Search

This article aims to review the current literature pertaining to the effects of eating local seasonal food on sustainable consumption. To this end, we examined definitions of seasonal and local food, the methodological approaches adopted to study the impact of seasonal consumption on sustainability, and sustainability dimensions investigated in journal articles. Highlighting what seasonal and local means, it is crucial to evaluate the effect of the consumption of these foods on sustainability. A systematic review of the literature was conducted using Scopus and Clarivate's Web of Science database in line with the recommendations from the Preferred Reporting Items for Systematic Reviews and Meta Analyses (PRISMA) guidelines. Our findings suggest that the concept of local seasonality provides relevant information to the study of sustainable consumption. However, for better use of this concept, it is crucial to define what is local. At this point, regulation of labels based on geographic proximity or political boundaries proves pertinent.

The objective of this experiment was to determine whether there is a difference between Warner-Blatzler shear force values of round (WBSF) and square (WBsSF) cross-section cores for assessment of beef tenderness. To compare the effect of core sampling, Longissimus thoracis muscles were obtained from 43 beef carcasses at 1, 14, and 28days postmortem. For each sample, tenderness was assessed by a trained sensory panel and by WBSF and WBsSF techniques. There was a strong and linear relationship (R 2 =0.77) between WBSF and WBsSF, but the average shear force of square cores were (P<0.05) greater than those of round cores. The WBsSF had greater repeatability (R=0.85 vs 0.81) and explained slightly more of the variation in sensory panel perception of beef tenderness (76% vs 74%) than WBSF. The results indicate that WBsSF seems to be a more precise method of measuring shear force, being little more sensitive for detecting tenderness differences than WBSF., (Copyright © 2016 Elsevier Ltd. All rights reserved.)

Xenografts--as simplified animal models of cancer-differ substantially in vasculature and stromal architecture when compared to clinical tumours. This makes mathematical model-based predictions of clinical outcome challenging. Our objective is to further understand differences in tumour progression and physiology between animal models and the clinic. To achieve that, we propose a mathematical model based upon tumour pathophysiology, where oxygen--as a surrogate for endocrine delivery--is our main focus. The Oxygen-Driven Model (ODM), using oxygen diffusion equations, describes tumour growth, hypoxia and necrosis. The ODM describes two key physiological parameters. Apparent oxygen uptake rate (k'R) represents the amount of oxygen cells seem to need to proliferate. The more oxygen they appear to need, the more the oxygen transport. k'R gathers variability from the vasculature, stroma and tumour morphology. Proliferating rate (kp) deals with cell line specific factors to promote growth. The KH,KN describe the switch of hypoxia and necrosis. Retrospectively, using archived data, we looked at longitudinal tumour volume datasets for 38 xenografted cell lines and 5 patient-derived xenograft-like models. Exploration of the parameter space allows us to distinguish 2 groups of parameters. Group 1 of cell lines shows a spread in values of k'R and lower kp, indicating that tumours are poorly perfused and slow growing. Group 2 share the value of the oxygen uptake rate (k'R) and vary greatly in kp, which we interpret as having similar oxygen transport, but more tumour intrinsic variability in growth. However, the ODM has some limitations when tested in explant-like animal models, whose complex tumour-stromal morphology may not be captured in the current version of the model. Incorporation of stroma in the ODM will help explain these discrepancies. We have provided an example. The ODM is a very simple -and versatile- model suitable for the design of preclinical experiments, which can be modified and enhanced whilst maintaining confidence in its predictions.

The major fungal pathogen of humans, Candida albicans, mounts robust responses to oxidative stress that are critical for its virulence. These responses counteract the reactive oxygen species (ROS) that are generated by host immune cells in an attempt to kill the invading fungus. Knowledge of the dynamical processes that instigate C. albicans oxidative stress responses is required for a proper understanding of fungus-host interactions. Therefore, we have adopted an interdisciplinary approach to explore the dynamical responses of C. albicans to hydrogen peroxide (H2O2). Our deterministic mathematical model integrates two major oxidative stress signalling pathways (Cap1 and Hog1 pathways) with the three major antioxidant systems (catalase, glutathione and thioredoxin systems) and the pentose phosphate pathway, which provides reducing equivalents required for oxidative stress adaptation. The model encapsulates existing knowledge of these systems with new genomic, proteomic, transcriptomic, molecular and cellular datasets. Our integrative approach predicts the existence of alternative states for the key regulators Cap1 and Hog1, thereby suggesting novel regulatory behaviours during oxidative stress. The model reproduces both existing and new experimental observations under a variety of scenarios. Time- and dose-dependent predictions of the oxidative stress responses for both wild type and mutant cells have highlighted the different temporal contributions of the various antioxidant systems during oxidative stress adaptation, indicating that catalase plays a critical role immediately following stress imposition. This is the first model to encapsulate the dynamics of the transcriptional response alongside the redox kinetics of the major antioxidant systems during H2O2 stress in C. albicans.

