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We present 50-fs, single-shot measurements of the x-ray thermal diffuse scattering (TDS) from copper foils that have been shocked via nanosecond laser-ablation up to pressures above 135~GPa. We hence deduce the x-ray Debye-Waller (DW) factor, providing a temperature measurement. The targets were laser-shocked with the DiPOLE 100-X laser at the High Energy Density (HED) endstation of the European X-ray Free-Electron Laser (EuXFEL). Single x-ray pulses, with a photon energy of 18 keV, were scattered from the samples and recorded on Varex detectors. Despite the targets being highly textured (as evinced by large variations in the elastic scattering), and with such texture changing upon compression, the absolute intensity of the azimuthally averaged inelastic TDS between the Bragg peaks is largely insensitive to these changes, and, allowing for both Compton scattering and the low-level scattering from a sacrificial ablator layer, provides a reliable measurement of $T/\Theta_D^2$, where $\Theta_D$ is the Debye temperature. We compare our results with the predictions of the SESAME 3336 and LEOS 290 equations of state for copper, and find good agreement within experimental errors. We thus demonstrate that single-shot temperature measurements of dynamically compressed materials can be made via thermal diffuse scattering of XFEL radation., Comment: 17 pages, 9 figures in main article; 10 pages, 5 figures in supplementary material

This paper focuses on a Vision-based Landing task and presents the design and the validation of a dataset that would comply with the Operational Design Domain (ODD) of a Machine-Learning (ML) system. Relying on emerging certification standards, we describe the process for establishing ODDs at both the system and image levels. In the process, we present the translation of high-level system constraints into actionable image-level properties, allowing for the definition of verifiable Data Quality Requirements (DQRs). To illustrate this approach, we use the Landing Approach Runway Detection (LARD) dataset which combines synthetic imagery and real footage, and we focus on the steps required to verify the DQRs. The replicable framework presented in this paper addresses the challenges of designing a dataset compliant with the stringent needs of ML-based systems certification in safety-critical applications., Comment: 12th European Congress on Embedded Real Time Software and Systems, Jun 2024, Toulouse, France. arXiv admin note: text overlap with arXiv:2304.09938

Machine Learning (ML) seems to be one of the most promising solution to automate partially or completely some of the complex tasks currently realized by humans, such as driving vehicles, recognizing voice, etc. It is also an opportunity to implement and embed new capabilities out of the reach of classical implementation techniques. However, ML techniques introduce new potential risks. Therefore, they have only been applied in systems where their benefits are considered worth the increase of risk. In practice, ML techniques raise multiple challenges that could prevent their use in systems submitted to certification constraints. But what are the actual challenges? Can they be overcome by selecting appropriate ML techniques, or by adopting new engineering or certification practices? These are some of the questions addressed by the ML Certification 3 Workgroup (WG) set-up by the Institut de Recherche Technologique Saint Exup\'ery de Toulouse (IRT), as part of the DEEL Project., Comment: 113 pages, White paper

Causal mediation analysis aims to estimate the natural direct and indirect effects under clearly specified assumptions. Traditional mediation analysis based on Ordinary Least Squares (OLS) relies on the absence of unmeasured causes of the putative mediator and outcome. When this assumption cannot be justified, Instrumental Variables (IV) estimators can be used in order to produce an asymptotically unbiased estimator of the mediator-outcome link. However, provided that valid instruments exist, bias removal comes at the cost of variance inflation for standard IV procedures such as Two-Stage Least Squares (TSLS). A Semi-Parametric Stein-Like (SPSL) estimator has been proposed in the literature that strikes a natural trade-off between the unbiasedness of the TSLS procedure and the relatively small variance of the OLS estimator. Moreover, the SPSL has the advantage that its shrinkage parameter can be directly estimated from the data. In this paper, we demonstrate how this Stein-like estimator can be implemented in the context of the estimation of natural direct and natural indirect effects of treatments in randomized controlled trials. The performance of the competing methods is studied in a simulation study, in which both the strength of hidden confounding and the strength of the instruments are independently varied. These considerations are motivated by a trial in mental health evaluating the impact of a primary care-based intervention to reduce depression in the elderly., Comment: 26 pages, 6 figures, 1 table. Presented at the conference of the International Society for Clinical Biostatistics (ISCB 2017)

