances antibiotic resistance in both laboratory and clinical nalB-type isolates of Pseudomonas aeruginosa

Resistance-Nodulation-Division (RND) efflux pumps are responsible for multidrug resistance in Pseudomonas aeruginosa. In this study, we demonstrate that CpxR, previously identified as a regulator of the cell envelope stress response in Escherichia coli, is directly involved in activation of expression of RND efflux pump MexAB-OprM in P. aeruginosa. A conserved CpxR binding site was identified upstream of the mexA promoter in all genome-sequenced P. aeruginosa strains. CpxR is required to enhance mexAB-oprM expression and drug resistance, in the absence of repressor MexR, in P. aeruginosa strains PA14. As defective mexR is a genetic trait associated with the clinical emergence of nalB-type multidrug resistance in P. aeruginosa during antibiotic treatment, we investigated the involvement of CpxR in regulating multidrug resistance among resistant isolates generated in the laboratory via antibiotic treatment and collected in clinical settings. CpxR is required to activate expression of mexAB-oprM and enhances drug resistance, in the absence or presence of MexR, in ofloxacin-cefsulodin-resistant isolates generated in the laboratory. Furthermore, CpxR was also important in the mexR-defective clinical isolates. The newly identified regulatory linkage between CpxR and the MexAB-OprM efflux pump highlights the presence of a complex regulatory network modulating multidrug resistance in P. aeruginosa.

Hexagonal patterns in finite domains

In many mathematical models for pattern formation, a regular hexagonal pattern is stable in an infinite region. However, laboratory and numerical experiments are carried out in finite domains, and this imposes certain constraints on the possible patterns. In finite rectangular domains, it is shown that a regular hexagonal pattern cannot occur if the aspect ratio is rational. In practice, it is found experimentally that in a rectangular region, patterns of irregular hexagons are often observed. This work analyses the geometry and dynamics of irregular hexagonal patterns. These patterns occur in two different symmetry types, either with a reflection symmetry, involving two wavenumbers, or without symmetry, involving three different wavenumbers. The relevant amplitude equations are studied to investigate the detailed bifurcation structure in each case. It is shown that hexagonal patterns can bifurcate subcritically either from the trivial solution or from a pattern of rolls. Numerical simulations of a model partial differential equation are also presented to illustrate the behaviour.

Waves, bumps, and patterns in neural field theories

Neural field models of firing rate activity have had a major impact in helping to develop an understanding of the dynamics seen in brain slice preparations. These models typically take the form of integro-differential equations. Their non-local nature has led to the development of a set of analytical and numerical tools for the study of waves, bumps and patterns, based around natural extensions of those used for local differential equation models. In this paper we present a review of such techniques and show how recent advances have opened the way for future studies of neural fields in both one and two dimensions that can incorporate realistic forms of axo-dendritic interactions and the slow intrinsic currents that underlie bursting behaviour in single neurons.

Modeling electrocortical activity through improved local approximations of integral neural field equations

Neural field models of firing rate activity typically take the form of integral equations with space-dependent axonal delays. Under natural assumptions on the synaptic connectivity we show how one can derive an equivalent partial differential equation (PDE) model that properly treats the axonal delay terms of the integral formulation. Our analysis avoids the so-called long-wavelength approximation that has previously been used to formulate PDE models for neural activity in two spatial dimensions. Direct numerical simulations of this PDE model show instabilities of the homogeneous steady state that are in full agreement with a Turing instability analysis of the original integral model. We discuss the benefits of such a local model and its usefulness in modeling electrocortical activity. In particular we are able to treat "patchy'" connections, whereby a homogeneous and isotropic system is modulated in a spatially periodic fashion. In this case the emergence of a "lattice-directed" traveling wave predicted by a linear instability analysis is confirmed by the numerical simulation of an appropriate set of coupled PDEs. Article published and (c) American Physical Society 2007

Higher-order variational problems of Herglotz type

We obtain a generalized Euler–Lagrange differential equation and transversality optimality conditions for Herglotz-type higher-order variational problems. Illustrative examples of the new results are given.

