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Current techniques for exoplanet detection, such as radial ... [more ▼]The search for exoplanets has gained much interest since the first discovery of a planet orbiting the star 51 Peg by Mayor and Queloz in 1995. Current techniques for exoplanet detection, such as radial velocity measurements, are well suited to detect Jupiter-sized planets, but do not have enough sensitivity to discover planets similar to our Earth. The IRSI-Darwin space mission is aimed at filling this gap, by means of nulling interferometry. This special kind of interferometry is intended to suppress all the light coming from a blinding star by means of destructive interference, in order to reveal the star's potential planetary companions. Once the starlight has been properly cancelled, the thermal emission from zodiacal and exo-zodiacal dust clouds becomes the main obstacle to planet detection. Internal modulation is a recent technique devised to suppress such spurious signals. It relies on rapid modulation between the outputs of two nulling interferometers sharing the same telescopes. In the present thesis, a comprehensive investigation of possible configurations of a telescope array with internal modulation has been undertaken, leading to a number of new configurations. As compared to the current {\sc Darwin} configuration, the sensitivity of the interferometer to the planetary signal has been improved by a factor of two, resulting in a fourfold speedup in the detection and characterization of exoplanets. The possibility of designing a nulling interferometer on ESO's Very Large Telescope Interferometer as a technological prerequisite to {\sc Darwin} has also been considered. Signal-to-noise calculations have shown that this instrument could be used to characterize exo-zodiacal clouds down to the 10-zodi level. [less ▲]Detailed reference viewed: 84 (10 ULg) Nulling interferometry with IRSI-Darwin: further study of the aperture configurationsAbsil, Olivier in Surdej, Jean; Swings, Jean-Pierre; Caro, Denise (Eds.) et al 36th Liège International Astrophysics Colloquium (2001)After a brief introduction to nulling interferometry, we emphasize the limitations of this technique for the detection of exoplanets, and the need for internal modulation, a recent technique for fast ... [more ▼]After a brief introduction to nulling interferometry, we emphasize the limitations of this technique for the detection of exoplanets, and the need for internal modulation, a recent technique for fast signal chopping. The principles of internal modulation are then discussed and illustrated with an example. Our contribution to the Darwin mission deals with the study of new aperture configurations using internal modulation. the best two configurations identified among an infinity of new possibilities are presented. As compared to the current Darwin configuration, the sensitivity to the planetary signal is improved by a factor of two, resulting in a fourfold speedup in the detection and characterization of exoplanets. [less ▲]Detailed reference viewed: 15 (2 ULg) Nulling interferometry: impact of exozodiacal clouds on the performance of future life-finding space missionsDefrere, Denis ; Absil, Olivier ; den Hartog, Roland et alin Astronomy and Astrophysics (2010), 509Earth-sized planets around nearby stars are being detected for the first time by ground-based radial velocity and space-based transit surveys. This milestone is opening the path towards the definition of ... [more ▼]Earth-sized planets around nearby stars are being detected for the first time by ground-based radial velocity and space-based transit surveys. This milestone is opening the path towards the definition of missions able to directly detect the light from these planets, with the identification of bio-signatures as one of the main objectives. In that respect, both ESA and NASA have identified nulling interferometry as one of the most promising techniques. The ability to study distant planets will however depend on exozodiacal dust clouds surrounding the target stars. In this paper, we assess the impact of exozodiacal dust clouds on the performance of an infrared nulling interferometer in the Emma X-array configuration. For the nominal mission architecture with 2-m aperture telescopes, we found that point-symmetric exozodiacal dust discs about 100 times denser than the solar zodiacal cloud can be tolerated in order to survey at least 150 targets during the mission lifetime. Considering modeled resonant structures created