A Bayesian framework for optimal motion planning with uncertainty

Modeling robot motion planning with uncertainty in a Bayesian framework leads to a computationally intractable stochastic control problem. We seek hypotheses that can justify a separate implementation of control, localization and planning. In the end, we reduce the stochastic control problem to path- planning in the extended space of poses x covariances; the transitions between states are modeled through the use of the Fisher information matrix. In this framework, we consider two problems: minimizing the execution time, and minimizing the final covariance, with an upper bound on the execution time. Two correct and complete algorithms are presented. The first is the direct extension of classical graph-search algorithms in the extended space. The second one is a back-projection algorithm: uncertainty constraints are propagated backward from the goal towards the start state

Variational principle for the Wheeler-Feynman electrodynamics

We adapt the formally-defined Fokker action into a variational principle for the electromagnetic two-body problem. We introduce properly defined boundary conditions to construct a Poincare-invariant-action-functional of a finite orbital segment into the reals. The boundary conditions for the variational principle are an endpoint along each trajectory plus the respective segment of trajectory for the other particle inside the lightcone of each endpoint. We show that the conditions for an extremum of our functional are the mixed-type-neutral-equations with implicit state-dependent-delay of the electromagnetic-two-body problem. We put the functional on a natural Banach space and show that the functional is Frechet-differentiable. We develop a method to calculate the second variation for C2 orbital perturbations in general and in particular about circular orbits of large enough radii. We prove that our functional has a local minimum at circular orbits of large enough radii, at variance with the limiting Kepler action that has a minimum at circular orbits of arbitrary radii. Our results suggest a bifurcation at some radius below which the circular orbits become saddle-point extrema. We give a precise definition for the distributional-like integrals of the Fokker action and discuss a generalization to a Sobolev space of trajectories where the equations of motion are satisfied almost everywhere. Last, we discuss the existence of solutions for the state-dependent delay equations with slightly perturbated arcs of circle as the boundary conditions and the possibility of nontrivial solenoidal orbits

Expectations For an Interferometric Sunyaev-Zel'dovich Effect Survey for Galaxy Clusters

Non-targeted surveys for galaxy clusters using the Sunyaev-Zel'dovich effect (SZE) will yield valuable information on both cosmology and evolution of the intra-cluster medium (ICM). The redshift distribution of detected clusters will constrain cosmology, while the properties of the discovered clusters will be important for studies of the ICM and galaxy formation. Estimating survey yields requires a detailed model for both cluster properties and the survey strategy. We address this by making mock observations of galaxy clusters in cosmological hydrodynamical simulations. The mock observatory consists of an interferometric array of ten 2.5 m diameter telescopes, operating at a central frequency of 30 GHz with a bandwidth of 8 GHz. We find that clusters with a mass above $2.5 \times 10^{14} h_{50}^{-1} M_\odot$ will be detected at any redshift, with the exact limit showing a very modest redshift dependence. Using a Press-Schechter prescription for evolving the number densities of clusters with redshift, we determine that such a survey should find hundreds of galaxy clusters per year, many at high redshifts and relatively low mass -- an important regime uniquely accessible to SZE surveys. Currently favored cosmological models predict roughly 25 clusters per square degree.Comment: revised to match published versio

Testing Primordial Black Holes as Dark Matter through LISA

The idea that primordial black holes (PBHs) can comprise most of the dark matter of the universe has recently reacquired a lot of momentum. Observational constraints, however, rule out this possibility for most of the PBH masses, with a notable exception around $10^{-12} M_\odot$. These light PBHs may be originated when a sizeable comoving curvature perturbation generated during inflation re-enters the horizon during the radiation phase. During such a stage, it is unavoidable that gravitational waves (GWs) are generated. Since their source is quadratic in the curvature perturbations, these GWs are generated fully non-Gaussian. Their frequency today is about the mHz, which is exactly the range where the LISA mission has the maximum of its sensitivity. This is certainly an impressive coincidence. We show that this scenario of PBHs as dark matter can be tested by LISA by measuring the GW two-point correlator. On the other hand, we show that the short observation time (as compared to the age of the universe) and propagation effects of the GWs across the perturbed universe from the production point to the LISA detector suppress the bispectrum to an unobservable level. This suppression is completely general and not specific to our model.Comment: 22 pages, 12 figures. v3: matching published versio

Minimizers with discontinuous velocities for the electromagnetic variational method

