Ordinal Arithmetic: A Case Study for Rippling in a Higher Order Domain

This paper reports a case study in the use of proof planning in the context of higher order syntax. Rippling is a heuristic for guiding rewriting steps in induction that has been used successfully in proof planning inductive proofs using first order representations. Ordinal arithmetic provides a natural set of higher order examples on which transfinite induction may be attempted using rippling. Previously Boyer-Moore style automation could not be applied to such domains. We demonstrate that a higher-order extension of the rippling heuristic is sufficient to plan such proofs automatically. Accordingly, ordinal arithmetic has been implemented in lambda-clam, a higher order proof planning system for induction, and standard undergraduate text book problems have been successfully planned. We show the synthesis of a fixpoint for normal ordinal functions which demonstrates how our automation could be extended to produce more interesting results than the textbook examples tried so far.

Structural and Biochemical Characterization of Peroxiredoxin Q beta from Xylella fastidiosa CATALYTIC MECHANISM and HIGH REACTIVITY

The phytopathogenic bacterium Xylella fastidiosa is the etiological agent of various plant diseases. To survive under oxidative stress imposed by the host, microorganisms express antioxidant proteins, including cysteine-based peroxidases named peroxiredoxins. This work is a comprehensive analysis of the catalysis performed by PrxQ from X. fastidiosa (XfPrxQ) that belongs to a peroxiredoxin class still poorly characterized and previously considered as moderately reactive toward hydroperoxides. Contrary to these assumptions, our competitive kinetics studies have shown that the second-order rate constants of the peroxidase reactions of XfPrxQ with hydrogen peroxide and peroxynitrite are in the order of 107 and 106 M(-1) s(-1), respectively, which are as fast as the most efficient peroxidases. The XfPrxQ disulfides were only slightly reducible by dithiothreitol; therefore, the identification of a thioredoxin system as the probable biological reductant of XfPrxQ was a relevant finding. We also showed by site-specific mutagenesis and mass spectrometry that an intramolecular disulfide bond between Cys-47 and Cys-83 is generated during the catalytic cycle. Furthermore, we elucidated the crystal structure of XfPrxQ C47S in which Ser-47 and Cys-83 lie similar to 12.3 angstrom apart. Therefore, significant conformational changes are required for disulfide bond formation. In fact, circular dichroism data indicated that there was a significant redox-dependent unfolding of alpha-helices, which is probably triggered by the peroxidatic cysteine oxidation. Finally, we proposed a model that takes data from this work as well data as from the literature into account.

Phase transitions in gene networks evolved under different selection rules

Mathematical models of gene regulation are a powerful tool for understanding the complex features of genetic control. While various modeling efforts have been successful at explaining gene expression dynamics, much less is known about how evolution shapes the structure of these networks. An important feature of gene regulatory networks is their stability in response to environmental perturbations. Regulatory systems are thought to have evolved to exist near the transition between stability and instability, in order to have the required stability to environmental fluctuations while also being able to achieve a wide variety of functions (corresponding to different dynamical patterns). We study a simplified model of gene network evolution in which links are added via different selection rules. These growth models are inspired by recent work on `explosive' percolation which shows that when network links are added through competitive rather than random processes, the connectivity phase transition can be significantly delayed, and when it is reached, it appears to be first order (discontinuous, e.g., going from no failure at all to large expected failure) instead of second order (continuous, e.g., going from no failure at all to very small expected failure). We find that by modifying the traditional framework for networks grown via competitive link addition to capture how gene networks evolve to avoid damage propagation, we also see significant delays in the transition that depend on the selection rules, but the transitions always appear continuous rather than `explosive'.

Avaliação da resposta ao stress de gatas hospitalizadas no período pós-cirúrgico em distintas condições de macroambiente

Dissertação de Mestrado Integrado em Medicina Veterinária

Estudo comparativo do desempenho de controladores robustos aplicados a um sistema de tanques acoplados.

