Direct dynamical test for deterministic chaos and optimal embedding of a chaotic time-series

We propose here a local exponential divergence plot which is capable of providing an alternative means of characterizing a complex time series. The suggested plot defines a time-dependent exponent and a ''plus'' exponent. Based on their changes with the embedding dimension and delay time, a criterion for estimating simultaneously the minimal acceptable embedding dimension, the proper delay time, and the largest Lyapunov exponent has been obtained. When redefining the time-dependent exponent LAMBDA(k) curves on a series of shells, we have found that whether a linear envelope to the LAMBDA(k) curves exists can serve as a direct dynamical method of distinguishing chaos from noise.

Local exponential divergence plot and optimal embedding of a chaotic time-series

we propose here a local exponential divergence plot which is capable of providing a new means of characterizing chaotic time series. The suggested plot defines a time dependent exponent LAMBDA and a ''plus'' exponent LAMBDA+ which serves as a criterion for estimating simultaneously the minimal acceptable embedding dimension, the proper delay time and the largest Lyapunov exponent.

Application of Entropy and Fractal Dimension Analyses to the Pattern Recognition of Contaminated Fish Responses in Aquaculture

The objective of the work was to develop a non-invasive methodology for image acquisition, processing and nonlinear trajectory analysis of the collective fish response to a stochastic event. Object detection and motion estimation were performed by an optical flow algorithm in order to detect moving fish and simultaneously eliminate background, noise and artifacts. The Entropy and the Fractal Dimension (FD) of the trajectory followed by the centroids of the groups of fish were calculated using Shannon and permutation Entropy and the Katz, Higuchi and Katz-Castiglioni's FD algorithms respectively. The methodology was tested on three case groups of European sea bass (Dicentrarchus labrax), two of which were similar (C1 control and C2 tagged fish) and very different from the third (C3, tagged fish submerged in methylmercury contaminated water). The results indicate that Shannon entropy and Katz-Castiglioni were the most sensitive algorithms and proved to be promising tools for the non-invasive identification and quantification of differences in fish responses. In conclusion, we believe that this methodology has the potential to be embedded in online/real time architecture for contaminant monitoring programs in the aquaculture industry.

An enactive and dynamical systems theory account of dyadic relationships

Many social relationships are a locus of struggle and suffering, either at the individual or interactional level. In this paper we explore why this is the case and suggest a modeling approach for dyadic interactions and the well-being of the participants. To this end we bring together an enactive approach to self with dynamical systems theory. Our basic assumption is that the quality of any social interaction or relationship fundamentally depends on the nature and constitution of the individuals engaged in these interactions. From an enactive perspective the self is conceived as an embodied and socially enacted autonomous system striving to maintain an identity. This striving involves a basic two-fold goal: the ability to exist as an individual in one's own right, while also being open to and affected by others. In terms of dynamical systems theory one can thus consider the individual self as a self-other organized system represented by a phase space spanned by the dimensions of distinction and participation, where attractors can be defined. Based on two everyday examples of dyadic relationship we propose a simple model of relationship dynamics, in which struggle or well-being in the dyad is analyzed in terms of movements of dyadic states that are in tension or in harmony with individually developed attractors. Our model predicts that relationships can be sustained when the dyad develops a new joint attractor toward which dyadic states tend to move, and well-being when this attractor is in balance with the individuals' attractors. We outline how this can inspire research on psychotherapy. The psychotherapy process itself provides a setting that supports clients to become aware how they fare with regards to the two-fold norm of distinction and participation and develop, through active engagement between client (or couple) and therapist, strategies to co-negotiate their self-organization.

