Power Law Behavior and Self-similarity in Modern Industrial Accidents

Advances in technology have produced more and more intricate industrial systems, such as nuclear power plants, chemical centers and petroleum platforms. Such complex plants exhibit multiple interactions among smaller units and human operators, rising potentially disastrous failure, which can propagate across subsystem boundaries. This paper analyzes industrial accident data-series in the perspective of statistical physics and dynamical systems. Global data is collected from the Emergency Events Database (EM-DAT) during the time period from year 1903 up to 2012. The statistical distributions of the number of fatalities caused by industrial accidents reveal Power Law (PL) behavior. We analyze the evolution of the PL parameters over time and observe a remarkable increment in the PL exponent during the last years. PL behavior allows prediction by extrapolation over a wide range of scales. In a complementary line of thought, we compare the data using appropriate indices and use different visualization techniques to correlate and to extract relationships among industrial accident events. This study contributes to better understand the complexity of modern industrial accidents and their ruling principles.

Integer and Fractional Order Entropy Analysis of Earthquake Data-series

This paper studies the statistical distributions of worldwide earthquakes from year 1963 up to year 2012. A Cartesian grid, dividing Earth into geographic regions, is considered. Entropy and the Jensen–Shannon divergence are used to analyze and compare real-world data. Hierarchical clustering and multi-dimensional scaling techniques are adopted for data visualization. Entropy-based indices have the advantage of leading to a single parameter expressing the relationships between the seismic data. Classical and generalized (fractional) entropy and Jensen–Shannon divergence are tested. The generalized measures lead to a clear identification of patterns embedded in the data and contribute to better understand earthquake distributions.

Bipedal Locomotion: A Fractional CPG for Generating Patterns

Proceedings of the 10th Conference on Dynamical Systems Theory and Applications

Échantillonnage dynamique de champs markoviens

L'un des modèles d'apprentissage non-supervisé générant le plus de recherche active est la machine de Boltzmann --- en particulier la machine de Boltzmann restreinte, ou RBM. Un aspect important de l'entraînement ainsi que l'exploitation d'un tel modèle est la prise d'échantillons. Deux développements récents, la divergence contrastive persistante rapide (FPCD) et le herding, visent à améliorer cet aspect, se concentrant principalement sur le processus d'apprentissage en tant que tel. Notamment, le herding renonce à obtenir un estimé précis des paramètres de la RBM, définissant plutôt une distribution par un système dynamique guidé par les exemples d'entraînement. Nous généralisons ces idées afin d'obtenir des algorithmes permettant d'exploiter la distribution de probabilités définie par une RBM pré-entraînée, par tirage d'échantillons qui en sont représentatifs, et ce sans que l'ensemble d'entraînement ne soit nécessaire. Nous présentons trois méthodes: la pénalisation d'échantillon (basée sur une intuition théorique) ainsi que la FPCD et le herding utilisant des statistiques constantes pour la phase positive. Ces méthodes définissent des systèmes dynamiques produisant des échantillons ayant les statistiques voulues et nous les évaluons à l'aide d'une méthode d'estimation de densité non-paramétrique. Nous montrons que ces méthodes mixent substantiellement mieux que la méthode conventionnelle, l'échantillonnage de Gibbs.

Role of Nuclear Angiotensin-II Receptor Mediated Signalling in Cardiovascular Remodelling