Currently the uncertain system has attracted much academic community from the standpoint of scientific research and also practical applications. A series of mathematical approaches emerge in order to troubleshoot the uncertainties of real physical systems. In this context, the work presented here focuses on the application of control theory in a nonlinear dynamical system with parametric variations in order and robustness. We used as the practical application of this work, a system of tanks Quanser associates, in a configuration, whose mathematical model is represented by a second order system with input and output (SISO). The control system is performed by PID controllers, designed by various techniques, aiming to achieve robust performance and stability when subjected to parameter variations. Other controllers are designed with the intention of comparing the performance and robust stability of such systems. The results are obtained and compared from simulations in Matlab-simulink.

Just imaginary: delimiting social inclusion in higher education

This paper explores the notion of a 'just imaginary' for social inclusion in higher education. It responds to the current strategy of OECD nations to expand higher education and increase graduate numbers, as a way of securing a competitive advantage in the global knowledge economy. The Australian higher education system provides the case for analysis. Three dilemmas for social inclusion policy in this context are identified: questions of sustainability, aspiration and opportunity. The paper argues that while social inclusion policy has 'first-order' effects in higher education, a just imaginary is required for more inclusive 'second-order' effects to be realized. It concludes that transformation of the current imaginary will require a more robust theorization of relations between social inclusion and higher education, to give new and unifying meaning to existing practices and to generate new ones. Short of this, social inclusion may be little more than just imaginary.

Strain localisation patterns under equal-channel angular pressing

Instabilities of plastic flow in the form of localised shear bands were experimentally observed to result from equal-channel angular pressing (ECAP) of magnesium alloy AZ31. The appearance of shear bands and their spacing were dependent on velocity of the pressing and applied back-pressure. A generic gradient plasticity theory involving second-order strain gradient terms in a constitutive model was applied to the case of AZ31 deformed by ECAP. Linear stability analysis was applied to the set of equations describing the deformation behaviour in the process zone idealised as a planar shear zone. A full analytical solution providing a dispersion relation between the rate of growth of a perturbation and the wave number was obtained. It was shown that the pattern of incipient localised shear bands exhibits a spectrum of characteristic lengths corresponding to admissible wave numbers. The interval of the spectrum of wave numbers of viable, i.e. growing, perturbations predicted by linear stability analysis was shown to be in good agreement with the experimentally observed spectrum. The effect of back-pressure applied during ECAP was also considered. The predicted displacement of the shear band spectrum towards lower wave numbers, shown to be a result of the decreased shear strain rate in the shear zone, was consistent with the experimentally observed increase of the band spacing with increased back-pressure. A good predictive capability of the general modelling frame used in conjunction with linear stability analysis was thus demonstrated in the instance of the particular alloy system and the specific processing conditions considered.

Hybrid Monte Carlo algorithm for the double exchange model

The Hybrid Monte Carlo algorithm is adapted to the simulation of a system of classical degrees of freedom coupled to non self-interacting lattices fermions. The diagonalization of the Hamiltonian matrix is avoided by introducing a path-integral formulation of the problem, in d + 1 Euclidean space–time. A perfect action formulation allows to work on the continuum Euclidean time, without need for a Trotter–Suzuki extrapolation. To demonstrate the feasibility of the method we study the Double Exchange Model in three dimensions. The complexity of the algorithm grows only as the system volume, allowing to simulate in lattices as large as 163 on a personal computer. We conclude that the second order paramagnetic–ferromagnetic phase transition of Double Exchange Materials close to half-filling belongs to the Universality Class of the three-dimensional classical Heisenberg model.

Variational mean-field approach to the double-exchange model

It has been recently shown that the double exchange Hamiltonian, with weak antiferromagnetic interactions, has a richer variety of first- and second-order transitions than previously anticipated, and that such transitions are consistent with the magnetic properties of manganites. Here we present a thorough discussion of the variational mean-field approach that leads to these results. We also show that the effect of the Berry phase turns out to be crucial to produce first-order paramagnetic-ferromagnetic transitions near half filling with transition temperatures compatible with the experimental situation. The computation relies on two crucial facts: the use of a mean-field ansatz that retains the complexity of a system of electrons with off-diagonal disorder, not fully taken into account by the mean-field techniques, and the small but significant antiferromagnetic superexchange interaction between the localized spins.

