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The purpose of this paper is to illustrate the many aspects of Poincare recurrence time theorem for an archetype of a complex system, the logistic map.

At the beginning of the twentieth century, Poincare's recurrence theorem had revolutionized modern mechanics and statistical physics. However, this theorem did not attract considerable attention, at least from a numerical and computational point of view. In a series of relatively recent papers, Balakrishnan, Nicolis and Nicolis have addressed the recurrence time problem in a firm basis, introducing notation, theory, and numerical studies. Motivated by this call, the paper proposes to illustrate the many aspects of Poincare recurrence time theorem for an archetype of a complex system, the logistic map. The authors propose here in different tests and computations, each one illuminating the many aspects of the problem of recurrence. The paper ends up with a short discussion and conclusions.

In this paper, the authors obtain new results on computations, each one illuminating the many aspects of the problem of recurrence. One striking aspect of this detailed work, is that when the sizes of the cells in the phase space became considerable, then the recurrence times assume ordinary values.

The paper extends previous results on chaotic maps to the logistic map, enhancing comprehension, making possible connections with number theory, combinatorics and cryptography.

Consumers are inclined to join longer queues due to social interactions in service consumptions. This purchase behavior brings in operational challenges in terms of capacity planning, which affects consumers’ demand, leading to an unstable and fluctuated arrival process. This paper aims to investigate the dynamic characteristics of the arrival process of a service system with boundedly rational consumers whose purchase decisions are influenced by the queue length under social interactions.

Consumers’ bounded rationality is modeled based on the random utility theory. Due to social interactions, the equilibrium queue length and its interaction with the expected waiting time affect consumers’ value perception. The authors first analyze the optimal service capacity decision with or without considering the influence of social interactions in a static setting. They then focus on the dynamic characteristics of the arrival process by a one-dimensional dynamical model in terms of the arrival rate.

This paper finds that the service system can behave chaotic in terms of arrival rate dynamics under social interactions. The results highlight the dynamical complexity of a simple service system due to consumers’ behavioral factors and the influence of social interactions, which may be the critical drivers leading to fluctuated and uneven demand.

The findings demonstrate that due to consumers’ limited cognitive ability and the influence of social interactions, the demand to a service system can be stable, periodic or even chaotic in terms of the arrival process. This study provides an alternative explanation to the observed demand fluctuations in various service processes under the influence of social interactions, which is important for service providers to effectively manage service capacity to achieve a stable service process and improve operational efficiency.

Some necessary and sufficient conditions allowing a previously unknown space to be explored through scanning operators are reexamined with respect to measure theory. Some generalized concepts of distances and dimensionality evaluation are proposed, together with their conditions of validity and range of application to topological spaces. The existence of a Boolean lattice with fractal properties originating from non‐wellfounded properties of the empty set is demonstrated. This lattice provides a substratum with both discrete and continuous properties from which existence of physical universes can be proved, up to the function of conscious perception. Space‐time emerges as an ordered sequence of mappings of closed 3D Poincaré sections of a topological four‐space provided by the lattice, and the function of conscious perception is founded on the same properties. Self‐evaluation of a system is possible against indecidability barriers through anticipatory mental imaging occurring in biological brain systems; then our embedding universe should be in principle accessible to knowledge. The possibility of existence of spaces with fuzzy dimension or with adjoined parts with decreasing dimensions is raised, together with possible tools for their study. The work presented here provides the introductory foundations supporting a new theory of space whose physical predictions (suppressing the opposition of quantum and relativistic approaches) and experimental proofs are presented in detail in Parts 2 and 3 of the study.

The purpose of this paper is to explore new mathematical results to advance the understanding of the picture of a chaotic unimodal map.

Ever since Poicare, deterministic chaos is ultimately connected with exponential divergence of nearby trajectories, unpredictability and erratic behaviour. Here, the authors propose an alternative approach in terms of complexity theory and transcendence.

In this paper, the authors were able to reproduce previous results easily, due to new theorems.

