Capacity sharing and stealing in serverbased real-time systems

A dynamic scheduler that supports the coexistence of guaranteed and non-guaranteed bandwidth servers is proposed. Overloads are handled by an efficient reclaiming of residual capacities originated by early completions as well as by allowing reserved capacity stealing of non-guaranteed bandwidth servers. The proposed dynamic budget accounting mechanism ensures that at a particular time the currently executing server is using a residual capacity, its own capacity or is stealing some reserved capacity, eliminating the need of additional server states or unbounded queues. The server to which the budget accounting is going to be performed is dynamically determined at the time instant when a capacity is needed. This paper describes and evaluates the proposed scheduling algorithm, showing that it can efficiently reduce the mean tardiness of periodic jobs. The achieved results become even more significant when tasks’ computation times have a large variance.

Diagnóstico de avarias em máquinas rotativas utilizando a análise de órbitas

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia Mecânica Perfil Manutenção e Produção

X Radiation dose implications in screening patients with ferromagnetic IOFBs prior to MRI: a literary review

Patients scheduled for a magnetic resonance imaging (MRI) scan sometimes require screening for ferromagnetic Intra Orbital Foreign Bodies (IOFBs). To assess this, they are required to fill out a screening protocol questionnaire before their scan. If it is established that a patient is at high risk, radiographic imaging is necessary. This review examines literature to evaluate which imaging modality should be used to screen for IOFBs, considering that the eye is highly sensitive to ionising radiation and any dose should be minimised. Method: Several websites and books were searched for information, these were as follows: PubMed, Science Direct, Web of Knowledge and Google Scholar. The terms searched related to IOFB, Ionising radiation, Magnetic Resonance Imaging Safety, Image Quality, Effective Dose, Orbits and X-ray. Thirty five articles were found, several were rejected due to age or irrelevance; twenty eight were eventually accepted. Results: There are several imaging techniques that can be used. Some articles investigated the use of ultrasound for investigation of ferromagnetic IOFBs of the eye and others discussed using Computed Tomography (CT) and X-ray. Some gaps in the literature were identified, mainly that there are no articles which discuss the lowest effective dose while having adequate image quality for orbital imaging. Conclusion: X-ray is the best method to identify IOFBs. The only problem is that there is no research which highlights exposure factors that maintain sufficient image quality for viewing IOFBs and keep the effective dose to the eye As Low As Reasonably Achievable (ALARA).

On chaos, transient chaos and ghosts in single populations models with allee effects

Density-dependent effects, both positive or negative, can have an important impact on the population dynamics of species by modifying their population per-capita growth rates. An important type of such density-dependent factors is given by the so-called Allee effects, widely studied in theoretical and field population biology. In this study, we analyze two discrete single population models with overcompensating density-dependence and Allee effects due to predator saturation and mating limitation using symbolic dynamics theory. We focus on the scenarios of persistence and bistability, in which the species dynamics can be chaotic. For the chaotic regimes, we compute the topological entropy as well as the Lyapunov exponent under ecological key parameters and different initial conditions. We also provide co-dimension two bifurcation diagrams for both systems computing the periods of the orbits, also characterizing the period-ordering routes toward the boundary crisis responsible for species extinction via transient chaos. Our results show that the topological entropy increases as we approach to the parametric regions involving transient chaos, being maximum when the full shift R(L)(infinity) occurs, and the system enters into the essential extinction regime. Finally, we characterize analytically, using a complex variable approach, and numerically the inverse square-root scaling law arising in the vicinity of a saddle-node bifurcation responsible for the extinction scenario in the two studied models. The results are discussed in the context of species fragility under differential Allee effects. (C) 2011 Elsevier Ltd. All rights reserved.

Topological entropy of catalytic sets: Hypercycles revisited

The dynamics of catalytic networks have been widely studied over the last decades because of their implications in several fields like prebiotic evolution, virology, neural networks, immunology or ecology. One of the most studied mathematical bodies for catalytic networks was initially formulated in the context of prebiotic evolution, by means of the hypercycle theory. The hypercycle is a set of self-replicating species able to catalyze other replicator species within a cyclic architecture. Hypercyclic organization might arise from a quasispecies as a way to increase the informational containt surpassing the so-called error threshold. The catalytic coupling between replicators makes all the species to behave like a single and coherent evolutionary multimolecular unit. The inherent nonlinearities of catalytic interactions are responsible for the emergence of several types of dynamics, among them, chaos. In this article we begin with a brief review of the hypercycle theory focusing on its evolutionary implications as well as on different dynamics associated to different types of small catalytic networks. Then we study the properties of chaotic hypercycles with error-prone replication with symbolic dynamics theory, characterizing, by means of the theory of topological Markov chains, the topological entropy and the periods of the orbits of unimodal-like iterated maps obtained from the strange attractor. We will focus our study on some key parameters responsible for the structure of the catalytic network: mutation rates, autocatalytic and cross-catalytic interactions.