A staggered approach for the coupling of Cahn–Hilliard type diffusion and finite strain elasticity

We develop an algorithm and computational implementation for simulation of problems that combine Cahn–Hilliard type diffusion with finite strain elasticity. We have in mind applications such as the electro-chemo- mechanics of lithium ion (Li-ion) batteries. We concentrate on basic computational aspects. A staggered algorithm is pro- posed for the coupled multi-field model. For the diffusion problem, the fourth order differential equation is replaced by a system of second order equations to deal with the issue of the regularity required for the approximation spaces. Low order finite elements are used for discretization in space of the involved fields (displacement, concentration, nonlocal concentration). Three (both 2D and 3D) extensively worked numerical examples show the capabilities of our approach for the representation of (i) phase separation, (ii) the effect of concentration in deformation and stress, (iii) the effect of Electronic supplementary material The online version of this article (doi:10.1007/s00466-015-1235-1) contains supplementary material, which is available to authorized users. B P. Areias pmaa@uevora.pt 1 Department of Physics, University of Évora, Colégio Luís António Verney, Rua Romão Ramalho, 59, 7002-554 Évora, Portugal 2 ICIST, Lisbon, Portugal 3 School of Engineering, Universidad de Cuenca, Av. 12 de Abril s/n. 01-01-168, Cuenca, Ecuador 4 Institute of Structural Mechanics, Bauhaus-University Weimar, Marienstraße 15, 99423 Weimar, Germany strain in concentration, and (iv) lithiation. We analyze con- vergence with respect to spatial and time discretization and found that very good results are achievable using both a stag- gered scheme and approximated strain interpolation.

Constructive development of the solutions of linear equations in introductory ordinary differential equations

The solution of linear ordinary differential equations (ODEs) is commonly taught in first year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognising what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to tables of solutions, is an important skill for students to carry with them to advanced studies in mathematics. In this study we describe a teaching and learning strategy that replaces the traditional algorithmic, transmission presentation style for solving ODEs with a constructive, discovery based approach where students employ their existing skills as a framework for constructing the solutions of first and second order linear ODEs. We elaborate on how the strategy was implemented and discuss the resulting impact on a first year undergraduate class. Finally we propose further improvements to the strategy as well as suggesting other topics which could be taught in a similar manner.

Developing an integrative model for understanding innovation adoption

We develop and test a theoretically-based integrative model of organizational innovation adoption. Confirmatory factor analyses using responses from 134 organizations showed that the hypothesized second-order model was a better fit to the data than the traditional model of independent factors. Furthermore, although not all elements were significant, the hypothesized model fit adoption better than the traditional model.

Patterns of query reformulation during web searching

Query reformulation is a key user behavior during Web search. Our research goal is to develop predictive models of query reformulation during Web searching. This article reports results from a study in which we automatically classified the query-reformulation patterns for 964,780 Web searching sessions, composed of 1,523,072 queries, to predict the next query reformulation. We employed an n-gram modeling approach to describe the probability of users transitioning from one query-reformulation state to another to predict their next state. We developed first-, second-, third-, and fourth-order models and evaluated each model for accuracy of prediction, coverage of the dataset, and complexity of the possible pattern set. The results show that Reformulation and Assistance account for approximately 45% of all query reformulations; furthermore, the results demonstrate that the first- and second-order models provide the best predictability, between 28 and 40% overall and higher than 70% for some patterns. Implications are that the n-gram approach can be used for improving searching systems and searching assistance.