A preliminary account and review of the simple methods for determining the operational parameters of fishing gear, underwater, with notes on its application

An account and review of the simple methods for determining the operational parameters of fishing gear, underwater, such a tilt of otter boards (outwards or inwards, forwards or afterwards), vertical height of net, its horizontal spread, angle of divergence at bosom, spread between wing tips, angle of inclination of danlenos, butterfly, slope of legs and sweep-line has been given. The relationship of distance between the otter boards spread and the vertical height of net has been obtained as generally linear. The possibilities of regulating the vertical height of net (dependent variate) and spread of otter boards (independent variate) for increasing the fishing efficiency has been discussed. The angle of attack of oval shaped otter boards used during the operations still remain undetermined, however, it has been explained how the best angle of attack for increasing the efficiency of gear can be obtained by regulating the ratio of depth to warp for a given net. The inadequacy of the mere indices of catch per hour of trawling in comparing the relative efficiency of trawls in gear research studies has been indicated. The importance of estimating the operational parameters and its application to commercial fisheries depending upon the distribution pattern of fish and in gear research has been discussed. The efficiency of the jelly bottle method has been compared statistically with the observations made on the trawl gear underwater with instruments.

Measurements of triggering and transient growth in a model lean-premixed gas turbine combustor

Instability triggering and transient growth of thermoacoustic oscillations were experimentally investigated in combination with linear/nonlinear flame transfer function (FTF) methodology in a model lean-premixed gas turbine combustor operated with CH 4 and air at atmospheric pressure. A fully premixed flame with 10kW thermal power and an equivalence ratio of 0.60 was chosen for detailed characterization of the nonlinear transient behaviors. Flame transfer functions were experimentally determined by simultaneous measurements of inlet velocity fluctuations and heat release rate oscillations using a constant temperature anemometer and OH */CH * chemiluminescence emissions, respectively. The phase-resolved variation of the local flame structure at a limit cycle was measured by planar laser-induced fluorescence of OH. Simultaneous measurements of inlet velocity, OH */CH * emission, and acoustic pressure were performed to investigate the temporal evolution of the system from a stable to a limit cycle operation. This measurement allows us to describe an unsteady instability triggering event in terms of several distinct stages: (i) initiation of a small perturbation, (ii) exponential amplification, (iii) saturation, (iv) nonlinear evolution of the perturbations towards a new unstable periodic state, (v) quasi-steady low-amplitude periodic oscillation, and (vi) fully-developed high-amplitude limit cycle oscillation. Phase-plane portraits of instantaneous inlet velocity and heat release rate clearly show the presence of two different attractors. Depending on its initial position in phase space at infinitesimally small amplitude, the system evolves towards either a high-amplitude oscillatory state or a low-amplitude oscillatory state. This transient phenomenon was analyzed using frequency- and amplitude-dependent damping mechanisms, and compared to subcritical and supercritical bifurcation theories. The results presented in this paper experimentally demonstrate the hypothesis proposed by Preetham et al. based on analytical and computational solutions of the nonlinear G-equation [J. Propul. Power 24 (2008) 1390-1402]. Good quantitative agreement was obtained between measurements and predictions in terms of the conditions for the onset of triggering and the amplitude of triggered combustion instabilities. © 2011 The Combustion Institute.

The Synthesis of Arbitrary Stable Dynamics in Non-linear Neural Networks II: Feedback and Universality

We wish to construct a realization theory of stable neural networks and use this theory to model the variety of stable dynamics apparent in natural data. Such a theory should have numerous applications to constructing specific artificial neural networks with desired dynamical behavior. The networks used in this theory should have well understood dynamics yet be as diverse as possible to capture natural diversity. In this article, I describe a parameterized family of higher order, gradient-like neural networks which have known arbitrary equilibria with unstable manifolds of known specified dimension. Moreover, any system with hyperbolic dynamics is conjugate to one of these systems in a neighborhood of the equilibrium points. Prior work on how to synthesize attractors using dynamical systems theory, optimization, or direct parametric. fits to known stable systems, is either non-constructive, lacks generality, or has unspecified attracting equilibria. More specifically, We construct a parameterized family of gradient-like neural networks with a simple feedback rule which will generate equilibrium points with a set of unstable manifolds of specified dimension. Strict Lyapunov functions and nested periodic orbits are obtained for these systems and used as a method of synthesis to generate a large family of systems with the same local dynamics. This work is applied to show how one can interpolate finite sets of data, on nested periodic orbits.