We report on the structural, optical, and magnetic properties of α,β-NiMoO4 nanorods synthesized by annealing the NiMoO4:nH2O precursor at 600°C for 10 minutes in a domestic microwave. The crystalline structure properties of α,β-NiMoO4 were investigated using X-ray diffraction (XRD), Fourier transform infrared (FTIR), and Raman (FT-Raman) spectroscopies. The particle morphologies and size distributions were identified by field emission microscopy (FE-SEM). Experimental data were obtained by magnetization measurements for different applied magnetic fields. Optical properties were analyzed by ultraviolet-visible (UV-vis) and photoluminescence (PL) measurements. Our results revealed that the oxygen atoms occupy different positions and are very disturbed in the lattice and exhibit a particular characteristic related to differences in the length of the chemical bonds (Ni-O and Mo-O) of the cluster structure or defect densities in the crystalline α,β-NiMoO4 nanorods, which are the key to a deeper understanding of the exploitable physical and chemical properties in this study.

Eukaryotic genomes are replicated from multiple DNA replication origins. We present complementary deep sequencing approaches to measure origin location and activity in Saccharomyces cerevisiae. Measuring the increase in DNA copy number during a synchronous S-phase allowed the precise determination of genome replication. To map origin locations, replication forks were stalled close to their initiation sites; therefore, copy number enrichment was limited to origins. Replication timing profiles were generated from asynchronous cultures using fluorescence-activated cell sorting. Applying this technique we show that the replication profiles of haploid and diploid cells are indistinguishable, indicating that both cell types use the same cohort of origins with the same activities. Finally, increasing sequencing depth allowed the direct measure of replication dynamics from an exponentially growing culture. This is the first time this approach, called marker frequency analysis, has been successfully applied to a eukaryote. These data provide a high-resolution resource and methodological framework for studying genome biology.

This study evaluates the perceptions of teachers in charge of coordinating health education in schools: the School Health Coordinators (SHCs). It addresses the success and barriers of the development and implementation regarding the first year of healthy eating programmes in their schools. This research is based on 16 face-to-face semi-structured interviews with SHCs from Portuguese public schools offering from fifth to ninth grades. A thematic analysis was performed and themes were identified, taking into consideration similarities and differences among the participants' opinions. The results showed that the schools in this study often involved a set of separate healthy diet promotion activities with a low level of joint effort from all members of the school. Nevertheless, in Portugal, health education is based on the broad concept that school health promotion is compulsory for all schools. Two main barriers were identified in order to explain this divergence: structural and political idiosyncrasies among schools and the food environment inside and outside the schools. The results are discussed considering the wide range of factors influencing young people's eating behaviours and recommendations are made for the different agents interacting with them in order to promote appropriate eating habits.

Eukaryotic genome replication is stochastic, and each cell uses a different cohort of replication origins. We demonstrate that interpreting high-resolution Saccharomyces cerevisiae genome replication data with a mathematical model allows quantification of the stochastic nature of genome replication, including the efficiency of each origin and the distribution of termination events. Single-cell measurements support the inferred values for stochastic origin activation time. A strain, in which three origins were inactivated, confirmed that the distribution of termination events is primarily dictated by the stochastic activation time of origins. Cell-to-cell variability in origin activity ensures that termination events are widely distributed across virtually the whole genome. We propose that the heterogeneity in origin usage contributes to genome stability by limiting potentially deleterious events from accumulating at particular loci., (Copyright © 2013 The Authors. Published by Elsevier Inc. All rights reserved.)

Inside the nucleus, DNA replication is organized at discrete sites called replication factories, consisting of DNA polymerases and other replication proteins. Replication factories play important roles in coordinating replication and in responding to replication stress. However, it remains unknown how replicons are organized for processing at each replication factory. Here we address this question using budding yeast. We analyze how individual replicons dynamically organized a replication factory using live-cell imaging and investigate how replication factories were structured using super-resolution microscopy. Surprisingly, we show that the grouping of replicons within factories is highly variable from cell to cell. Once associated, however, replicons stay together relatively stably to maintain replication factories. We derive a coherent genome-wide mathematical model showing how neighboring replicons became associated stochastically to form replication factories, which was validated by independent microscopy-based analyses. This study not only reveals the fundamental principles promoting replication factory organization in budding yeast, but also provides insight into general mechanisms by which chromosomes organize sub-nuclear structures.