by an Earth-like planet orbiting at 1 AU around a Sun-like star, we show that the tolerable dust density for planet detection goes down to about 15 times the solar zodiacal density for face-on systems and decreases with the disc inclination. The upper limits on the tolerable exozodiacal dust density derived in this study must be considered as rather pessimistic, but still give a realistic estimation of the typical sensitivity that we will need to reach on exozodiacal discs in order to prepare the scientific programme of future Earth-like planet characterisation missions. [less ▲]Detailed reference viewed: 22 (3 ULg) Nulling interferometry: performance comparison between Antarctica and other ground-based sitesAbsil, Olivier ; Coudé Du Foresto, V.; Barillot, M. et alin Astronomy and Astrophysics (2007), 475Context: Detecting the presence of circumstellar dust around nearby solar-type main sequence stars is an important pre-requisite for the design of future life-finding space missions such as ESA's Darwin ... [more ▼]Context: Detecting the presence of circumstellar dust around nearby solar-type main sequence stars is an important pre-requisite for the design of future life-finding space missions such as ESA's Darwin or NASA's Terrestrial Planet Finder (TPF). The high Antarctic plateau may provide appropriate conditions to perform such a survey from the ground. Aims: We investigate the performance of a nulling interferometer optimised for the detection of exozodiacal discs at Dome C, on the high Antarctic plateau, and compare it to the expected performance of similar instruments at temperate sites. Methods: Based on the currently available measurements of the atmospheric turbulence characteristics at Dome C, we adapt the GENIEsim software (Absil et al. 2006, A&A, 448, 787) to simulate the performance of a nulling interferometer on the high Antarctic plateau. To feed a realistic instrumental configuration into the simulator, we propose a conceptual design for ALADDIN, the Antarctic L-band Astrophysics Discovery Demonstrator for Interferometric Nulling. We assume that this instrument can be placed above the 30-m thick boundary layer, where most of the atmospheric turbulence originates. Results: We show that an optimised nulling interferometer operating on a pair of 1-m class telescopes located 30 m above the ground could achieve a better sensitivity than a similar instrument working with two 8-m class telescopes at a temperate site such as Cerro Paranal. The detection of circumstellar discs about 20 times as dense as our local zodiacal cloud seems within reach for typical Darwin/TPF targets in an integration time of a few hours. Moreover, the exceptional turbulence conditions significantly relax the requirements on real-time control loops, which has favourable consequences on the feasibility of the nulling instrument. Conclusions: The perspectives for high dynamic range, high angular resolution infrared astronomy on the high Antarctic plateau look very promising. [less ▲]Detailed reference viewed: 54 (8 ULg) Nulling interferometry: performance comparison between space and ground-based sites for exozodiacal disc detectionDefrere, Denis ; Absil, Olivier ; Coudé Du Foresto, V. et alin Astronomy and Astrophysics (2008), 490Context: Characterising the circumstellar dust around nearby main sequence stars is a necessary step in understanding the planetary formation process and is crucial for future life-finding space missions ... [more ▼]Context: Characterising the circumstellar dust around nearby main sequence stars is a necessary step in understanding the planetary formation process and is crucial for future life-finding space missions such as ESA's Darwin or NASA's terrestrial planet finder (TPF). Besides paving the technological way to Darwin/TPF, the space-based infrared interferometers Pegase and FKSI (Fourier-Kelvin Stellar Interferometer) will be valuable scientific precursors. Aims: We investigate the performance of Pegase and FKSI for exozodiacal disc detection and compare the results with ground-based nulling interferometers. Methods: We used the GENIEsim software (Absil et al. 2006, A&A, 448, 787) which was designed and validated to study the performance of ground-based nulling interferometers. The software has been adapted to simulate the performance of space-based nulling interferometers by disabling all atmospheric effects and by thoroughly implementing the perturbations induced by payload vibrations in the ambient space environment. Results: Despite using relatively small