Mandelbrot's 1/f fractional renewal models of 1963-67: The non-ergodic missing link between change points and long range dependence

The problem of 1/f noise has been with us for about a century. Because it is so often framed in Fourier spectral language, the most famous solutions have tended to be the stationary long range dependent (LRD) models such as Mandelbrot's fractional Gaussian noise. In view of the increasing importance to physics of non-ergodic fractional renewal models, I present preliminary results of my research into the history of Mandelbrot's very little known work in that area from 1963-67. I speculate about how the lack of awareness of this work in the physics and statistics communities may have affected the development of complexity science, and I discuss the differences between the Hurst effect, 1/f noise and LRD, concepts which are often treated as equivalent.Comment: 11 pages. Corrected and improved version of a manuscript submitted to ITISE 2016 meeting in Granada, Spai

Superaging correlation function and ergodicity breaking for Brownian motion in logarithmic potentials

We consider an overdamped Brownian particle moving in a confining asymptotically logarithmic potential, which supports a normalized Boltzmann equilibrium density. We derive analytical expressions for the two-time correlation function and the fluctuations of the time-averaged position of the particle for large but finite times. We characterize the occurrence of aging and nonergodic behavior as a function of the depth of the potential, and support our predictions with extensive Langevin simulations. While the Boltzmann measure is used to obtain stationary correlation functions, we show how the non-normalizable infinite covariant density is related to the super-aging behavior.Comment: 16 pages, 6 figure

Residence Time Statistics for Normal and Fractional Diffusion in a Force Field

We investigate statistics of occupation times for an over-damped Brownian particle in an external force field. A backward Fokker-Planck equation introduced by Majumdar and Comtet describing the distribution of occupation times is solved. The solution gives a general relation between occupation time statistics and probability currents which are found from solutions of the corresponding problem of first passage time. This general relationship between occupation times and first passage times, is valid for normal Markovian diffusion and for non-Markovian sub-diffusion, the latter modeled using the fractional Fokker-Planck equation. For binding potential fields we find in the long time limit ergodic behavior for normal diffusion, while for the fractional framework weak ergodicity breaking is found, in agreement with previous results of Bel and Barkai on the continuous time random walk on a lattice. For non-binding potential rich physical behaviors are obtained, and classification of occupation time statistics is made possible according to whether or not the underlying random walk is recurrent and the averaged first return time to the origin is finite. Our work establishes a link between fractional calculus and ergodicity breaking.Comment: 12 page

Риски, вызовы и механизмы ESG-трансформации систем управления

Purpose: the article aims at justification and identification of the factors hindering the effective implementation of the management systems ESG-transformation, taking into account new risks and threats to sustainable development, and substantiation of the mechanisms that ensure its implementation.Methods: along with the traditional methods of scientific analysis, interdisciplinary approach typical for the study of sustainable development problems and the diagnosis of key factors associated with ESG-transformation of management systems, carried out a review of scientific literature, used various rating models, regulatory documents and guidelines for sustainable development, corporate social responsibility and diagnostics of ESG-factors.Results: the article performed diagnostics of managed and unmanaged risks of ESG-transformation of management systems, identified trends in the development of managerial personnel competencies that carry out such a transformation, and disclosed the features of achieving sustainable development goals. The essence of the author's position is that in order to achieve any of the sustainable development goals, two mandatory conditions must be met: ensuring effective interaction between the state, business and civil society and applying an integrated approach to considering economic, social and environmental aspects that reflect its specifics.Сonclusions and Relevance: the proposed approach makes it possible to develop scientifically based tools for minimizing risks and mechanisms for achieving sustainable development goals based on the ESG-transformation of management systems. Results obtained in the article may be useful for the professional community interested in promoting the ESG-agenda and achieving sustainable development goals based on the ESG-transformation of public and corporate governance.Цель статьи – выявление и идентификация факторов, препятствующих эффективному проведению ESGтрансформации систем управления, с учетом новых рисков и вызовов устойчивому развитию, и обоснование механизмов, обеспечивающих ее реализацию.Методы или методология проведения работы. Наряду с традиционными методами научного анализа, а также междисциплинарного подхода, характерного для исследования проблем устойчивого развития и диагностики ключевых факторов, связанных с ESG-трансформацией систем управления, в работе выполнен обзор научной литературы. В рамках исследования использовались различные рейтинговые модели, нормативные документы и руководящие принципы устойчивого развития, корпоративной социальной ответственности и диагностики ESG-факторов.Результаты работы. В работе проведена диагностика управляемых и неуправляемых рисков ESGтрансформации систем управления, определены тренды развития компетенций управленческих кадров, такую трансформацию осуществляющих, и раскрыты особенности достижения целей устойчивого развития. Суть авторской позиции заключается в том, что для достижения любой из целей устойчивого развития необходимо выполнение двух обязательных условий: обеспечение эффективного взаимодействия государства, бизнеса и гражданского общества и применение комплексного подхода к рассмотрению экономических, социальных и экологических аспектов, отражающих ее специфику.Выводы. Предложенный подход дает возможность разработки научно обоснованного инструментария минимизации рисков и механизмов достижения целей устойчивого развития на основе ESG-трансформации систем управления. Результаты, полученные в статье, могут быть использованы профессиональным сообществом, заинтересованном в продвижении ESG-повестки и достижении целей устойчивого развития на основе ESG-трансформации государственного и корпоративного управления

Weakly non-ergodic Statistical Physics

We find a general formula for the distribution of time averaged observables for weakly non-ergodic systems. Such type of ergodicity breaking is known to describe certain systems which exhibit anomalous fluctuations, e.g. blinking quantum dots and the sub-diffusive continuous time random walk model. When the fluctuations become normal we recover usual ergodic statistical mechanics. Examples of a particle undergoing fractional dynamics in a binding force field are worked out in detail. We briefly discuss possible physical applications in single particle experiments

Reverse Engineering Gene Networks with ANN: Variability in Network Inference Algorithms

Motivation :Reconstructing the topology of a gene regulatory network is one of the key tasks in systems biology. Despite of the wide variety of proposed methods, very little work has been dedicated to the assessment of their stability properties. Here we present a methodical comparison of the performance of a novel method (RegnANN) for gene network inference based on multilayer perceptrons with three reference algorithms (ARACNE, CLR, KELLER), focussing our analysis on the prediction variability induced by both the network intrinsic structure and the available data. Results: The extensive evaluation on both synthetic data and a selection of gene modules of "Escherichia coli" indicates that all the algorithms suffer of instability and variability issues with regards to the reconstruction of the topology of the network. This instability makes objectively very hard the task of establishing which method performs best. Nevertheless, RegnANN shows MCC scores that compare very favorably with all the other inference methods tested. Availability: The software for the RegnANN inference algorithm is distributed under GPL3 and it is available at the corresponding author home page (http://mpba.fbk.eu/grimaldi/regnann-supmat