In the presence of confounders, the ordinary least squares (OLS) estimator is known to be biased. This problem can be remedied by using the two-stage least squares (TSLS) estimator, based on the availability of valid instrumental variables (IVs). This reduction in bias, however, is offset by an increase in variance. Under standard assumptions, the OLS has indeed a larger bias than the TSLS estimator; and moreover, one can prove that the sample variance of the OLS estimator is no greater than the one of the TSLS. Therefore, it is natural to ask whether one could combine the desirable properties of the OLS and TSLS estimators. Such a trade-off can be achieved through a convex combination of these two estimators, thereby producing our proposed convex least squares (CLS) estimator. The relative contribution of the OLS and TSLS estimators is here chosen to minimize a sample estimate of the mean squared error (MSE) of their convex combination. This proportion parameter is proved to be unique, whenever the OLS and TSLS differ in MSEs. Remarkably, we show that this proportion parameter can be estimated from the data, and that the resulting CLS estimator is consistent. We also show how the CLS framework can incorporate other asymptotically unbiased estimators, such as the jackknife IV estimator (JIVE). The finite-sample properties of the CLS estimator are investigated using Monte Carlo simulations, in which we independently vary the amount of confounding and the strength of the instrument. Overall, the CLS estimator is found to outperform the TSLS estimator in terms of MSE. The method is also applied to a classic data set from econometrics, which models the financial return to education., Comment: 33 pages. 8 figures, 1 table. To be presented at UK-CIM (Causal Inference Meeting) in Bristol, in April 2015

In recent years, it has become common practice in neuroscience to use networks to summarize relational information in a set of measurements, typically assumed to be reflective of either functional or structural relationships between regions of interest in the brain. One of the most basic tasks of interest in the analysis of such data is the testing of hypotheses, in answer to questions such as "Is there a difference between the networks of these two groups of subjects?" In the classical setting, where the unit of interest is a scalar or a vector, such questions are answered through the use of familiar two-sample testing strategies. Networks, however, are not Euclidean objects, and hence classical methods do not directly apply. We address this challenge by drawing on concepts and techniques from geometry, and high-dimensional statistical inference. Our work is based on a precise geometric characterization of the space of graph Laplacian matrices and a nonparametric notion of averaging due to Fr\'echet. We motivate and illustrate our resulting methodologies for testing in the context of networks derived from functional neuroimaging data on human subjects from the 1000 Functional Connectomes Project. In particular, we show that this global test is more statistical powerful, than a mass-univariate approach. In addition, we have also provided a method for visualizing the individual contribution of each edge to the overall test statistic., Comment: 34 pages. 5 figures

We consider the problem of distinguishing classical (Erd\H{o}s-R\'{e}nyi) percolation from explosive (Achlioptas) percolation, under noise. A statistical model of percolation is constructed allowing for the birth and death of edges as well as the presence of noise in the observations. This graph-valued stochastic process is composed of a latent and an observed non-stationary process, where the observed graph process is corrupted by Type I and Type II errors. This produces a hidden Markov graph model. We show that for certain choices of parameters controlling the noise, the classical (ER) percolation is visually indistinguishable from the explosive (Achlioptas) percolation model. In this setting, we compare two different criteria for discriminating between these two percolation models, based on a quantile difference (QD) of the first component's size and on the maximal size of the second largest component. We show through data simulations that this second criterion outperforms the QD of the first component's size, in terms of discriminatory power. The maximal size of the second component therefore provides a useful statistic for distinguishing between the ER and Achlioptas models of percolation, under physically motivated conditions for the birth and death of edges, and under noise. The potential application of the proposed criteria for percolation detection in clinical neuroscience is also discussed., Comment: 9 pages and 8 figures. Submitted to Physics Review, Series E

Comparing weighted networks in neuroscience is hard, because the topological properties of a given network are necessarily dependent on the number of edges of that network. This problem arises in the analysis of both weighted and unweighted networks. The term density is often used in this context, in order to refer to the mean edge weight of a weighted network, or to the number of edges in an unweighted one. Comparing families of networks is therefore statistically difficult because differences in topology are necessarily associated with differences in density. In this review paper, we consider this problem from two different perspectives, which include (i) the construction of summary networks, such as how to compute and visualize the mean network from a sample of network-valued data points; and (ii) how to test for topological differences, when two families of networks also exhibit significant differences in density. In the first instance, we show that the issue of summarizing a family of networks can be conducted by adopting a mass-univariate approach, which produces a statistical parametric network (SPN). In the second part of this review, we then highlight the inherent problems associated with the comparison of topological functions of families of networks that differ in density. In particular, we show that a wide range of topological summaries, such as global efficiency and network modularity are highly sensitive to differences in density. Moreover, these problems are not restricted to unweighted metrics, as we demonstrate that the same issues remain present when considering the weighted versions of these metrics. We conclude by encouraging caution, when reporting such statistical comparisons, and by emphasizing the importance of constructing summary networks., Comment: 16 pages, 5 figures

