Role of noise in population dynamics cycles

Noise is an intrinsic feature of population dynamics and plays a crucial role in oscillations called phase-forgetting quasicycles by converting damped into sustained oscillations. This function of noise becomes evident when considering Langevin equations whose deterministic part yields only damped oscillations. We formulate here a consistent and systematic approach to population dynamics, leading to a Fokker-Planck equation and the associate Langevin equations in accordance with this conceptual framework, founded on stochastic lattice-gas models that describe spatially structured predator-prey systems. Langevin equations in the population densities and predator-prey pair density are derived in two stages. First, a birth-and-death stochastic process in the space of prey and predator numbers and predator-prey pair number is obtained by a contraction method that reduces the degrees of freedom. Second, a van Kampen expansion in the inverse of system size is then performed to get the Fokker-Planck equation. We also study the time correlation function, the asymptotic behavior of which is used to characterize the transition from the cyclic coexistence of species to the ordinary coexistence.

Evolutionary dynamics on rugged fitness landscapes: Exact dynamics and information theoretical aspects

The parallel mutation-selection evolutionary dynamics, in which mutation and replication are independent events, is solved exactly in the case that the Malthusian fitnesses associated to the genomes are described by the random energy model (REM) and by a ferromagnetic version of the REM. The solution method uses the mapping of the evolutionary dynamics into a quantum Ising chain in a transverse field and the Suzuki-Trotter formalism to calculate the transition probabilities between configurations at different times. We find that in the case of the REM landscape the dynamics can exhibit three distinct regimes: pure diffusion or stasis for short times, depending on the fitness of the initial configuration, and a spin-glass regime for large times. The dynamic transition between these dynamical regimes is marked by discontinuities in the mean-fitness as well as in the overlap with the initial reference sequence. The relaxation to equilibrium is described by an inverse time decay. In the ferromagnetic REM, we find in addition to these three regimes, a ferromagnetic regime where the overlap and the mean-fitness are frozen. In this case, the system relaxes to equilibrium in a finite time. The relevance of our results to information processing aspects of evolution is discussed.

Inverse aerodynamic design applications using the MGM hybrid formulation

The well-known modified Garabedian-Mcfadden (MGM) method is an attractive alternative for aerodynamic inverse design, for its simplicity and effectiveness (P. Garabedian and G. Mcfadden, Design of supercritical swept wings, AIAA J. 20(3) (1982), 289-291; J.B. Malone, J. Vadyak, and L.N. Sankar, Inverse aerodynamic design method for aircraft components, J. Aircraft 24(2) (1987), 8-9; Santos, A hybrid optimization method for aerodynamic design of lifting surfaces, PhD Thesis, Georgia Institute of Technology, 1993). Owing to these characteristics, the method has been the subject of several authors over the years (G.S. Dulikravich and D.P. Baker, Aerodynamic shape inverse design using a Fourier series method, in AIAA paper 99-0185, AIAA Aerospace Sciences Meeting, Reno, NV, January 1999; D.H. Silva and L.N. Sankar, An inverse method for the design of transonic wings, in 1992 Aerospace Design Conference, No. 92-1025 in proceedings, AIAA, Irvine, CA, February 1992, 1-11; W. Bartelheimer, An Improved Integral Equation Method for the Design of Transonic Airfoils and Wings, AIAA Inc., 1995). More recently, a hybrid formulation and a multi-point algorithm were developed on the basis of the original MGM. This article discusses applications of those latest developments for airfoil and wing design. The test cases focus on wing-body aerodynamic interference and shock wave removal applications. The DLR-F6 geometry is picked as the baseline for the analysis.

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.

Complex dynamics in the trajectory control of redundant manipulators

Redundant manipulators allow the trajectory optimization, the obstacle avoidance, and the resolution of singularities. For this type of manipulators, the kinematic control algorithms adopt generalized inverse matrices that may lead to unpredictable responses. Motivated by these problems this paper studies the complexity revealed by the trajectory planning scheme when controlling redundant manipulators. The results reveal fundamental properties of the chaotic phenomena and give a deeper insight towards the development of superior trajectory control algorithms.

