On the analytical solutions of the Hindmarsh-Rose neuronal model

In this article we analytically solve the Hindmarsh-Rose model (Proc R Soc Lond B221:87-102, 1984) by means of a technique developed for strongly nonlinear problems-the step homotopy analysis method. This analytical algorithm, based on a modification of the standard homotopy analysis method, allows us to obtain a one-parameter family of explicit series solutions for the studied neuronal model. The Hindmarsh-Rose system represents a paradigmatic example of models developed to qualitatively reproduce the electrical activity of cell membranes. By using the homotopy solutions, we investigate the dynamical effect of two chosen biologically meaningful bifurcation parameters: the injected current I and the parameter r, representing the ratio of time scales between spiking (fast dynamics) and resting (slow dynamics). The auxiliary parameter involved in the analytical method provides us with an elegant way to ensure convergent series solutions of the neuronal model. Our analytical results are found to be in excellent agreement with the numerical simulations.

Inverse dynamics based predictive control for unified power flow controllers without DC bus

This paper presents a new predictive digital control method applied to Matrix Converters (MC) operating as Unified Power Flow Controllers (UPFC). This control method, based on the inverse dynamics model equations of the MC operating as UPFC, just needs to compute the optimal control vector once in each control cycle, in contrast to direct dynamics predictive methods that needs 27 vector calculations. The theoretical principles of the inverse dynamics power flow predictive control of the MC based UPFC with input filter are established. The proposed inverse dynamics predictive power control method is tested using Matlab/Simulink Power Systems toolbox and the obtained results show that the designed power controllers guarantees decoupled active and reactive power control, zero error tracking, fast response times and an overall good dynamic and steady-state response.

Reversible current power supply for fast-field cycling nuclear magnetic resonance equipment

The Fast Field-Cycling Nuclear Magnetic Resonance (FFC-NMR) is a technique used to study the molecular dynamics of different types of materials. The main elements of this equipment are a magnet and its power supply. The magnet used as reference in this work is basically a ferromagnetic core with two sets of coils and an air-gap where the materials' sample is placed. The power supply should supply the magnet being the magnet current controlled in order to perform cycles. One of the technical issues of this type of solution is the compensation of the non-linearities associated to the magnetic characteristic of the magnet and to parasitic magnetic fields. To overcome this problem, this paper describes and discusses a solution for the FFC-NMR power supply based on a four quadrant DC/DC converter.

Chaos and crises in a model for cooperative hunting: A symbolic dynamics approach

In this work we investigate the population dynamics of cooperative hunting extending the McCann and Yodzis model for a three-species food chain system with a predator, a prey, and a resource species. The new model considers that a given fraction sigma of predators cooperates in prey's hunting, while the rest of the population 1-sigma hunts without cooperation. We use the theory of symbolic dynamics to study the topological entropy and the parameter space ordering of the kneading sequences associated with one-dimensional maps that reproduce significant aspects of the dynamics of the species under several degrees of cooperative hunting. Our model also allows us to investigate the so-called deterministic extinction via chaotic crisis and transient chaos in the framework of cooperative hunting. The symbolic sequences allow us to identify a critical boundary in the parameter spaces (K, C-0) and (K, sigma) which separates two scenarios: (i) all-species coexistence and (ii) predator's extinction via chaotic crisis. We show that the crisis value of the carrying capacity K-c decreases at increasing sigma, indicating that predator's populations with high degree of cooperative hunting are more sensitive to the chaotic crises. We also show that the control method of Dhamala and Lai [Phys. Rev. E 59, 1646 (1999)] can sustain the chaotic behavior after the crisis for systems with cooperative hunting. We finally analyze and quantify the inner structure of the target regions obtained with this control method for wider parameter values beyond the crisis, showing a power law dependence of the extinction transients on such critical parameters.

Pricing intraday dynamics across EUAS and CERS markets

The relative contribution of European Union Allowances (EUAs) and Certified Emission Reductions (CERs) to the price discovery of their common true value has been empirically studied using daily data with inconclusive results. In this paper, we study the short-run and long-run price dynamics between EUAs and CERs future contracts using intraday data. We report a bidirectional feedback causality relationship both in the short-run and in the long-run, with the EUA's market being the leader.

