Uncovering the dynamics of cardiac systems using stochastic pacing and frequency domain analyses

Alternans of cardiac action potential duration (APD) is a well-known arrhythmogenic mechanism which results from dynamical instabilities. The propensity to alternans is classically investigated by examining APD restitution and by deriving APD restitution slopes as predictive markers. However, experiments have shown that such markers are not always accurate for the prediction of alternans. Using a mathematical ventricular cell model known to exhibit unstable dynamics of both membrane potential and Ca2+ cycling, we demonstrate that an accurate marker can be obtained by pacing at cycle lengths (CLs) varying randomly around a basic CL (BCL) and by evaluating the transfer function between the time series of CLs and APDs using an autoregressive-moving-average (ARMA) model. The first pole of this transfer function corresponds to the eigenvalue (λalt) of the dominant eigenmode of the cardiac system, which predicts that alternans occurs when λalt≤−1. For different BCLs, control values of λalt were obtained using eigenmode analysis and compared to the first pole of the transfer function estimated using ARMA model fitting in simulations of random pacing protocols. In all versions of the cell model, this pole provided an accurate estimation of λalt. Furthermore, during slow ramp decreases of BCL or simulated drug application, this approach predicted the onset of alternans by extrapolating the time course of the estimated λalt. In conclusion, stochastic pacing and ARMA model identification represents a novel approach to predict alternans without making any assumptions about its ionic mechanisms. It should therefore be applicable experimentally for any type of myocardial cell.

Position information but not force information is used in adapting to changes in environmental dynamics

This study investigated how movement error is evaluated and used to change feedforward commands following a change in the environmental dynamics. In particular, we addressed the question of whether only position-error information is used or whether information about the force-field direction can also be used for rapid adaptation to changes in the environmental dynamics. Subjects learned to move in a position-dependent force field (PF) with a parabolic profile and the dynamics of a negative spring, which produced lateral force to the left of the target hand path. They adapted very rapidly, dramatically reducing lateral error after a single trial. Several times during training, the strength of the PF was unexpectedly doubled (PF2) for two trials. This again created a large leftward deviation, which was greatly reduced on the second PF2 trial, and an aftereffect when the force field subsequently returned to its original strength. The aftereffect was abolished if the second PF2 trial was replaced by an oppositely directed velocity-dependent force field (VF). During subsequent training in the VF, immediately after having adapted to the PF, subjects applied a force that assisted the force field for similar to 15 trials, indicating that they did not use information about the force-field direction. We concluded that the CNS uses only the position error for updating the internal model of the environmental dynamics and modifying feedforward commands. Although this strategy is not necessarily optimal, it may be the most reliable strategy for iterative improvement in performance.

Habitat complexity, spatial interference, and "minimum risk distribution": a framework for population stability

In the past century, the debate over whether or not density-dependent factors regulate populations has generally focused on changes in mean population density, ignoring the spatial variance around the mean as unimportant noise. In an attempt to provide a different framework for understanding population dynamics based on individual fitness, this paper discusses the crucial role of spatial variability itself on the stability of insect populations. The advantages of this method are the following: (1) it is founded on evolutionary principles rather than post hoc assumptions; (2) it erects hypotheses that can be tested; and (3) it links disparate ecological schools, including spatial dynamics, behavioral ecology, preference-performance, and plant apparency into an overall framework. At the core of this framework, habitat complexity governs insect spatial variance. which in turn determines population stability. First, the minimum risk distribution (MRD) is defined as the spatial distribution of individuals that results in the minimum number of premature deaths in a population given the distribution of mortality risk in the habitat (and, therefore, leading to maximized population growth). The greater the divergence of actual spatial patterns of individuals from the MRD, the greater the reduction of population growth and size from high, unstable levels. Then, based on extensive data from 29 populations of the processionary caterpillar, Ochrogaster lunifer, four steps are used to test the effect of habitat interference on population growth rates. (1) The costs (increasing the risk of scramble competition) and benefits (decreasing the risk of inverse density-dependent predation) of egg and larval aggregation are quantified. (2) These costs and benefits, along with the distribution of resources, are used to construct the MRD for each habitat. (3) The MRD is used as a benchmark against which the actual spatial pattern of individuals is compared. The degree of divergence of the actual spatial pattern from the MRD is quantified for each of the 29 habitats. (4) Finally, indices of habitat complexity are used to provide highly accurate predictions of spatial divergence from the MRD, showing that habitat interference reduces population growth rates from high, unstable levels. The reason for the divergence appears to be that high levels of background vegetation (vegetation other than host plants) interfere with female host-searching behavior. This leads to a spatial distribution of egg batches with high mortality risk, and therefore lower population growth. Knowledge of the MRD in other species should be a highly effective means of predicting trends in population dynamics. Species with high divergence between their actual spatial distribution and their MRD may display relatively stable dynamics at low population levels. In contrast, species with low divergence should experience high levels of intragenerational population growth leading to frequent habitat-wide outbreaks and unstable dynamics in the long term. Six hypotheses, erected under the framework of spatial interference, are discussed, and future tests are suggested.

