Geometry-aware Manipulability Learning, Tracking and Transfer

Body posture influences human and robots performance in manipulation tasks, as appropriate poses facilitate motion or force exertion along different axes. In robotics, manipulability ellipsoids arise as a powerful descriptor to analyze, control and design the robot dexterity as a function of the articulatory joint configuration. This descriptor can be designed according to different task requirements, such as tracking a desired position or apply a specific force. In this context, this paper presents a novel \emph{manipulability transfer} framework, a method that allows robots to learn and reproduce manipulability ellipsoids from expert demonstrations. The proposed learning scheme is built on a tensor-based formulation of a Gaussian mixture model that takes into account that manipulability ellipsoids lie on the manifold of symmetric positive definite matrices. Learning is coupled with a geometry-aware tracking controller allowing robots to follow a desired profile of manipulability ellipsoids. Extensive evaluations in simulation with redundant manipulators, a robotic hand and humanoids agents, as well as an experiment with two real dual-arm systems validate the feasibility of the approach.Comment: Accepted for publication in the Intl. Journal of Robotics Research (IJRR). Website: https://sites.google.com/view/manipulability. Code: https://github.com/NoemieJaquier/Manipulability. 24 pages, 20 figures, 3 tables, 4 appendice

Learning Task Priorities from Demonstrations

Bimanual operations in humanoids offer the possibility to carry out more than one manipulation task at the same time, which in turn introduces the problem of task prioritization. We address this problem from a learning from demonstration perspective, by extending the Task-Parameterized Gaussian Mixture Model (TP-GMM) to Jacobian and null space structures. The proposed approach is tested on bimanual skills but can be applied in any scenario where the prioritization between potentially conflicting tasks needs to be learned. We evaluate the proposed framework in: two different tasks with humanoids requiring the learning of priorities and a loco-manipulation scenario, showing that the approach can be exploited to learn the prioritization of multiple tasks in parallel.Comment: Accepted for publication at the IEEE Transactions on Robotic

redMaPPer III: A Detailed Comparison of the Planck 2013 and SDSS DR8 RedMaPPer Cluster Catalogs

We compare the Planck Sunyaev-Zeldovich (SZ) cluster sample (PSZ1) to the Sloan Digital Sky Survey (SDSS) redMaPPer catalog, finding that all Planck clusters within the redMaPPer mask and within the redshift range probed by redMaPPer are contained in the redMaPPer cluster catalog. These common clusters define a tight scaling relation in the richness-SZ mass ($\lambda$--$M_{SZ}$) plane, with an intrinsic scatter in richness of $\sigma_{\lambda|M_{SZ}} = 0.266 \pm 0.017$. The corresponding intrinsic scatter in true cluster halo mass at fixed richness is $\approx 21\%$. The regularity of this scaling relation is used to identify failures in both the redMaPPer and Planck cluster catalogs. Of the 245 galaxy clusters in common, we identify three failures in redMaPPer and 36 failures in the PSZ1. Of these, at least 12 are due to clusters whose optical counterpart was correctly identified in the PSZ1, but where the quoted redshift for the optical counterpart in the external data base used in the PSZ1 was incorrect. The failure rates for redMaPPer and the PSZ1 are $1.2\%$ and $14.7\%$ respectively, or 9.8% in the PSZ1 after subtracting the external data base errors. We have further identified 5 PSZ1 sources that suffer from projection effects (multiple rich systems along the line-of-sight of the SZ detection) and 17 new high redshift ($z\gtrsim 0.6$) cluster candidates of varying degrees of confidence. Should all of the high-redshift cluster candidates identified here be confirmed, we will have tripled the number of high redshift Planck clusters in the SDSS region. Our results highlight the power of multi-wavelength observations to identify and characterize systematic errors in galaxy cluster data sets, and clearly establish photometric data both as a robust cluster finding method, and as an important part of defining clean galaxy cluster samples.Comment: comments welcom

Orientation bias of optically selected galaxy clusters and its impact on stacked weak-lensing analyses

Weak-lensing measurements of the averaged shear profiles of galaxy clusters binned by some proxy for cluster mass are commonly converted to cluster mass estimates under the assumption that these cluster stacks have spherical symmetry. In this paper, we test whether this assumption holds for optically selected clusters binned by estimated optical richness. Using mock catalogues created from N-body simulations populated realistically with galaxies, we ran a suite of optical cluster finders and estimated their optical richness. We binned galaxy clusters by true cluster mass and estimated optical richness and measure the ellipticity of these stacks. We find that the processes of optical cluster selection and richness estimation are biased, leading to stacked structures that are elongated along the line of sight. We show that weak-lensing alone cannot measure the size of this orientation bias. Weak-lensing masses of stacked optically selected clusters are overestimated by up to 3–6 per cent when clusters can be uniquely associated with haloes. This effect is large enough to lead to significant biases in the cosmological parameters derived from large surveys like the Dark Energy Survey, if not calibrated via simulations or fitted simultaneously. This bias probably also contributes to the observed discrepancy between the observed and predicted Sunyaev–Zel’dovich signal of optically selected clusters

Una descomposición tendencia-ciclo con histéresis

Las fluctuaciones económicas pueden estimarse como producto de perturbaciones que no necesitan desagregarse entre choques de oferta y demanda. Choques conjuntos de oferta y demanda (S&D) pueden ayudar a estimar el ciclo de la brecha del producto, así como un ciclo en el producto tendencial. El modelo es una descomposición ciclo-tendencia univariada con histéresis en el producto tendencial, que permite la estimación de la brecha del producto y el producto tendencial en 81 economías en frecuencia trimestral desde 1995Q1 y en 184 economías en frecuencia anual desde 1975. La volatilidad, dispersión y frecuencia de choques conjuntos grandes fueron bajos durante el período de la Época Dorada; altos durante el período entre guerras, aún más en economías avanzadas (AD) en comparación con las emergentes y en desarrollo (EMDE); y bajo en las economías AD y alto en las economías EMDE en la segunda postguerra. En contraste con otros estimativos existentes del producto tendencial, los de la descomposición tendencia-ciclo con histéresis no evolucionan de forma suave, no resultan en un boom artificial antes de las recesiones y son menos sensibles a los datos nuevos.Business fluctuations can be estimated as the product of perturbations that do not need to be broken down into supply and demand shocks. Joint supply and demand (S&D) shocks can help estimate the cycle in the output gap as well as a cycle in trend output. The model is a univariate trend-cycle decomposition with hysteresis in trend output, that enables the estimation of the output gap and trend output in 81 economies in quarterly frequency, since 1995Q1; and 184 economies in yearly frequency, in several cases since 1950, and in a few cases since 1820. Volatility and dispersion, as well as the frequency of large joint trend-cycle shocks, were low during the Gilded Age period; high during the interwar period, even more so in advanced (AD) economies compared to emerging market and developing economies (EMDE); and low in AD economies and high in EMDE economies in the post WWII period. In contrast with other existing estimates of trend output, those from the trend-cycle decomposition with hysteresis do not evolve smoothly, do not result in an artificial boom before recessions and are less sensitive to new data.Enfoque De acuerdo con el enfoque keynesiano tradicional, las fluctuaciones económicas son causadas por choques que afectan la brecha del producto mientras que el producto tendencial evoluciona de forma suave. En contraste nosotros argumentamos que, tanto en economías avanzadas como en las emergentes y en desarrollo, la tendencia muestra ciclos. Aún más, argumentamos que las fluctuaciones económicas son causadas por choques que no son choques puros de demanda sino choques conjuntos a la oferta y a la demanda, que afectan tanto el producto tendencial como la brecha del producto. Como son choques conjuntos, son tratados como un todo que, para el propósito de analizar el ciclo de los negocios, no necesita ser desagregado entre sus componentes de oferta y demanda. Entonces, el producto tendencial y la brecha del producto son impulsados por choques conjuntos de oferta y demanda y ambos pueden ser vistos como partes del ciclo económico. Contribución El ciclo de los negocios es el ciclo en la brecha del producto y también en el producto tendencial si éste está definido en forma estacionaria. Además, tanto la brecha del producto como la medida estacionaria de producto tendencial son impulsados por choques conjuntos de oferta y demanda. En la descomposición ciclo tendencia con histéresis el producto tendencial tiene algunas características importantes. La primera es que no evoluciona de forma suave; de hecho, puede colapsar al comienzo de las recesiones, como por ejemplo en la mayoría de las economías al comienzo de la recesión de la pandemia del COVID-19. La segunda es que la brecha del producto no necesariamente sugiere un auge antes de cada recesión, como sucede con filtros como el de tendencia lineal local o el de Hodrick-Prescott. La tercera es que la brecha del producto cambia menos a medida que hay más datos disponibles, también en contraste con los filtros citados en donde el producto tendencial evoluciona de forma suave. Resultados La estimación muestra que durante la crisis financiera de 2008-2009 en las economías avanzadas el producto tendencial evidenció una importante histéresis. Este no fue el caso en las economías emergentes y en desarrollo. En contraste, durante la recesión del COVID-19 el producto tendencial registró importante histéresis tanto en las economías avanzadas como en las economías emergentes y en desarrollo. Con base en la volatilidad y dispersión de las fluctuaciones económicas, tres períodos históricos saltan a la vista: el período relativamente tranquilo de 1870-1910, conocido como la Época Dorada; el período relativamente turbulento de 1910-1950, que llamamos el período de guerras y entre guerras; y el período posterior a la segunda guerra mundial, 1950-, relativamente tranquilo en las economías avanzadas y relativamente turbulento en una cantidad de países emergentes y en desarrollo. El crecimiento de largo plazo del producto tendencial aumentó considerablemente durante la expansión económica de la segunda postguerra. Desde los años setenta el crecimiento de largo plazo del producto tendencial bajó junto con la reducción del crecimiento de la productividad. Al contrastar la brecha del producto de la descomposición ciclo-tendencia con la estimada por medio de otras metodologías en frecuencia anual y disponible en algunas bases de datos públicas, se hacen evidentes las ventajas de la descomposición ciclo-tendencia con histéresis; a saber, el producto tendencial no evoluciona de forma suave, la brecha del producto no necesariamente muestra un auge antes de cada recesión, y la brecha del producto registra revisiones menores a medida que se incorporan datos nuevos. Estas ventajas se obtienen al costo de una brecha del producto que es un poco menos variable y un producto tendencial que es variable; la desviación estándar de la brecha del producto es menor en alrededor de un quinto. Frase destacada: Las fluctuaciones económicas son causadas por choques que no son choques puros de demanda sino choques conjuntos a la oferta y a la demanda, que afectan tanto el producto tendencial como la brecha del producto

