Asymptotic normality of kernel estimates in a regression model for random fields

We establish the asymptotic normality of the regression estimator in a fixed-design setting when the errors are given by a field of dependent random variables. The result applies to martingale-difference or strongly mixing random fields. On this basis, a statistical test that can be applied to image analysis is also presented.Comment: 20 page

Maximum a posteriori estimation through simulated annealing for binary asteroid orbit determination

This paper considers a new method for the binary asteroid orbit determination problem. The method is based on the Bayesian approach with a global optimisation algorithm. The orbital parameters to be determined are modelled through an a posteriori distribution made of a priori and likelihood terms. The first term constrains the parameters space and it allows the introduction of available knowledge about the orbit. The second term is based on given observations and it allows us to use and compare different observational error models. Once the a posteriori model is built, the estimator of the orbital parameters is computed using a global optimisation procedure: the simulated annealing algorithm. The maximum a posteriori (MAP) techniques are verified using simulated and real data. The obtained results validate the proposed method. The new approach guarantees independence of the initial parameters estimation and theoretical convergence towards the global optimisation solution. It is particularly useful in these situations, whenever a good initial orbit estimation is difficult to get, whenever observations are not well-sampled, and whenever the statistical behaviour of the observational errors cannot be stated Gaussian like.Comment: Accepted for publication in Monthly Notices of the Royal Astronomical Societ

Photometric redshift galaxies as tracers of the filamentary network

Galaxy filaments are the dominant feature in the overall structure of the cosmic web. The study of the filamentary web is an important aspect in understanding galaxy evolution and the evolution of matter in the Universe. A map of the filamentary structure is an adequate probe of the web. We propose that photometric redshift galaxies are significantly positively associated with the filamentary structure detected from the spatial distribution of spectroscopic redshift galaxies. The catalogues of spectroscopic and photometric galaxies are seen as point-process realisations in a sphere, and the catalogue of filamentary spines is proposed to be a realisation of a random set in a sphere. The positive association between these sets was studied using a bivariate $J-$function, which is a summary statistics studying clustering. A quotient $D$ was built to estimate the distance distribution of the filamentary spine to galaxies in comparison to the distance distribution of the filamentary spine to random points in $3-$dimensional Euclidean space. This measure gives a physical distance scale to the distances between filamentary spines and the studied sets of galaxies. The bivariate $J-$function shows a statistically significant clustering effect in between filamentary spines and photometric redshift galaxies. The quotient $D$ confirms the previous result that smaller distances exist with higher probability between the photometric galaxies and filaments. The trend of smaller distances between the objects grows stronger at higher redshift. Additionally, the quotient $D$ for photometric galaxies gives a rough estimate for the filamentary spine width of about $1$~Mpc. Photometric redshift galaxies are positively associated with filamentary spines detected from the spatial distribution of spectroscopic galaxies.Comment: Accepted to Astronomy & Astrophysics. 13 pages and 9 figure

Method and Apparatus for Simultaneous Processing of Multiple Functions

Electronic logic gates that operate using N logic state levels, where N is greater than 2, and methods of operating such gates. The electronic logic gates operate according to truth tables. At least two input signals each having a logic state that can range over more than two logic states are provided to the logic gates. The logic gates each provide an output signal that can have one of N logic states. Examples of gates described include NAND/NAND gates having two inputs A and B and NAND/NAND gates having three inputs A, B, and C, where A, B and C can take any of four logic states. Systems using such gates are described, and their operation illustrated. Optical logic gates that operate using N logic state levels are also described

The bivariate J-function to analyse positive association between galaxies and galaxy filaments

International audienceThe compelling and intrinsic network of galaxies builds up a complex structure for the Universe. In this work positive association between long bridging structures named galaxy filaments and a photometric redshift galaxy dataset is under investigation. Possible positive association is studied by the use of a bivariate J-function.Le réseau de filaments formé par la position des galaxies est une des structures les plus fascinantes dans notre Univers. Dans cet article, nous étudions des possibles associations entre le réseau de filaments déjà détecté et des nouvelles observations. Ces observations très récentes sont obtenues à partir des mesures du décalage vers le rouge photométrique. L'utilisation de la fonction J-bivariée tend à indiquer une association positive entre les filaments existants et les nouvelles observations

Statistically bias-minimized peculiar velocity catalogs from Gibbs point processes and Bayesian inference

Galaxy peculiar velocities are excellent cosmological probes provided that biases inherent to their measurements are contained before any study. This paper proposes a new algorithm based on an object point process model whose probability density is built to statistically reduce the effects of Malmquist biases and uncertainties due to lognormal errors in radial peculiar velocity catalogs. More precisely, a simulated annealing algorithm permits maximizing the probability density describing the point process model. The resulting configurations are bias-minimized catalogs. Tests are conducted on synthetic catalogs mimicking the second and third distance modulus catalogs of the Cosmicflows project from which peculiar velocity catalogs are derived. By reducing the local peculiar velocity variance in catalogs by an order of magnitude, the algorithm permits recovering the expected one while preserving the small-scale velocity correlation. It also permits retrieving the expected clustering. The algorithm is then applied to the observational catalogs. The large-scale structure reconstructed with the Wiener-filter technique applied to the bias-minimized observational catalogs matches with great success the local cosmic web as depicted by redshift surveys of local galaxies. These new bias-minimized versions of peculiar velocity catalogs can be used as a starting point for several studies from possibly estimating the most probable Hubble constant, H0, value to the production of simulations constrained to reproduce the local Universe.Comment: Accepted for publication in A&A, 26 pages, 22 figures, 3 table