Methylglyoxal (MG) elicits activation of K(+) efflux systems to protect cells against the toxicity of the electrophile. ChIP-chip targeting RNA polymerase, supported by a range of other biochemical measurements and mutant creation, was used to identify genes transcribed in response to MG and which complement this rapid response. The SOS DNA repair regulon is induced at cytotoxic levels of MG, even when exposure to MG is transient. Glyoxalase I alone among the core MG protective systems is induced in response to MG exposure. Increased expression is an indirect consequence of induction of the upstream nemRA operon, encoding an enzyme system that itself does not contribute to MG detoxification. Moreover, this induction, via nemRA only occurs when cells are exposed to growth inhibitory concentrations of MG. We show that the kdpFABCDE genes are induced and that this expression occurs as a result of depletion of cytoplasmic K(+) consequent upon activation of the KefGB K(+) efflux system. Finally, our analysis suggests that the transcriptional changes in response to MG are a culmination of the damage to DNA and proteins, but that some integrate specific functions, such as DNA repair, to augment the allosteric activation of the main protective system, KefGB., (© 2013 The Authors. Molecular Microbiology published by John Wiley & Sons Ltd.)

Pathogenic microbes exist in dynamic niches and have evolved robust adaptive responses to promote survival in their hosts. The major fungal pathogens of humans, Candida albicans and Candida glabrata, are exposed to a range of environmental stresses in their hosts including osmotic, oxidative and nitrosative stresses. Significant efforts have been devoted to the characterization of the adaptive responses to each of these stresses. In the wild, cells are frequently exposed simultaneously to combinations of these stresses and yet the effects of such combinatorial stresses have not been explored. We have developed a common experimental platform to facilitate the comparison of combinatorial stress responses in C. glabrata and C. albicans. This platform is based on the growth of cells in buffered rich medium at 30°C, and was used to define relatively low, medium and high doses of osmotic (NaCl), oxidative (H(2)O(2)) and nitrosative stresses (e.g., dipropylenetriamine (DPTA)-NONOate). The effects of combinatorial stresses were compared with the corresponding individual stresses under these growth conditions. We show for the first time that certain combinations of combinatorial stress are especially potent in terms of their ability to kill C. albicans and C. glabrata and/or inhibit their growth. This was the case for combinations of osmotic plus oxidative stress and for oxidative plus nitrosative stress. We predict that combinatorial stresses may be highly significant in host defences against these pathogenic yeasts.

Background: Saccharomyces cerevisiae senses hyperosmotic conditions via the HOG signaling network that activates the stress-activated protein kinase, Hog1, and modulates metabolic fluxes and gene expression to generate appropriate adaptive responses. The integral control mechanism by which Hog1 modulates glycerol production remains uncharacterized. An additional Hog1-independent mechanism retains intracellular glycerol for adaptation. Candida albicans also adapts to hyperosmolarity via a HOG signaling network. However, it remains unknown whether Hog1 exerts integral or proportional control over glycerol production in C. albicans., Results: We combined modeling and experimental approaches to study osmotic stress responses in S. cerevisiae and C. albicans. We propose a simple ordinary differential equation (ODE) model that highlights the integral control that Hog1 exerts over glycerol biosynthesis in these species. If integral control arises from a separation of time scales (i.e. rapid HOG activation of glycerol production capacity which decays slowly under hyperosmotic conditions), then the model predicts that glycerol production rates elevate upon adaptation to a first stress and this makes the cell adapts faster to a second hyperosmotic stress. It appears as if the cell is able to remember the stress history that is longer than the timescale of signal transduction. This is termed the long-term stress memory. Our experimental data verify this. Like S. cerevisiae, C. albicans mimimizes glycerol efflux during adaptation to hyperosmolarity. Also, transient activation of intermediate kinases in the HOG pathway results in a short-term memory in the signaling pathway. This determines the amplitude of Hog1 phosphorylation under a periodic sequence of stress and non-stressed intervals. Our model suggests that the long-term memory also affects the way a cell responds to periodic stress conditions. Hence, during osmohomeostasis, short-term memory is dependent upon long-term memory. This is relevant in the context of fungal responses to dynamic and changing environments., Conclusions: Our experiments and modeling have provided an example of identifying integral control that arises from time-scale separation in different processes, which is an important functional module in various contexts.

We show that common circulatory diseases, such as stenoses and aneurysms, generate chaotic advection of blood particles. This phenomenon has major consequences on the way the biochemical particles behave. Chaotic advection leads to a peculiar filamentary particle distribution, which in turn creates a favorable environment for particle reactions. Furthermore, we argue that the enhanced stretching dynamics induced by chaos can lead to the activation of platelets, particles involved in the thrombus formation. In particular, we vary the size of both stenoses and aneurysms, and model them under resting and exercising conditions. We show that the filamentary particle distribution, governed by the fractal skeleton, depends on the size of the vessel wall irregularity, and investigate how it varies under resting or exercising conditions., (Copyright © 2011 Elsevier Ltd. All rights reserved.)

DNA replication is an essential process in biology and its timing must be robust so that cells can divide properly. Random fluctuations in the formation of replication starting points, called origins, and the subsequent activation of proteins lead to variations in the replication time. We analyze these stochastic properties of DNA and derive the positions of origins corresponding to the minimum replication time. We show that under some conditions the minimization of replication time leads to the grouping of origins, and relate this to experimental data in a number of species showing origin grouping.

