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## Observational evidence in favor of scale free evolution of sunspot groups

The hypothesis stating that the distribution of sunspot groups versus their size ($\varphi$) follows a power law in the domain of small groups was recently highlighted but rejected in favor of a Weibull distribution. In this paper we re-consider this question, and are led to the opposite conclusion. We suggest a new definition of group size, namely the spatio-temporal ``volume'' ($V$) obtained as the sum of the observed daily areas instead of a single area associated with each group. With this new definition of ``size'', the width of the power-law part of the distribution increases from 1.5 to 2.5. The exponent of the power-law is close to 1. The width of the power-law part and its exponent are stable with respect to the different catalogues and computational procedures used to reduce errors in the data. The observed distribution is not fit adequately by a Weibull distribution. The existence of a wide power-law part of the distribution suggests that self-organized criticality underlies the generation and evolution of sunspot groups and that the mechanism responsible for it is scale-free over a large range of sizes.

The contribution of electron–phonon scattering to conductivity of a quantum cylinder in a lon-gitudinal magnetic field has been studied. It has been shown that the conductivity of the nanotube undergoes Aharonov–Bohm oscillations with variations in the magnetic flux through the nanotube cross section. The formulas describing the temperature dependence of the resistance of the nanostructure both in the case of an isotropic phonon spectrum and with allowance for the effects of phonon confinement have been obtained in the analytical form.

This book constitutes the refereed proceedings of the 10th International Conference on Formal Concept Analysis, ICFCA 2012, held in Leuven, Belgium in May 2012. The 20 revised full papers presented together with 6 invited talks were carefully reviewed and selected from 68 submissions. The topics covered in this volume range from recent advances in machine learning and data mining; mining terrorist networks and revealing criminals; concept-based process mining; to scalability issues in FCA and rough sets.

In this paper we propose the software system CORDIET-Helthcare which we are currently developing in collaboration with the Katholieke Universiteit Leuven, Moscow Higher School of Economics and the GZA-hospital group located in Antwerp. The main aim of this system is to offer healthcare management staff a user-friendly and powerful data analysis environment. Using state of the art techniques from computer science and mathematics we show how CORDIET-Helthcare can be used to gain insight in existing care processes and reveal actionable knowledge which can be used to improve the current way of working.

This book constitutes the second part of the refereed proceedings of the 10th International Conference on Formal Concept Analysis, ICFCA 2012, held in Leuven, Belgium in May 2012. The topics covered in this volume range from recent advances in machine learning and data mining; mining terrorist networks and revealing criminals; concept-based process mining; to scalability issues in FCA and rough sets.

We define, calculate and analyze irregularity indices λISSN of daily series of the International Sunspot Number ISSN as a function of increasing smoothing from *N* = 162 to 648 days. The irregularity indices λ are computed within 4-year sliding windows, with embedding dimensions *m* = 1 and 2. λISSN displays Schwabe cycles with ~5.5-year variations ("half Schwabe variations" HSV). The mean of λISSN undergoes a downward step and the amplitude of its variations strongly decreases around 1930. We observe changes in the ratio *R* of the mean amplitude of λ peaks at solar cycle minima with respect to peaks at solar maxima as a function of date, embedding dimension and, importantly, smoothing parameter *N*. We identify two distinct regimes, called Q1 and Q2, defined mainly by the evolution of *R* as a function of *N*: Q1, with increasing HSV behavior and *R* value as *N* is increased, occurs before 1915–1930; and Q2, with decreasing HSV behavior and *R* value as *N* is increased, occurs after ~1975. We attempt to account for these observations with an autoregressive (order 1) model with Poissonian noise and a mean modulated by two sine waves of periods *T*1 and *T*2 (*T*1 = 11 years, and intermediate *T*2 is tuned to mimic quasi-biennial oscillations QBO). The model can generate both Q1 and Q2 regimes. When *m* = 1, HSV appears in the absence of *T*2 variations. When *m* = 2, Q1 occurs when *T*2 variations are present, whereas Q2 occurs when *T*2 variations are suppressed. We propose that the HSV behavior of the irregularity index of ISSN may be linked to the presence of strong QBO before 1915–1930, a transition and their disappearance around 1975, corresponding to a change in regime of solar activity.

This is a textbook in data analysis. Its contents are heavily influenced by the idea that data analysis should help in enhancing and augmenting knowledge of the domain as represented by the concepts and statements of relation between them. According to this view, two main pathways for data analysis are summarization, for developing and augmenting concepts, and correlation, for enhancing and establishing relations. Visualization, in this context, is a way of presenting results in a cognitively comfortable way. The term *summarization* is understood quite broadly here to embrace not only simple summaries like totals and means, but also more complex summaries such as the principal components of a set of features or cluster structures in a set of entities.

The material presented in this perspective makes a unique mix of subjects from the fields of statistical data analysis, data mining, and computational intelligence, which follow different systems of presentation.

We describe FCART software system, a universal integrated environment for knowledge and data engineers with a set of research tools based on Formal Concept Analysis. The system is intended for knowledge discovery from big dynamic data collections, including text collections. FCART allows the user to load structured and unstructured data (texts and various metainformation) from heterogeneous data sources, build data snapshots, compose queries, generate and visualize concept lattices, clusters, attribute dependencies, and other useful analytical artifacts. Full preprocessing scenario is considered.

Formal Concept Analysis Research Toolbox (FCART) is an integrated environment for knowledge and data engineers with a set of research tools based on Formal Concept Analysis. FCART allows a user to load structured and unstructured data (including texts with various metadata) from heterogeneous data sources into local data storage, compose scaling queries for data snapshots, and then research classical and some innovative FCA artifacts in analytic sessions.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.