Automated image analysis of lung branching morphogenesis

Regulating mechanisms of branchingmorphogenesis of fetal lung rat explants have been an essential tool formolecular research.This work presents a new methodology to accurately quantify the epithelial, outer contour, and peripheral airway buds of lung explants during cellular development frommicroscopic images. Methods.Theouter contour was defined using an adaptive and multiscale threshold algorithm whose level was automatically calculated based on an entropy maximization criterion. The inner lung epithelium was defined by a clustering procedure that groups small image regions according to the minimum description length principle and local statistical properties. Finally, the number of peripheral buds was counted as the skeleton branched ends from a skeletonized image of the lung inner epithelia. Results. The time for lung branching morphometric analysis was reduced in 98% in contrast to themanualmethod. Best results were obtained in the first two days of cellular development, with lesser standard deviations. Nonsignificant differences were found between the automatic and manual results in all culture days. Conclusions. The proposed method introduces a series of advantages related to its intuitive use and accuracy, making the technique suitable to images with different lighting characteristics and allowing a reliable comparison between different researchers.

Quantifying chaos for ecological stoichiometry

The theory of ecological stoichiometry considers ecological interactions among species with different chemical compositions. Both experimental and theoretical investigations have shown the importance of species composition in the outcome of the population dynamics. A recent study of a theoretical three-species food chain model considering stoichiometry [B. Deng and I. Loladze, Chaos 17, 033108 (2007)] shows that coexistence between two consumers predating on the same prey is possible via chaos. In this work we study the topological and dynamical measures of the chaotic attractors found in such a model under ecological relevant parameters. By using the theory of symbolic dynamics, we first compute the topological entropy associated with unimodal Poincareacute return maps obtained by Deng and Loladze from a dimension reduction. With this measure we numerically prove chaotic competitive coexistence, which is characterized by positive topological entropy and positive Lyapunov exponents, achieved when the first predator reduces its maximum growth rate, as happens at increasing delta(1). However, for higher values of delta(1) the dynamics become again stable due to an asymmetric bubble-like bifurcation scenario. We also show that a decrease in the efficiency of the predator sensitive to prey's quality (increasing parameter zeta) stabilizes the dynamics. Finally, we estimate the fractal dimension of the chaotic attractors for the stoichiometric ecological model.

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.

Measuring and Controlling the Chaotic Motion of Profits

The study of economic systems has generated deep interest in exploring the complexity of chaotic motions in economy. Due to important developments in nonlinear dynamics, the last two decades have witnessed strong revival of interest in nonlinear endogenous business chaotic models. The inability to predict the behavior of dynamical systems in the presence of chaos suggests the application of chaos control methods, when we are more interested in obtaining regular behavior. In the present article, we study a specific economic model from the literature. More precisely, a system of three ordinary differential equations gather the variables of profits, reinvestments and financial flow of borrowings in the structure of a firm. Firstly, using results of symbolic dynamics, we characterize the topological entropy and the parameter space ordering of kneading sequences, associated with one-dimensional maps that reproduce significant aspects of the model dynamics. The analysis of the variation of this numerical invariant, in some realistic system parameter region, allows us to quantify and to distinguish different chaotic regimes. Finally, we show that complicated behavior arising from the chaotic firm model can be controlled without changing its original properties and the dynamics can be turned into the desired attracting time periodic motion (a stable steady state or into a regular cycle). The orbit stabilization is illustrated by the application of a feedback control technique initially developed by Romeiras et al. [1992]. This work provides another illustration of how our understanding of economic models can be enhanced by the theoretical and numerical investigation of nonlinear dynamical systems modeled by ordinary differential equations.

Dynamical behaviour on the parameter space: new populational growth models proportional to beta densities

We present new populational growth models, generalized logistic models which are proportional to beta densities with shape parameters p and 2, where p > 1, with Malthusian parameter r. The complex dynamical behaviour of these models is investigated in the parameter space (r, p), in terms of topological entropy, using explicit methods, when the Malthusian parameter r increases. This parameter space is split into different regions, according to the chaotic behaviour of the models.

Genus and Braid Index Associated to Sequences of Renormalizable Lorenz Maps

We describe the Lorenz links generated by renormalizable Lorenz maps with reducible kneading invariant (K(f)(-), = K(f)(+)) = (X, Y) * (S, W) in terms of the links corresponding to each factor. This gives one new kind of operation that permits us to generate new knots and links from the ones corresponding to the factors of the *-product. Using this result we obtain explicit formulas for the genus and the braid index of this renormalizable Lorenz knots and links. Then we obtain explicit formulas for sequences of these invariants, associated to sequences of renormalizable Lorenz maps with kneading invariant (X, Y) * (S,W)*(n), concluding that both grow exponentially. This is specially relevant, since it is known that topological entropy is constant on the archipelagoes of renormalization.

Re-entrant phase behaviour of network fluids: A patchy particle model with temperature-dependent valence

We study a model consisting of particles with dissimilar bonding sites ("patches"), which exhibits self-assembly into chains connected by Y-junctions, and investigate its phase behaviour by both simulations and theory. We show that, as the energy cost epsilon(j) of forming Y-junctions increases, the extent of the liquid-vapour coexistence region at lower temperatures and densities is reduced. The phase diagram thus acquires a characteristic "pinched" shape in which the liquid branch density decreases as the temperature is lowered. To our knowledge, this is the first model in which the predicted topological phase transition between a fluid composed of short chains and a fluid rich in Y-junctions is actually observed. Above a certain threshold for epsilon(j), condensation ceases to exist because the entropy gain of forming Y-junctions can no longer offset their energy cost. We also show that the properties of these phase diagrams can be understood in terms of a temperature-dependent effective valence of the patchy particles. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3605703]

