Inference of multivariate exponential Hawkes processes with inhibition and application to neuronal activity

The multivariate Hawkes process is a past-dependent point process used to model the relationship of event occurrences between different phenomena.Although the Hawkes process was originally introduced to describe excitation effects, which means that one event increases the chances of another occurring, there has been a growing interest in modelling the opposite effect, known as inhibition.In this paper, we focus on how to infer the parameters of a multidimensional exponential Hawkes process with both excitation and inhibition effects. Our first result is to prove the identifiability of this model under a few sufficient assumptions. Then we propose a maximum likelihood approach to estimate the interaction functions, which is, to the best of our knowledge, the first exact inference procedure in the frequentist framework.Our method includes a variable selection step in order to recover the support of interactions and therefore to infer the connectivity graph.A benefit of our method is to provide an explicit computation of the log-likelihood, which enables in addition to perform a goodness-of-fit test for assessing the quality of estimations.We compare our method to standard approaches, which were developed in the linear framework and are not specifically designed for handling inhibiting effects.We show that the proposed estimator performs better on synthetic data than alternative approaches. We also illustrate the application of our procedure to a neuronal activity dataset, which highlights the presence of both exciting and inhibiting effects between neurons.Comment: Statistics and Computing, 202

L'effet tunnel assisté par le chaos comme nouvel outil pour la simulation quantique

L'effet tunnel est une manifestation emblématique de la nature ondulatoire de la matière. Il décrit le passage de particules quantiques à travers des barrières de potentiel classiquement infranchissables. Lorsqu'il se produit dans des systèmes dont la dynamique classique est mixte, c'est-à-dire intermédiaire entre chaotique et régulière, l'effet tunnel est un processus bien plus riche que celui présenté dans les livres d'introduction à la mécanique quantique. En effet, dans l'espace des phases classique de ces systèmes, les orbites régulières s'organisent en îlots stables entourés par un mer d'orbites chaotiques instables. L'effet tunnel entre les îlots réguliers est alors partiellement médié par des états ergodiques dans la mer chaotique. Une des signatures emblématiques de cet effet tunnel assisté par le chaos est l'existence de résonances de la fréquence d'oscillation entre deux îlots symétriques. Dans ce manuscrit nous rapportons, en collaboration avec un groupe d'expérimentateurs et expérimentatrice du LCAR à Toulouse, la première observation de ces résonances dans un système quantique, avec une expérience d'atomes froids. Nous présentons également une généralisation de ce mécanisme de transport à des réseaux optiques modulés dans le temps qui forment dans l'espace des phases une chaîne d'îlots d'orbites stables immergés dans une même mer de trajectoires chaotiques. Nous montrons que l'effet tunnel assisté par le chaos s'y traduit par des couplages à longue portée entre les îlots et démontrons que les propriétés de fluctuation statistique de ces couplages sont universelles. De tels couplages à longue portée pourraient servir dans le champ de la simulation quantique pour accéder expérimentalement à de nouvelles classes de systèmes difficiles à réaliser autrement, notamment des systèmes désordonnés critiques. La dernière partie de ce manuscrit est consacrée à l'étude de tels systèmes désordonnés critiques, comme au seuil de la transition d'Anderson, dont les états quantiques sont multifractals : ils sont délocalisés mais non ergodiques et possèdent des fluctuations invariantes d'échelle. Nous caractérisons la dynamique de ces systèmes en décrivant le rôle de la multifractalité sur la diffusion cohérente d'une onde plane. Cette étude est une étape importante vers la caractérisation expérimentale de la multifractalité dans un système quantique, qui reste à ce jour très difficile par d'autres méthodes.Tunneling is an emblematic manifestation of the wave nature of matter. It describes the passage of quantum particles through classically forbidden barriers of energy. When it occurs in systems whose classical dynamics is mixed, that is to say intermediate between chaotic and regular, tunneling is a much richer process than presented in introductory books to quantum mechanics. Indeed, in the classical phase space of such systems, regular orbits organize themselves into stable islands surrounded by a sea of unstable chaotic orbits. Tunneling between regular islands is then partially mediated by ergodic states in the chaotic sea. One of the striking signatures of this chaos-assisted tunneling is the existence of resonances of the oscillation frequency between two neighboring sites. In this thesis we report, in collaboration with an experimental team at LCAR in Toulouse, the first observation of these resonances in a quantum system, with a a cold atom experiment. We also present a generalization of this transport mechanism to driven optical lattices that form in phase space a chain of stable islands surrounded by the same chaotic sea. We show that chaos- assisted tunneling results in very long-range couplings between islands, whose fluctuations statistical propreties are universal. These long-range couplings could be used in the field of quantum simulation to experimentally access new classes of systems, difficult to achieve otherwise, in particular critical disordered systems. The last part of this manuscript is devoted to the study of such critical disordered systems, e.g. at the Anderson transition, whose quantum states are multifractals: they are delocalized but not ergodic and have remarkable scaling properties. We characterize the dynamics of these systems by describing the role of multifractality on the coherent scattering of a plane wave. This study is an important step towards the experimental characterization of multifractality in a quantum system, which remains up to now very difficult by other methods

