3 results
(Almost) complete characterization of the stability of a discrete-time Hawkes process with inhibition and memory of length two
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- Manon Costa, Pascal Maillard, Anthony Muraro
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- Journal:
- Journal of Applied Probability , First View
- Published online by Cambridge University Press:
- 24 May 2024, pp. 1-22
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We consider a Poisson autoregressive process whose parameters depend on the past of the trajectory. We allow these parameters to take negative values, modelling inhibition. More precisely, the model is the stochastic process $(X_n)_{n\ge0}$ with parameters $a_1,\ldots,a_p \in \mathbb{R}$, $p\in\mathbb{N}$, and $\lambda \ge 0$, such that, for all $n\ge p$, conditioned on $X_0,\ldots,X_{n-1}$, $X_n$ is Poisson distributed with parameter $(a_1 X_{n-1} + \cdots + a_p X_{n-p} + \lambda)_+$. This process can be regarded as a discrete-time Hawkes process with inhibition and a memory of length p. In this paper we initiate the study of necessary and sufficient conditions of stability for these processes, which seems to be a hard problem in general. We consider specifically the case $p = 2$, for which we are able to classify the asymptotic behavior of the process for the whole range of parameters, except for boundary cases. In particular, we show that the process remains stochastically bounded whenever the solution to the linear recurrence equation $x_n = a_1x_{n-1} + a_2x_{n-2} + \lambda$ remains bounded, but the converse is not true. Furthermore, the criterion for stochastic boundedness is not symmetric in $a_1$ and $a_2$, in contrast to the case of non-negative parameters, illustrating the complex effects of inhibition.
X-ray powder diffraction investigation of new oxynitride precursors: rare earth oxide compounds of fluorite- and sheelite-type structures in the Yb-(Zr,W)-O system
- Pascal Maillard, Patricia Bénard-Rocherullé, Thierry Roisnel, Franck Tessier
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- Journal:
- Powder Diffraction / Volume 22 / Issue 4 / December 2007
- Published online by Cambridge University Press:
- 01 March 2012, pp. 344-351
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Nanocrystallized oxide precursors of colored (oxy)nitrides related to the system Yb-(Zr-W)-O have been successfully prepared using a chimie douce process—the amorphous citrate route. The process involves first a formation of fine and homogeneous powdered solids obtained by calcination at 600 °C, a temperature much lower than that of the conventional solid-state method. At this stage, the X-ray diffraction patterns exhibit large line broadening effects. Finally, two well-crystallized and pure quaternary oxides have been readily obtained by heating and under annealing conditions at 850 and 900 °C for 12 h. For one of the patterns, all the X-ray diffraction lines can be easily indexed to a cubic phase with the fluorite structure conforming to the Fm3m space group [Yb2Zr1.21W0.41O6.65◻1.35 called C-phase: a=5.1864(2) Å]. The second phase adopts the sheelite-type structure [Yb2ZrWO8 called T-phase: space group I41/a, a=5.1584(5), and c=10.8246(6) Å]. By taking into account the present compositions determined by EDS measurements, Rietveld structure refinements produce final RB factors of 0.015 and 0.044, and Rwp factors of 0.069 and 0.089, respectively. In order to characterize the microstructure of the materials (crystallite size and lattice distortion) at the nanometer scale, a study based on diffraction line broadening analysis applying the whole pattern refinement method was also undertaken with confidence. The results show smooth angular variations of the values of FWHMs, indicating that the microstructural properties are isotropic for the cubic and tetragonal oxides. More precisely, the results indicate that whatever the profile fitting approach used (“profile matching” procedure and Rietveld method), the reliability factors Rwp are systematically better with a combined size strain than with zero strain considerations. The strain magnitudes observed for the C-phase-850 °C as well as for the T-phase-900 °C should be viewed as realistic strain.