Chaos Dynamics in the Trajectory Conjtrol of Redundant Manipulators

Nonlinear Dynamics, chaos, Control, and Their Applications to Engineering Sciences: Vol. 6 - Applications of nonlinear phenomena

Analysis of the EEG Dynamics of Epileptic Activity in Gelastic Seizures Using Decomposition in Independent Components

Objective: Gelastic seizures are a frequent and well established manifestation of the epilepsy associated with hypothalamic hamartomas. The scalp EEG recordings very seldom demonstrate clear spike activity and the information about the ictal epilepsy dynamics is limited. In this work, we try to isolate epileptic rhythms in gelastic seizures and study their generators. Methods: We extracted rhythmic activity from EEG scalp recordings of gelastic seizures using decomposition in independent components (ICA) in three patients, two with hypothalamic hamartomas and one with no hypothalamic lesion. Time analysis of these rhythms and inverse source analysis was done to recover their foci of origin and temporal dynamics. Results: In the two patients with hypothalamic hamartomas consistent ictal delta (2–3 Hz) rhythms were present, with subcortical generators in both and a superficial one in a single patient. The latter pattern was observed in the patient with no hypothalamic hamartoma visible in MRI. The deep generators activated earlier than the superficial ones, suggesting a consistent sub-cortical origin of the rhythmical activity. Conclusions: Our data is compatible with early and brief epileptic generators in deep sub-cortical regions and more superficial ones activating later. Significance: Gelastic seizures express rhythms on scalp EEG compatible with epileptic activity originating in sub-cortical generators and secondarily involving cortical ones.

A musculoskeletal shoulder model based on pseudo-inverse and null-space optimization.

The goal of the present work was assess the feasibility of using a pseudo-inverse and null-space optimization approach in the modeling of the shoulder biomechanics. The method was applied to a simplified musculoskeletal shoulder model. The mechanical system consisted in the arm, and the external forces were the arm weight, 6 scapulo-humeral muscles and the reaction at the glenohumeral joint, which was considered as a spherical joint. The muscle wrapping was considered around the humeral head assumed spherical. The dynamical equations were solved in a Lagrangian approach. The mathematical redundancy of the mechanical system was solved in two steps: a pseudo-inverse optimization to minimize the square of the muscle stress and a null-space optimization to restrict the muscle force to physiological limits. Several movements were simulated. The mathematical and numerical aspects of the constrained redundancy problem were efficiently solved by the proposed method. The prediction of muscle moment arms was consistent with cadaveric measurements and the joint reaction force was consistent with in vivo measurements. This preliminary work demonstrated that the developed algorithm has a great potential for more complex musculoskeletal modeling of the shoulder joint. In particular it could be further applied to a non-spherical joint model, allowing for the natural translation of the humeral head in the glenoid fossa.

Setting boundaries: brain dynamics of modal and amodal illusory shape completion in humans.

Normal visual perception requires differentiating foreground from background objects. Differences in physical attributes sometimes determine this relationship. Often such differences must instead be inferred, as when two objects or their parts have the same luminance. Modal completion refers to such perceptual "filling-in" of object borders that are accompanied by concurrent brightness enhancement, in turn termed illusory contours (ICs). Amodal completion is filling-in without concurrent brightness enhancement. Presently there are controversies regarding whether both completion processes use a common neural mechanism and whether perceptual filling-in is a bottom-up, feedforward process initiating at the lowest levels of the cortical visual pathway or commences at higher-tier regions. We previously examined modal completion (Murray et al., 2002) and provided evidence that the earliest modal IC sensitivity occurs within higher-tier object recognition areas of the lateral occipital complex (LOC). We further proposed that previous observations of IC sensitivity in lower-tier regions likely reflect feedback modulation from the LOC. The present study tested these proposals, examining the commonality between modal and amodal completion mechanisms with high-density electrical mapping, spatiotemporal topographic analyses, and the local autoregressive average distributed linear inverse source estimation. A common initial mechanism for both types of completion processes (140 msec) that manifested as a modulation in response strength within higher-tier visual areas, including the LOC and parietal structures, is demonstrated, whereas differential mechanisms were evident only at a subsequent time period (240 msec), with amodal completion relying on continued strong responses in these structures.