Comparative analysis of corporate risk management practices in Croatian and Slovenian companies

The paper explores differences as well as commonalities in corporate risk management practices and risk exposures in the large non-financial Slovenian and Croatian companies. Comparative analysis of survey results have revealed that the majority of analysed companies in both Croatia and Slovenia are using some form of risk management to manage interest-rate, foreign exchange, or commodity price risk. Regarding the intensity of influence of financial risks on the performance of the analysed companies, the results have shown that the price risk has the highest influence among the Slovenian as well as the Croatian companies. Croatian companies are more affected by currency risk than the Slovenian companies, while the interest-rate risk has been ranged as less important in comparison with commodity price and currency risks. The survey’s results have clearly indicated that Croatian and Slovenian non-financial companies manage financial risks primarily with simple risk management instruments such as natural hedging. In the case of derivatives use, forwards and swaps are by far the most important instruments in both countries, but futures as representatives of standardised derivatives and structured derivatives are more important in the Slovenian than in the Croatian companies.

Looking backwards to look forwards: the role of natural history in temperate reef ecology

Temperate reefs are superb tractable systems for testing hypotheses in ecology and evolutionary biology. Accordingly there is a rich history of research stretching back over 100 years, which has made major contributions to general ecological and evolutionary theory as well as providing better understanding of how littoral systems work by linking pattern with process. A brief resumé of the history of temperate reef ecology is provided to celebrate this rich heritage. As a community, temperate reef ecologists generally do well designed experiments and test well formulated hypotheses. Increasingly large datasets are being collected, collated and subjected to complex meta-analyses and used for modelling. These datasets do not happen spontaneously – the burgeoning subject of macroecology is possible only because of the efforts of dedicated natural historians whether it be observing birds, butterflies, or barnacles. High-quality natural history and old-fashioned field craft enable surveys or experiments to be stratified (i.e. replicates are replicates and not a random bit of rock) and lead to the generation of more insightful hypotheses. Modern molecular approaches have led to the discovery of cryptic species and provided phylogeographical insights, but natural history is still required to identify species in the field. We advocate a blend of modern approaches with old school skills and a fondness for temperate reefs in all their splendour.

Echolocation signals and pinnae movement in the fruitbat Rousettus aegyptiacus

The fruit bat Rousettus aegyptiacus has highly mobile pinnae. Little is known about the role that such movements play in sound localisation however and whether they interact with the process of echolocation in this species. Here we report the correspondence of echolocation signals in free flight with the downward wingbeat and forward movement of the pinnae, and demonstrate that the ears have a greater sensitivity to click stimuli in front of the animal when directed forwards than when back and to the side. The potential significance of the production of echolocation signals whilst the ears are moving from their least sensitive to their most sensitive position is discussed.

Remembering forwards: or how to live together in the future with divided memories

Memory is thought to be about the past. The past is a problem in conflict transformation. This lecture suggests memory can also be about the future. It introduces the notion of remembering forwards, which is contrasted with remembering backwards. The distinction between these two forms of remembering defines the burden of memory in post-conflict societies generally and specifically in Ireland. In societies emerging out of conflict, where divided memories in part constituted the conflict, social memory privileges remembering backward. Collective and personal memories elide within social memory to perpetuate divided group identities and contested personal narratives. Above all, social memory works to arbitrate the future, by predisposing an extreme memory culture that locks people into the past. Forgetting the past is impossible and undesirable. What is needed in societies emerging out of conflict is to be released from the hold that oppressive and haunting memories have over people. This lecture will suggest that this is found in the idea of remembering forwards. This is not the same as forgetting. It is remembering to cease to remember oppressive and haunting memories. It does not involve non-remembrance but active remembering: remembering to cease to remember the past. While the past lives in us always, remembering forwards assists us in not living in the past. Remembering forwards thus allows us to live in tolerance in the future despite the reality that divided memories endure and live on. The lecture further argues that these enduring divided memories need to be reimagined by the application of truth, tolerance, togetherness and trajectory. The lecture suggests that it is through remembering forwards with truth, tolerance, togetherness and trajectory that people in post-conflict societies can inherit the future despite their divided pasts and live in tolerance in the midst of contested memories.

