Extensions of tempered representations

Let $\pi, \pi'$ be irreducible tempered representations of an affine Hecke algebra H with positive parameters. We compute the higher extension groups $Ext_H^n (\pi,\pi')$ explicitly in terms of the representations of analytic R-groups corresponding to $\pi$ and $\pi'$. The result has immediate applications to the computation of the Euler-Poincar\'e pairing $EP(\pi,\pi')$, the alternating sum of the dimensions of the Ext-groups. The resulting formula for $EP(\pi,\pi')$ is equal to Arthur's formula for the elliptic pairing of tempered characters in the setting of reductive p-adic groups. Our proof applies equally well to affine Hecke algebras and to reductive groups over non-archimedean local fields of arbitrary characteristic. This sheds new light on the formula of Arthur and gives a new proof of Kazhdan's orthogonality conjecture for the Euler-Poincar\'e pairing of admissible characters.Comment: This paper grew out of "A formula of Arthur and affine Hecke algebras" (arXiv:1011.0679). In the second version some minor points were improve

Spitzer Mid-Infrared Photometry of 500 - 750 K Brown Dwarfs

Mid-infrared data, including Spitzer warm-IRAC [3.6] and [4.5] photometry, is critical for understanding the cold population of brown dwarfs now being found, objects which have more in common with planets than stars. As effective temperature (T_eff) drops from 800 K to 400 K, the fraction of flux emitted beyond 3 microns increases rapidly, from about 40% to >75%. This rapid increase makes a color like H-[4.5] a very sensitive temperature indicator, and it can be combined with a gravity- and metallicity-sensitive color like H-K to constrain all three of these fundamental properties, which in turn gives us mass and age for these slowly cooling objects. Determination of mid-infrared color trends also allows better exploitation of the WISE mission by the community. We use new Spitzer Cycle 6 IRAC photometry, together with published data, to present trends of color with type for L0 to T10 dwarfs. We also use the atmospheric and evolutionary models of Saumon & Marley to investigate the masses and ages of 13 very late-type T dwarfs, which have H-[4.5] > 3.2 and T_eff ~ 500 K to 750 K.Comment: To be published in the on-line version of the Proceedings of Cool Stars 16 (ASP Conference Series). This is an updated version of Leggett et al. 2010 ApJ 710 1627; a photometry compilation is available at http://www.gemini.edu/staff/slegget

Extending the Canada-France brown Dwarfs Survey to the near-infrared: first ultracool brown dwarfs from CFBDSIR

We present the first results of the ongoing Canada-France Brown Dwarfs Survey-InfraRed, hereafter CFBDSIR, a Near InfraRed extension to the optical wide-field survey CFBDS. Our final objectives are to constrain ultracool atmosphere physics by finding a statistically significant sample of objects cooler than 650K and to explore the ultracool brown dwarf mass function building on a well defined sample of such objects. Candidates are identified in CFHT/WIRCam J and CFHT/MegaCam z' images using optimised psf-fitting, and we follow them up with pointed near infrared imaging with SOFI at NTT. We finally obtain low resolution spectroscopy of the coolest candidates to characterise their atmospheric physics. We have so far analysed and followed up all candidates on the first 66 square degrees of the 335 square degrees survey. We identified 55 T-dwarfs candidates with z'-J > 3:5 and have confirmed six of them as T-dwarfs, including 3 that are strong later-than-T8 candidates, based on their far-red and NIR colours. We also present here the NIR spectra of one of these ultracool dwarfs, CFBDSIR1458+1013 which confirms it as one of the coolest brown dwarf known, possibly in the 550-600K temperature range. From the completed survey we expect to discover 10 to 15 dwarfs later than T8, more than doubling the known number of such objects. This will enable detailed studies of their extreme atmospheric properties and provide a stronger statistical base for studies of their luminosity function.Comment: A&A, Accepte

The SPHERE data center: a reference for high contrast imaging processing

The objective of the SPHERE Data Center is to optimize the scientific return of SPHERE at the VLT, by providing optimized reduction procedures, services to users and publicly available reduced data. This paper describes our motivation, the implementation of the service (partners, infrastructure and developments), services, description of the on-line data, and future developments. The SPHERE Data Center is operational and has already provided reduced data with a good reactivity to many observers. The first public reduced data have been made available in 2017. The SPHERE Data Center is gathering a strong expertise on SPHERE data and is in a very good position to propose new reduced data in the future, as well as improved reduction procedures.Comment: SF2A proceeding

Meson Condensation in Dense Matter Revisited

The results for meson condensation in the literature vary markedly depending on whether one uses chiral perturbation theory or the current-algebra-plus-PCAC approach. To elucidate the origin of this discrepancy, we re-examine the role of the sigma-term in meson condensation. We find that the resolution of the existing discrepancy requires a knowledge of terms in the Lagrangian that are higher order in density than hitherto considered.Comment: 10pages, USC(NT)-94-