Le remodelage cardiaque est le processus par lequel la structure ou la fonction cardiaque change en réponse à un déséquilibre pathophysiologique tel qu'une maladie cardiaque, un contexte d'arythmie prolongée ou une modification de l'équilibre hormonal. Le système rénine-angiotensine (SRA) est un système hormonal largement étudié et il est impliqué dans de nombreuses activités associées au remodelage cardiovasculaire. L’existence d'un système circulatoire couplé à un système de tissus locaux est une représentation classique, cependant de nouvelles données suggèrent un SRA indépendant et fonctionnellement actif à l'échelle cellulaire. La compréhension de l'activité intracellulaire du SRA pourrait mener à de nouvelles pistes thérapeutiques qui pourraient prévenir un remodelage cardiovasculaire défavorable. L'objectif de cette thèse était d'élucider le rôle du SRA intracellulaire dans les cellules cardiaques. Récemment, les récepteurs couplés aux protéines G (RCPG), les protéines G et leurs effecteurs ont été détectés sur des membranes intracellulaires, y compris sur la membrane nucléaire, et les concepts de RCPG intracellulaires fonctionnels sont en voie d'être acceptés comme une réalité. Nous avons dès lors fait l'hypothèse que la signalisation du SRA délimitant le noyau était impliquée dans le contrôle de l'expression des gènes cardiaques. Nous avons démontré la présence de récepteurs d'angiotensine de type-1 (AT1R) et de type-2 (AT2R) nucléaires dans les cardiomyocytes ventriculaires adultes et dans une fraction nucléaire purifiée de tissu cardiaque. Des quantités d'Ang II ont été détectées dans du lysat de cardiomyocytes et des microinjections d'Ang-II-FITC ont donné lieu à des liaisons préférentielles aux sites nucléaires. L'analyse transcriptionnelle prouve que la synthèse d'ARN de novo dans des noyaux isolés stimulés à l'Ang-II, et l'expression des ARNm de NF-κB étaient beaucoup plus importants lorsque les noyaux étaient exposés à de l'Ang II par rapport aux cardiomyocytes intacts. La stimulation des AT1R nucléaires a engendré une mobilisation de Ca2+ via les récepteurs de l'inositol trisphosphate (IP3R), et le blocage des IP3R a diminué la réponse transcriptionnelle. Les méthodes disponibles actuellement pour l'étude de la signalisation intracrine sont limitées aux méthodes indirectes. L'un des objectifs de cette thèse était de synthétiser et caractériser des analogues d'Ang-II cellule-perméants afin d’étudier spécifiquement dans les cellules intactes l'activité intracellulaire du SRA. Nous avons synthétisé et caractérisé pharmacologiquement des analogues photosensibles Ang-II encapsulée en incorporant un groupement 4,5-diméthoxy-2-nitrobenzyl (DMNB) photoclivable sur les sites actifs identifiés du peptide. Chacun des trois analogues d'Ang II encapsulée synthétisés et purifiés: [Tyr(DMNB)4]Ang-II, Ang-II-ODMNB et [Tyr(DMNB)4]Ang-II-ODMNB a montré une réduction par un facteur deux ou trois de l'affinité de liaison envers AT1R et AT2R dans les dosages par liaison compétitive et une activité réduite dans la contraction de l'aorte thoracique. La photostimulation de [Tyr(DMNB)4]Ang-II dans des cellules HEK a augmenté la phosphorylation d'ERK1/2 (via AT1R) et la production de cGMP (via AT2R) alors que dans les cardiomyocytes isolés elle générait une augmentation de Ca2+ nucléoplasmique et initiait la synthèse d'ARNr 18S et d'ARNm du NF-κB. Les fibroblastes sont les principaux générateurs de remodelage cardiaque structurel, et les fibroblastes auriculaires sont plus réactifs aux stimuli profibrotiques que les fibroblastes ventriculaires. Nous avons émis l'hypothèse que l’Ang-II intracellulaire et l'activation des AT1R et AT2R nucléaires associés contrôlaient les profils d'expression des gènes des fibroblastes via des systèmes de signalisation distincts et de ce fait jouaient un rôle majeur dans le développement de la fibrose cardiaque. Nous avons remarqué que les fibroblastes auriculaires expriment l’AT1R et l’AT2R nucléaire et l'Ang-II au niveau intracellulaire. L’expression d'AT1R nucléaire a été régulés positivement dans les cas d’insuffisance cardiaque (IC), tandis que l'AT2R nucléaire a été glycosylé post-traductionnellement. La machinerie protéique des protéines G, y compris Gαq/11, Gαi/3, et Gβ, a été observée dans des noyaux isolés de fibroblastes. AT1R et AT2R régulent l'initiation de la transcription du fibroblaste via les voies de transduction de signal d'IP3R et du NO. La photostimulation de [Tyr(DMNB)4]Ang-II dans une culture de fibroblastes auriculaire déclenche la libération de Ca2+ nucléoplasmique, la prolifération, et la synthèse et sécrétion de collagène qui ne sont pas inhibées par les bloqueurs d'AT1R et/ou AT2R extracellulaires.

Numerical study of reverse period doubling route from chaos to stability in a two-mode intracavity doubled Nd-YAG laser

We have numerically studied the behavior of a two-mode Nd-YAG laser with an intracavity KTP crystal. It is found that when the parameter, which is a measure of the relative orientations of the KTP crystal with respect to the Nd-YAG crystal, is varied continuously, the output intensity fluctuations change from chaotic to stable behavior through a sequence of reverse period doubling bifurcations. The graph of the intensity in the X-polarized mode against that in the Y-polarized mode shows a complex pattern in the chaotic regime. The Lyapunov exponent is calculated for the chaotic and periodic regions.