Fast optimum-predictive control and capacitor voltage balancing strategy for bipolar back-to-back NPC converters in high-voltage direct current transmission systems

Multilevel power converters have been introduced as the solution for high-power high-voltage switching applications where they have well-known advantages. Recently, full back-to-back connected multilevel neutral point diode clamped converters (NPC converter) have been used inhigh-voltage direct current (HVDC) transmission systems. Bipolar-connected back-to-back NPC converters have advantages in long-distance HVDCtransmission systems over the full back-to-back connection, but greater difficulty to balance the dc capacitor voltage divider on both sending and receiving end NPC converters. This study shows that power flow control and dc capacitor voltage balancing are feasible using fast optimum-predictive-based controllers in HVDC systems using bipolar back-to-back-connected five-level NPC multilevel converters. For both converter sides, the control strategytakes in account active and reactive power, which establishes ac grid currents in both ends, and guarantees the balancing of dc bus capacitor voltages inboth NPC converters. Additionally, the semiconductor switching frequency is minimised to reduce switching losses. The performance and robustness of the new fast predictive control strategy, and its capability to solve the DC capacitor voltage balancing problem of bipolar-connected back-to-back NPCconverters are evaluated.

Autoinhibition of TBCB regulates EB1-mediated microtubule dynamics

Tubulin cofactors (TBCs) participate in the folding, dimerization, and dissociation pathways of the tubulin dimer. Among them, TBCB and TBCE are two CAP-Gly domain-containing proteins that together efficiently interact with and dissociate the tubulin dimer. In the study reported here we showed that TBCB localizes at spindle and midzone microtubules during mitosis. Furthermore, the motif DEI/M-COO− present in TBCB, which is similar to the EEY/F-COO− element characteristic of EB proteins, CLIP-170, and α-tubulin, is required for TBCE–TBCB heterodimer formation and thus for tubulin dimer dissociation. This motif is responsible for TBCB autoinhibition, and our analysis suggests that TBCB is a monomer in solution. Mutants of TBCB lacking this motif are derepressed and induce microtubule depolymerization through an interaction with EB1 associated with microtubule tips. TBCB is also able to bind to the chaperonin complex CCT containing α-tubulin, suggesting that it could escort tubulin to facilitate its folding and dimerization, recycling or degradation.

Symbolic dynamics and renormalization of non-autonomous k periodic dynamical systems

The purpose of this paper was to introduce the symbolic formalism based on kneading theory, which allows us to study the renormalization of non-autonomous periodic dynamical systems.

An Extension of Gompertzian Growth Dynamics Weibull and Frechet Models

In this work a new probabilistic and dynamical approach to an extension of the Gompertz law is proposed. A generalized family of probability density functions, designated by Beta* (p, q), which is proportional to the right hand side of the Tsoularis-Wallace model, is studied. In particular, for p = 2, the investigation is extended to the extreme value models of Weibull and Frechet type. These models, described by differential equations, are proportional to the hyper-Gompertz growth model. It is proved that the Beta* (2, q) densities are a power of betas mixture, and that its dynamics are determined by a non-linear coupling of probabilities. The dynamical analysis is performed using techniques of symbolic dynamics and the system complexity is measured using topological entropy. Generally, the natural history of a malignant tumour is reflected through bifurcation diagrams, in which are identified regions of regression, stability, bifurcation, chaos and terminus.

Topological Complexity and Predictability in the Dynamics of a Tumor Growth Model with Shilnikov's Chaos

Dynamical systems modeling tumor growth have been investigated to determine the dynamics between tumor and healthy cells. Recent theoretical investigations indicate that these interactions may lead to different dynamical outcomes, in particular to homoclinic chaos. In the present study, we analyze both topological and dynamical properties of a recently characterized chaotic attractor governing the dynamics of tumor cells interacting with healthy tissue cells and effector cells of the immune system. By using the theory of symbolic dynamics, we first characterize the topological entropy and the parameter space ordering of kneading sequences from one-dimensional iterated maps identified in the dynamics, focusing on the effects of inactivation interactions between both effector and tumor cells. The previous analyses are complemented with the computation of the spectrum of Lyapunov exponents, the fractal dimension and the predictability of the chaotic attractors. Our results show that the inactivation rate of effector cells by the tumor cells has an important effect on the dynamics of the system. The increase of effector cells inactivation involves an inverse Feigenbaum (i.e. period-halving bifurcation) scenario, which results in the stabilization of the dynamics and in an increase of dynamics predictability. Our analyses also reveal that, at low inactivation rates of effector cells, tumor cells undergo strong, chaotic fluctuations, with the dynamics being highly unpredictable. Our findings are discussed in the context of tumor cells potential viability.