Solubility of Ethene in Water and in a Medium for the Cultivation of a Bacterial Strain

The solubility of ethene in water and in the fermentation medium of Xanthobacter Py(2) was determined with a Ben-Naim-Baer type apparatus. The solubility measurements were carried out in the temperature range of (293.15 to 323.15) K and at atmospheric pressure with a precision of about +/- 0.3 %. The Ostwald coefficients, the mole fractions of the dissolved ethene, at the gas partial pressure of 101.325 kPa, and the Henry coefficients, at the water vapor pressure, were calculated using accurate thermodynamic relations. A comparison between the solubility of ethene in water and in the cultivation medium has shown that this gas is about 2.4 % more soluble in pure water. On the other hand, from the solubility temperature dependence, the Gibbs energy, enthalpy, and entropy changes for the process of transferring the solute from the gaseous phase to the liquid solutions were also determined. Moreover, the perturbed-chain statistical associating fluid theory equation of state (PC-SAFT EOS) model was used for the prediction of the solubility of ethene in water. New parameters, k(ij), are proposed for this system, and it was found that using a ky temperature-dependent PC-SAFT EOS describes more accurately the behavior solubilities of ethene in water at 101.325 kPa, improving the deviations to 1 %.

Trends in properties of para-substituted 3-(phenylhydrazo)pentane-2,4-diones

Trends between the Hammett's sigma(p) and related normal sigma(n)(p), inductive sigma(I), resonance sigma(R), negative sigma(-)(p) and positive sigma(+)(p) polar conjugation and Taft's sigma(o)(p) substituent constants and the N-H center dot center dot center dot O distance, delta(N-H) NMR chemical shift, oxidation potential (E-p/2(ox), measured in this study by cyclic voltammetry (CV)) and thermodynamic parameters (pK, Delta G(0), Delta H-0 and Delta S-0) of the dissociation process of unsubstituted 3-(phenylhydrazo)pentane-2,4-dione (HL1) and its para-substituted chloro (HL2), carboxy (HL3), fluoro (HL4) and nitro (HL5) derivatives were recognized. The best fits were found for sigma(p) and/or sigma(-)(p) in the cases of d(N center dot center dot center dot O), delta(N-H) and E-p/2(ox), showing the importance of resonance and conjugation effects in such properties, whereas for the above thermodynamic properties the inductive effects (sigma(I)) are dominant. HL2 exists in the hydrazo form in DMSO solution and in the solid state and contains an intramolecular H-bond with the N center dot center dot center dot O distance of 2.588(3)angstrom. It was also established that the dissociation process of HL1-5 is non-spontaneous, endothermic and entropically unfavourable, and that the increase in the inductive effect (sigma(I)) of para-substitutents (-H < -Cl < -COOH < -F < -NO2) leads to the corresponding growth of the N center dot center dot center dot O distance and decrease of the pK and of the changes of Gibbs free energy, of enthalpy and of entropy for the HL1-5 acid dissociation process. The electrochemical behaviour of HL1-5 was interpreted using theoretical calculations at the DFT/HF hybrid level, namely in terms of HOMO and LUMO compositions, and of reactivities induced by anodic and cathodic electron-transfers. Copyright (C) 2010 John Wiley & Sons, Ltd.

Dynamical analysis of compositions

This paper analyzes musical opus from the point of view of two mathematical tools, namely the entropy and the multidimensional scaling (MDS). The Fourier analysis reveals a fractional dynamics, but the time rhythm variations are diluted along the spectrum. The combination of time-window entropy and MDS copes with the time characteristics and is well suited to treat a large volume of data. The experiments focus on a large number of compositions classified along three sets of musical styles, namely “Classical”, “Jazz”, and “Pop & Rock” compositions. Without lack of generality, the present study describes the application of the tools and the sets of musical compositions in a methodology leading to clear conclusions, but extensions to other possibilities are straightforward. The results reveal significant differences in the musical styles, demonstrating the feasibility of the proposed strategy and motivating further developments toward a dynamical analysis of musical compositions.

A multidimensional scaling analysis of musical sounds based on pseudo phase plane

This paper studies musical opus from the point of view of three mathematical tools: entropy, pseudo phase plane (PPP), and multidimensional scaling (MDS). The experiments analyze ten sets of different musical styles. First, for each musical composition, the PPP is produced using the time series lags captured by the average mutual information. Second, to unravel hidden relationships between the musical styles the MDS technique is used. The MDS is calculated based on two alternative metrics obtained from the PPP, namely, the average mutual information and the fractal dimension. The results reveal significant differences in the musical styles, demonstrating the feasibility of the proposed strategy and motivating further developments towards a dynamical analysis of musical sounds.

Dynamical analysis in growth models: Blumberg’s equation

We present a new dynamical approach to the Blumberg's equation, a family of unimodal maps. These maps are proportional to Beta(p, q) probability densities functions. Using the symmetry of the Beta(p, q) distribution and symbolic dynamics techniques, a new concept of mirror symmetry is defined for this family of maps. The kneading theory is used to analyze the effect of such symmetry in the presented models. The main result proves that two mirror symmetric unimodal maps have the same topological entropy. Different population dynamics regimes are identified, when the intrinsic growth rate is modified: extinctions, stabilities, bifurcations, chaos and Allee effect. To illustrate our results, we present a numerical analysis, where are demonstrated: monotonicity of the topological entropy with the variation of the intrinsic growth rate, existence of isentropic sets in the parameters space and mirror symmetry.

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.

Modelling the distribution of cetaceans using opportunistic presence-only data in S. Miguel Island (Azores)

25th Annual Conference of the European Cetacean Society, Cadiz, Spain 21-23 March 2011.