In-Flight Collision Avoidance Controller Based Only on OS4 Embedded Sensors

The major goal of this research was the development and implementation of a control system able to avoid collisions during the flight for a mini-quadrotor helicopter, based only on its embedded sensors without changing the environment. However, it is important to highlight that the design aspects must be seriously considered in order to overcome hardware limitations and achieve control simplification. The controllers of a UAV (Unmanned Aerial Vehicle) robot deal with highly unstable dynamics and strong axes coupling. Furthermore, any additional embedded sensor increases the robot total weight and therefore, decreases its operating time. The best balance between embedded electronics and robot operating time is desired. This paper focuses not only on the development and implementation of a collision avoidance controller for a mini-robotic helicopter using only its embedded sensors, but also on the mathematical model that was essential for the controller developing phases. Based on this model we carried out the development of a simulation tool based on MatLab/Simulink that was fundamental for setting the controllers' parameters. This tool allowed us to simulate and improve the OS4 controllers in different modeled environments and test different approaches. After that, the controllers were embedded in the real robot and the results proved to be very robust and feasible. In addition to this, the controller has the advantage of being compatible with future path planners that we are developing.

Novel strategies in feedforward adaptation to a position-dependent perturbation

To investigate the control mechanisms used in adapting to position-dependent forces, subjects performed 150 horizontal reaching movements over 25 cm in the presence of a position-dependent parabolic force field (PF). The PF acted only over the first 10 cm of the movement. On every fifth trial, a virtual mechanical guide (double wall) constrained subjects to move along a straight-line path between the start and target positions. Its purpose was to register lateral force to track formation of an internal model of the force field, and to look for evidence of possible alternative adaptive strategies. The force field produced a force to the right, which initially caused subjects to deviate in that direction. They reacted by producing deviations to the left, into the force field, as early as the second trial. Further adaptation resulted in rapid exponential reduction of kinematic error in the latter portion of the movement, where the greatest perturbation to the handpath was initially observed, whereas there was little modification of the handpath in the region where the PF was active. Significant force directed to counteract the PF was measured on the first guided trial, and was modified during the first half of the learning set. The total force impulse in the region of the PF increased throughout the learning trials, but it always remained less than that produced by the PF. The force profile did not resemble a mirror image of the PF in that it tended to be more trapezoidal than parabolic in shape. As in previous studies of force-field adaptation, we found that changes in muscle activation involved a general increase in the activity of all muscles, which increased arm stiffness, and selectively-greater increases in the activation of muscles which counteracted the PF. With training, activation was exponentially reduced, albeit more slowly than kinematic error. Progressive changes in kinematics and EMG occurred predominantly in the region of the workspace beyond the force field. We suggest that constraints on muscle mechanics limit the ability of the central nervous system to employ an inverse dynamics model to nullify impulse-like forces by generating mirror-image forces. Consequently, subjects adopted a strategy of slightly overcompensating for the first half of the force field, then allowing the force field to push them in the opposite direction. Muscle activity patterns in the region beyond the boundary of the force field were subsequently adjusted because of the relatively-slow response of the second-order mechanics of muscle impedance to the force impulse.