Analysis of System Signals Based on Cross Recurrence Method for System Dynamics Characterization

Natural systems are inherently non linear. Recurrent behaviours are typical of natural systems. Recurrence is a fundamental property of non linear dynamical systems which can be exploited to characterize the system behaviour effectively. Cross recurrence based analysis of sensor signals from non linear dynamical system is presented in this thesis. The mutual dependency among relatively independent components of a system is referred as coupling. The analysis is done for a mechanically coupled system specifically designed for conducting experiment. Further, cross recurrence method is extended to the actual machining process in a lathe to characterize the chatter during turning. The result is verified by permutation entropy method. Conventional linear methods or models are incapable of capturing the critical and strange behaviours associated with the dynamical process. Hence any effective feature extraction methodologies should invariably gather information thorough nonlinear time series analysis. The sensor signals from the dynamical system normally contain noise and non stationarity. In an effort to get over these two issues to the maximum possible extent, this work adopts the cross recurrence quantification analysis (CRQA) methodology since it is found to be robust against noise and stationarity in the signals. The study reveals that the CRQA is capable of characterizing even weak coupling among system signals. It also divulges the dependence of certain CRQA variables like percent determinism, percent recurrence and entropy to chatter unambiguously. The surrogate data test shows that the results obtained by CRQA are the true properties of the temporal evolution of the dynamics and contain a degree of deterministic structure. The results are verified using permutation entropy (PE) to detect the onset of chatter from the time series. The present study ascertains that this CRP based methodology is capable of recognizing the transition from regular cutting to the chatter cutting irrespective of the machining parameters or work piece material. The results establish this methodology to be feasible for detection of chatter in metal cutting operation in a lathe.

Studies of stability of fluid flowa using variational methods

The study of stability problems is relevant to the study of structure of a physical system. It 1S particularly important when it is not possible to probe into its interior and obtain information on its structure by a direct method. The thesis states about stability theory that has become of dominant importance in the study of dynamical systems. and has many applications in basic fields like meteorology, oceanography, astrophysics and geophysics- to mention few of them. The definition of stability was found useful 1n many situations, but inadequate in many others so that a host of other important concepts have been introduced in past many years which are more or less related to the first definition and to the common sense meaning of stability. In recent years the theoretical developments in the studies of instabilities and turbulence have been as profound as the developments in experimental methods. The study here Points to a new direction for stability studies based on Lagrangian formulation instead of the Hamiltonian formulation used by other authors.

Some non- linear problems in theoretical physics

An immense variety of problems in theoretical physics are of the non-linear type. Non~linear partial differential equations (NPDE) have almost become the rule rather than an exception in diverse branches of physics such as fluid mechanics, field theory, particle physics, statistical physics and optics, and the construction of exact solutions of these equations constitutes one of the most vigorous activities in theoretical physics today. The thesis entitled ‘Some Non-linear Problems in Theoretical Physics’ addresses various aspects of this problem at the classical level. For obtaining exact solutions we have used mathematical tools like the bilinear operator method, base equation technique and similarity method with emphasis on its group theoretical aspects. The thesis deals with certain methods of finding exact solutions of a number of non-linear partial differential equations of importance to theoretical physics. Some of these new solutions are of relevance from the applications point of view in diverse branches such as elementary particle physics, field theory, solid state physics and non-linear optics and give some insight into the stable or unstable behavior of dynamical Systems The thesis consists of six chapters.

Studies on integrability of some perturbed nonlinear evolution equations

Usually typical dynamical systems are non integrable. But few systems of practical interest are integrable. The soliton concept is a sophisticated mathematical construct based on the integrability of a class ol' nonlinear differential equations. An important feature in the clevelopment. of the theory of solitons and of complete integrability has been the interplay between mathematics and physics. Every integrable system has a lo11g list of special properties that hold for integrable equations and only for them. Actually there is no specific definition for integrability that is suitable for all cases. .There exist several integrable partial clillerential equations( pdes) which can be derived using physically meaningful asymptotic teclmiques from a very large class of pdes. It has been established that many 110nlinear wa.ve equations have solutions of the soliton type and the theory of solitons has found applications in many areas of science. Among these, well-known equations are Korteweg de-Vries(KdV), modified KclV, Nonlinear Schr6dinger(NLS), sine Gordon(SG) etc..These are completely integrable systems. Since a small change in the governing nonlinear prle may cause the destruction of the integrability of the system, it is interesting to study the effect of small perturbations in these equations. This is the motivation of the present work.