Studies of functional MRI data are increasingly concerned with the estimation of differences in spatio-temporal networks across groups of subjects or experimental conditions. Unsupervised clustering and independent component analysis (ICA) have been used to identify such spatio-temporal networks. While these approaches have been useful for estimating these networks at the subject-level, comparisons over groups or experimental conditions require further methodological development. In this paper, we tackle this problem by showing how self-organizing maps (SOMs) can be compared within a Frechean inferential framework. Here, we summarize the mean SOM in each group as a Frechet mean with respect to a metric on the space of SOMs. We consider the use of different metrics, and introduce two extensions of the classical sum of minimum distance (SMD) between two SOMs, which take into account the spatio-temporal pattern of the fMRI data. The validity of these methods is illustrated on synthetic data. Through these simulations, we show that the three metrics of interest behave as expected, in the sense that the ones capturing temporal, spatial and spatio-temporal aspects of the SOMs are more likely to reach significance under simulated scenarios characterized by temporal, spatial and spatio-temporal differences, respectively. In addition, a re-analysis of a classical experiment on visually-triggered emotions demonstrates the usefulness of this methodology. In this study, the multivariate functional patterns typical of the subjects exposed to pleasant and unpleasant stimuli are found to be more similar than the ones of the subjects exposed to emotionally neutral stimuli. Taken together, these results indicate that our proposed methods can cast new light on existing data by adopting a global analytical perspective on functional MRI paradigms., Comment: 23 pages, 5 figures, 4 tables. Submitted to Neuroimage

The Frechet mean or barycenter generalizes the idea of averaging in spaces where pairwise addition is not well-defined. In general metric spaces, the Frechet sample mean is not a consistent estimator of the theoretical Frechet mean. For graph-valued random variables, for instance, the Frechet sample mean may fail to converge to a unique value. Hence, it becomes necessary to consider the convergence of sequences of sets of graphs. We show that a specific type of almost sure convergence for the Frechet sample mean previously introduced by Ziezold (1977) is, in fact, equivalent to the Kuratowski outer limit of a sequence of Frechet sample means. Equipped with this outer limit, we provide a new proof of the strong consistency of the Frechet sample mean for graph-valued random variables in separable (pseudo-)metric space. Our proof strategy exploits the fact that the metric of interest is bounded, since we are considering graphs over a finite number of vertices. In this setting, we describe two strong laws of large numbers for both the restricted and unrestricted Frechet sample means of all orders, thereby generalizing a previous result, due to Sverdrup-Thygeson (1981)., Comment: 21 pages, 3 figures

In this short note, we study the properties of the weighted Frechet mean as a convex combination operator on an arbitrary metric space, (Y,d). We show that this binary operator is commutative, non-associative, idempotent, invariant to multiplication by a constant weight and possesses an identity element. We also treat the properties of the weighted cumulative Frechet mean. These tools allow us to derive several types of median inequalities for abstract metric spaces that hold for both negative and positive Alexandrov spaces. In particular, we show through an example that these bounds cannot be improved upon in general metric spaces. For weighted Frechet means, however, such inequalities can solely be derived for weights equal or greater than one. This latter limitation highlights the inherent difficulties associated with working with abstract-valued random variables., Comment: 7 pages, 1 figure. Submitted to Probability and Statistics Letters

In a recent paper, Bassett et al. (2011) have analyzed the static and dynamic organization of functional brain networks in humans. We here focus on the first claim made in this paper, which states that the static modular structure of such networks is nested with respect to time. Bassett et al. (2011) argue that this graded structure underlines a "multiscale modular structure". In this letter, however, we show that such a relationship is substantially mediated by an increase in the random variation of the correlation coefficients computed at different time scales., Comment: Submitted as a letter to the Proceedings of the National Academy of Sciences (PNAS)