Small-scale genetic structure of Cerastoderma glaucum in a lagoonal environment: potential significance of habitat discontinuity and unstable population dynamics

Environmental heterogeneity in coastal lagoons is expected to facilitate local adaptation in response to different ecological conditions, causing significant genetic structuring within lagoon populations at a small scale and also differentiation between lagoons. However, these patterns and processes of genetic structuring are still poorly understood. The aims of our study were (1) to seek genetic structure at a small scale in Cerastoderma glaucum inside the Mar Menor coastal lagoon using a mitochondrial DNA marker (COI) that has previously detected genetic differentiation inside the lagoon in other species and (2) to evaluate the influence of extreme environmental conditions and habitat discontinuity on its genetic composition. The results indicate high levels of haplotype diversity and low values of nucleotide diversity. COI data provide evidence of significant population differentiation among some localities within the lagoon. Limited gene flow and unstable population dynamics (i.e. fluctuations in population size caused by local extinction and recolonization), probably due to the high environmental heterogeneity, could generate the small-scale genetic divergence detected between populations within the lagoon.

A partial velocity approach to subcycling structural dynamics

Subcycling, or the use of different timesteps at different nodes, can be an effective way of improving the computational efficiency of explicit transient dynamic structural solutions. The method that has been most widely adopted uses a nodal partition. extending the central difference method, in which small timestep updates are performed interpolating on the displacement at neighbouring large timestep nodes. This approach leads to narrow bands of unstable timesteps or statistical stability. It also can be in error due to lack of momentum conservation on the timestep interface. The author has previously proposed energy conserving algorithms that avoid the first problem of statistical stability. However, these sacrifice accuracy to achieve stability. An approach to conserve momentum on an element interface by adding partial velocities is considered here. Applied to extend the central difference method. this approach is simple. and has accuracy advantages. The method can be programmed by summing impulses of internal forces, evaluated using local element timesteps, in order to predict a velocity change at a node. However, it is still only statistically stable, so an adaptive timestep size is needed to monitor accuracy and to be adjusted if necessary. By replacing the central difference method with the explicit generalized alpha method. it is possible to gain stability by dissipating the high frequency response that leads to stability problems. However. coding the algorithm is less elegant, as the response depends on previous partial accelerations. Extension to implicit integration, is shown to be impractical due to the neglect of remote effects of internal forces acting across a timestep interface. (C) 2002 Elsevier Science B.V. All rights reserved.

Using attractor dynamics to generate decentralized motion control of two mobile robots transporting a long object in coordination

Dynamical systems theory is used here as a theoretical language and tool to design a distributed control architecture for a team of two mobile robots that must transport a long object and simultaneously avoid obstacles. In this approach the level of modeling is at the level of behaviors. A “dynamics” of behavior is defined over a state space of behavioral variables (heading direction and path velocity). The environment is also modeled in these terms by representing task constraints as attractors (i.e. asymptotically stable states) or reppelers (i.e. unstable states) of behavioral dynamics. For each robot attractors and repellers are combined into a vector field that governs the behavior. The resulting dynamical systems that generate the behavior of the robots may be nonlinear. By design the systems are tuned so that the behavioral variables are always very close to one attractor. Thus the behavior of each robot is controled by a time series of asymptotically stable states. Computer simulations support the validity of our dynamic model architectures.

Population Dynamics Modeling of Arapaima gigas

Pirarucu (Arapaima gigas) has been of the most important natural fishing resources of the Amazon region. Due to its economic importance, and the necessity to preserve the species hand, field research concerning the habits and behavior of the pirarucu has been increasing for the last 20 years. The aim of this paper is to present a mathematical model for the pirarucu population dynamics considering the species peculiarities, particularly the male parental care over the offspring. The solution of the dynamical systems indicates three possible equilibrium points for the population. The first corresponds to extinction; the third corresponds to a stable population close to the environmental carrying capacity. The second corresponds to an unstable equilibrium located between extinction and full use of the carrying capacity. It is shown that lack of males’ parental care closes the gap between the point corresponding to the unstable equilibrium and the point of stable non-trivial equilibrium. If guarding failure reaches a critical point the two points coincide and the population tends irreversibly to extinction. If some event tends to destabilize the population equilibrium, as for instance inadequate parental care, the model responds in such a way as to restore the trajectory towards the stable equilibrium point avoiding the route to extinction. The parameters introduced to solve the system of equations are partially derived from limited but reliable field data collected at the Mamirauá Sustainable Development Reserve (MSDR) in the Brazilian Amazonian Region.