The Effects of Halo Assembly Bias on Self-Calibration in Galaxy Cluster Surveys

Self-calibration techniques for analyzing galaxy cluster counts utilize the abundance and the clustering amplitude of dark matter halos. These properties simultaneously constrain cosmological parameters and the cluster observable-mass relation. It was recently discovered that the clustering amplitude of halos depends not only on the halo mass, but also on various secondary variables, such as the halo formation time and the concentration; these dependences are collectively termed assembly bias. Applying modified Fisher matrix formalism, we explore whether these secondary variables have a significant impact on the study of dark energy properties using the self-calibration technique in current (SDSS) and the near future (DES, SPT, and LSST) cluster surveys. The impact of the secondary dependence is determined by (1) the scatter in the observable-mass relation and (2) the correlation between observable and secondary variables. We find that for optical surveys, the secondary dependence does not significantly influence an SDSS-like survey; however, it may affect a DES-like survey (given the high scatter currently expected from optical clusters) and an LSST-like survey (even for low scatter values and low correlations). For an SZ survey such as SPT, the impact of secondary dependence is insignificant if the scatter is 20% or lower but can be enhanced by the potential high scatter values introduced by a highly correlated background. Accurate modeling of the assembly bias is necessary for cluster self-calibration in the era of precision cosmology.Comment: 13 pages, 5 figures, replaced to match published versio

Primordial Gravity Waves and Weak Lensing

Inflation produces a primordial spectrum of gravity waves in addition to the density perturbations which seed structure formation. We compute the signature of these gravity waves in the large scale shear field. In particular, the shear can be divided into a gradient mode (G or E) and a curl mode (C or B). The former is produced by both density perturbations and gravity waves, while the latter is produced only by gravity waves, so the observations of a non-zero curl mode could be seen as evidence for inflation. We find that the expected signal from inflation is small, peaking on the largest scales at $l(l+1)C_l/2\pi < 10^{-11}$ at $l=2$ and falling rapidly there after. Even for an all-sky deep survey, this signal would be below noise at all multipoles. Part of the reason for the smallness of the signal is a cancellation on large scales of the standard line-of-sight effect and the effect of ``metric shear.''Comment: 4 pages, 1 figur