The efficient computation of transition state resonances and reaction rates from a quantum normal form

A quantum version of a recent formulation of transition state theory in {\em phase space} is presented. The theory developed provides an algorithm to compute quantum reaction rates and the associated Gamov-Siegert resonances with very high accuracy. The algorithm is especially efficient for multi-degree-of-freedom systems where other approaches are no longer feasible.Comment: 4 pages, 3 figures, revtex

Detecting Pilot's Engagement Using fNIRS Connectivity Features in an Automated vs. Manual Landing Scenario

Monitoring pilot's mental states is a relevant approach to mitigate human error and enhance human machine interaction. A promising brain imaging technique to perform such a continuous measure of human mental state under ecological settings is Functional Near-InfraRed Spectroscopy (fNIRS). However, to our knowledge no study has yet assessed the potential of fNIRS connectivity metrics as long as passive Brain Computer Interfaces (BCI) are concerned. Therefore, we designed an experimental scenario in a realistic simulator in which 12 pilots had to perform landings under two contrasted levels of engagement (manual vs. automated). The collected data were used to benchmark the performance of classical oxygenation features (i.e., Average, Peak, Variance, Skewness, Kurtosis, Area Under the Curve, and Slope) and connectivity features (i.e., Covariance, Pearson's, and Spearman's Correlation, Spectral Coherence, and Wavelet Coherence) to discriminate these two landing conditions. Classification performance was obtained by using a shrinkage Linear Discriminant Analysis (sLDA) and a stratified cross validation using each feature alone or by combining them. Our findings disclosed that the connectivity features performed significantly better than the classical concentration metrics with a higher accuracy for the wavelet coherence (average: 65.3/59.9 %, min: 45.3/45.0, max: 80.5/74.7 computed for HbO/HbR signals respectively). A maximum classification performance was obtained by combining the area under the curve with the wavelet coherence (average: 66.9/61.6 %, min: 57.3/44.8, max: 80.0/81.3 computed for HbO/HbR signals respectively). In a general manner all connectivity measures allowed an efficient classification when computed over HbO signals. Those promising results provide methodological cues for further implementation of fNIRS-based passive BCIs

Quantum breaking time near classical equilibrium points

By using numerical and semiclassical methods, we evaluate the quantum breaking, or Ehrenfest time for a wave packet localized around classical equilibrium points of autonomous one-dimensional systems with polynomial potentials. We find that the Ehrenfest time diverges logarithmically with the inverse of the Planck constant whenever the equilibrium point is exponentially unstable. For stable equilibrium points, we have a power law divergence with exponent determined by the degree of the potential near the equilibrium point.Comment: 4 pages, 5 figure

Determination of set-membership identifiability sets

International audienceThis paper concerns the concept of set-membership identifiability introduced in \cite{jauberthie}. Given a model, a set-membership identifiable set is a connected set in the parameter domain of the model such that its corresponding trajectories are distinct to trajectories arising from its complementary. For obtaining the so-called set-membership identifiable sets, we propose an algorithm based on interval analysis tools. The proposed algorithm is decomposed into three parts namely {\it mincing}, {\it evaluating} and {\it regularization} (\cite{jaulin2}). The latter step has been modified in order to obtain guaranteed set-membership identifiable sets. Our algorithm will be tested on two examples

Pre-stimulus antero-posterior EEG connectivity predicts performance in a UAV monitoring task

Long monitoring tasks without regular actions, are becoming increasingly common from aircraft pilots to train conductors as these systems grow more automated. These task contexts are challenging for the human operator because they require inputs at irregular and highly interspaced moments even though these actions are often critical. It has been shown that such conditions lead to divided and distracted attentional states which in turn reduce the processing of external stimuli (e.g. alarms) and may lead to miss critical events. In this study we explored to which extent it is possible to predict an operator’s behavioural performance in a Unmanned Aerial Vehicle (UAV) monitoring task using electroencephalographic (EEG) activity. More specifically we investigated the relevance of large-scale EEG connectivity for performance prediction by correlating relative coherence with reaction times (RT). We show that long-range EEG relative coherence, i.e. between occipital and frontal electrodes, is significantly correlated with RT and that different frequency bands exhibit opposite effects. More specifically we observed that coherence between occipital and frontal electrodes was: negatively correlated with RT at 6Hz (theta band), more coherence leading to better performance, and positively correlated with RT at 8Hz (lower alpha band), more coherence leading to worse performance. Our results suggest that EEG connectivity measures could be useful in predicting an operator’s attentional state and her/his performances in ecological settings. Hence these features could potentially be used in a neuro-adaptive interface to improve operator-system interaction and safety in critical systems