Stochastic modelling of financial time series with memory and multifractal scaling

Financial processes may possess long memory and their probability densities may display heavy tails. Many models have been developed to deal with this tail behaviour, which reflects the jumps in the sample paths. On the other hand, the presence of long memory, which contradicts the efficient market hypothesis, is still an issue for further debates. These difficulties present challenges with the problems of memory detection and modelling the co-presence of long memory and heavy tails. This PhD project aims to respond to these challenges. The first part aims to detect memory in a large number of financial time series on stock prices and exchange rates using their scaling properties. Since financial time series often exhibit stochastic trends, a common form of nonstationarity, strong trends in the data can lead to false detection of memory. We will take advantage of a technique known as multifractal detrended fluctuation analysis (MF-DFA) that can systematically eliminate trends of different orders. This method is based on the identification of scaling of the q-th-order moments and is a generalisation of the standard detrended fluctuation analysis (DFA) which uses only the second moment; that is, q = 2. We also consider the rescaled range R/S analysis and the periodogram method to detect memory in financial time series and compare their results with the MF-DFA. An interesting finding is that short memory is detected for stock prices of the American Stock Exchange (AMEX) and long memory is found present in the time series of two exchange rates, namely the French franc and the Deutsche mark. Electricity price series of the five states of Australia are also found to possess long memory. For these electricity price series, heavy tails are also pronounced in their probability densities. The second part of the thesis develops models to represent short-memory and longmemory financial processes as detected in Part I. These models take the form of continuous-time AR(∞) -type equations whose kernel is the Laplace transform of a finite Borel measure. By imposing appropriate conditions on this measure, short memory or long memory in the dynamics of the solution will result. A specific form of the models, which has a good MA(∞) -type representation, is presented for the short memory case. Parameter estimation of this type of models is performed via least squares, and the models are applied to the stock prices in the AMEX, which have been established in Part I to possess short memory. By selecting the kernel in the continuous-time AR(∞) -type equations to have the form of Riemann-Liouville fractional derivative, we obtain a fractional stochastic differential equation driven by Brownian motion. This type of equations is used to represent financial processes with long memory, whose dynamics is described by the fractional derivative in the equation. These models are estimated via quasi-likelihood, namely via a continuoustime version of the Gauss-Whittle method. The models are applied to the exchange rates and the electricity prices of Part I with the aim of confirming their possible long-range dependence established by MF-DFA. The third part of the thesis provides an application of the results established in Parts I and II to characterise and classify financial markets. We will pay attention to the New York Stock Exchange (NYSE), the American Stock Exchange (AMEX), the NASDAQ Stock Exchange (NASDAQ) and the Toronto Stock Exchange (TSX). The parameters from MF-DFA and those of the short-memory AR(∞) -type models will be employed in this classification. We propose the Fisher discriminant algorithm to find a classifier in the two and three-dimensional spaces of data sets and then provide cross-validation to verify discriminant accuracies. This classification is useful for understanding and predicting the behaviour of different processes within the same market. The fourth part of the thesis investigates the heavy-tailed behaviour of financial processes which may also possess long memory. We consider fractional stochastic differential equations driven by stable noise to model financial processes such as electricity prices. The long memory of electricity prices is represented by a fractional derivative, while the stable noise input models their non-Gaussianity via the tails of their probability density. A method using the empirical densities and MF-DFA will be provided to estimate all the parameters of the model and simulate sample paths of the equation. The method is then applied to analyse daily spot prices for five states of Australia. Comparison with the results obtained from the R/S analysis, periodogram method and MF-DFA are provided. The results from fractional SDEs agree with those from MF-DFA, which are based on multifractal scaling, while those from the periodograms, which are based on the second order, seem to underestimate the long memory dynamics of the process. This highlights the need and usefulness of fractal methods in modelling non-Gaussian financial processes with long memory.

Fundamental solution and discrete random walk model for time-space fractional diffusion equation

In this paper, we consider a time-space fractional diffusion equation of distributed order (TSFDEDO). The TSFDEDO is obtained from the standard advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α∈(0,1], the first-order and second-order space derivatives by the Riesz fractional derivatives of orders β 1∈(0,1) and β 2∈(1,2], respectively. We derive the fundamental solution for the TSFDEDO with an initial condition (TSFDEDO-IC). The fundamental solution can be interpreted as a spatial probability density function evolving in time. We also investigate a discrete random walk model based on an explicit finite difference approximation for the TSFDEDO-IC.