The science of EChO
- Giovanna Tinetti, James Y-K. Cho, Caitlin A. Griffith, Olivier Grasset, Lee Grenfell, Tristan Guillot, Tommi T. Koskinen, Julianne I. Moses, David Pinfield, Jonathan Tennyson, Marcell Tessenyi, Robin Wordsworth, Alan Aylward, Roy van Boekel, Angioletta Coradini, Therese Encrenaz, Ignas Snellen, Maria R. Zapatero-Osorio, Jeroen Bouwman, Vincent Coudé du Foresto, Mercedes Lopez-Morales, Ingo Mueller-Wodarg, Enric Pallé, Franck Selsis, Alessandro Sozzetti, Jean-Philippe Beaulieu, Thomas Henning, Michael Meyer, Giuseppina Micela, Ignasi Ribas, Daphne Stam, Mark Swain, Oliver Krause, Marc Ollivier, Emanuele Pace, Bruce Swinyard, Peter A.R. Ade, Nick Achilleos, Alberto Adriani, Craig B. Agnor, Cristina Afonso, Carlos Allende Prieto, Gaspar Bakos, Robert J. Barber, Michael Barlow, Peter Bernath, Bruno Bézard, Pascal Bordé, Linda R. Brown, Arnaud Cassan, Céline Cavarroc, Angela Ciaravella, Charles Cockell, Athéna Coustenis, Camilla Danielski, Leen Decin, Remco De Kok, Olivier Demangeon, Pieter Deroo, Peter Doel, Pierre Drossart, Leigh N. Fletcher, Matteo Focardi, Francois Forget, Steve Fossey, Pascal Fouqué, James Frith, Marina Galand, Patrick Gaulme, Jonay I. González Hernández, Davide Grassi, Matt J. Griffin, Ulrich Grözinger, Manuel Guedel, Pactrick Guio, Olivier Hainaut, Robert Hargreaves, Peter H. Hauschildt, Kevin Heng, David Heyrovsky, Ricardo Hueso, Pat Irwin, Lisa Kaltenegger, Patrick Kervella, David Kipping, Geza Kovacs, Antonino La Barbera, Helmut Lammer, Emmanuel Lellouch, Giuseppe Leto, Mercedes Lopez Morales, Miguel A. Lopez Valverde, Manuel Lopez-Puertas, Christophe Lovi, Antonio Maggio, Jean-Pierre Maillard, Jesus Maldonado Prado, Jean-Baptiste Marquette, Francisco J. Martin-Torres, Pierre Maxted, Steve Miller, Sergio Molinari, David Montes, Amaya Moro-Martin, Olivier Mousis, Napoléon Nguyen Tuong, Richard Nelson, Glenn S. Orton, Eric Pantin, Enzo Pascale, Stefano Pezzuto, Ennio Poretti, Raman Prinja, Loredana Prisinzano, Jean-Michel Réess, Ansgar Reiners, Benjamin Samuel, Jorge Sanz Forcada, Dimitar Sasselov, Giorgio Savini, Bruno Sicardy, Alan Smith, Lars Stixrude, Giovanni Strazzulla, Gautam Vasisht, Sandrine Vinatier, Serena Viti, Ingo Waldmann, Glenn J. White, Thomas Widemann, Roger Yelle, Yuk Yung, Sergey Yurchenko
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- Journal:
- Proceedings of the International Astronomical Union / Volume 6 / Issue S276 / October 2010
- Published online by Cambridge University Press:
- 10 November 2011, pp. 359-370
- Print publication:
- October 2010
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The science of extra-solar planets is one of the most rapidly changing areas of astrophysics and since 1995 the number of planets known has increased by almost two orders of magnitude. A combination of ground-based surveys and dedicated space missions has resulted in 560-plus planets being detected, and over 1200 that await confirmation. NASA's Kepler mission has opened up the possibility of discovering Earth-like planets in the habitable zone around some of the 100,000 stars it is surveying during its 3 to 4-year lifetime. The new ESA's Gaia mission is expected to discover thousands of new planets around stars within 200 parsecs of the Sun. The key challenge now is moving on from discovery, important though that remains, to characterisation: what are these planets actually like, and why are they as they are?
In the past ten years, we have learned how to obtain the first spectra of exoplanets using transit transmission and emission spectroscopy. With the high stability of Spitzer, Hubble, and large ground-based telescopes the spectra of bright close-in massive planets can be obtained and species like water vapour, methane, carbon monoxide and dioxide have been detected. With transit science came the first tangible remote sensing of these planetary bodies and so one can start to extrapolate from what has been learnt from Solar System probes to what one might plan to learn about their faraway siblings. As we learn more about the atmospheres, surfaces and near-surfaces of these remote bodies, we will begin to build up a clearer picture of their construction, history and suitability for life.
The Exoplanet Characterisation Observatory, EChO, will be the first dedicated mission to investigate the physics and chemistry of Exoplanetary Atmospheres. By characterising spectroscopically more bodies in different environments we will take detailed planetology out of the Solar System and into the Galaxy as a whole.
EChO has now been selected by the European Space Agency to be assessed as one of four M3 mission candidates.