Uncovering the spatial structure of mobility networks

The extraction of a clear and simple footprint of the structure of large, weighted and directed networks is a general problem that has many applications. An important example is given by origin-destination matrices which contain the complete information on commuting flows, but are difficult to analyze and compare. We propose here a versatile method which extracts a coarse-grained signature of mobility networks, under the form of a $2\times 2$ matrix that separates the flows into four categories. We apply this method to origin-destination matrices extracted from mobile phone data recorded in thirty-one Spanish cities. We show that these cities essentially differ by their proportion of two types of flows: integrated (between residential and employment hotspots) and random flows, whose importance increases with city size. Finally the method allows to determine categories of networks, and in the mobility case to classify cities according to their commuting structure.Comment: 10 pages, 5 figures +Supplementary informatio

From mobile phone data to the spatial structure of cities

Pervasive infrastructures, such as cell phone networks, enable to capture large amounts of human behavioral data but also provide information about the structure of cities and their dynamical properties. In this article, we focus on these last aspects by studying phone data recorded during 55 days in 31 Spanish metropolitan areas. We first define an urban dilatation index which measures how the average distance between individuals evolves during the day, allowing us to highlight different types of city structure. We then focus on hotspots, the most crowded places in the city. We propose a parameter free method to detect them and to test the robustness of our results. The number of these hotspots scales sublinearly with the population size, a result in agreement with previous theoretical arguments and measures on employment datasets. We study the lifetime of these hotspots and show in particular that the hierarchy of permanent ones, which constitute the "heart" of the city, is very stable whatever the size of the city. The spatial structure of these hotspots is also of interest and allows us to distinguish different categories of cities, from monocentric and "segregated" where the spatial distribution is very dependent on land use, to polycentric where the spatial mixing between land uses is much more important. These results point towards the possibility of a new, quantitative classification of cities using high resolution spatio-temporal data.Comment: 14 pages, 15 figure

Coherent forward scattering as a robust probe of multifractality in critical disordered media

We study coherent forward scattering (CFS) in critical disordered systems, whose eigenstates are multifractals. We give general and simple arguments that make it possible to fully characterize the dynamics of the shape and height of the CFS peak. We show that the dynamics is governed by multifractal dimensions $D_1$ and $D_2$, which suggests that CFS could be used as an experimental probe for quantum multifractality. Our predictions are universal and numerically verified in three paradigmatic models of quantum multifractality: Power-law Random Banded Matrices (PRBM), the Ruijsenaars-Schneider ensembles (RS), and the three-dimensional kicked-rotor (3DKR). In the strong multifractal regime, we show analytically that these universal predictions exactly coincide with results from standard perturbation theory applied to the PRBM and RS models.Comment: 24 pages, 10 figure

Exploring the Influence of Price and Convenience on Perceived Usefulness of On-line Banking within the TAM Framework: A Cross National (Canada and Spain) Decision Model

Nowadays, the Internet is a powerful mean to complement the traditional marketing channels used by banks. Based on the Technology Acceptance Model, this paper explores the importance of two external latent variables—‘Price’ and ‘Convenience’ —as antecedents of ‘Perceived Usefulness’ and consumer acceptance of on-line banking in a Canadian and Spanish environment; the results highlight the predictive power and accuracy of the model cross-nationally. In fact, the findings were quite similar in the Canadian and Spanish samples, and stress that ‘Perceived Usefulness’ and ‘Attitude’ are the key drivers of the consumers’ on-line banking acceptance. Conclusions and recommendations for future research are also provided

Nopol: Automatic Repair of Conditional Statement Bugs in Java Programs

International audienceWe propose NOPOL, an approach to automatic repair of buggy conditional statements (i.e., if-then-else statements). This approach takes a buggy program as well as a test suite as input and generates a patch with a conditional expression as output. The test suite is required to contain passing test cases to model the expected behavior of the program and at least one failing test case that reveals the bug to be repaired. The process of NOPOL consists of three major phases. First, NOPOL employs angelic fix localization to identify expected values of a condition during the test execution. Second, runtime trace collection is used to collect variables and their actual values, including primitive data types and objected-oriented features (e.g., nullness checks), to serve as building blocks for patch generation. Third, NOPOL encodes these collected data into an instance of a Satisfiability Modulo Theory (SMT) problem; then a feasible solution to the SMT instance is translated back into a code patch. We evaluate NOPOL on 22 real-world bugs (16 bugs with buggy IF conditions and 6 bugs with missing preconditions) on two large open-source projects, namely Apache Commons Math and Apache Commons Lang. Empirical analysis on these bugs shows that our approach can effectively fix bugs with buggy IF conditions and missing preconditions. We illustrate the capabilities and limitations of NOPOL using case studies of real bug fixes

A Spiking Neural Network for Gas Discrimination using a Tin Oxide Sensor Array

International audienceWe propose a bio-inspired signal processing method for odor discrimination. A spiking neural network is trained with a supervised learning rule so as to classify the analog outputs from a monolithic 4×4 tin oxide gas sensor array implemented in our in-house 5 µm process. This scheme has been sucessfully tested on a discrimination task between 4 gases (hydrogen, ethanol, carbon monoxide, methane). Performance compares favorably to the one obtained with a common statistical classifier. Moreover, the simplicity of our method makes it well suited for building dedicated hardware for processing data from gas sensor arrays