Analytical Studies on Diffusion and lntermittency in Chaotic Maps

The study of simple chaotic maps for non-equilibrium processes in statistical physics has been one of the central themes in the theory of chaotic dynamical systems. Recently, many works have been carried out on deterministic diffusion in spatially extended one-dimensional maps This can be related to real physical systems such as Josephson junctions in the presence of microwave radiation and parametrically driven oscillators. Transport due to chaos is an important problem in Hamiltonian dynamics also. A recent approach is to evaluate the exact diffusion coefficient in terms of the periodic orbits of the system in the form of cycle expansions. But the fact is that the chaotic motion in such spatially extended maps has two complementary aspects- - diffusion and interrnittency. These are related to the time evolution of the probability density function which is approximately Gaussian by central limit theorem. It is noticed that the characteristic function method introduced by Fujisaka and his co-workers is a very powerful tool for analysing both these aspects of chaotic motion. The theory based on characteristic function actually provides a thermodynamic formalism for chaotic systems It can be applied to other types of chaos-induced diffusion also, such as the one arising in statistics of trajectory separation. It was noted that there is a close connection between cycle expansion technique and characteristic function method. It was found that this connection can be exploited to enhance the applicability of the cycle expansion technique. In this way, we found that cycle expansion can be used to analyse the probability density function in chaotic maps. In our research studies we have successfully applied the characteristic function method and cycle expansion technique for analysing some chaotic maps. We introduced in this connection, two classes of chaotic maps with variable shape by generalizing two types of maps well known in literature.

Chaotic, memory, and cooling rate effects in spin glasses: Evaluation of the Edwards-Anderson model

We investigate chaotic, memory, and cooling rate effects in the three-dimensional Edwards-Anderson model by doing thermoremanent (TRM) and ac susceptibility numerical experiments and making a detailed comparison with laboratory experiments on spin glasses. In contrast to the experiments, the Edwards-Anderson model does not show any trace of reinitialization processes in temperature change experiments (TRM or ac). A detailed comparison with ac relaxation experiments in the presence of dc magnetic field or coupling distribution perturbations reveals that the absence of chaotic effects in the Edwards-Anderson model is a consequence of the presence of strong cooling rate effects. We discuss possible solutions to this discrepancy, in particular the smallness of the time scales reached in numerical experiments, but we also question the validity of the Edwards-Anderson model to reproduce the experimental results.

The Logical Problem of Language Change

This paper considers the problem of language change. Linguists must explain not only how languages are learned but also how and why they have evolved along certain trajectories and not others. While the language learning problem has focused on the behavior of individuals and how they acquire a particular grammar from a class of grammars ${cal G}$, here we consider a population of such learners and investigate the emergent, global population characteristics of linguistic communities over several generations. We argue that language change follows logically from specific assumptions about grammatical theories and learning paradigms. In particular, we are able to transform parameterized theories and memoryless acquisition algorithms into grammatical dynamical systems, whose evolution depicts a population's evolving linguistic composition. We investigate the linguistic and computational consequences of this model, showing that the formalization allows one to ask questions about diachronic that one otherwise could not ask, such as the effect of varying initial conditions on the resulting diachronic trajectories. From a more programmatic perspective, we give an example of how the dynamical system model for language change can serve as a way to distinguish among alternative grammatical theories, introducing a formal diachronic adequacy criterion for linguistic theories.

Robust fault detection using consistency techniques for uncertainty handling

Often practical performance of analytical redundancy for fault detection and diagnosis is decreased by uncertainties prevailing not only in the system model, but also in the measurements. In this paper, the problem of fault detection is stated as a constraint satisfaction problem over continuous domains with a big number of variables and constraints. This problem can be solved using modal interval analysis and consistency techniques. Consistency techniques are then shown to be particularly efficient to check the consistency of the analytical redundancy relations (ARRs), dealing with uncertain measurements and parameters. Through the work presented in this paper, it can be observed that consistency techniques can be used to increase the performance of a robust fault detection tool, which is based on interval arithmetic. The proposed method is illustrated using a nonlinear dynamic model of a hydraulic system

SQualTrack: A Tool for Robust Fault Detection

One of the techniques used to detect faults in dynamic systems is analytical redundancy. An important difficulty in applying this technique to real systems is dealing with the uncertainties associated with the system itself and with the measurements. In this paper, this uncertainty is taken into account by the use of intervals for the parameters of the model and for the measurements. The method that is proposed in this paper checks the consistency between the system's behavior, obtained from the measurements, and the model's behavior; if they are inconsistent, then there is a fault. The problem of detecting faults is stated as a quantified real constraint satisfaction problem, which can be solved using the modal interval analysis (MIA). MIA is used because it provides powerful tools to extend the calculations over real functions to intervals. To improve the results of the detection of the faults, the simultaneous use of several sliding time windows is proposed. The result of implementing this method is semiqualitative tracking (SQualTrack), a fault-detection tool that is robust in the sense that it does not generate false alarms, i.e., if there are false alarms, they indicate either that the interval model does not represent the system adequately or that the interval measurements do not represent the true values of the variables adequately. SQualTrack is currently being used to detect faults in real processes. Some of these applications using real data have been developed within the European project advanced decision support system for chemical/petrochemical manufacturing processes and are also described in this paper