telescopes (<=0.5 m), Pegase and FKSI are very efficient for exozodiacal disc detection. They are capable of detecting exozodiacal discs 5 and 1 time respectively, as dense as the solar zodiacal cloud, and they outperform any ground-based instrument. Unlike Pegase, FKSI can achieve this sensitivity for most targets of the Darwin/TPF catalogue thanks to an appropriate combination of baseline length and observing wavelength. The sensitivity of Pegase could, however, be significantly boosted by considering a shorter interferometric baseline length. Conclusions: Besides their main scientific goal (characterising hot giant extrasolar planets), the space-based nulling interferometers Pegase and FKSI will be very efficient in assessing within a few minutes the level of circumstellar dust in the habitable zone around nearby main sequence stars down to the density of the solar zodiacal cloud. These space-based interferometers would be complementary to Antarctica-based instruments in terms of sky coverage and would be ideal instruments for preparing future life-finding space missions. [less ▲]Detailed reference viewed: 24 (3 ULg) Nullité et réduction, note sous Rb. Gent, 4 février 2002Biquet, Christine in Journal des Juges de Paix = Tijdschrift van de Vrederecters (2003)Detailed reference viewed: 17 (10 ULg) Number and relative size of thenar motor units estimated by an adapted multiple point stimulation method.Wang, François-Charles ; Delwaide, Paul in Muscle & nerve (1995), 18(9), 969-79An adapted multiple point stimulation (AMPS) method is described for estimating the number and relative size of thenar motor units. With this method, the median nerve was stimulated at various sites from ... [more ▼]An adapted multiple point stimulation (AMPS) method is described for estimating the number and relative size of thenar motor units. With this method, the median nerve was stimulated at various sites from the wrist to the elbow. To avoid alternation, only two or three clearly identifiable surface-recorded motor unit action potentials (S-MUAPs) were recruited at each point by incremental stimulation. A total of 10 S-MUAPs, elicited from four to five distinct stimulation points, was used to calculate the average S-MUAP size. By dividing the maximum M-potential size by that value, a motor unit number estimate (MUNE) was derived. In 59 healthy volunteers, from 19 to 87 years old, the mean average S-MUAP size was 87 +/- 27.6 microV.ms and the mean MUNE was 278 +/- 113 motor units. When performed repeatedly, the results were reproducible. The number of motor units declined exponentially with age while average S-MUAP sizes increased only moderately. To assess the validity of the AMPS method, its results were correlated with those obtained using the F-response technique. The correlation coefficient was 0.83 (P < 0.001). [less ▲]Detailed reference viewed: 10 (2 ULg) Number and relative size of thenar motor units in ALS patients: application of the adapted multiple point stimulation method.Wang, François-Charles ; Delwaide, Paul in Electroencephalography and Clinical Neurophysiology (1998), 109(1), 36-43In the present study, the adapted multiple point stimulation (AMPS) method was first applied to median innervated thenar muscles in 22 amyotrophic lateral sclerosis (ALS) patients who did not received any ... [more ▼]In the present study, the adapted multiple point stimulation (AMPS) method was first applied to median innervated thenar muscles in 22 amyotrophic lateral sclerosis (ALS) patients who did not received any treatment. In all patients, a motor unit number estimate (MUNE) and an average surface-recorded motor unit action potential (S-MUAP) size have been derived even if the denervation was severe; and the results were reproducible. The thenar MUNE was less than the normal lower limit for age in 17 patients, and the mean MUNE (67.1 +/- 90.6) was significantly different from that estimated in control subjects (263.3 +/- 116.8). The mean S-MUAP size in the 22 ALS patients was 352.9 +/- 328.4 microV x ms versus 94.1 +/- 30.3 microV x ms in healthy volunteers. A control AMPS was achieved in 8 patients after 2 and 6 months of a glutamate-release antagonist (riluzole) treatment. The mean loss of motor units, based on control thenar MUNEs realized after 6 months of treatment, was 53%. In conclusion, we propose AMPS as a manageable, reproducible and non-invasive procedure which permits one to quantify peripheral denervation and to appreciate the effectiveness of collateral reinnervation in ALS patients. [less ▲]Detailed reference viewed: 7 (0 ULg) Number of iterations when comparing MLEM/OSEM with FBPSeret, Alain in Journal of Nuclear Medicine : Official Publication, Society of Nuclear Medicine (2004), 45(12), 2125-2125Detailed reference viewed: 60 (5 ULg) Number of representations of a power of a prime by certain integral quaternary quadratic formsPays, Isabelle Conference (1988, June)Detailed reference viewed: 9 (0 ULg) THE NUMBER OF STRUCTURES COMPATIBLE WITH A GIVEN SMALL-ANGLE SCATTERING PATTERNGommes, Cédric Poster (2012, November)Detailed reference viewed: 3 (0 ULg) The number of structures compatible with any correlation functionGommes, Cédric Conference (2013, July)A two-point correlation function provides a crucial yet an incomplete characterization of a microstructure because distinctly different microstructures may have the same correlation function. We address ... [more ▼]A two-point correlation function provides a crucial yet an incomplete characterization of a microstructure because distinctly different microstructures may have the same correlation function. We address here the microstructural degeneracy question: What is the number of microstructures compatible with a specified correlation function? We compute this degeneracy in the framework of reconstruction methods, which enables us to map the problem to the determination of ground-state degeneracies. Since the configuration space of a reconstruction problem is a hypercube on which a Hamming distance is defined, we can calculate analytically the energy profile of any reconstruction problem, corresponding to the average energy of all microstructures at a given Hamming distance from a ground state. The steepness of the energy profile is a measure of the roughness of the energy landscape associated with the reconstruction problem, which can be used as a proxy for the ground-state degeneracy. The relationship between this roughness metric and the ground-state degeneracy is calibrated using a Monte Carlo algorithm for determining the ground-state degeneracy of a variety of microstructures (e.g., realizations of hard disks and Poisson point processes at various densities), as well as with microstructures with a known degeneracy (e.g., single disks of various sizes and a particular crystalline microstructure). We show that our results can be expressed in terms of the information content of the two-point correlation functions. From this perspective, the a priori condition for a reconstruction to be accurate is that the information content, expressed in bits, should be comparable to the number of pixels in the unknown microstructure. We provide a formula to calculate the information content of any two-point correlation function, which makes our results directly applicable by other researchers in the field. [less ▲]Detailed reference viewed: 15 (4 ULg) The number of structures compatible with any given correlation functionGommes, Cédric Conference (2013)Detailed reference viewed: 10 (2 ULg) The number of structures compatible with any given correlation functionGommes, Cédric Scientific conference (2012)Detailed reference viewed: 5 (1 ULg) The Number of Structures Compatible with any Specified Correlation FunctionGommes, Cédric Conference (2015, September)Detailed reference viewed: 12 (1 ULg) The number of subsets required for OSEM reconstruction in nuclear cardiologySeret, Alain in European Journal of Nuclear Medicine and Molecular Imaging (2006), 33(2), 231-231Detailed reference viewed: 51 (2 ULg) Number-Set Representations for Infinite-State VerificationBoigelot, Bernard in Proceedings of VISSAS 2005 (2006)In order to compute the reachability set of infinite-state models, one needs a technique for exploring infinite sequences of transitions in finite time, as well as a symbolic representation for the finite ... [more ▼]In order to compute the reachability set of infinite-state models, one needs a technique for exploring infinite sequences of transitions in finite time, as well as a symbolic representation for the finite and infinite sets of configurations that are to be handled. The representation problem can be solved by automata-based methods, which consist in representing a set by a finite-state machine recognizing its elements, suitably encoded as words over a finite alphabet. Automata-based set representations have many advantages: They are expressive, easy to manipulate, and admit a canonical form. In this survey, we describe two automata-based structures that have been developed for representing sets of numbers (or, more