We study the collision probability p of particles advected by open flows with chaotic advection. We show that p scales with the particle size (or, alternatively, reaction distance) δ as a power law whose coefficient is determined by the fractal dimensions of the invariant sets defined by the advection dynamics. We also argue that this same scaling also holds for the reaction rate of active particles in the low-density regime. These analytical results are compared to numerical simulations, and they are found to agree very well.

Nanorods and nanoplates of Y(2)O(3):Eu(3+) powders were synthesized through the thermal decomposition of the Y(OH)(3) precursors using a microwave-hydrothermal method in a very short reaction time. These powders were analyzed by X-ray diffraction, field emission scanning electron microscopy, Fourrier transform Raman, as well as photoluminescence measurements. Based on these results, these materials presented nanoplates and nanorods morphologies. The broad emission band between 300 and 440 nm ascribed to the photoluminescence of Y(2)O(3) matrix shifts as the procedure used in the microwave-hydrothermal assisted method changes in the Y(2)O(3):Eu(3+) samples. The presence of Eu(3+) and the hydrothermal treatment time are responsible for the band shifts in Y(2)O(3):Eu(3+) powders, since in the pure Y(2)O(3) matrix this behavior was not observed. Y(2)O(3):Eu(3+) powders also show the characteristic Eu(3+) emission lines at 580, 591, 610, 651 and 695 nm, when excited at 393 nm. The most intense band at 610 nm is responsible for the Eu(3+) red emission in these materials, and the Eu(3+) lifetime for this transition presented a slight increase as the time used in the microwave-hydrothermal assisted method increases., (© Springer Science+Business Media, LLC 2011)

DNA damage is a hazard all cells must face, and evolution has created a number of mechanisms to repair damaged bases in the chromosome. Paradoxically, many of these repair mechanisms can create double-strand breaks in the DNA molecule which are fatal to the cell. This indicates that the connection between DNA repair and death is far from straightforward, and suggests that the repair mechanisms can be a double-edged sword. In this report, we formulate a mathematical model of the dynamics of DNA damage and repair, and we obtain analytical expressions for the death rate. We predict a counterintuitive relationship between survival and repair. We can discriminate between two phases: below a critical threshold in the number of repair enzymes, the half-life decreases with the number of repair enzymes, but becomes independent of the number of repair enzymes above the threshold. We are able to predict quantitatively the dependence of the death rate on the damage rate and other relevant parameters. We verify our analytical results by simulating the stochastic dynamics of DNA damage and repair. Finally, we also perform an experiment with Escherichia coli cells to test one of the predictions of our model., (Copyright © 2011 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Hyperornithinemia-hyperammonemia-homocitrullinuria (HHH) syndrome is an autosomal recessive disorder caused by a defect in the mitochondrial ornithine transporter, leading to accumulation of ornithine (Orn), homocitrulline (Hcit) and ammonia. Progressive neurological regression whose pathogenesis is not well established is common in this disease. The present work investigated the in vivo effects of intracerebroventricular administration of Orn and Hcit on important parameters of oxidative stress and energy metabolism in cerebral cortex from young rats. Orn and Hcit significantly increased thiobarbituric acid-reactive substances values and carbonyl formation, indicators of lipid and protein oxidative damage, respectively. Furthermore, N-acetylcysteine and the combination of the free radical scavengers ascorbic acid plus α-tocopherol attenuated the lipid oxidation and totally prevented the protein oxidative damage provoked by Orn and Hcit, suggesting that reactive species were involved in these effects. Hcit, but not Orn administration, also decreased glutathione concentrations, as well as the activity of catalase and glutathione peroxidase, indicating that Hcit provokes a reduction of brain antioxidant defenses. As regards to the parameters of energy metabolism, we verified that Orn and Hcit significantly inhibited the citric acid cycle function (inhibition of CO(2) synthesis from [1-(14)C] acetate), the aerobic glycolytic pathway (reduced CO(2) production from [U-(14)C] glucose) and complex I-III activity of the respiratory chain. Hcit also inhibited the activity of aconitase, an enzyme very susceptible to free radical attack. Taken together, our data indicate that mitochondrial homeostasis is disturbed by Orn and especially by Hcit. It is presumed that the impairment of brain bioenergetics and the oxidative damage induced by these metabolites may possibly contribute to the brain deterioration and neurological symptoms affecting patients with HHH syndrome., (Copyright © 2010 Elsevier B.V. All rights reserved.)