Chaotic dynamics in credit constrained emerging economies

This paper analyzes the role of financial development as a source of endogenous instability in small open economies. By assuming that firms face credit constraints, our model displays a complex dynamic behavior for intermediate values of the parameter representing the level of financial development of the economy. The basic implication of our model is that economies experiencing a process of financial development are more unstable than both very underdeveloped and very developed economies. Our instability concept means that small shocks have a persistent effect on the long run behavior of the model and also that economies can exhibit cycles with a very high period or even chaotic dynamic patterns.

A geometric mechanism of diffusion: Rigorous verification in a priori unstable Hamiltonian systems

In this paper we consider a representative a priori unstable Hamiltonian system with 2+1/2 degrees of freedom, to which we apply the geometric mechanism for diffusion introduced in the paper Delshams et al., Mem.Amer.Math. Soc. 2006, and generalized in Delshams and Huguet, Nonlinearity 2009, and provide explicit, concrete and easily verifiable conditions for the existence of diffusing orbits. The simplification of the hypotheses allows us to perform explicitly the computations along the proof, which contribute to present in an easily understandable way the geometric mechanism of diffusion. In particular, we fully describe the construction of the scattering map and the combination of two types of dynamics on a normally hyperbolic invariant manifold.

Adaptive dynamics and the implementation problem with complete information

This paper studies the equilibrating process of several implementationmechanisms using naive adaptive dynamics. We show that the dynamics convergeand are stable, for the canonical mechanism of implementation in Nash equilibrium.In this way we cast some doubt on the criticism of ``complexity'' commonlyused against this mechanism. For mechanisms that use more refined equilibrium concepts,the dynamics converge but are not stable. Some papers in the literatureon implementation with refined equilibrium concepts have claimed that themechanisms they propose are ``simple'' and implement ``everything'' (incontrast with the canonical mechanism). The fact that some of these ``simple''mechanisms have unstable equilibria suggests that these statements shouldbe interpreted with some caution.

Decay of an unstable state in the presence of multiplicative noise

The phenomenon of anomalous fluctuations associated with the decay of an unstable state is analyzed in the presence of multiplicative noise. A theory is presented and compared with a numerical simulation. Our results allow us to distinguish the roles of additive and multiplicative noise in the nonlinear relaxation process. We suggest the use of experiments on transient dynamics to understand the effect of these two sources of noise in problems in which parametric noise is thought to be important, such as dye lasers.

Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study

We study the singular effects of vanishingly small surface tension on the dynamics of finger competition in the Saffman-Taylor problem, using the asymptotic techniques described by Tanveer [Philos. Trans. R. Soc. London, Ser. A 343, 155 (1993)] and Siegel and Tanveer [Phys. Rev. Lett. 76, 419 (1996)], as well as direct numerical computation, following the numerical scheme of Hou, Lowengrub, and Shelley [J. Comput. Phys. 114, 312 (1994)]. We demonstrate the dramatic effects of small surface tension on the late time evolution of two-finger configurations with respect to exact (nonsingular) zero-surface-tension solutions. The effect is present even when the relevant zero-surface-tension solution has asymptotic behavior consistent with selection theory. Such singular effects, therefore, cannot be traced back to steady state selection theory, and imply a drastic global change in the structure of phase-space flow. They can be interpreted in the framework of a recently introduced dynamical solvability scenario according to which surface tension unfolds the structurally unstable flow, restoring the hyperbolicity of multifinger fixed points.