FABP4 Dynamics in Obesity: Discrepancies in Adipose Tissue and Liver Expression Regarding Circulating Plasma Levels.

BACKGROUND FABP4 is predominantly expressed in adipose tissue, and its circulating levels are linked with obesity and a poor atherogenic profile. OBJECTIVE In patients with a wide BMI range, we analyze FABP4 expression in adipose and hepatic tissues in the settings of obesity and insulin resistance. Associations between FABP4 expression in adipose tissue and the FABP4 plasma level as well as the main adipogenic and lipolytic genes expressed in adipose tissue were also analyzed. METHODS The expression of several lipogenic, lipolytic, PPAR family and FABP family genes was analyzed by real time PCR. FABP4 protein expression in total adipose tissues and its fractions were determined by western blot. RESULTS In obesity FABP4 expression was down-regulated (at both mRNA and protein levels), with its levels mainly predicted by ATGL and inversely by the HOMA-IR index. The BMI appeared as the only determinant of the FABP4 variation in both adipose tissue depots. FABP4 plasma levels showed a significant progressive increase according to BMI but no association was detected between FABP4 circulating levels and SAT or VAT FABP4 gene expression. The gene expression of FABP1, FABP4 and FABP5 in hepatic tissue was significantly higher in tissue from the obese IR patients compared to the non-IR group. CONCLUSION The inverse pattern in FABP4 expression between adipose and hepatic tissue observed in morbid obese patients, regarding the IR context, suggests that both tissues may act in a balanced manner. These differences may help us to understand the discrepancies between circulating plasma levels and adipose tissue expression in obesity.

Gender and weight shape brain dynamics during food viewing.

Hemodynamic imaging results have associated both gender and body weight to variation in brain responses to food-related information. However, the spatio-temporal brain dynamics of gender-related and weight-wise modulations in food discrimination still remain to be elucidated. We analyzed visual evoked potentials (VEPs) while normal-weighted men (n = 12) and women (n = 12) categorized photographs of energy-dense foods and non-food kitchen utensils. VEP analyses showed that food categorization is influenced by gender as early as 170 ms after image onset. Moreover, the female VEP pattern to food categorization co-varied with participants' body weight. Estimations of the neural generator activity over the time interval of VEP modulations (i.e. by means of a distributed linear inverse solution [LAURA]) revealed alterations in prefrontal and temporo-parietal source activity as a function of image category and participants' gender. However, only neural source activity for female responses during food viewing was negatively correlated with body-mass index (BMI) over the respective time interval. Women showed decreased neural source activity particularly in ventral prefrontal brain regions when viewing food, but not non-food objects, while no such associations were apparent in male responses to food and non-food viewing. Our study thus indicates that gender influences are already apparent during initial stages of food-related object categorization, with small variations in body weight modulating electrophysiological responses especially in women and in brain areas implicated in food reward valuation and intake control. These findings extend recent reports on prefrontal reward and control circuit responsiveness to food cues and the potential role of this reactivity pattern in the susceptibility to weight gain.

Angiostrongylus cantonensis infection in molluscs in the municipality of São Gonçalo, a metropolitan area of Rio de Janeiro, Brazil: role of the invasive species Achatina fulica in parasite transmission dynamics

The aim of this study was to analyse the infection dynamics ofAngiostrongylus cantonensisin its possible intermediate hosts over two years in an urban area in the state of Rio de Janeiro where the presence ofA. cantonensis had been previously recorded in molluscs. Four of the seven mollusc species found in the study were exotic.Bradybaena similariswas the most abundant, followed byAchatina fulica, Streptaxissp., Subulina octona, Bulimulus tenuissimus, Sarasinula linguaeformisand Leptinaria unilamellata. Only A. fulicaand B. similariswere parasitised by A. cantonensis and both presented co-infection with other helminths. The prevalence of A. cantonensisin A. fulicawas more than 50% throughout the study. There was an inverse correlation between the population size ofA. fulicaand the prevalence of A. cantonensisand abundance of the latter was negatively related to rainfall. The overall prevalence of A. cantonensisin B. similariswas 24.6%. A. fulicawas the most important intermediary host of A. cantonensisin the studied area andB. similariswas secondary in importance for A. cantonensistransmission dynamics.

