Pareto law of the expenditure of a person in convenience stores

We study the statistical laws of the expenditure of a person in convenience stores by analysing around 100 million receipts. The density function of expenditure exhibits a fat tail that follows a power law. We observe the Pareto principle where both the top 25% and 2% of the customers account for 80% and 25% of the store's sales, respectively. Using the Lorenz curve, the Gini coefficient is estimated to be 0.70; this implies a strong economic inequality.Comment: 8 pages, 3 figures, Proceedings of APFA

A new web-based system to improve the monitoring of snow avalanche hazard in France

International audienceSnow avalanche data in the French Alps and Pyrenees have been recorded for more than 100 years in several databases. The increasing amount of observed data required a more integrative and automated service. Here we report the comprehensive web-based Snow Avalanche Information System newly developed to this end for three important data sets: an avalanche chronicle (Enquete Permanente sur les Avalanches, EPA), an avalanche map (Carte de Localisation des Phenomenes d'Avalanche, CLPA) and a compilation of hazard and vulnerability data recorded on selected paths endangering human settlements (Sites Habites Sensibles aux Avalanches, SSA). These data sets are now integrated into a common database, enabling full interoperability between all different types of snow avalanche records: digitized geographic data, avalanche descriptive parameters, eyewitness reports, photographs, hazard and risk levels, etc. The new information system is implemented through modular components using Java-based web technologies with Spring and Hibernate frameworks. It automates the manual data entry and improves the process of information collection and sharing, enhancing user experience and data quality, and offering new outlooks to explore and exploit the huge amount of snow avalanche data available for fundamental research and more applied risk assessment

Can Avalanche Deposits be Effectively Detected by Deep Learning on Sentinel-1 Satellite SAR Images?

International audienceAchieving reliable observations of avalanche debris is crucial for many applications including avalanche forecasting. The ability to continuously monitor the avalanche activity, in space and time, would provide indicators on the potential instability of the snowpack and would allow a better characterization of avalanche risk periods and zones. In this work, we use Sentinel-1 SAR (synthetic aperture radar) data and an independent in-situ avalanche inventory (ground truth) to automatically detect avalanche debris in the French Alps during the remarkable winter season 2017-18. Convolutional neural networks are applied on SAR image patches to locate avalanche debris signatures. We are able to successfully locate new avalanche deposits with as much as 77% confidence on the most susceptible mountain zone (compared to 53% with a baseline method). One of the challenges of this study is to make an efficient use of remote sensing measurements on a complex terrain. It explores the following questions: to what extent can deep learning methods improve the detection of avalanche deposits and help us to derive relevant avalanche activity statistics at different scales (in time and space) that could be useful for a large number of users (researchers, forecasters, government operators)

Power Law of Customers' Expenditures in Convenience Stores

In a convenience store chain, a tail of the cumulative density function of the expenditure of a person during a single shopping trip follows a power law with an exponent of -2.5. The exponent is independent of the location of the store, the shopper's age, the day of week, and the time of day.Comment: 9 pages, 5 figures. Accepted for publication in Journal of the Physical Society of Japan Vol.77No.

Endogenous and exogenous dynamics in the fluctuations of capital fluxes: An empirical analysis of the Chinese stock market

A phenomenological investigation of the endogenous and exogenous dynamics in the fluctuations of capital fluxes is investigated on the Chinese stock market using mean-variance analysis, fluctuation analysis and their generalizations to higher orders. Non-universal dynamics have been found not only in $\alpha$ exponents different from the universal value 1/2 and 1 but also in the distributions of the ratios $\eta_i = \sigma_i^{\rm{exo}} / \sigma_i^{\rm{endo}}$. Both the scaling exponent $\alpha$ of fluctuations and the Hurst exponent $H_i$ increase in logarithmic form with the time scale $\Delta t$ and the mean traded value per minute $$, respectively. We find that the scaling exponent $\alpha^{\rm{endo}}$ of the endogenous fluctuations is found to be independent of the time scale, while the exponent of exogenous fluctuations $\alpha^{\rm{exo}}=1$. Multiscaling and multifractal features are observed in the data as well. However, the inhomogeneous impact model is not verified.Comment: 9 Latx pages for EPJB including 13 figure

Hierarchy of Temporal Responses of Multivariate Self-Excited Epidemic Processes

We present the first exact analysis of some of the temporal properties of multivariate self-excited Hawkes conditional Poisson processes, which constitute powerful representations of a large variety of systems with bursty events, for which past activity triggers future activity. The term "multivariate" refers to the property that events come in different types, with possibly different intra- and inter-triggering abilities. We develop the general formalism of the multivariate generating moment function for the cumulative number of first-generation and of all generation events triggered by a given mother event (the "shock") as a function of the current time $t$. This corresponds to studying the response function of the process. A variety of different systems have been analyzed. In particular, for systems in which triggering between events of different types proceeds through a one-dimension directed or symmetric chain of influence in type space, we report a novel hierarchy of intermediate asymptotic power law decays $\sim 1/t^{1-(m+1)\theta}$ of the rate of triggered events as a function of the distance $m$ of the events to the initial shock in the type space, where $0 < \theta <1$ for the relevant long-memory processes characterizing many natural and social systems. The richness of the generated time dynamics comes from the cascades of intermediate events of possibly different kinds, unfolding via a kind of inter-breeding genealogy.Comment: 40 pages, 8 figure

Generation-by-Generation Dissection of the Response Function in Long Memory Epidemic Processes

In a number of natural and social systems, the response to an exogenous shock relaxes back to the average level according to a long-memory kernel $\sim 1/t^{1+\theta}$ with $0 \leq \theta <1$. In the presence of an epidemic-like process of triggered shocks developing in a cascade of generations at or close to criticality, this "bare" kernel is renormalized into an even slower decaying response function $\sim 1/t^{1-\theta}$. Surprisingly, this means that the shorter the memory of the bare kernel (the larger $1+\theta$), the longer the memory of the response function (the smaller $1-\theta$). Here, we present a detailed investigation of this paradoxical behavior based on a generation-by-generation decomposition of the total response function, the use of Laplace transforms and of "anomalous" scaling arguments. The paradox is explained by the fact that the number of triggered generations grows anomalously with time at $\sim t^\theta$ so that the contributions of active generations up to time $t$ more than compensate the shorter memory associated with a larger exponent $\theta$. This anomalous scaling results fundamentally from the property that the expected waiting time is infinite for $0 \leq \theta \leq 1$. The techniques developed here are also applied to the case $\theta >1$ and we find in this case that the total renormalized response is a {\bf constant} for $t < 1/(1-n)$ followed by a cross-over to $\sim 1/t^{1+\theta}$ for $t \gg 1/(1-n)$.Comment: 27 pages, 4 figure

Analyse des fluctuations spatio-temporelles des nombres d’avalanches dans les Alpes du Nord à partir de l’enquête permanente sur les avalanches (EPA)

L'enquête permanente sur les avalanches (EPA) est une chronique très détaillée d'événements d'avalanche sur près de cinq mille sites sélectionnés en France. Source d’information extrêmement précieuse pour les gestionnaires du risque en montagne, ses données sont utilisées ici par des chercheurs pour quantifier et étudier les variations de l’activité avalancheuse dans l’espace et dans le temps, et ce afin de mieux comprendre la structure spatiale des avalanches et sa réponse aux variations du climat. Les résultats obtenus dans cette étude, une fois confrontés à des données climatiques, pourront aider à mieux anticiper l’évolution future de l’activité avalancheuse

Propagation des ultrasons dans les milieux disperses. Application a la metrologie des sols geles

SIGLEINIST T 76790 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc