Chaotic Kabanov formula for the Azéma martingales

We derive the chaotic expansion of the product of nth- and first-order multiple stochastic integrals with respect to certain normal martingales. This is done by application of the classical and quantum product formulae for multiple stochastic integrals. Our approach extends existing results on chaotic calculus for normal martingales and exhibits properties, relative to multiple stochastic integrals, polynomials and Wick products, that characterize the Wiener and Poisson processes.

Chaotic dynamics and team effectiveness: evidence from professional basketball

Considering teams as complex adaptive systems (CAS) this study deals with changes in team effectiveness over time in a specific context: professional basketball. The sample comprised 23 basketball teams whose outcomes were analysed over a 12-year period according to two objective measures. The results reveal that all the teams showed chaotic dynamics, one of the key characteristics of CAS. A relationship was also found between teams showing low-dimensional chaotic dynamics and better outcomes, supporting the idea of healthy variability in organizational behaviour. The stability of the squad was likewise found to influence team outcomes, although it was not associated with the chaotic dynamics in team effectiveness. It is concluded that studying teams as CAS enables fluctuations in team effectiveness to be explained, and that the techniques derived from nonlinear dynamical systems, developed specifically for the study of CAS, are useful for this purpose.

The link between land-use management and fluvial flood risk : a chaotic conception?

There is much policy interest in the possible linkages that might exist between land use and downstream fluvial flood risk. On the one hand, this position is sustained by observations from plot- and field-scale studies that suggest land management does affect runoff. On the other, upscaling these effects to show that land-management activities impact upon flood risk at larger catchment scales has proved to be elusive. This review considers the reasons for why this upscaling is problematic. We argue that, rather than it reflecting methodological challenges associated with the difficulties of modelling hydrological processes over very large areas and during extreme runoff events, it reflects the fact that any linkage between land management and flood risk cannot be generalized and taken out of its specific spatial (catchment) and temporal (flood event) context. We use Sayer's (1992) notion of a `chaotic conception' to describe the belief that there is a simple and general association between land management and downstream flood risk rather than the impacts of land management being spatially and temporally contingent in relation to the particular geographical location, time period and scale being considered. Our argument has important practical consequences because it implies that land-management activities to reduce downstream flood risk will be different to traditional flood-reduction interventions such as levees. The purpose of demonstration projects then needs careful consideration such that conclusions made for one project are not transferred uncritically to other scales of analysis or geographical locations.

Chaotic dynamics and team effectiveness: evidence from professional basketball

Considering teams as complex adaptive systems (CAS) this study deals with changes in team effectiveness over time in a specific context: professional basketball. The sample comprised 23 basketball teams whose outcomes were analysed over a 12-year period according to two objective measures. The results reveal that all the teams showed chaotic dynamics, one of the key characteristics of CAS. A relationship was also found between teams showing low-dimensional chaotic dynamics and better outcomes, supporting the idea of healthy variability in organizational behaviour. The stability of the squad was likewise found to influence team outcomes, although it was not associated with the chaotic dynamics in team effectiveness. It is concluded that studying teams as CAS enables fluctuations in team effectiveness to be explained, and that the techniques derived from nonlinear dynamical systems, developed specifically for the study of CAS, are useful for this purpose.

Amplification and displacement of chaotic attractors by means of unidirectional chaotic driving

Chaotic systems, when used to drive copies of themselves (or parts of themselves) may induce interesting behaviors in the driven system. In case the later exhibits invariance under amplification or translation, they may show amplification (reduction), or displacement of the attractor. It is shown how the behavior to be obtained is implied by the symmetries involved. Two explicit examples are studied to show how these phenomena manifest themselves under perfect and imperfect coupling.

Synchronization of symmetric chaotic systems

This paper contains a study of the synchronization by homogeneous nonlinear driving of systems that are symmetric in phase space. The main consequence of this symmetry is the ability of the response to synchronize in more than just one way to the driving systems. These different forms of synchronization are to be understood as generalized synchronization states in which the motions of drive and response are in complete correlation, but the phase space distance between them does not converge to zero. In this case the synchronization phenomenon becomes enriched because there is multistability. As a consequence, there appear multiple basins of attraction and special responses to external noise. It is shown, by means of a computer simulation of various nonlinear systems, that: (i) the decay to the generalized synchronization states is exponential, (ii) the basins of attraction are symmetric, usually complicated, frequently fractal, and robust under the changes in the parameters, and (iii) the effect of external noise is to weaken the synchronization, and in some cases to produce jumps between the various synchronization states available

Amplitude envelope synchronization in coupled chaotic oscillators.

A peculiar type of synchronization has been found when two Van der PolDuffing oscillators, evolving in different chaotic attractors, are coupled. As the coupling increases, the frequencies of the two oscillators remain different, while a synchronized modulation of the amplitudes of a signal of each system develops, and a null Lyapunov exponent of the uncoupled systems becomes negative and gradually larger in absolute value. This phenomenon is characterized by an appropriate correlation function between the returns of the signals, and interpreted in terms of the mutual excitation of new frequencies in the oscillators power spectra. This form of synchronization also occurs in other systems, but it shows up mixed with or screened by other forms of synchronization, as illustrated in this paper by means of the examples of the dynamic behavior observed for three other different models of chaotic oscillators.