Dynamics of the control of Aedes (Stegomyia) aegypti Linnaeus (Diptera, Culicidae) by Bacillus thuringiensis var israelensis, related with temperature, density and concentration of insecticide

The dynamics of the control of Aedes (Stegomyia) aegypti Linnaeus, (Diptera, Culicidae) by Bacillus thuringiensis var israelensis has been related with the temperature, density and concentration of the insecticide. A mathematical model for biological control of Aedes aegypti with Bacillus thuringiensis var israelensis (Bti) was constructed by using data from the literature regarding the biology of the vector. The life cycle was described by differential equations. Lethal concentrations (LC50 and LC95) of Bti were determined in the laboratory under different experimental conditions. Temperature, colony, larvae density and bioinsecticide concentration presented marked differences in the analysis of the whole set of variables; although when analyzed individually, only the temperature and concentration showed changes. The simulations indicated an inverse relationship between temperature and mosquito population, nonetheless, faster growth of populations is reached at higher temperatures. As conclusion, the model suggests the use of integrated control strategies for immature and adult mosquitoes in order to achieve a reduction of Aedes aegypti.

Deficit, human capital and economic growth dynamics

Long-run economic growth arouses a great interest since it can shed light on the income-path of an economy and try to explain the large differences in income we observe across countries and over time. The neoclassical model has been followed by several endogenous growth models which, contrarily to the former, seem to predict that economies with similar preferences and technological level, do not necessarily tend to converge to similar per capita income levels. This paper attempts to show a possible mechanismthrough which macroeconomic disequilibria and inefficiencies, represented by budget deficits, may hinder human capital accumulation and therefore economic growth. Using a mixed education system, deficit is characterized as a bug agent which may end up sharply reducing the resources devoted to education and training. The paper goes a step further from the literature on deficit by introducing a rich dynamic analysis of the effects of a deficit reduction on different economic aspects.Following a simple growth model and allowing for slight changes in the law of human capital accumulation, we reach a point where deficit might sharply reduce human capital accumulation. On the other hand, a deficit reduction carried on for a long time, taking that reduction as a more efficient management of the economy, may prove useful in inducing endogenous growth. Empirical evidence for a sample of countries seems to support the theoretical assumptions in the model: (1) evidence on an inverse relationship betweendeficit and human capital accumulation, (2) presence of a strongly negative associationbetween the quantity of deficit in the economy and the rate of growth. They may prove a certain role for budget deficit in economic growth

Deficit, human capital and economic growth dynamics

Long-run economic growth arouses a great interest since it can shed light on the income-path of an economy and try to explain the large differences in income we observe across countries and over time. The neoclassical model has been followed by several endogenous growth models which, contrarily to the former, seem to predict that economies with similar preferences and technological level, do not necessarily tend to converge to similar per capita income levels. This paper attempts to show a possible mechanismthrough which macroeconomic disequilibria and inefficiencies, represented by budget deficits, may hinder human capital accumulation and therefore economic growth. Using a mixed education system, deficit is characterized as a bug agent which may end up sharply reducing the resources devoted to education and training. The paper goes a step further from the literature on deficit by introducing a rich dynamic analysis of the effects of a deficit reduction on different economic aspects.Following a simple growth model and allowing for slight changes in the law of human capital accumulation, we reach a point where deficit might sharply reduce human capital accumulation. On the other hand, a deficit reduction carried on for a long time, taking that reduction as a more efficient management of the economy, may prove useful in inducing endogenous growth. Empirical evidence for a sample of countries seems to support the theoretical assumptions in the model: (1) evidence on an inverse relationship betweendeficit and human capital accumulation, (2) presence of a strongly negative associationbetween the quantity of deficit in the economy and the rate of growth. They may prove a certain role for budget deficit in economic growth