Recent advances in the field of chaotic advection provide the impetus to revisit the dynamics of particles transported by blood flow in the presence of vessel wall irregularities. The irregularity, being either a narrowing or expansion of the vessel, mimicking stenoses or aneurysms, generates abnormal flow patterns that lead to a peculiar filamentary distribution of advected particles, which, in the blood, would include platelets. Using a simple model, we show how the filamentary distribution depends on the size of the vessel wall irregularity, and how it varies under resting or exercise conditions. The particles transported by blood flow that spend a long time around a disturbance either stick to the vessel wall or reside on fractal filaments. We show that the faster flow associated with exercise creates widespread filaments where particles can get trapped for a longer time, thus allowing for the possible activation of such particles. We argue, based on previous results in the field of active processes in flows, that the non-trivial long-time distribution of transported particles has the potential to have major effects on biochemical processes occurring in blood flow, including the activation and deposition of platelets. One aspect of the generality of our approach is that it also applies to other relevant biological processes, an example being the coexistence of plankton species investigated previously.

The dynamics of escape from an attractive state due to random perturbations is of central interest to many areas in science. Previous studies of escape in chaotic systems have rather focused on the case of unbounded noise, usually assumed to have Gaussian distribution. In this paper, we address the problem of escape induced by bounded noise. We show that the dynamics of escape from an attractor's basin is equivalent to that of a closed system with an appropriately chosen "hole." Using this equivalence, we show that there is a minimum noise amplitude above which escape takes place, and we derive analytical expressions for the scaling of the escape rate with noise amplitude near the escape transition. We verify our analytical predictions through numerical simulations of two well-known two-dimensional maps with noise.

All chromosomes must be completely replicated prior to cell division, a requirement that demands the activation of a sufficient number of appropriately distributed DNA replication origins. Here we investigate how the activity of multiple origins on each chromosome is coordinated to ensure successful replication. We present a stochastic model for whole chromosome replication where the dynamics are based upon the parameters of individual origins. Using this model we demonstrate that mean replication time at any given chromosome position is determined collectively by the parameters of all origins. Combining parameter estimation with extensive simulations we show that there is a range of model parameters consistent with mean replication data, emphasising the need for caution in interpreting such data. In contrast, the replicated-fraction at time points through S phase contains more information than mean replication time data and allowed us to use our model to uniquely estimate many origin parameters. These estimated parameters enable us to make a number of predictions that showed agreement with independent experimental data, confirming that our model has predictive power. In summary, we demonstrate that a stochastic model can recapitulate experimental observations, including those that might be interpreted as deterministic such as ordered origin activation times.

A great number of physical processes are described within the context of Hamiltonian scattering. Previous studies have rather been focused on trajectories starting outside invariant structures, since the ones starting inside are expected to stay trapped there forever. This is true though only for the deterministic case. We show however that, under finitely small random fluctuations of the field, trajectories starting inside Kolmogorov-Arnold-Moser (KAM) islands escape within finite time. The nonhyperbolic dynamics gains then hyperbolic characteristics due to the effect of the random perturbed field. As a consequence, trajectories which are started inside KAM curves escape with hyperboliclike time decay distribution, and the fractal dimension of a set of particles that remain in the scattering region approaches that for hyperbolic systems. We show a universal quadratic power law relating the exponential decay to the amplitude of noise. We present a random walk model to relate this distribution to the amplitude of noise, and investigate these phenomena with a numerical study applying random maps.

Optical properties of highly transparent blends formed by bisphenol A polycarbonate (PC) and poly(methyl methacrylate) (PMMA) and doped with either europium(III) thenoyltrifluoroacetone hydrate [Eu(TTA)(3)-hydrate] or terbium(III) acetylacetonate hydrate [Tb(ACAC)(3)-hydrate] were studied. From the absorption/emission spectra (200 to 800 nm), percolation limits of less than 0.4 wt/wt% for Eu and above 0.7 wt/wt% for Tb were found. Lifetimes for 20/80 and 60/40 Tb-doped blends were from 1.0 to 1.5 ms, respectively, about 5 times longer than for a similar blend prepared with Langmuir-Blodgett film. For blends doped with Eu, the lifetimes were from 0.4 to 0.8 ms, almost double that for the pure complex. The results indicated interactions between the PC/PMMA blends and the rare-earth ion complex. Particularly, photoluminescent spectra evidenced the incorporation of the Eu(3+) and Tb(3+) ions into the blend, with quenching observed near 1.0 wt/wt%, except for the 20/80 blend doped with Eu ion, in which luminescence increased to 5 wt/wt %.

The topological structure of basin boundaries plays a fundamental role in the sensitivity to the final state in chaotic dynamical systems. Herewith we present a study on the dynamics of dissipative systems close to the Hamiltonian limit, emphasizing the increasing number of periodic attractors, and on the structural changes in their basin boundaries as the dissipation approaches zero. We show numerically that a power law with nontrivial exponent describes the growth of the total number of periodic attractors as the damping is decreased. We also establish that for small scales the dynamics is governed by effective dynamical invariants, whose measure depends not only on the region of the phase space but also on the scale under consideration. Therefore, our results show that the concept of effective invariants is also relevant for dissipative systems.