How Complex, Probable, and Predictable is Genetically Driven Red Queen Chaos?

Coevolution between two antagonistic species has been widely studied theoretically for both ecologically- and genetically-driven Red Queen dynamics. A typical outcome of these systems is an oscillatory behavior causing an endless series of one species adaptation and others counter-adaptation. More recently, a mathematical model combining a three-species food chain system with an adaptive dynamics approach revealed genetically driven chaotic Red Queen coevolution. In the present article, we analyze this mathematical model mainly focusing on the impact of species rates of evolution (mutation rates) in the dynamics. Firstly, we analytically proof the boundedness of the trajectories of the chaotic attractor. The complexity of the coupling between the dynamical variables is quantified using observability indices. By using symbolic dynamics theory, we quantify the complexity of genetically driven Red Queen chaos computing the topological entropy of existing one-dimensional iterated maps using Markov partitions. Co-dimensional two bifurcation diagrams are also built from the period ordering of the orbits of the maps. Then, we study the predictability of the Red Queen chaos, found in narrow regions of mutation rates. To extend the previous analyses, we also computed the likeliness of finding chaos in a given region of the parameter space varying other model parameters simultaneously. Such analyses allowed us to compute a mean predictability measure for the system in the explored region of the parameter space. We found that genetically driven Red Queen chaos, although being restricted to small regions of the analyzed parameter space, might be highly unpredictable.

Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth models

In this paper, motivated by the interest and relevance of the study of tumor growth models, a central point of our investigation is the study of the chaotic dynamics and the bifurcation structure of Weibull-Gompertz-Fréchet's functions: a class of continuousdefined one-dimensional maps. Using symbolic dynamics techniques and iteration theory, we established that depending on the properties of this class of functions in a neighborhood of a bifurcation point PBB, in a two-dimensional parameter space, there exists an order regarding how the infinite number of periodic orbits are born: the Sharkovsky ordering. Consequently, the corresponding symbolic sequences follow the usual unimodal kneading sequences in the topological ordered tree. We verified that under some sufficient conditions, Weibull-Gompertz-Fréchet's functions have a particular bifurcation structure: a big bang bifurcation point PBB. This fractal bifurcations structure is of the so-called "box-within-a-box" type, associated to a boxe ω1, where an infinite number of bifurcation curves issues from. This analysis is done making use of fold and flip bifurcation curves and symbolic dynamics techniques. The present paper is an original contribution in the framework of the big bang bifurcation analysis for continuous maps.

Nonautonomous Graphs and Topological Entropy of Nonautonomous Lorenz Systems

In this work, we associate a p-periodic nonautonomous graph to each p-periodic nonautonomous Lorenz system with finite critical orbits. We develop Perron-Frobenius theory for nonautonomous graphs and use it to calculate their entropy. Finally, we prove that the topological entropy of a p-periodic nonautonomous Lorenz system is equal to the entropy of its associated nonautonomous graph.

Strange Dynamics in a Fractional Derivative of Complex-Order Network of Chaotic Oscillators

We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z3 × Z5 cyclic symmetry group. The complex derivative Dα±jβ, with α, β ∈ R+ is a generalization of the concept of integer order derivative, where α = 1, β = 0. Each cell is modeled by the Chen oscillator. Numerical simulations of the coupled cell system associated with the network expose patterns such as equilibria, periodic orbits, relaxation oscillations, quasiperiodic motion, and chaos, in one or in two rings of cells. In addition, fixing β = 0.8, we perceive differences in the qualitative behavior of the system, as the parameter c ∈ [13, 24] of the Chen oscillator and/or the real part of the fractional derivative, α ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, are varied. Some patterns produced by the coupled system are constrained by the network architecture, but other features are only understood in the light of the internal dynamics of each cell, in this case, the Chen oscillator. What is more important, architecture and/or internal dynamics?

