Nonnegative 3-way tensor factorization via conjugate gradient with globally optimal stepsize

International audienceThis paper deals with the minimal polyadic decomposition (also known as canonical decomposition or Parafac) of a 3-way array, assuming each entry is positive. In this case, the low-rank approximation problem becomes well-posed. The suggested approach consists of taking into account the nonnegative nature of the loading matrices directly in the problem parameterization. Then, the three gradient components are derived allowing to efficiently implement the decomposition using classical optimization algorithms. In our case, we focus on the conjugate gradient algorithm, well matched to large problems. The good behaviour of the proposed approach is illustrated through computer simulations in the context of data analysis and compared to other existing approaches

Computing the nonnegative 3-way tensor factorization using Tikhonov regularization

International audienceThis paper deals with the minimum polyadic decomposition of a nonnegative three-way array. The main advantage of the nonnegativity constraint is that the approximation problem becomes well posed. To tackle this problem, we suggest the use of a cost function including penalty terms built with matrix exponentials. Gradient components are then derived, allowing to efficiently implement the decomposition using classical optimization algorithms. In our case, Alternating Least Squares (ALS) and conjugate gradient algorithms are studied and compared with another existing algorithm, thanks to computer simulations performed in the context of data analysis

Computing the polyadic decomposition of nonnegative third order tensors

International audienceComputing the minimal polyadic decomposition (also often referred to as canonical decomposition, or sometimes Parafac) amounts to finding the global minimum of a coercive polynomial in many variables. In the case of arrays with nonnegative entries, the low-rank approximation problem is well posed. In addition, due to the large dimension of the problem, the decomposition can be rather efficiently calculated with the help of preconditioned nonlinear conjugate gradient algorithms, as subsequently shown, if equipped with an algebraic calculation of the globally optimal stepsize in low dimension. Other algorithms are also studied (gradient and quasi-Newton approaches) for comparisons. Two versions of each algorithm are considered: the Enhanced Line Search version (ELS), and the backtracking version alternating with ELS. Computer simulations are provided and demonstrate the good behavior of these algorithms dedicated to nonnegative arrays, compared to others put forward in the literature. Finally, applications in the context of data analysis illustrate various algorithms. The main advantage of the suggested approach is to explicitly take into account the nonnegative nature of the loading matrices in the problem parameterization, instead of enforcing positive entries by projection. According to the experiments we have run, such an approach also happens to be more robust with respect to possible modeling errors

Error Analysis of Low-rank Three-Way Tensor Factorization Approach to Blind Source Separation

International audienceIn tensor factorization approaches to blind separation of multidimensional sources, two formulas for calculating the source tensor have emerged. In practice, it is observed that these two schemes exhibit different levels of robustness against perturbations of the factors involved in the tensor model. Motivated by both practical reasons and the will to better figure this out, we present error analyses in source tensor estimation performed by low-rank factorization of three-way tensors. To that aim, computer simulations as well as the analytical calculation of the theoretical error are carried out. The conclusions drawn from these numerical and analytical error analyses are supported by the results obtained thanks to tensor-based blind decomposition of an experimental multispectral image of a skin tumor

Water analysis with the help of tensor canonical decompositions

Coopération universitaire et scientifique Franco-VietnamienneInternational audienceRaw data are collected in five measurement locations along the Var river. It is assumed that some locations interact with each other, whereas others do not. In such a context, we are interested in determining the contribution of each location and in better understanding the water exchanges that are involved. Organic components can also be identified thanks to methods such as Canonical Polyadic decompositions (CP) (sometimes known as Parafac), applied to 3D fluorescence spectra calculated from the collected samples. The expected impact is a more efficient detection of polluting matters in water

The SuperCam Instrument Suite on the Mars 2020 Rover: Science Objectives and Mast-Unit Description