In this paper we argue that the effects of irregular chaotic motion of particles transported by blood can play a major role in the development of serious circulatory diseases. Vessel wall irregularities modify the flow field, changing in a nontrivial way the transport and activation of biochemically active particles. We argue that blood particle transport is often chaotic in realistic physiological conditions. We also argue that this chaotic behavior of the flow has crucial consequences for the dynamics of important processes in the blood, such as the activation of platelets which are involved in the thrombus formation.

We show that bifurcations in chaotic scattering manifest themselves through the appearance of an infinitely fine-scale structure of singularities in the cross section. These "rainbow singularities" are created in a cascade, which is closely related to the bifurcation cascade undergone by the set of trapped orbits (the chaotic saddle). This cascade provides a signature in the differential cross section of the complex pattern of bifurcations of orbits underlying the transition to chaotic scattering. We show that there is a power law with a universal coefficient governing the sequence of births of rainbow singularities and we verify this prediction by numerical simulations.

In this paper we investigate the transition to chaos in the motion of particles advected by open flows with obstacles. By means of a topological argument, we show that the separation points on the surface of the obstacle imply the existence of a saddle point downstream from the obstacle, with an associated heteroclinic orbit. We argue that as soon as the flow becomes time periodic, these orbits give rise to heteroclinic tangles, causing passively advected particles to experience transient chaos. The transition to chaos thus coincides with the onset of time dependence in open flows with stagnant points, in contrast with flows with no stagnant points. We also show that the nonhyperbolic nature of the dynamics near the walls causes anomalous scalings in the vicinity of the transition. These results are confirmed by numerical simulations of the two-dimensional flow around a cylinder.

We show the existence of strange nonchaotic repellers--that is, systems with transient dynamics whose nonattracting invariant set is fractal, but whose maximum Lyapunov coefficient is zero. We introduce the concept using a simple one-dimensional map and argue that strange nonchaotic repellers are a general phenomenon, occurring in bifurcation points of transient chaotic systems. All strange nonchaotic systems studied to date have been attractors; here, it is revealed that strange nonchaotic sets are also present in transient systems.

Aerosols under chaotic advection often approach a strange attractor. They move chaotically on this fractal set but, in the presence of gravity, they have a net vertical motion downwards. In practical situations, observational data may be available only at a given level, for example, at the ground level. We uncover two fractal signatures of chaotic advection of aerosols under the action of gravity. Each one enables the computation of the fractal dimension D(0) of the strange attractor governing the advection dynamics from data obtained solely at a given level. We illustrate our theoretical findings with a numerical experiment and discuss their possible relevance to meteorology.

The study of the information flow through communication networks, such as the Internet, is of great importance. In the Internet, information flows in discrete units ("packets"), and the capacity of storage and processing of information of computers is finite. Thus if there are many packets walking on the network at the same time, they will interfere with each other. To understand this, we propose an idealized model, in which many particles move randomly on the network, and the nodes support limited numbers of particles. The maximum number of packets supported by a node can be any positive integer, and can be different for each node. We analyze the statistical properties of this model, obtaining analytical expressions for the mean occupation of each node, for different network topologies. The analytical results are shown to be in agreement with numerical simulations.

We study the effects of finite-sizeness on small, neutrally buoyant, spherical particles advected by open chaotic flows. We show that, when observed in the configuration or physical space, the advected finite-size particles disperse about the unstable manifold of the chaotic saddle that governs the passive advection. Using a discrete-time system for the dynamics, we obtain an expression predicting the dispersion of the finite-size particles in terms of their Stokes parameter at the onset of the finite-size induced dispersion. We test our theory in a system derived from a flow and find remarkable agreement between our expression and the numerically measured dispersion.

A modified version of the Watts-Strogatz (WS) network model is proposed, in which the number of shortcuts scales with the network size N as Nalpha, with alpha < 1. In these networks, the ratio of the number of shortcuts to the network size approaches zero as N --> infinity, whereas in the original WS model, this ratio is constant. We call such networks "thin Watts-Strogatz networks." We show that even though the fraction of shortcuts becomes vanishingly small for large networks, they still cause a kind of small-world effect, in the sense that the length L of the network increases sublinearly with the size. We develop a mean-field theory for these networks, which predicts that the length scales as N1-alpha ln N for large N. We also study how a search using only local information works in thin WS networks. We find that the search performance is enhanced compared to the regular network, and we predict that the search time tau scales as N1-alpha/2. These theoretical results are tested using numerical simulations. We comment on the possible relevance of thin WS networks for the design of high-performance low-cost communication networks.

We propose a scheme to induce chaos in nonlinear oscillators that either are by themselves incapable of exhibiting chaos or are far away from parameter regions of chaotic behaviors. Our idea is to make use of small, judiciously chosen perturbations in the form of weak periodic signals with time-varying frequency and phase, and to drive the system into a hierarchy of nonlinear resonant states and eventually into chaos. We demonstrate this method by using numerical examples and a laboratory experiment with a Duffing type of electronic circuit driven by a phase-locked loop. The phase-locked loop can track the instantaneous frequency and phase of the Duffing circuit and deliver resonant perturbations to generate robust chaos.