Parameter ensembles or sets of point estimates constitute one of the cornerstones of modern statistical practice. This is especially the case in Bayesian hierarchical models, where different decision-theoretic frameworks can be deployed to summarize such parameter ensembles. The estimation of these parameter ensembles may thus substantially vary depending on which inferential goals are prioritised by the modeller. In this note, we consider the problem of classifying the elements of a parameter ensemble above or below a given threshold. Two threshold classification losses (TCLs) --weighted and unweighted-- are formulated. The weighted TCL can be used to emphasize the estimation of false positives over false negatives or the converse. We prove that the weighted and unweighted TCLs are optimized by the ensembles of unit-specific posterior quantiles and posterior medians, respectively. In addition, we relate these classification loss functions on parameter ensembles to the concepts of posterior sensitivity and specificity. Finally, we find some relationships between the unweighted TCL and the absolute value loss, which explain why both functions are minimized by posterior medians., Comment: Submitted to Probability and Statistics Letters

Parameter ensembles or sets of random effects constitute one of the cornerstones of modern statistical practice. This is especially the case in Bayesian hierarchical models, where several decision theoretic frameworks can be deployed. The estimation of these parameter ensembles may substantially vary depending on which inferential goals are prioritised by the modeller. Since one may wish to satisfy a range of desiderata, it is therefore of interest to investigate whether some sets of point estimates can simultaneously meet several inferential objectives. In this thesis, we will be especially concerned with identifying ensembles of point estimates that produce good approximations of (i) the true empirical quantiles and empirical quartile ratio (QR) and (ii) provide an accurate classification of the ensemble's elements above and below a given threshold. For this purpose, we review various decision-theoretic frameworks, which have been proposed in the literature in relation to the optimisation of different aspects of the empirical distribution of a parameter ensemble. This includes the constrained Bayes (CB), weighted-rank squared error loss (WRSEL), and triple-goal (GR) ensembles of point estimates. In addition, we also consider the set of maximum likelihood estimates (MLEs) and the ensemble of posterior means --the latter being optimal under the summed squared error loss (SSEL). Firstly, we test the performance of these different sets of point estimates as plug-in estimators for the empirical quantiles and empirical QR under a range of synthetic scenarios encompassing both spatial and non-spatial simulated data sets. Performance evaluation is here conducted using the posterior regret. Secondly, two threshold classification losses (TCLs) --weighted and unweighted-- are formulated and formally optimised. The performance of these decision-theoretic tools is also evaluated on real data sets., Comment: Imperial College London PhD thesis

A statistically principled way of conducting weighted network analysis is still lacking. Comparison of different populations of weighted networks is hard because topology is inherently dependent on wiring cost, where cost is defined as the number of edges in an unweighted graph. In this paper, we evaluate the benefits and limitations associated with using cost-integrated topological metrics. Our focus is on comparing populations of weighted undirected graphs using global efficiency. We evaluate different approaches to the comparison of weighted networks that differ in mean association weight. Our key result shows that integrating over cost is equivalent to controlling for any monotonic transformation of the weight set of a weighted graph. That is, when integrating over cost, we eliminate the differences in topology that may be due to a monotonic transformation of the weight set. Our result holds for any unweighted topological measure. Cost-integration is therefore helpful in disentangling differences in cost from differences in topology. By contrast, we show that the use of the weighted version of a topological metric does not constitute a valid approach to this problem. Indeed, we prove that, under mild conditions, the use of the weighted version of global efficiency is equivalent to simply comparing weighted costs. Thus, we recommend the reporting of (i) differences in weighted costs and (ii) differences in cost-integrated topological measures. We demonstrate the application of these techniques in a re-analysis of an fMRI working memory task. Finally, we discuss the limitations of integrating topology over cost, which may pose problems when some weights are zero, when multiplicities exist in the ranks of the weights, and when one expects subtle cost-dependent topological differences, which could be masked by cost-integration., Comment: Accepted for publication in PLoS one, in June 2011

Graph theory is increasingly commonly utilised in genetics, proteomics and neuroimaging. In such fields, the data of interest generally constitute weighted graphs. Analysis of such weighted graphs often require the integration of topological metrics with respect to the density of the graph. Here, density refers to the proportion of the number of edges present in that graph. When topological metrics based on shortest paths are of interest, such density-integration usually necessitates the iterative application of Dijkstra's algorithm in order to compute the shortest path matrix at each density level. In this short note, we describe a recursive shortest path algorithm based on single edge updating, which replaces the need for the iterative use of Dijkstra's algorithm. Our proposed procedure is based on pairs of breadth-first searches around each of the vertices incident to the edge added at each recursion. An algorithmic analysis of the proposed technique is provided. When the graph of interest is coded as an adjacency list, our algorithm can be shown to be more efficient than an iterative use of Dijkstra's algorithm.