Temporal and spatial dynamics of benthic invertebrate communities in an alpine glacier-fed alluvial system

Summary The present thesis work focused on the ecology of benthic invertebrates in the proglacial floodplain of the Rhone in the Swiss Alps. The main glacial Rhone River and a smaller glacial tributary, the Mutt River, joined and entered a braiding multi-thread area. A first part concentrated on the disruption of the longitudinal patterns of environmental conditions and benthic invertebrate fauna in the Rhone by its tributary the Mutt. The Mutt had less harsh environmental conditions, higher taxonomic richness and more abundant zoobenthos compared to the Rhone upstream of the confluence. Although the habitat conditions in the main stream were little modified by the tributary, the fauna was richer and more diverse below the confluence. Colonisation from the Mutt induced the occurrence of faunal elements uncommon of glacial streams in the upper Rhone, where water temperature remains below 4°C. Although the glacial Rhone dominated the system with regard to hydrology and certain environmental conditions, the Mutt tributary has to be seen as the faunal driver of the system. The second part of the study concerned the spatio-temporal differentiation of the habitats and the benthic communities along and across the flood plain. No longitudinal differentiation was found. The spatial transversal differentiation of three habitat types with different environmental characteristics was successfully reflected in the spatial variability of benthic assemblages. This typology separated marginal sites of the flood plain, left bank sites under the influence of the Mutt, and the right bank sites under the influence of the Rh6ne. Faunistic spatial differences were emphasized by the quantitative structure of the fauna, richness, abundances and Simpson index of diversity. Seasonal environmental variability was positively related with Simpson index of diversity and the total richness per site. Low flow conditions were the most favourable season for the fauna and November was characterized by low spatial environmental heterogeneity, high spatial heterogeneity of faunal assemblage, maximum taxonomic richness, a particular taxonomic composition, highest abundances, as well as the highest primary food resources. The third part studied the egg development of three species of Ephemeroptera in the laboratory at 1.5 to 7°C and the ecological implications in the field. Species revealed very contrasting development strategies. Baetis alpinus has a synchronous and efficient egg development, which is faster in warmer habitats, enabling it to exploit short periods of favourable conditions in the floodplain. Ecdyonurus picteti has a very long development time slightly decreasing in warmer conditions. The high degree of individual variation suggests a genetic determination of the degree-days demand. Combined with the glacial local conditions, this strategy leads to an extreme delay of hatching and allows it to develop in very unpredictable habitats. Rhithrogena nivata is the second cold adapted species in Ephemeroptera. The incubation duration is long and success largely depends on the timing of hatching and the discharge conditions. This species is able to exploit extremely unstable and cold habitats where other species are limited by low water temperatures. The fourth part dealt with larval development in different habitats of the floodplain. Addition of data on egg development allowed the description of the life histories of the species from oviposition until emergence. Rhithrogena nivata and loyolaea generally have a two-year development, with the first winter passed as eggs and the second one as larvae. Development of Ecdyonurus picteti is difficult to document but appears to be efficient in a harsh and unpredictable environment. Baetis alpinus was studied separately in four habitats of the floodplain system with contrasting thermal regimes. Differences in success and duration of larval development and in growth rates are emphasised. Subvention mechanisms between habitats by migration of young or grown larvae were demonstrated. Development success and persistence of the populations in the system were thus increased. Emergence was synchronised to the detriment of the optimisation of the adult's size and fecundity. These very different development strategies induce a spatial and temporal distribution in the use of food resources and ecological niches. The last part of this work aimed at the synthesis of the characteristics and the ecological features of three distinct compartments of the system that are the upper Rhone, the Mutt and the floodplain. Their particular role as well as their inter-dependence concerning the structure and the dynamics of the benthic communities was emphasised. Résumé Ce travail de thèse est consacré à l'écologie des invertébrés benthiques dans la zone alluviale proglaciaire du Rhône