Strong and weak Allee effects and chaotic dynamics in Richards' growths

In this paper we define and investigate generalized Richards' growth models with strong and weak Allee effects and no Allee effect. We prove the transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, depending on the implicit conditions, which involve the several parameters considered in the models. New classes of functions describing the existence or not of Allee effect are introduced, a new dynamical approach to Richards' populational growth equation is established. These families of generalized Richards' functions are proportional to the right hand side of the generalized Richards' growth models proposed. Subclasses of strong and weak Allee functions and functions with no Allee effect are characterized. The study of their bifurcation structure is presented in detail, this analysis is done based on the configurations of bifurcation curves and symbolic dynamics techniques. Generically, the dynamics of these functions are classified in the following types: extinction, semi-stability, stability, period doubling, chaos, chaotic semistability and essential extinction. We obtain conditions on the parameter plane for the existence of a weak Allee effect region related to the appearance of cusp points. To support our results, we present fold and flip bifurcations curves and numerical simulations of several bifurcation diagrams.

Vertex component analysis: a fast algorithm to extract endmembers spectra from hyperspectral data

Chapter in Book Proceedings with Peer Review First Iberian Conference, IbPRIA 2003, Puerto de Andratx, Mallorca, Spain, JUne 4-6, 2003. Proceedings

Vertex component analysis: a fast algorithm to unmix hyperspectral data

Given a set of mixed spectral (multispectral or hyperspectral) vectors, linear spectral mixture analysis, or linear unmixing, aims at estimating the number of reference substances, also called endmembers, their spectral signatures, and their abundance fractions. This paper presents a new method for unsupervised endmember extraction from hyperspectral data, termed vertex component analysis (VCA). The algorithm exploits two facts: (1) the endmembers are the vertices of a simplex and (2) the affine transformation of a simplex is also a simplex. In a series of experiments using simulated and real data, the VCA algorithm competes with state-of-the-art methods, with a computational complexity between one and two orders of magnitude lower than the best available method.

Fast growing fungi: a problem to be solved to achieve characterization of occupational exposure to fungi in cork industry

Chrysonilia sitophila is a common mould in cork industry and has been identified as a cause of IgE sensitization and occupational asthma. This fungal species have a fast growth rate that may inhibit others species’ growth causing underestimated data from characterization of occupational fungal exposure. Aiming to ascertain occupational exposure to fungi in cork industry, were analyzed papers from 2000 about the best air sampling method, to obtain quantification and identification of all airborne culturable fungi, besides the ones that have fast-growing rates. Impaction method don’t allows the collection of a representative air volume, because even with some media that restricts the growth of the colonies, in environments with higher fungal load, such as cork industry, the counting of the colonies is very difficult. Otherwise, impinger method permits the collection of a representative air volume, since we can make dilution of the collected volume. Besides culture methods that allows fungal identification trough macro- and micro-morphology, growth features, thermotolerance and ecological data, we can apply molecular biology with the impinger method, to detect the presence of non-viable particles and potential mycotoxin producers’ strains, and also to detect mycotoxins presence with ELISA or HPLC. Selection of the best air sampling method in each setting is crucial to achieve characterization of occupational exposure to fungi. Information about the prevalent fungal species in each setting and also the eventual fungal load it’s needed for a criterious selection.

Dynamics and orchestral effects in late Eighteenth-Century portuguese organ music: the works of José Marques e Silva (1782-1837) and the organs of António Xavier Machado e Cerveira (1756-1828)

A maioria dos órgãos históricos portugueses data dos finais do século XVIII ou do princípio do século XIX. Durante este período foi construído um invulgar número de instrumentos em Lisboa e nas áreas circundantes por António Xavier Machado e Cerveira (1756-1828) e outros organeiros menos prolíficos. O estudo desses órgãos, muitos dos quais (restaurados ou não) se encontram próximos das condições originais, permite a identificação de um tipo de instrumento com uma morfologia específica, claramente emancipada do chamado «órgão ibérico». No entanto, até muito recentemente, não era conhecida música que se adaptasse às idiossincrasisas daqueles instrumentos. O recente estudo das obras para órgão de José Marques e Silva (1782-1837) permitiu clarificar esta situação. Bem conhecido durante a sua vida como organista e compositor, José Marques e Silva foi um dos ultimos mestres do Seminário Patriarcal. A importância da sua produção musical reside não só num substancial número de obras com autoria firmemente estabelecida – escritas, na maior parte, para coro misto com acompanhamento de órgão obbligato – mas também na íntima relação entre a sua escrita e a morfologia dos órgãos construídos em Portugal durante a sua vida. Este artigo enfatiza a importância de José Marques e Silva (indubitavelmente, o mais significativo compositor português para órgão do seu tempo) sublinhando a relevância das suas obras para órgão solo, cujo uso extensivo de escrita idiomática e indicações de registação fazem delas um dos mais importantes documentos só início do século XIX sobre a prática organística em Portugal.