generally, of vectors): The Number Decision Diagram (NDD) for integer values, and the Real Vector Automaton (RVA) for real numbers. We discuss the expressiveness of these structures, present some construction algorithms, and give a brief introduction to some related acceleration techniques. [less ▲]Detailed reference viewed: 12 (2 ULg) A numeration point of view on the HD0L periodicity problemCharlier, Emilie Scientific conference (2011, January)A HD0L system is a 5-tuple G = (∆, Γ, f, g, w) where • ∆ and Γ are alphabet; • f : ∆^∗ → ∆^∗ is a morphism; • g : ∆^∗ → Γ^∗ is a morphism; • w is a finite word over ∆. If w is a prefix of f(w) and if g(f ... [more ▼]A HD0L system is a 5-tuple G = (∆, Γ, f, g, w) where • ∆ and Γ are alphabet; • f : ∆^∗ → ∆^∗ is a morphism; • g : ∆^∗ → Γ^∗ is a morphism; • w is a finite word over ∆. If w is a prefix of f(w) and if g(f^ω(w)) is an infinite word over Γ, where f^ω(w) denotes the limit lim_{n→+∞}f^n(w), then we define the infinite word generated by G to be ω(G) = g(f^ω(w)). The question is to decide whether the infinite word ω(G) is ultimately periodic. This open problem is called the HD0L periodicity problem. It is not hard to see that we may assume that w is a letter. Furthermore, it is well known that we can assume that f is a non-erasing morphism and g is a coding. Therefore we will always consider that all these additional hypotheses hold. On the one hand, if f is uniform of length b, then ω(G) is b-automatic. In that particular case the problem is known to be decidable. Various proofs of this result have been given by several authors. On the other hand, in the general case, when f is not necessarily uniform, ω(G) is S-automatic for some abstract numeration system S. Therefore the HD0L periodicity problem is equivalent to the following problem involving numeration systems. Given an abstract numeration system S, is it decidable whether an S-recognizable set X ⊆ N is ultimately periodic? The numeration language L and the set X are given through DFAs accepting L and rep_S(X) respectively. Thanks to this numeration point of view, we can give decision procedures for large classes of numeration systems. In this talk, I will discuss some techniques used to provide such decision procedures. [less ▲]Detailed reference viewed: 23 (1 ULg) Numeration systems on a regular language : Arithmetic operations, Recognizability and Formal power seriesRigo, Michel in Theoretical Computer Science (2001), 269Generalizations of numeration systems in which $$\N$$ is recognizable by a finite automaton are obtained by describing a lexicographically ordered infinite regular language $$L\subset \Sigma^*$$. For ... [more ▼]Generalizations of numeration systems in which $$\N$$ is recognizable by a finite automaton are obtained by describing a lexicographically ordered infinite regular language $$L\subset \Sigma^*$$. For these systems, we obtain a characterization of recognizable sets of integers in terms of $\N$-rational formal series. After a study of the polynomial regular languages, we show that, if the complexity of $$L$$ is $$\Theta (n^l)$$ (resp. if $$L$$ is the complement of a polynomial language), then multiplication by $$\lambda\in \N$$ preserves recognizability only if $$\lambda=\beta^{l+1}$$ (resp. if $$\lambda\neq (\#\Sigma)^\beta$$) for some $$\beta\in \N$$. Finally, we obtain sufficient conditions for the notions of recognizability for abstract systems and some positional number systems to be equivalent. [less ▲]Detailed reference viewed: 29 (2 ULg) Numeration systems: a link between number theory and formal language theoryRigo, Michel Scientific conference (2012, November 28)In this talk, we survey facts mostly emerging from the seminal results of Alan Cobham obtained in the late sixties and early seventies about sets of integers whose base k expansions are recognized by some ... [more ▼]In this talk, we survey facts mostly emerging from the seminal results of Alan Cobham obtained in the late sixties and early seventies about sets of integers whose base k expansions are recognized by some finite automaton. We do not expect any background from the audience, so we will present the basic definitions and many examples. We will not attempt to be exhaustive but try instead to present some actual research directions about numeration systems, recognizable sets of integers and automatic sequences. If there is enough time, we will brieﬂy sketch some results about transcendence related to the representation of real numbers. [less ▲]Detailed reference viewed: 70 (6 ULg)