Evolution of networks

We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of such a kind came into existence recently. This opens a wide field for the study of their topology, evolution, and complex processes occurring in them. Such networks possess a rich set of scaling properties. A number of them are scale-free and show striking resilience against random breakdowns. In spite of large sizes of these networks, the distances between most their vertices are short -- a feature known as the ``small-world'' effect. We discuss how growing networks self-organize into scale-free structures and the role of the mechanism of preferential linking. We consider the topological and structural properties of evolving networks, and percolation in these networks. We present a number of models demonstrating the main features of evolving networks and discuss current approaches for their simulation and analytical study. Applications of the general results to particular networks in Nature are discussed. We demonstrate the generic connections of the network growth processes with the general problems of non-equilibrium physics, econophysics, evolutionary biology, etc.Comment: 67 pages, updated, revised, and extended version of review, submitted to Adv. Phy

Modeling and predicting time series of social activities with fat-tailed distributions

Fat-tailed distributions, characterized by the relation P(x) ∝ x^{−α−1}, are an emergent statistical signature of many complex systems, and in particular of social activities. These fat-tailed distributions are the outcome of dynamical processes that, contrary to the shape of the distributions, is in most cases are unknown. Knowledge of these processes’ properties sheds light on how the events in these fat tails, i.e. extreme events, appear and if it is possible to anticipate them. In this Thesis, we study how to model the dynamics that lead to fat-tailed distributions and the possibility of an accurate prediction in this context. To approach these problems, we focus on the study of attention to items (such as videos, forum posts or papers) in the Internet, since human interactions through the online media leave digital traces that can be analysed quantitatively. We collected four sets of time series of online activity that show fat tails and we characterize them. Of the many features that items in the datasets have, we need to know which ones are the most relevant to describe the dynamics, in order to include them in a model; we select the features that show high predictability, i.e. the capacity of realizing an accurate prediction based on that information. To quantify predictability we propose to measure the quality of the optimal forecasting method for extreme events, and we construct this measure. Applying these methods to data, we find that more extreme events (i.e. higher value of activity) are systematically more predictable, indicating that the possibility of discriminate successful items is enhanced. The simplest model that describes the dynamics of activity is to relate linearly the increment of activity with the last value of activity recorded. This starting point is known as proportional effect, a celebrated and widely used class of growth models in complex systems, which leads to a distribution of activity that is fat-tailed. On the one hand, we show that this process can be described and generalized in the framework of Stochastic Differential Equations (SDE) with Normal noise; moreover, we formalize the methods to estimate the parameters of such SDE. On the other hand, we show that the fluctuations of activity resulting from these models are not compatible with the data. We propose a model with proportional effect and Lévy-distributed noise, that proves to be superior describing the fluctuations around the average of the data and predicting the possibility of an item to become an extreme event. However, it is possible to model the dynamics using more than just the last value of activity; we generalize the growth models used previously, and perform an analysis that indicates that the most relevant variable for a model is the last increment in activity. We propose a new model using only this variable and the fat-tailed noise, and we find that, in our data, this model is superior to the previous models, including the one we proposed. These results indicate that, even if present, the relevance of proportional effect as a generative mechanism for fat-tailed distributions is greatly reduced, since the dynamical equations of our models contain this feature in the noise. The implications of this new interpretation of growth models to the quantification of predictability are discussed along with applications to other complex systems

Dedication to Professor Michael Tribelsky

Professor Tribelsky's accomplishments are highly appreciated by the international community. The best indications of this are the high citation rates of his publications, and the numerous awards and titles he has received. He has made numerous fundamental contributions to an extremely broad area of physics and mathematics, including (but not limited to) quantum solid-state physics, various problems in light–matter interaction, liquid crystals, physical hydrodynamics, nonlinear waves, pattern formation in nonequilibrium systems and transition to chaos, bifurcation and probability theory, and even predictions of the dynamics of actual market prices. This book presents several extensions of his results, based on his inspiring publications

Image Simulation in Remote Sensing

Remote sensing is being actively researched in the fields of environment, military and urban planning through technologies such as monitoring of natural climate phenomena on the earth, land cover classification, and object detection. Recently, satellites equipped with observation cameras of various resolutions were launched, and remote sensing images are acquired by various observation methods including cluster satellites. However, the atmospheric and environmental conditions present in the observed scene degrade the quality of images or interrupt the capture of the Earth's surface information. One method to overcome this is by generating synthetic images through image simulation. Synthetic images can be generated by using statistical or knowledge-based models or by using spectral and optic-based models to create a simulated image in place of the unobtained image at a required time. Various proposed methodologies will provide economical utility in the generation of image learning materials and time series data through image simulation. The 6 published articles cover various topics and applications central to Remote sensing image simulation. Although submission to this Special Issue is now closed, the need for further in-depth research and development related to image simulation of High-spatial and spectral resolution, sensor fusion and colorization remains.I would like to take this opportunity to express my most profound appreciation to the MDPI Book staff, the editorial team of Applied Sciences journal, especially Ms. Nimo Lang, the assistant editor of this Special Issue, talented authors, and professional reviewers