An accident of misidentification has brought to light the interesting system HD 191588, a new RS CVn-type spectroscopic binary. A radial-velocity study of the primary star, the only seen component, carried out at the Observatoire de Haute-Provence with the Coravel instrument and subsequently at the Cambridge Observatories with a similar one, reveals two orbital motions: a short-period orbit (60 days) and a long-period one (about 4.5 years), so this star is a triple system. The following orbital elements are obtained: (1) for the long-period orbit P = 1667+/-17 days, T = 50901 +/-67 MJD, Gamma = +2.09 +/-0.07 km/s, K = 2.51 +/-0.13 km/s, e = 0.18 +/-0.04, omega = 228deg +/- 14 deg, a1 sin i = 56.7 +/- 3.0 Gm, f(m) = 0.0026 +/-0.0004 M_sun, and (2) for the short-period orbit P = 60.0269 +/-0.0016 days, T = 50482.6 +/-3.3 MJD, gamma is var., K = 24.03 +/- 0.09 km/s, e = 0.012 +/-0.004, omega = 233 deg +/-19deg, a1 sin i = 19.83 +/-0.07 Gm, f(m) = 0.0865 +/-0.0009 M_sun. From near-infrared observations we refine the classification of the primary component and we found a spectral type of K2.5 III, and a spectrum obtained in the blue--near-UV spectral region reveals strong H and K emission lines of Ca II. The unseen secondary should be a solar-type star (F or G V); the minimum mass of the third body is that of a dwarf M star. Probably, the primary component rotates in synchronism with the orbital motion in the inner orbit; a model, based upon that hypothesis, is proposed for the system, and finally the connection of the inner binary to the long-period RS CVn group (Hall 1976) is discussed., Comment: 8 pages

The results of long-term surveys of radial velocities of cool Ap and Am stars are presented. There are two samples, one of about 100 Ap stars and the other of 86 Am stars. Both have been observed with the CORAVEL scanner from Observatoire de Haute-Provence (CNRS), France. The conspicuous lack of short-period binaries among cool Ap stars seems confirmed, although this may be the result of an observational bias; one system has a period as short as 1.6 days. A dozen new orbits could be determined, including that of one SB2 system. Considering the mass functions of 68 binaries from the literature and from our work, we conclude that the distribution of the mass ratios is the same for the Bp-Ap stars than for normal G dwarfs. Among the Am stars, we found 52 binaries, i.e. 60%; an orbit could be computed for 29 of them. Among these 29, there are 7 SB2 systems, one triple and one quadruple system. The 21 stars with an apparently constant radial velocity may show up later as long-period binaries with a high eccentricity. The mass functions of the SB1 systems are compatible with cool main-sequence companions, also suggested by ongoing spectral observations., Comment: 5 pages, 2 figures, to appear in: Proc. of the 26th workshop of the European Working Group on CP stars, Contrib. Astr. Obs. Skalnate Pleso Vol. 27, No 3

Orbital elements are presented for the Tc-poor S stars HR 363 (= HD 7351) and HD 191226. With an orbital period of 4592 d (=12.6 y), HR 363 has the longest period known among S stars, and yet it is a strong X-ray source. Its X-ray flux is similar to that of HD 35155, an S star with one of the shortest orbital periods (640 d). This surprising result is put in perspective with other diagnostics of binary interaction observed in binary S stars. They reveal that there is no correlation between the level of binary interaction and the orbital period. This situation may be accounted for if the wind mass-loss rate from the giant is the principal factor controlling the activity level in these (detached) systems, via a stream of matter funneled through the inner Lagragian point., Comment: Astronomy & Astrophysics Supplements, 6 pages, 2 figures, 4 tables (LaTeX A&A). Also available at: http://obswww.unige.ch/~udry/cine/barium/barium.html

We present the first results of a radial-velocity survey of cool Ap and Am stars. HD 8441 is not only a double system with P = 106.357 days, but is a triple one, the third companion having an orbital period larger than 5000 days. Improved orbital elements are given for the classical Ap star HD 137909 = beta CrB by combining our radial velocities with published ones. We yield new orbital elements of the two Am, SB2 binaries HD 43478 and HD 96391. Good estimates of the individual masses of the components of HD 43478 can be given thanks to the eclipses of this system, for which an approximate photometric solution is also proposed., Comment: 10 pages, 10 figures, accepted for publication in A&AS