A multiscale time-Laplace method to extract relaxation times from non-stationary dynamic light scattering signals.

Dynamic Light Scattering (DLS) is a well-known technique to study the relaxation times of systems at equilibrium. In many soft matter systems, we actually have to consider non-equilibrium or non-stationary situations. We discuss here the principles, the signal processing techniques we developed, based on regularized inverse Laplace transform, sliding with time, and the light scattering signal acquisition, which enable us to use DLS experiments in this general situation. In this article, we show how to obtain such a time-Laplace analysis. We claim that this method can be adapted to numerous DLS experiments dealing with non-equilibrium systems so as to extract the non-stationary distribution of relaxation times. To prove that, we test this time-Laplace method on three different non-equilibrium processes or systems investigated by means of the DLS technique: the cooling kinetics of a colloidal particle solution, the sol-gel transition and the internal dynamics of a living cell nucleus.

Semi-automatic Extraction of Functional Dynamic Networks Describing Patient's Epileptic Seizures.

Intracranial electroencephalography (EEG) studies using stereotactic EEG (SEEG) have shown that during seizures, epileptic activity spreads across several anatomical regions from the seizure onset zone toward remote brain areas. A full and objective characterization of this patient-specific time-varying network is crucial for optimal surgical treatment. Functional connectivity (FC) analysis of SEEG signals recorded during seizures enables to describe the statistical relations between all pairs of recorded signals. However, extracting meaningful information from those large datasets is time consuming and requires high expertise. In the present study, we first propose a novel method named Brain-wide Time-varying Network Decomposition (BTND) to characterize the dynamic epileptogenic networks activated during seizures in individual patients recorded with SEEG electrodes. The method provides a number of pathological FC subgraphs with their temporal course of activation. The method can be applied to several seizures of the patient to extract reproducible subgraphs. Second, we compare the activated subgraphs obtained by the BTND method with visual interpretation of SEEG signals recorded in 27 seizures from nine different patients. As a whole, we found that activated subgraphs corresponded to brain regions involved during the course of the seizures and their time course was highly consistent with classical visual interpretation. We believe that the proposed method can complement the visual analysis of SEEG signals recorded during seizures by highlighting and characterizing the most significant parts of epileptic networks with their activation dynamics.

Spatial and temporal regularization to estimate COVID-19 reproduction number R(t): Promoting piecewise smoothness via convex optimization.

Among the different indicators that quantify the spread of an epidemic such as the on-going COVID-19, stands first the reproduction number which measures how many people can be contaminated by an infected person. In order to permit the monitoring of the evolution of this number, a new estimation procedure is proposed here, assuming a well-accepted model for current incidence data, based on past observations. The novelty of the proposed approach is twofold: 1) the estimation of the reproduction number is achieved by convex optimization within a proximal-based inverse problem formulation, with constraints aimed at promoting piecewise smoothness; 2) the approach is developed in a multivariate setting, allowing for the simultaneous handling of multiple time series attached to different geographical regions, together with a spatial (graph-based) regularization of their evolutions in time. The effectiveness of the approach is first supported by simulations, and two main applications to real COVID-19 data are then discussed. The first one refers to the comparative evolution of the reproduction number for a number of countries, while the second one focuses on French departments and their joint analysis, leading to dynamic maps revealing the temporal co-evolution of their reproduction numbers.

Who benefits most from Lyon's bike sharing system?

Bike sharing systems (BSS) have been growing fast all over the world, along with the number of articles analyzing such systems. However the lack of databases at the individual level and covering several years has limited the analysis of BSS users' behavior in the long term. This article gives a first detailed description of the temporal evolution of individual customers. Using a 5-year dataset covering 120,827 distinct year-long subscribers, we show the heterogeneous individual trajectories masked by the overall system stability. Users follow two main trajectories: about half remain in the system for at most one year, showing a low median activity (47 trips); the remaining half corresponds to more active users (median activity of 91 trips in their first year) that remain continuously active for several years (mean time = 2.9 years). We show that users from urban cores, middle-aged and male are over represented among these long-term users, which profit most from the BSS. This provides further support for the view that BSS mostly benefit the already privileged.

Multi-scale structural community organisation of the human genome.

BACKGROUND: Structural interaction frequency matrices between all genome loci are now experimentally achievable thanks to high-throughput chromosome conformation capture technologies. This ensues a new methodological challenge for computational biology which consists in objectively extracting from these data the structural motifs characteristic of genome organisation. RESULTS: We deployed the fast multi-scale community mining algorithm based on spectral graph wavelets to characterise the networks of intra-chromosomal interactions in human cell lines. We observed that there exist structural domains of all sizes up to chromosome length and demonstrated that the set of structural communities forms a hierarchy of chromosome segments. Hence, at all scales, chromosome folding predominantly involves interactions between neighbouring sites rather than the formation of links between distant loci. CONCLUSIONS: Multi-scale structural decomposition of human chromosomes provides an original framework to question structural organisation and its relationship to functional regulation across the scales. By construction the proposed methodology is independent of the precise assembly of the reference genome and is thus directly applicable to genomes whose assembly is not fully determined.

2D Prony-Huang transform: a new tool for 2D spectral analysis.

This paper provides an extension of the 1D Hilbert Huang transform for the analysis of images using recent optimization techniques. The proposed method consists of: 1) adaptively decomposing an image into oscillating parts called intrinsic mode functions (IMFs) using a mode decomposition procedure and 2) providing a local spectral analysis of the obtained IMFs in order to get the local amplitudes, frequencies, and orientations. For the decomposition step, we propose two robust 2D mode decompositions based on nonsmooth convex optimization: 1) a genuine 2D approach, which constrains the local extrema of the IMFs and 2) a pseudo-2D approach, which separately constrains the extrema of lines, columns, and diagonals. The spectral analysis step is an optimization strategy based on Prony annihilation property and applied on small square patches of the IMFs. The resulting 2D Prony­Huang transform is validated on simulated and real data.

Bootstrapping under constraint for the assessment of group behavior in human contact networks.

The increasing availability of time- and space-resolved data describing human activities and interactions gives insights into both static and dynamic properties of human behavior. In practice, nevertheless, real-world data sets can often be considered as only one realization of a particular event. This highlights a key issue in social network analysis: the statistical significance of estimated properties. In this context, we focus here on the assessment of quantitative features of specific subset of nodes in empirical networks. We present a method of statistical resampling based on bootstrapping groups of nodes under constraints within the empirical network. The method enables us to define acceptance intervals for various null hypotheses concerning relevant properties of the subset of nodes under consideration in order to characterize by a statistical test its behavior as "normal" or not. We apply this method to a high-resolution data set describing the face-to-face proximity of individuals during two colocated scientific conferences. As a case study, we show how to probe whether colocating the two conferences succeeded in bringing together the two corresponding groups of scientists.