Chaotic systems with a null conditional Lyapunov exponent under nonlinear driving.

Control of a chaotic system by homogeneous nonlinear driving, when a conditional Lyapunov exponent is zero, may give rise to special and interesting synchronizationlike behaviors in which the response evolves in perfect correlation with the drive. Among them, there are the amplification of the drive attractor and the shift of it to a different region of phase space. In this paper, these synchronizationlike behaviors are discussed, and demonstrated by computer simulation of the Lorentz model [E. N. Lorenz, J. Atmos. Sci. 20 130 (1963)] and the double scroll [T. Matsumoto, L. O. Chua, and M. Komuro, IEEE Trans. CAS CAS-32, 798 (1985)].

Vacuum-assisted closure device for the management of infected postpneumonectomy chest cavities.

BACKGROUND: Infected postpneumonectomy chest cavities may be related to chronic postpneumonectomy empyema or arise in rare situations of necrotizing pneumonia with complete lung destruction where pneumonectomy and pleural debridement are required. We evaluated the safety and efficacy of an intrathoracic vacuum-assisted closure device (VAC) for the treatment of infected postpneumonectomy chest cavities. METHOD: A retrospective single institution review of all patients with infected postpneumonectomy chest cavities treated by VAC between 2005 and 2013. Patients underwent surgical debridement of the thoracic cavity, muscle flap closure of the bronchial stump when a fistula was present, and repeated intrathoracic VAC dressings until granulation tissue covered the entire chest cavity. After this, the cavity was obliterated by a Clagett procedure and closed. RESULTS: Twenty-one patients (14 men and 7 women) underwent VAC treatment of their infected postpneumonectomy chest cavity. Twelve patients presented with a chronic postpneumonectomy empyema (10 of them with a bronchopleural fistula) and 9 patients with an empyema occurring in the context of necrotizing pneumonia treated by pneumonectomy. In-hospital mortality was 23%. The median duration of VAC therapy was 23 days (range, 4-61 days) and the median number of VAC changes per patient was 6 (range, 2-14 days). Infection control and successful chest cavity closure was achieved in all surviving patients. One adverse VAC treatment-related event was identified (5%). CONCLUSIONS: The intrathoracic VAC application is a safe and efficient treatment of infected postpneumonectomy chest cavities and allows the preservation of chest wall integrity.

Treatment of pleural malignancies by photo-induction combined to systemic chemotherapy: Proof of concept on rodent lung tumors and feasibility study on porcine chest cavities.

BACKGROUND: Low-dose, Visudyne®-mediated photodynamic therapy (photo-induction) was shown to selectively enhance tumor vessel transport causing increased uptake of systemically administered chemotherapy in various tumor types grown on rodent lungs. The present experiments explore the efficacy of photo-induced vessel modulation combined to intravenous (IV) liposomal cisplatin (Lipoplatin®) on rodent lung tumors and the feasibility/toxicity of this approach in porcine chest cavities. MATERIAL AND METHODS: Three groups of Fischer rats underwent orthotopic sarcoma (n = 14), mesothelioma (n = 14), or adenocarcinoma (n = 12) implantation on the left lung. Half of the animals of each group had photo-induction (0.0625 mg/kg Visudyne®, 10 J/cm(2) ) followed by IV administration of Lipoplatin® (5 mg/kg) and the other half received Lipoplatin® without photo-induction. Then, two groups of minipigs underwent intrapleural thoracoscopic (VATS) photo-induction (0.0625 mg/kg Visudyne®; 30 J/cm(2) hilum; 10 J/cm(2) apex/diaphragm) with in situ light dosimetry in combination with IV Lipoplatin® administration (5 mg/kg). Protocol I (n = 6) received Lipoplatin® immediately after light delivery and Protocol II (n = 9) 90 minutes before light delivery. Three additional animals received Lipoplatin® and VATS pleural biopsies but no photo-induction (controls). Lipoplatin® concentrations were analyzed in blood and tissues before and at regular intervals after photo-induction using inductively coupled plasma mass spectrometry. RESULTS: Photo-induction selectively increased Lipoplatin® uptake in all orthotopic tumors. It significantly increased the ratio of tumor to lung Lipoplatin® concentration in sarcoma (P = 0.0008) and adenocarcinoma (P = 0.01) but not in mesothelioma, compared to IV drug application alone. In minipigs, intrapleural photo-induction combined to systemic Lipoplatin® was well tolerated with no toxicity at 7 days for both treatment protocols. The pleural Lipoplatin® concentrations were not significantly different at 10 and 30 J/cm(2) locations but they were significantly higher in protocol I compared to II (2.37 ± 0.7 vs. 1.37 ± 0.7 ng/mg, P  < 0.001). CONCLUSION: Visudyne®-mediated photo-induction selectively enhances the uptake of IV administered Lipoplatin® in rodent lung tumors. Intrapleural VATS photo-induction with identical treatment conditions combined to IV Lipoplatin chemotherapy is feasible and well tolerated in a porcine model. Lasers Surg. Med. 47:807-816, 2015. © 2015 Wiley Periodicals, Inc.