Model spaces and Toeplitz kernels in reflexive Hardy spaces

This paper considers model spaces in an Hp setting. The existence of unbounded functions and the characterisation of maximal functions in a model space are studied, and decomposition results for Toeplitz kernels, in terms of model spaces, are established

Bifurcations of homoclinic tangency in two-dimensional area-preserving and reversible maps

Report for the scientific sojourn at the Research Institute for Applied Mathematics and Cybernetics, Nizhny Novgorod, Russia, from July to September 2006. Within the project, bifurcations of orbit behavior in area-preserving and reversible maps with a homoclinic tangency were studied. Finitely smooth normal forms for such maps near saddle fixed points were constructed and it was shown that they coincide in the main order with the analytical Birkhoff-Moser normal form. Bifurcations of single-round periodic orbits for two-dimensional symplectic maps close to a map with a quadratic homoclinic tangency were studied. The existence of one- and two-parameter cascades of elliptic periodic orbits was proved.

A General and Intuitive Envelope Theorem

We present an envelope theorem for establishing first-order conditions in decision problems involving continuous and discrete choices. Our theorem accommodates general dynamic programming problems, even with unbounded marginal utilities. And, unlike classical envelope theorems that focus only on differentiating value functions, we accommodate other endogenous functions such as default probabilities and interest rates. Our main technical ingredient is how we establish the differentiability of a function at a point: we sandwich the function between two differentiable functions from above and below. Our theory is widely applicable. In unsecured credit models, neither interest rates nor continuation values are globally differentiable. Nevertheless, we establish an Euler equation involving marginal prices and values. In adjustment cost models, we show that first-order conditions apply universally, even if optimal policies are not (S,s). Finally, we incorporate indivisible choices into a classic dynamic insurance analysis.

L'albedo lunar i els satèl·lits: Recerca sobre els efectes de l'albedo lunar en les plaques solars d'un satèl·lit artificial que orbita al voltant de la Lluna

Treball de recerca realitzat per una alumna d'ensenyament secundari i guardonat amb un Premi CIRIT per fomentar l'esperit científic del Jovent l'any 2009. L’albedo lunar i els satèl•lits és un treball que relaciona l’enginyeria aeroespacial amb l’astronomia. El seu objectiu principal investigar si l’albedo lunar, els rajos de sol reflectits a la superfície lunar, pot modificar significativament la temperatura de les plaques solars d’un satèl•lit artificial que orbiti la Lluna i, en conseqüència, afectar-ne el rendiment. El segon objectiu del treball és calcular si seria possible fer un mapa d’albedo lunar, a partir de la temperatura d’un satèl•lit en òrbita al voltant de la Lluna, que permetria conèixer amb més precisió la composició de la superfície lunar. Després d’adquirir els fonaments teòrics necessaris per a realitzar el treball, del procés per a trobar la manera de dur a terme els càlculs i d’efectuar els càlculs en si, les conclusions del treball són que l’albedo lunar causa un augment de temperatura en els satèl•lits prou significatiu per afectar-ne el rendiment; i que amb les temperatures enregistrades per un satèl•lit en òrbita al voltant de la Lluna es podria crear un mapa d’albedo. Aquesta recerca ha estat feta per suggeriment i sota la supervisió del CTAE (Centre de Tecnologia Aeroespacial) per analitzar si els resultats són aplicables al satèl•lit que s’enviarà a la Lluna, Lunar Mission BW1.

Exponentially small splitting of separatrices in the perturbed McMillan map

The McMillan map is a one-parameter family of integrable symplectic maps of the plane, for which the origin is a hyperbolic fixed point with a homoclinic loop, with small Lyapunov exponent when the parameter is small. We consider a perturbation of the McMillan map for which we show that the loop breaks in two invariant curves which are exponentially close one to the other and which intersect transversely along two primary homoclinic orbits. We compute the asymptotic expansion of several quantities related to the splitting, namely the Lazutkin invariant and the area of the lobe between two consecutive primary homoclinic points. Complex matching techniques are in the core of this work. The coefficients involved in the expansion have a resurgent origin, as shown in [MSS08].

Generic Nekhoroshev theory without small divisors

In this article, we present a new approach of Nekhoroshev theory for a generic unperturbed Hamiltonian which completely avoids small divisors problems. The proof is an extension of a method introduced by P. Lochak which combines averaging along periodic orbits with simultaneous Diophantine approximation and uses geometric arguments designed by the second author to handle generic integrable Hamiltonians. This method allows to deal with generic non-analytic Hamiltonians and to obtain new results of generic stability around linearly stable tori.