Extrasolar planets and brown dwarfs around A--F type stars. VIII. A giant planet orbiting the young star HD113337

In the frame of the search for extrasolar planets and brown dwarfs around early-type main-sequence stars, we present the detection of a giant planet around the young F-type star HD113337. We estimated the age of the system to be 150 +100/-50 Myr. Interestingly, an IR excess attributed to a cold debris disk was previously detected on this star. The SOPHIE spectrograph on the 1.93m telescope at Observatoire de Haute-Provence was used to obtain ~300 spectra over 6 years. We used our SAFIR tool, dedicated to the spectra analysis of A and F stars, to derive the radial velocity variations. The data reveal a 324.0 +1.7/-3.3 days period that we attribute to a giant planet with a minimum mass of 2.83 +- 0.24 Mjup in an eccentric orbit with e=0.46 +- 0.04. A long-term quadratic drift, that we assign to be probably of stellar origin, is superimposed to the Keplerian solution.Comment: 7 pages, 4 figure

A Markovian event-based framework for stochastic spiking neural networks

In spiking neural networks, the information is conveyed by the spike times, that depend on the intrinsic dynamics of each neuron, the input they receive and on the connections between neurons. In this article we study the Markovian nature of the sequence of spike times in stochastic neural networks, and in particular the ability to deduce from a spike train the next spike time, and therefore produce a description of the network activity only based on the spike times regardless of the membrane potential process. To study this question in a rigorous manner, we introduce and study an event-based description of networks of noisy integrate-and-fire neurons, i.e. that is based on the computation of the spike times. We show that the firing times of the neurons in the networks constitute a Markov chain, whose transition probability is related to the probability distribution of the interspike interval of the neurons in the network. In the cases where the Markovian model can be developed, the transition probability is explicitly derived in such classical cases of neural networks as the linear integrate-and-fire neuron models with excitatory and inhibitory interactions, for different types of synapses, possibly featuring noisy synaptic integration, transmission delays and absolute and relative refractory period. This covers most of the cases that have been investigated in the event-based description of spiking deterministic neural networks

The SOPHIE search for northern extrasolar planets VIII. A warm Neptune orbiting HD164595

High-precision radial velocity surveys explore the population of low-mass exoplanets orbiting bright stars. This allows accurately deriving their orbital parameters such as their occurrence rate and the statistical distribution of their properties. Based on this, models of planetary formation and evolution can be constrained. The SOPHIE spectrograph has been continuously improved in past years, and thanks to an appropriate correction of systematic instrumental drift, it is now reaching 2 m/s precision in radial velocity measurements on all timescales. As part of a dedicated radial velocity survey devoted to search for low-mass planets around a sample of 190 bright solar-type stars in the northern hemisphere, we report the detection of a warm Neptune with a minimum mass of 16.1 +- 2.7 Mearth orbiting the solar analog HD164595 in 40 +- 0.24 days . We also revised the parameters of the multiplanetary system around HD190360. We discuss this new detection in the context of the upcoming space mission CHEOPS, which is devoted to a transit search of bright stars harboring known exoplanets.Comment: 11 pages, 9 figure

Numerical Solution of Differential Equations by the Parker-Sochacki Method

A tutorial is presented which demonstrates the theory and usage of the Parker-Sochacki method of numerically solving systems of differential equations. Solutions are demonstrated for the case of projectile motion in air, and for the classical Newtonian N-body problem with mutual gravitational attraction.Comment: Added in July 2010: This tutorial has been posted since 1998 on a university web site, but has now been cited and praised in one or more refereed journals. I am therefore submitting it to the Cornell arXiv so that it may be read in response to its citations. See "Spiking neural network simulation: numerical integration with the Parker-Sochacki method:" J. Comput Neurosci, Robert D. Stewart & Wyeth Bair and http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2717378

The SOPHIE search for northern extrasolar planets VIII. Follow-up of ELODIE candidates: long-period brown-dwarf companions

Long-period brown dwarf companions detected in radial velocity surveys are important targets for direct imaging and astrometry to calibrate the mass-luminosity relation of substellar objects. Through a 20-year radial velocity monitoring of solar-type stars that began with ELODIE and was extended with SOPHIE spectrographs, giant exoplanets and brown dwarfs with orbital periods longer than ten years are discovered. We report the detection of five new potential brown dwarfs with minimum masses between 32 and 83 Jupiter mass orbiting solar-type stars with periods longer than ten years. An upper mass limit of these companions is provided using astrometric Hipparcos data, high-angular resolution imaging made with PUEO, and a deep analysis of the cross-correlation function of the main stellar spectra to search for blend effects or faint secondary components. These objects double the number of known brown dwarf companions with orbital periods longer than ten years and reinforce the conclusion that the occurrence of such objects increases with orbital separation. With a projected separation larger than 100 mas, all these brown dwarf candidates are appropriate targets for high-contrast and high angular resolution imaging.Comment: 17 pages, 9 figures, accepted in A&