On the NASA 2020 rover mission to Jezero crater, the remote determination of the texture, mineralogy and chemistry of rocks is essential to quickly and thoroughly characterize an area and to optimize the selection of samples for return to Earth. As part of the Perseverance payload, SuperCam is a suite of five techniques that provide critical and complementary observations via Laser-Induced Breakdown Spectroscopy (LIBS), Time-Resolved Raman and Luminescence (TRR/L), visible and near-infrared spectroscopy (VISIR), high-resolution color imaging (RMI), and acoustic recording (MIC). SuperCam operates at remote distances, primarily 2-7 m, while providing data at sub-mm to mm scales. We report on SuperCam's science objectives in the context of the Mars 2020 mission goals and ways the different techniques can address these questions. The instrument is made up of three separate subsystems: the Mast Unit is designed and built in France; the Body Unit is provided by the United States; the calibration target holder is contributed by Spain, and the targets themselves by the entire science team. This publication focuses on the design, development, and tests of the Mast Unit; companion papers describe the other units. The goal of this work is to provide an understanding of the technical choices made, the constraints that were imposed, and ultimately the validated performance of the flight model as it leaves Earth, and it will serve as the foundation for Mars operations and future processing of the data.In France was provided by the Centre National d'Etudes Spatiales (CNES). Human resources were provided in part by the Centre National de la Recherche Scientifique (CNRS) and universities. Funding was provided in the US by NASA's Mars Exploration Program. Some funding of data analyses at Los Alamos National Laboratory (LANL) was provided by laboratory-directed research and development funds

A search for resonances decaying into a Higgs boson and a new particle X in the XH→qqbb final state with the ATLAS detector

A search for heavy resonances decaying into a Higgs boson ($H$) and a new particle ($X$) is reported, utilizing 36.1 fb$^{-1}$ of proton-proton collision data at $\sqrt{s} =$ 13 TeV collected during 2015 and 2016 with the ATLAS detector at the CERN Large Hadron Collider. The particle $X$ is assumed to decay to a pair of light quarks, and the fully hadronic final state $XH \rightarrow q\bar q'b\bar b$ is analysed. The search considers the regime of high $XH$ resonance masses, where the $X$ and $H$ bosons are both highly Lorentz-boosted and are each reconstructed using a single jet with large radius parameter. A two-dimensional phase space of $XH$ mass versus $X$ mass is scanned for evidence of a signal, over a range of $XH$ resonance mass values between 1 TeV and 4 TeV, and for $X$ particles with masses from 50 GeV to 1000 GeV. All search results are consistent with the expectations for the background due to Standard Model processes, and 95% CL upper limits are set, as a function of $XH$ and $X$ masses, on the production cross-section of the $XH\rightarrow q\bar q'b\bar b$ resonance

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements

TRY plant trait database – enhanced coverage and open access

Plant traits - the morphological, anatomical, physiological, biochemical and phenological characteristics of plants - determine how plants respond to environmental factors, affect other trophic levels, and influence ecosystem properties and their benefits and detriments to people. Plant trait data thus represent the basis for a vast area of research spanning from evolutionary biology, community and functional ecology, to biodiversity conservation, ecosystem and landscape management, restoration, biogeography and earth system modelling. Since its foundation in 2007, the TRY database of plant traits has grown continuously. It now provides unprecedented data coverage under an open access data policy and is the main plant trait database used by the research community worldwide. Increasingly, the TRY database also supports new frontiers of trait‐based plant research, including the identification of data gaps and the subsequent mobilization or measurement of new data. To support this development, in this article we evaluate the extent of the trait data compiled in TRY and analyse emerging patterns of data coverage and representativeness. Best species coverage is achieved for categorical traits - almost complete coverage for ‘plant growth form’. However, most traits relevant for ecology and vegetation modelling are characterized by continuous intraspecific variation and trait–environmental relationships. These traits have to be measured on individual plants in their respective environment. Despite unprecedented data coverage, we observe a humbling lack of completeness and representativeness of these continuous traits in many aspects. We, therefore, conclude that reducing data gaps and biases in the TRY database remains a key challenge and requires a coordinated approach to data mobilization and trait measurements. This can only be achieved in collaboration with other initiatives

Determination of the strong coupling constant αs from transverse energy–energy correlations in multijet events at s√=8 TeV using the ATLAS detector

Measurements of transverse energy–energy correlations and their associated asymmetries in multi-jet events using the ATLAS detector at the LHC are presented. The data used correspond to s√=8 TeV proton–proton collisions with an integrated luminosity of 20.2 fb−1 . The results are presented in bins of the scalar sum of the transverse momenta of the two leading jets, unfolded to the particle level and compared to the predictions from Monte Carlo simulations. A comparison with next-to-leading-order perturbative QCD is also performed, showing excellent agreement within the uncertainties. From this comparison, the value of the strong coupling constant is extracted for different energy regimes, thus testing the running of αs(μ) predicted in QCD up to scales over 1 TeV . A global fit to the transverse energy–energy correlation distributions yields αs(mZ)=0.1162±0.0011(exp.) +0.0084−0.0070(theo.) , while a global fit to the asymmetry distributions yields a value of αs(mZ)=0.1196±0.0013(exp.) +0.0075−0.0045(theo.)