The electromagnetic two-body problem has \emph{neutral differential delay} equations of motion that, for generic boundary data, can have solutions with \emph{discontinuous} derivatives. If one wants to use these neutral differential delay equations with \emph{arbitrary} boundary data, solutions with discontinuous derivatives must be expected and allowed. Surprisingly, Wheeler-Feynman electrodynamics has a boundary value variational method for which minimizer trajectories with discontinuous derivatives are also expected, as we show here. The variational method defines continuous trajectories with piecewise defined velocities and accelerations, and electromagnetic fields defined \emph{by} the Euler-Lagrange equations \emph{% on} trajectory points. Here we use the piecewise defined minimizers with the Li{\'{e}}nard-Wierchert formulas to define generalized electromagnetic fields almost everywhere (but on sets of points of zero measure where the advanced/retarded velocities and/or accelerations are discontinuous). Along with this generalization we formulate the \emph{generalized absorber hypothesis} that the far fields vanish asymptotically \emph{almost everywhere%} and show that localized orbits with far fields vanishing almost everywhere \emph{must} have discontinuous velocities on sewing chains of breaking points. We give the general solution for localized orbits with vanishing far fields by solving a (linear) neutral differential delay equation for these far fields. We discuss the physics of orbits with discontinuous derivatives stressing the differences to the variational methods of classical mechanics and the existence of a spinorial four-current associated with the generalized variational electrodynamics.Comment: corrected minor typo: piecewise differentiable on closed instead of open interval

An overview of the EXTraS project: Exploring the X-ray Transient and Variable Sky

The EXTraS project (Exploring the X-ray Transient and variable Sky) will harvest the hitherto unexplored temporal domain information buried in the serendipitous data collected by the European Photon Imaging Camera (EPIC) instrument onboard the ESA XMM-Newton X-ray observatory since its launch. This will include a search for fast transients, as well as a search and characterization of variability (both periodic and aperiodic) in hundreds of thousands of sources spanning more than nine orders of magnitude in time scale and six orders of magnitude in flux. X-ray results will be complemented by multiwavelength characterization of new discoveries. Phenomenological classification of variable sources will also be performed. All our results will be made available to the community. A didactic program in selected High Schools in Italy, Germany and the UK will also be implemented. The EXTraS project (2014-2016), funded within the EU/FP7 framework, is carried out by a collaboration including INAF (Italy), IUSS (Italy), CNR/IMATI (Italy), University of Leicester (UK), MPE (Germany) and ECAP (Germany).Comment: 6 pages, 1 figure. Proceedings of "Swift: 10 years of Discovery", to appear in Po

Supergiant Fast X-ray Transients uncovered by the EXTraS project: flares reveal the development of magnetospheric instability in accreting neutron stars

The low luminosity, X-ray flaring activity, of the sub-class of high mass X-ray binaries called Supergiant Fast X-ray Transients, has been investigated using XMM-Newton public observations, taking advantage of the products made publicly available by the EXTraS project. One of the goals of EXTraS was to extract from the XMM-Newton public archive information on the aperiodic variability of all sources observed in the soft X-ray range with EPIC (0.2-12 keV). Adopting a Bayesian block decomposition of the X-ray light curves of a sample of SFXTs, we picked out 144 X-ray flares, covering a large range of soft X-ray luminosities (1e32-1e36 erg/s). We measured temporal quantities, like the rise time to and the decay time from the peak of the flares, their duration and the time interval between adjacent flares. We also estimated the peak luminosity, average accretion rate and energy release in the flares. The observed soft X-ray properties of low-luminosity flaring activity from SFXTs is in qualitative agreement with what is expected by the application of the Rayleigh-Taylor instability model in accreting plasma near the neutron star magnetosphere. In the case of rapidly rotating neutron stars, sporadic accretion from temporary discs cannot be excluded.Comment: Accepted for publication in MNRAS (accepted 2019 May 1; received 2019 April 30; in original form 2019 February 25). 22 pages, 16 figures, 3 tables

Discovery of periodic dips in the brightest hard X-ray source of M31 with EXTraS

We performed a search for eclipsing and dipping sources in the archive of the EXTraS project - a systematic characterization of the temporal behaviour of XMM-Newton point sources. We discovered dips in the X-ray light curve of 3XMM J004232.1+411314, which has been recently associated with the hard X-ray source dominating the emission of M31. A systematic analysis of XMM-Newton observations revealed 13 dips in 40 observations (total exposure time $\sim$0.8 Ms). Among them, four observations show two dips, separated by $\sim$4.01 hr. Dip depths and durations are variable. The dips occur only during low-luminosity states (L$_{0.2-12}<1\times10^{38}$ erg s$^{-1}$), while the source reaches L$_{0.2-12}\sim2.8\times10^{38}$ erg s$^{-1}$. We propose this system to be a new dipping Low-Mass X-ray Binary in M31 seen at high inclination (60$^{\circ}$-80$^{\circ}$), the observed dipping periodicity is the orbital period of the system. A blue HST source within the Chandra error circle is the most likely optical counterpart of the accretion disk. The high luminosity of the system makes it the most luminous dipper known to date.Comment: 11 pages, 2 figures, 5 tables, accepted for publication in ApJ