Semi-classical analysis and passive imaging

Passive imaging is a new technique which has been proved to be very efficient, for example in seismology: the correlation of the noisy fields, computed from the fields recorded at different points, is strongly related to the Green function of the wave propagation. The aim of this paper is to provide a mathematical context for this approach and to show, in particular, how the methods of semi-classical analysis can be be used in order to find the asymptotic behaviour of the correlations.Comment: Invited paper to appear in NONLINEARITY; Accepted Revised versio

Spectral EEG-based classification for operator dyads workload and cooperation level estimation

There is a growing momentum to design online tools to measure mental workload for neuroergonomic purposes. Most of the research focuses on the monitoring of a single human operator. However, in real-life situations, human operators work in cooperation to optimize safety and performance. This is particularly the case in aviation whereby crews are composed of a pilot flying and a pilot monitoring. The motivation of this study is to evaluate the possibility to apply an hyperscanning approach to estimate the mental workload of crews composed of two operators. We designed an experimental protocol in which ten crews (i.e. 20 subjects) had to perform a modified version of the NASA MATBII during 8 five-minute blocks (i.e. 4 mental workload level configurations * 2 cooperation v. non cooperation conditions). Mental workload and cooperation level were classified using a traditional passive brain-computer interface pipeline that includes a spatial filtering step on frequency features. Our results disclosed that all mental states’ estimations were significantly above chance level. Intra-subject classification accuracy for mental workload (2 classes) was 63% for the pilot flying and 58% for the pilot monitoring. As for cooperation level, the binary classification reached 57% for the pilot flying and 60% for the pilot monitoring. Regarding the team, intra-team classification accuracy of the workload configuration of the team (4-class) reached 35%. As for the team cooperation level, the binary classifier reached 60% of accuracy. The results are discussed in terms of hyperscanning applications

Families of spherical caps: spectra and ray limit

We consider a family of surfaces of revolution ranging between a disc and a hemisphere, that is spherical caps. For this family, we study the spectral density in the ray limit and arrive at a trace formula with geodesic polygons describing the spectral fluctuations. When the caps approach the hemisphere the spectrum becomes equally spaced and highly degenerate whereas the derived trace formula breaks down. We discuss its divergence and also derive a different trace formula for this hemispherical case. We next turn to perturbative corrections in the wave number where the work in the literature is done for either flat domains or curved without boundaries. In the present case, we calculate the leading correction explicitly and incorporate it into the semiclassical expression for the fluctuating part of the spectral density. To the best of our knowledge, this is the first calculation of such perturbative corrections in the case of curvature and boundary.Comment: 28 pages, 7 figure

Dirac Operators and the Calculation of the Connes Metric on arbitrary (Infinite) Graphs

As an outgrowth of our investigation of non-regular spaces within the context of quantum gravity and non-commutative geometry, we develop a graph Hilbert space framework on arbitrary (infinite) graphs and use it to study spectral properties of graph-Laplacians and graph-Dirac-operators. We define a spectral triplet sharing most of the properties of what Connes calls a spectral triple. With the help of this scheme we derive an explicit expression for the Connes-distance function on general directed or undirected graphs. We derive a series of apriori estimates and calculate it for a variety of examples of graphs. As a possibly interesting aside, we show that the natural setting of approaching such problems may be the framework of (non-)linear programming or optimization. We compare our results (arrived at within our particular framework) with the results of other authors and show that the seeming differences depend on the use of different graph-geometries and/or Dirac operators.Comment: 27 pages, Latex, comlementary to an earlier paper, general treatment of directed and undirected graphs, in section 4 a series of general results and estimates concerning the Connes Distance on graphs together with examples and numerical estimate

Entropy of semiclassical measures for nonpositively curved surfaces

We study the asymptotic properties of eigenfunctions of the Laplacian in the case of a compact Riemannian surface of nonpositive sectional curvature. We show that the Kolmogorov-Sinai entropy of a semiclassical measure for the geodesic flow is bounded from below by half of the Ruelle upper bound. We follow the same main strategy as in the Anosov case (arXiv:0809.0230). We focus on the main differences and refer the reader to (arXiv:0809.0230) for the details of analogous lemmas.Comment: 20 pages. This note provides a detailed proof of a result announced in appendix A of a previous work (arXiv:0809.0230, version 2