Attracting cavities for docking. Replacing the rough energy landscape of the protein by a smooth attracting landscape.

Molecular docking is a computational approach for predicting the most probable position of ligands in the binding sites of macromolecules and constitutes the cornerstone of structure-based computer-aided drug design. Here, we present a new algorithm called Attracting Cavities that allows molecular docking to be performed by simple energy minimizations only. The approach consists in transiently replacing the rough potential energy hypersurface of the protein by a smooth attracting potential driving the ligands into protein cavities. The actual protein energy landscape is reintroduced in a second step to refine the ligand position. The scoring function of Attracting Cavities is based on the CHARMM force field and the FACTS solvation model. The approach was tested on the 85 experimental ligand-protein structures included in the Astex diverse set and achieved a success rate of 80% in reproducing the experimental binding mode starting from a completely randomized ligand conformer. The algorithm thus compares favorably with current state-of-the-art docking programs. © 2015 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

Chaotic dynamics of electric-field domains in periodically driven superlattices

Self-sustained time-dependent current oscillations under dc voltage bias have been observed in recent experiments on n-doped semiconductor superlattices with sequential resonant tunneling. The current oscillations are caused by the motion and recycling of the domain wall separating low- and high-electric-field regions of the superlattice, as the analysis of a discrete drift model shows and experimental evidence supports. Numerical simulation shows that different nonlinear dynamical regimes of the domain wall appear when an external microwave signal is superimposed on the dc bias and its driving frequency and driving amplitude vary. On the frequency-amplitude parameter plane, there are regions of entrainment and quasiperiodicity forming Arnold tongues. Chaos is demonstrated to appear at the boundaries of the tongues and in the regions where they overlap. Coexistence of up to four electric-field domains randomly nucleated in space is detected under ac+dc driving.

Multifractal dimension of chaotic attractors in a driven semiconductor superlattice

The multifractal dimension of chaotic attractors has been studied in a weakly coupled superlattice driven by an incommensurate sinusoidal voltage as a function of the driving voltage amplitude. The derived multifractal dimension for the observed bifurcation sequence shows different characteristics for chaotic, quasiperiodic, and frequency-locked attractors. In the chaotic regime, strange attractors are observed. Even in the quasiperiodic regime, attractors with a certain degree of strangeness may exist. From the observed multifractal dimensions, the deterministic nature of the chaotic oscillations is clearly identified.

Differential Evolution approach and parameter estimation of chaotic

Parameter estimation still remains a challenge in many important applications. There is a need to develop methods that utilize achievements in modern computational systems with growing capabilities. Owing to this fact different kinds of Evolutionary Algorithms are becoming an especially perspective field of research. The main aim of this thesis is to explore theoretical aspects of a specific type of Evolutionary Algorithms class, the Differential Evolution (DE) method, and implement this algorithm as codes capable to solve a large range of problems. Matlab, a numerical computing environment provided by MathWorks inc., has been utilized for this purpose. Our implementation empirically demonstrates the benefits of a stochastic optimizers with respect to deterministic optimizers in case of stochastic and chaotic problems. Furthermore, the advanced features of Differential Evolution are discussed as well as taken into account in the Matlab realization. Test "toycase" examples are presented in order to show advantages and disadvantages caused by additional aspects involved in extensions of the basic algorithm. Another aim of this paper is to apply the DE approach to the parameter estimation problem of the system exhibiting chaotic behavior, where the well-known Lorenz system with specific set of parameter values is taken as an example. Finally, the DE approach for estimation of chaotic dynamics is compared to the Ensemble prediction and parameter estimation system (EPPES) approach which was recently proposed as a possible solution for similar problems.

Chaotic Behaviour of Active Magnetic Bearing System by Time Series Analysis

Chaotic behaviour is one of the hardest problems that can happen in nonlinear dynamical systems with severe nonlinearities. It makes the system's responses unpredictable. It makes the system's responses to behave similar to noise. In some applications it should be avoided. One of the approaches to detect the chaotic behaviour is nding the Lyapunov exponent through examining the dynamical equation of the system. It needs a model of the system. The goal of this study is the diagnosis of chaotic behaviour by just exploring the data (signal) without using any dynamical model of the system. In this work two methods are tested on the time series data collected from AMB (Active Magnetic Bearing) system sensors. The rst method is used to nd the largest Lyapunov exponent by Rosenstein method. The second method is a 0-1 test for identifying chaotic behaviour. These two methods are used to detect if the data is chaotic. By using Rosenstein method it is needed to nd the minimum embedding dimension. To nd the minimum embedding dimension Cao method is used. Cao method does not give just the minimum embedding dimension, it also gives the order of the nonlinear dynamical equation of the system and also it shows how the system's signals are corrupted with noise. At the end of this research a test called runs test is introduced to show that the data is not excessively noisy.