dans les Alpes suisses. Le Rhône, torrent glaciaire principal, reçoit les eaux de la Mutt, affluent glaciaire secondaire, puis pénètre dans une zone de tressage formée de plusieurs bras. La première partie de l'étude se concentre sur la disruption par la Mutt des processus longitudinaux, tant environnementaux que faunistiques, existants dans le Rhône. Les conditions environnementales régnant dans la Mutt sont moins rudes, la richesse taxonomique plus élevée et le zoobenthos plus abondant que dans le Rhône en amont de la confluence. Bien que les conditions environnementales dans le torrent principal soient peu modifiées par l'affluent, la faune s'avère être plus riche et plus diversifiée en aval de la confluence. La colonisation depuis la Mutt permet l'occurrence de taxons inhabituels dans le Rhône en amont de la confluence, où la température de l'eau se maintient en dessous de 4°C. Bien que le Rhône, torrent glaciaire principal, domine le système du point de vu de l'hydrologie et de certains paramètres environnementaux, l'affluent Mutt doit être considéré comme l'élément structurant la faune dans le système. La deuxième partie concerne la différentiation spatiale et temporelle des habitats et des communautés benthiques à travers la plaine alluviale. Aucune différentiation longitudinale n'a été mise en évidence. La différentiation transversale de trois types d'habitats sur la base des caractéristiques environnementales a été confirmée par la variabilité spatiale de la faune. Cette typologie sépare les sites marginaux de la plaine alluviale, ceux sous l'influence de la Mutt (en rive gauche) et ceux sous l'influence du Rhône amont (en rive droite). Les différences spatiales de la faune sont mises en évidence par la structure quantitative de la faune, la richesse, les abondances et l'indice de diversité de Simpson. La variabilité saisonnière du milieu est positivement liée avec l'indice de diversité de Simpson et la richesse totale par site. L'étiage correspond à la période la plus favorable pour la faune et novembre réunit des conditions de faible hétérogénéité spatiale du milieu, de forte hétérogénéité spatiale de la faune, une richesse taxonomique maximale, une composition faunistique particulière, les abondances ainsi que les ressources primaires les plus élevées. La troisième partie est consacrée à l'étude du développement des oeufs de trois espèces d'Ephémères au laboratoire à des températures de 1.5 à 7°C, ainsi qu'aux implications écologiques sur le terrain. Ces espèces présentent des stratégies de développement très contrastées. Baetis alpinus a un développement synchrone et efficace, plus rapide en milieu plus chaud et lui permettant d'exploiter les courtes périodes de conditions favorables. Ecdyonurus picteti présente une durée de développement très longue, diminuant légèrement dans des conditions plus chaudes. L'importante variation interindividuelle suggère un déterminisme génétique de la durée de développement. Cette stratégie, associée aux conditions locales, conduit à un décalage extrême des éclosions et permet à l'espèce de se développer dans des habitats imprévisibles. Rhithrogena nivata est la seconde espèce d'Ephémères présentant une adaptation au froid. L'incubation des oeufs est longue et son succès dépend de la période des éclosions et des conditions hydrologiques. Cette espèce est capable d'exploiter des habitats extrêmement instables et froids, où la température est facteur limitant pour d'autres espèces. La quatrième partie traite du développement larvaire dans différents habitats de la plaine alluviale. Le développement complet est décrit pour les espèces étudiées de la ponte jusqu'à l'émergence. Rhithrogena nivata et loyolaea atteignent généralement le stade adulte en deux ans, le premier hiver étant passé sous forme d'oeuf et le second sous forme de larve. Le développement de Ecdyonurus picteti est difficile à documenter, mais s'avère cependant efficace dans un environnement rude et imprévisible. Baetis alpinus a été étudié séparément dans quatre habitats de la plaine ayant des régimes thermiques contrastés. La réussite et la durée du développement embryonnaire ainsi que les taux de croissance y sont variables. Des mécanismes de subvention entre habitats sont possibles par la migration de larves juvéniles ou plus développées, augmentant ainsi la réussite du développement et le maintien des populations dans le système. L'émergence devient synchrone, au détriment de l'optimisation de la taille et de la fécondité des adultes. Ces stratégies très différentes induisent une distribution spatiale et temporelle dans l'usage des ressources et des niches écologiques. La dernière partie synthétise les caractéristiques écologiques des trois compartiments du système que sont le Rhône amont, la Mutt et la zone alluviale. Leurs rôles particuliers et leurs interdépendances du point de vue de la structure et de la dynamique des communautés benthiques sont mis en avant.