Alcohol gel ingestion amongst homeless Eastern and Central Europeans in London: assessing the effects on cognitive functioning and psychological health

Background: Intentional consumption of alcohol based hand gels has been reported especially amongst non-UK national, alcohol dependent, homeless individuals in London. Whilst alcohol misuse is known to be associated with impaired cognitive functioning and mental health problems, the effects of additional ingestion of alcohol gel are unknown. Objectives: To explore cognitive and psychological functioning in users who intentionally ingest alcohol gel compared with ethyl-alcohol only misusers and controls. Methods: Male, Central and Eastern European alcohol only misusers, (n=14; mean age 39 years), alcohol gel users (n=14; mean age 43 years) and controls (n=12; mean age 31 years) were recruited from a London Homeless Service during 2013/14. Alcohol misusers, alcohol gel users and controls were compared on the Forwards and Backwards Digit Span Test; Block Design test; Retrospective and Prospective Memory Questionnaire (PRMQ) and the Hospital and Anxiety Depression Scale (HADS). Results: Alcohol gel users performed significantly worse on the Block Design task (p<0.01) and PRMQ (p<0.01) relative to both alcohol only and control groups, and significantly worse on the digit span relative to controls (p=0.01). Both alcohol misusing groups scored comparatively on digit span backwards (p<0.01), with both groups performing significantly worse than controls. The alcohol gel group reported significantly higher levels of anxiety relative to controls (p=0.02). Conclusions: Whilst there could be constitutional differences between alcohol misusers who additionally abuse alcohol gel, the findings suggest that alcohol gel ingestion may have a greater impact on psychological functioning than traditional alcohol misuse.

Position-specific Performance Indicators that Discriminate between Successful and Unsuccessful Teams in Elite Women’s Indoor Field Hockey: Implications for Coaching

The aim of this investigation was to establish median performance profiles for the six playing positions in elite women’s indoor hockey and then identify whether these position-specific profiles could discriminate between qualifying (top four), mid-table and relegated teams in the 2011-12 England Hockey premier league. Successful passing in relegated teams was significantly lower (p<0.008) than in mid-table and qualifying teams in four of the five outfield positions. Furthermore, the right backs of qualifying teams demonstrated significantly fewer (p<0.008) unsuccessful passes (x̃=15.5 ±CLs 15.0 and 10.0 respectively) and interceptions (x̃=4.0 ±CLs 4.0 and 3.0 respectively) than relegated teams (x̃=19.5 ±CLs 21.0 and 17.0; x̃=7.5 ±CLs 8.0 and 6.0 respectively). Finally, the right forwards of relegated teams demonstrated significantly fewer (p<0.008) successful interceptions (x̃=4.0 ±CLs 5.0 and 4.0 respectively) than qualifying teams (x̃=5.0 ±CLs 6.0 and 3.0 respectively) and significantly more (p<0.008) unsuccessful interceptions (x̃=5.5 ±CLs 6.0 and 4.0 respectively) than mid-table teams (x̃=3.0 ±CLs 3.0 and 2.0 respectively). Based on these findings, coaches should adapt tactical strategies and personnel deployment accordingly to enhance the likelihood of preparing a qualifying team. Research should build from these data to examine dribbling, pressing and patterns of play when outletting.