We propose an idealized model for traffic in a network, in which many particles move randomly from node to node, following the network's links, and it is assumed that at most one particle can occupy any given node. This is intended to mimic the finite forwarding capacity of nodes in communication networks, thereby allowing the possibility of congestion and jamming phenomena. We show that the particles behave like free fermions, with appropriately defined energy-level structure and temperature. The statistical properties of this system are thus given by the corresponding Fermi-Dirac distribution. We use this to obtain analytical expressions for dynamical quantities of interest, such as the mean occupation of each node and the transport efficiency, for different network topologies and particle densities. We show that the subnetwork of free nodes always fragments into small isolated clusters for a sufficiently large number of particles, implying a communication breakdown at some density for all network topologies. These results are compared to direct simulations.

An adequate characterization of the dynamics of Hamiltonian systems at physically relevant scales has been largely lacking. Here we investigate this fundamental problem and we show that the finite-scale Hamiltonian dynamics is governed by effective dynamical invariants, which are significantly different from the dynamical invariants that describe the asymptotic Hamiltonian dynamics. The effective invariants depend both on the scale of resolution and the region of the phase space under consideration, and they are naturally interpreted within a framework in which the nonhyperbolic dynamics of the Hamiltonian system is modeled as a chain of hyperbolic systems.

We study the reaction dynamics of active particles that are advected passively by 2D incompressible open flows, whose motion is nonhyperbolic. This nonhyperbolicity is associated with the presence of persistent vortices near the wake, wherein fluid is trapped. We show that the fractal equilibrium distribution of the reactants is described by an effective dimension d(eff) , which is a finite resolution approximation to the fractal dimension. Furthermore, d(eff) depends on the resolution epsilon and on the reaction rate 1/tau . As tau is increased, the equilibrium distribution goes through a series of transitions where the effective dimension increases abruptly. These transitions are determined by the complex structure of Cantori surrounding the Kolmogorov-Arnold-Moser (KAM) islands.

We study the dynamics of active particles advected by three-dimensional (3D) open incompressible flows, both analytically and numerically. We find that 3D reactive flows have fundamentally different dynamical features from those in 2D systems. In particular, we show that the reaction's productivity per reaction step can be enhanced, with respect to the 2D case, while the productivity per unit time in some 3D flows goes to zero in the limit of high mixing rates, in contrast to the 2D behavior, in which the productivity goes to a finite constant. These theoretical predictions are validated by numerical simulations on a generic map model.

We study a simple stochastic system with a "rich-get-richer" behavior, in which there are 2 states, and N particles that are successively assigned to one of the states, with a probability p(i) that depends on the states' occupation n(i) as p(i) = n(gamma)(i)/ n(gamma)(1) + n(gamma)(2)). We show that there is a phase transition as gamma crosses the critical value gamma(c) =1. For gamma<1, in the thermodynamic limit the occupations are approximately the same, n(1) approximately n(2). For gamma>1, however, a spontaneous symmetry breaking occurs, and the system goes to a highly clustered configuration, in which one of the states has almost all the particles. These results also hold for any finite number of states (not only two). We show that this "rich-get-richer" principle governs the growth dynamics in a simple model of gravitational aggregation, and we argue that the same is true in all growth processes mediated by long-range forces like gravity.

We study the dynamics of chemically or biologically active particles advected by open flows of chaotic time dependence, which can be modeled by a random time dependence of the parameters on a stroboscopic map. We develop a general theory for reactions in such random flows, and derive the reaction equation for this case. We show that there is a singular enhancement of the reaction in random flows, and this enhancement is increased as compared to the nonrandom case. We verify our theory in a model flow generated by four point vortices moving chaotically.

We study the average time it takes to find a desired node in the Watts-Strogatz family of networks. We consider the case when the look-up time can be neglected and when it is important, where the look-up time is the time needed to choose one among all the neighboring nodes of a node at each step in the search. We show that in both cases, the search time is minimum in the small-world regime, when an appropriate distance between the nodes is defined. Through an analytical model, we show that the search time scales as N(1/D(D+1)) for small-world networks, where N is the number of nodes and D is the dimension of the underlying lattice. This model is shown to be in agreement with numerical simulations.

A large computer program is typically divided into many hundreds or even thousands of smaller units, whose logical connections define a network in a natural way. This network reflects the internal structure of the program, and defines the "information flow" within the program. We show that (1) due to its growth in time this network displays a scale-free feature in that the probability of the number of links at a node obeys a power-law distribution, and (2) as a result of performance optimization of the program the network has a small-world structure. We believe that these features are generic for large computer programs. Our work extends the previous studies on growing networks, which have mostly been for physical networks, to the domain of computer software.