Instabilities in threshold-diffusion equations with delay

The introduction of delays into ordinary or partial differential equation models is well known to facilitate the production of rich dynamics ranging from periodic solutions through to spatio-temporal chaos. In this paper we consider a class of scalar partial differential equations with a delayed threshold nonlinearity which admits exact solutions for equilibria, periodic orbits and travelling waves. Importantly we show how the spectra of periodic and travelling wave solutions can be determined in terms of the zeros of a complex analytic function. Using this as a computational tool to determine stability we show that delays can have very different effects on threshold systems with negative as opposed to positive feedback. Direct numerical simulations are used to confirm our bifurcation analysis, and to probe some of the rich behaviour possible for mixed feedback.

Effects of Drive Speed Modulation on Dynamics of Slender Rotating Structures

Slender rotating structures are used in many mechanical systems. These structures can suffer from undesired vibrations that can affect the components and safety of a system. Furthermore, since some these structures can operate in a harsh environment, installation and operation of sensors that are needed for closed-loop and collocated control schemes may not be feasible. Hence, the need for an open-loop non-collocated scheme for control of the dynamics of these structures. In this work, the effects of drive speed modulation on the dynamics of slender rotating structures are studied. Slender rotating structures are a type of mechanical rotating structures, whose length to diameter ratio is large. For these structures, the torsion mode natural frequencies can be low. In particular, for isotropic structures, the first few torsion mode frequencies can be of the same order as the first few bending mode frequencies. These situations can be conducive for energy transfer amongst bending and torsion modes. Scenarios with torsional vibrations experienced by rotating structures with continuous rotor-stator contact occur in many rotating mechanical systems. Drill strings used in the oil and gas industry are an example of rotating structures whose torsional vibrations can be deleterious to the components of the drilling system. As a novel approach to mitigate undesired vibrations, the effects of adding a sinusoidal excitation to the rotation speed of a drill string are studied. A portion of the drill string located within a borewell is considered and this rotating structure has been modeled as an extended Jeffcott rotor and a sinusoidal excitation has been added to the drive speed of the rotor. After constructing a three-degree-of-freedom model to capture lateral and torsional motions, the equations of motions are reduced to a single differential equation governing torsional vibrations during continuous stator contact. An approximate solution has been obtained by making use of the Method of Direct Partition of Motions with the governing torsional equation of motion. The results showed that for a rotor undergoing forward or backward whirling, the addition of sinusoidal excitation to the drive speed can cause an increase in the equivalent torsional stiffness, smooth the discontinuous friction force at contact, and reduce the regions of negative slope in the friction coefficient variation with respect to speed. Experiments with a scaled drill string apparatus have also been conducted and the experimental results show good agreement with the numerical results obtained from the developed models. These findings suggest that the extended Jeffcott rotordynamics model can be useful for studies of rotor dynamics in situations with continuous rotor-stator contact. Furthermore, the results obtained suggest that the drive speed modulation scheme can have value for attenuating drill-string vibrations.

Credit risk & forward price models

Doutoramento em Gestão

Otimização evolucionária para problemas de transferência de calor em PCI usando MEC

Dissertação (mestrado)—Universidade de Brasília, Faculdade UnB Gama, Programa de Pós-graduação em Integridade de Materiais da Engenharia, 2015.

Symbolic dynamics generated by a hybrid chaotic systems

We consider piecewise defined differential dynamical systems which can be analysed through symbolic dynamics and transition matrices. We have a continuous regime, where the time flow is characterized by an ordinary differential equation (ODE) which has explicit solutions, and the singular regime, where the time flow is characterized by an appropriate transformation. The symbolic codification is given through the association of a symbol for each distinct regular system and singular system. The transition matrices are then determined as linear approximations to the symbolic dynamics. We analyse the dependence on initial conditions, parameter variation and the occurrence of global strange attractors.

Unbounded solutions for functional problems on the half-line

This paper presents an existence and localization result of unbounded solutions for a second-order differential equation on the half-line with functional boundary conditions. By applying unbounded upper and lower solutions, Green's functions and Schauder fixed point theorem, the existence of at least one solution is shown for the above problem. One example and one application to an Emden-Fowler equation are shown to illustrate our results.

Unbounded solutions for functional problems on the half-line

This paper presents an existence and localization result of unbounded solutions for a second-order differential equation on the half-line with functional boundary conditions. By applying unbounded upper and lower solutions, Green's functions and Schauder fixed point theorem, the existence of at least one solution is shown for the above problem. One example and one application to an Emden-Fowler equation are shown to illustrate our results.