The paper updates previous results and proposes a more complete understanding of the phenomenon of deterministic chaos, also making possible connections with number theory, combinatorics and possibly quantum mechanics, as in quantum mechanics there does not exist the notion on nearby trajectories.

Under this heading are published regularly abstracts of all Reports and Memoranda of the Aeronautical Research Committee, Reports and Technical Notes of the United States National Advisory Committee for Aeronautics and publications af other similar Research Bodies as issued.

The purpose of this paper is to characterize the nonlinear dynamical behaviour of a buck‐based power‐switching amplifier controlled by fixed frequency and pulse width modulation with a proportional‐integral compensator. The system has two forcing frequencies and one natural frequency and therefore it is characterized by three different scales of time. When the frequencies are far one from the other, quasi‐static approximation can be used. However, as the switching and the modulating frequencies become closer, this approximation is not valid and the results based on it lead to erroneous conclusions about the dynamics of the system.

A discrete time approach is used to reveal the interesting nonlinear phenomena that the system can exhibit. From numerical simulations using the switched model, it is shown that the system can present period‐doubling bifurcation at the fast scale (switching frequency).

An exact solution discrete‐time model is derived, able to predict accurately the nonlinear dynamical behaviour of the system.

The discrete time model is obtained without making quasi‐static approximation. The exact switched model is used to validate the discrete‐time model obtained. Finally, the effect of the switching frequency instabilities on the output voltage spectrum has been explored.

Aims to investigate the causative factors and clinical applicability of spontaneous regression of malignant tumours without treatment, a really paradoxical phenomenon with many therapeutic potentialities. Analyses past cases to find that the commonest cause is a preceding episode of high fever‐induced thermal fluctuation which produces fluctuation of biochemical/immunological parameters. Using Prigogine‐Glansdorff‐Langevin stability theory and biocybernetic principles, develops the theoretical foundation of a tumour’s self‐control, homeostasis and regression induced by thermal, radiation or oxygenation fluctuations. Derives a threshold condition of perturbations for producing regression. Presents some striking confirmation of such fluctuation‐induced regression in Ewing tumour, Clear cell cancer and Lewis lung carcinoma. Using experimental data on patients, elucidates a novel therapeutic approach of multi‐modal hyper‐fluctuation utilizing radiotherapeutic hyper‐fractionation, temperature and immune‐status.

Industries lament the current situation of approaches that have resulted in huge losses in the face of complex risks. The purpose of this study is therefore to review complexity theory in the context of risk management so that it is possible to research better approaches for managing complex risks.

The approach is to review complexity theory and highlight those aspects of complexity theory that have relevance for risk management. Then, the paper ends with a discussion on what direction of research that will be most promising for the aforementioned purpose.

The paper finds that the most challenging aspect is to identify the weak signals, and this implies that the current approaches of estimating probabilities are not going to produce the desired results. Big data may hold a solution in the future, but with legislation such as the General Data Protection Regulation, this seems impossible to implement on ethical grounds. Hence, the most prudent approach is to use a margin of safety as advocated by Graham roughly 70 years ago. Indeed, the approach may be to assume that a disaster will take place and use risk management tools to estimate the impact for a given object.

The literature review is a summary of a much larger work, and in so doing, the resulting simplification may run the risk of missing out on important details. However, with this risk in mind, the review holds rich enough discussion on complexity to be relevant for research about complex risk management.

The current implication for practice is that the paper strongly supports the notion of using a margin of safety as advocated by Graham and his most famous disciple Warren Buffet. This comes from the fact that because context is king, risk management approaches must be applied in their right domain. There is no one right way. In the future, the goal is to develop a quantitative approach that can help the industry in pricing complex risks.

The main contribution of the paper is to bring complexity theory more into the domain of risk management with sufficient details that should allow researchers to get conceptual ideas about what might work or not concerning complex risk management. If nothing else, it would be a significant contribution of the paper if it could help increasing the interest in complexity theory.