We study the topological structure of basin boundaries of open chaotic Hamiltonian systems in general. We show that basin boundaries can be classified as either type I or type II, according to their topology. Let B be the intersection of the boundary with a one-dimensional curve. In type I boundaries, B is a Cantor set, whereas in type II boundaries B is a Cantor set plus a countably infinite set of isolated points. We show that the occurrence of one or the other type of boundary is determined by the topology of the accessible configuration space, and also by the chosen definition of escapes. We show that the basin boundary may undergo a transition from type I to type II, as the system's energy crosses a critical value. We illustrate our results with a two-dimensional scattering system.

We argue that many major features in electronic transport in realistic quantum dots are not explainable by the usual semiclassical approach, due to the contributions of the quantum-mechanical tunneling of the electrons through the Kolmogorov-Arnol'd-Moser islands. We show that dynamical tunneling gives rise to a set of resonances characterized by two quantum numbers, which leads to conductance oscillations and concentration of wave functions near stable and unstable periodic orbits. Experimental results agree very well with our theoretical predictions, indicating that tunneling has to be taken into account to understand the physics of transport in generic nanostructures.

We define two words in a language to be connected if they express similar concepts. The network of connections among the many thousands of words that make up a language is important not only for the study of the structure and evolution of languages, but also for cognitive science. We study this issue quantitatively, by mapping out the conceptual network of the English language, with the connections being defined by the entries in a Thesaurus dictionary. We find that this network presents a small-world structure, with an amazingly small average shortest path, and appears to exhibit an asymptotic scale-free feature with algebraic connectivity distribution.

We study the effects of classical chaotic scattering on the differential cross section, which is the measurable quantity in most scattering experiments. We show that the fractal set of singularities in the deflection function is not, in general, reflected on the differential cross section. We show that there are systems in which, as the energy (or some other parameter) crosses a critical value, the system's differential cross-section changes from a singular function having an infinite set of rainbow singularities with structure in all scales to a smooth function with no singularities, the scattering being chaotic on both sides of the transition. We call this metamorphosis the rainbow transition. We exemplify this transition with a physically relevant class of systems. These results have important consequences for the problem of inverse scattering in chaotic systems and for the experimental observation of chaotic scattering.

We present a novel method for the calculation of the fractal dimension of boundaries in dynamical systems, which is in many cases many orders of magnitude more efficient than the uncertainty method. We call it the output function evaluation (OFE) method. We show analytically that the OFE method is much more efficient than the uncertainty method for boundaries with D<0.5, where D is the dimension of the intersection of the boundary with a one-dimensional manifold. We apply the OFE method to a scattering system, and compare it to the uncertainty method. We use the OFE method to study the behavior of the fractal dimension as the system's dynamics undergoes a topological transition.

We investigate Hamiltonian chaotic scattering in physically realistic three-dimensional potentials. We find that the basin topology of the scattering dynamics can undergo a metamorphosis from being totally disconnected to being connected as a system parameter, such as the particle energy, is varied through a critical value. The dynamical origin of the metamorphosis is investigated, and the topological change in the scattering basin is explained in terms of the change in the structure of the invariant set of nonescaping orbits. A dynamical consequence of this metamorphosis is that the fractal dimension of the chaotic set responsible for the chaotic scattering changes its behavior characteristically at the metamorphosis. This topological metamorphosis has no correspondence in two-degree-of-freedom open Hamiltonian systems.

We study the motion of light in the gravitational field of two Schwarzschild black holes, making the approximation that they are far apart, so that the motion of light rays in the neighborhood of one black hole can be considered to be the result of the action of each black hole separately. Using this approximation, the dynamics is reduced to a two-dimensional map, which we study both numerically and analytically. The map is found to be chaotic, with a fractal basin boundary separating the possible outcomes of the orbits (escape or falling into one of the black holes). In the limit of large separation distances, the basin boundary becomes a self-similar Cantor set, and we find that the box-counting dimension decays slowly with the separation distance, following a logarithmic decay law.

We study the escape dynamics of test particles in general-relativistic gravitational fields generated by core-shell models, which are used in astrophysics as idealized models to observed mass distributions, such as the interior of galaxies. As a general-relativistic core-halo system, we use exact axisymmetric static solutions of Einstein's field equations which represent the superposition of a central Schwarzschild black hole (the core) and multipolar fields from external masses (the halo). We are particularly interested in the occurrence of chaos in the escape, which is characterized by a great sensitivity of the choice of escape by a test particle to initial conditions. The motion of both material particles and zero rest mass particles is considered. Chaos is quantified by the fractal dimension of the boundary between the basins of the different escapes. We find chaos in the motion of both material particles and null geodesics, but its intensity depends strongly on the halo. We have found for all the cases we have considered that massless particles are less chaotic than massive particles.