Characterization of the unfolding of a weak focus and modulus of analytic classification

La thèse présente une description géométrique d’un germe de famille générique déployant un champ de vecteurs réel analytique avec un foyer faible à l’origine et son complexifié : le feuilletage holomorphe singulier associé. On montre que deux germes de telles familles sont orbitalement analytiquement équivalents si et seulement si les germes de familles de difféomorphismes déployant la complexification de leurs fonctions de retour de Poincaré sont conjuguées par une conjugaison analytique réelle. Le “caractère réel” de la famille correspond à sa Z2-équivariance dans R^4, et cela s’exprime comme l’invariance du plan réel sous le flot du système laquelle, à son tour, entraîne que l’expansion asymptotique de la fonction de Poincaré est réelle quand le paramètre est réel. Le pullback du plan réel après éclatement par la projection monoidal standard intersecte le feuilletage en une bande de Möbius réelle. La technique d’éclatement des singularités permet aussi de donner une réponse à la question de la “réalisation” d’un germe de famille déployant un germe de difféomorphisme avec un point fixe de multiplicateur égal à −1 et de codimension un comme application de semi-monodromie d’une famille générique déployant un foyer faible d’ordre un. Afin d’étudier l’espace des orbites de l’application de Poincaré, nous utilisons le point de vue de Glutsyuk, puisque la dynamique est linéarisable auprès des points singuliers : pour les valeurs réels du paramètre, notre démarche, classique, utilise une méthode géométrique, soit un changement de coordonée (coordonée “déroulante”) dans lequel la dynamique devient beaucoup plus simple. Mais le prix à payer est que la géométrie locale du plan complexe ambiante devient une surface de Riemann, sur laquelle deux notions de translation sont définies. Après avoir pris le quotient par le relèvement de la dynamique nous obtenons l’espace des orbites, ce qui s’avère être l’union de trois tores complexes plus les points singuliers (l’espace résultant est non-Hausdorff). Les translations, le caractère réel de l’application de Poincaré et le fait que cette application est un carré relient les différentes composantes du “module de Glutsyuk”. Cette propriété implique donc le fait qu’une seule composante de l’invariant Glutsyuk est indépendante.

Fixed point results for multivalued contractions on graphs and their applications

Nous présentons dans cette thèse des théorèmes de point fixe pour des contractions multivoques définies sur des espaces métriques, et, sur des espaces de jauges munis d’un graphe. Nous illustrons également les applications de ces résultats à des inclusions intégrales et à la théorie des fractales. Cette thèse est composée de quatre articles qui sont présentés dans quatre chapitres. Dans le chapitre 1, nous établissons des résultats de point fixe pour des fonctions multivoques, appelées G-contractions faibles. Celles-ci envoient des points connexes dans des points connexes et contractent la longueur des chemins. Les ensembles de points fixes sont étudiés. La propriété d’invariance homotopique d’existence d’un point fixe est également établie pour une famille de Gcontractions multivoques faibles. Dans le chapitre 2, nous établissons l’existence de solutions pour des systèmes d’inclusions intégrales de Hammerstein sous des conditions de type de monotonie mixte. L’existence de solutions pour des systèmes d’inclusions différentielles avec conditions initiales ou conditions aux limites périodiques est également obtenue. Nos résultats s’appuient sur nos théorèmes de point fixe pour des G-contractions multivoques faibles établis au chapitre 1. Dans le chapitre 3, nous appliquons ces mêmes résultats de point fixe aux systèmes de fonctions itérées assujettis à un graphe orienté. Plus précisément, nous construisons un espace métrique muni d’un graphe G et une G-contraction appropriés. En utilisant les points fixes de cette G-contraction, nous obtenons plus d’information sur les attracteurs de ces systèmes de fonctions itérées. Dans le chapitre 4, nous considérons des contractions multivoques définies sur un espace de jauges muni d’un graphe. Nous prouvons un résultat de point fixe pour des fonctions multivoques qui envoient des points connexes dans des points connexes et qui satisfont une condition de contraction généralisée. Ensuite, nous étudions des systèmes infinis de fonctions itérées assujettis à un graphe orienté (H-IIFS). Nous donnons des conditions assurant l’existence d’un attracteur unique à un H-IIFS. Enfin, nous appliquons notre résultat de point fixe pour des contractions multivoques définies sur un espace de jauges muni d’un graphe pour obtenir plus d’information sur l’attracteur d’un H-IIFS. Plus précisément, nous construisons un espace de jauges muni d’un graphe G et une G-contraction appropriés tels que ses points fixes sont des sous-attracteurs du H-IIFS.