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This paper quantitatively analyzes the usage of Gallica, a website platform for accessing the digital library of the Bibliothèque nationale de France (BnF). Our approach relies on the access logs retrieved from the Apache HTTP Servers of Gallica. The server access logs record all requests processed by the server and thus, contain the web pages and the timestamp of the requests along with the corresponding IP of the users. These access logs are augmented with additional structured data via The Open Archives Initiative Protocol for Metadata Harvesting in order to store, when it is possible, the metadata of consulted documents. Beyond straightforward statistics (such as the duration of a session, the number of documents consulted by each session, the most popular type of documents over all the Gallica users), our research aims to model user navigational behaviours by a Mixture of Continuous-Time Markov Chains. This model allows to cluster users into classes of typical paths of navigation on Gallica. The results provide relevant insights on the way the users interact with the interface of Gallica, highlighting the mean duration of some actions such as the interaction with the search engine or the consultation of documents. Even if our approach requires the use of additional informations in order to properly interpret the models and the correlation that it highlights, it allows the integration of all types of behaviour, including the most stealthy and the most difficult to catch in traditional surveys, giving them their fair weight in terms of audience. [ABSTRACT FROM AUTHOR]

The estimation of the slowness vector of infrasound waves propagating across an array is a critical process leading to the determination of parameters of interest such as the direction of arrival. The sensors of an array are often considered to be located in a horizontal plane. However, due to topography, the altitudes of the sensors are not identical and introduce a bias on the estimate if neglected. However, the unbiased 3D estimation procedure, while suppressing the bias, leads to an increase of the variance. Accounting for an a priori constraint on the slowness vector significantly reduces the variance and could therefore improve the performance of the estimation if the introduced bias by incorrect a priori information remains negligible. This study focuses on measuring the benefits of this approach with a thorough investigation of the bias and variance of the constrained 3D estimator, which is not available in the existing literature. This contribution provides such computations based on an asymptotic Gaussian approximation. Simulations are carried out to assess the theoretical results both with synthetic and real data. Thus, a constrained 3D estimator is proposed yielding the best bias/variance compromise if good knowledge of the propagation wave speed is accessible. [ABSTRACT FROM AUTHOR]

To estimate the slowness vector of infrasound waves propagating across an infrasound array, it is often considered that the sensors are located in a perfectly horizontal plane (2-D approximation). However, the arrays are not planar and differences between sensor altitudes cannot be neglected without introducing biases when estimating the parameters of interest (backazimuth and incidence). A closed-formula of this error depending on the geometry of the array and the wave incidence is presented. Since the unbiased 3-D estimation of the slowness parameters results in a significant alteration of the variance, a metric based on the mean square error is proposed. We found it useful to compare the 3-D to the 2-D processed results. We show the 3-D estimator does not always give the best estimates. We propose also a formulation of the boundary that allow us to choose between these two estimators depending on the situation (arrays, incidence and signal-to-noise ratios). Finally, we compare these two approaches (2-D/3-D) to all International Monitoring System arrays with synthetic data, and perform a comparative estimation of backazimuth for real data. [ABSTRACT FROM PUBLISHER]