A Novel Distribution for Representation of 6D Pose Uncertainty

The 6D Pose estimation is a crux in many applications, such as visual perception, autonomous navigation, and spacecraft motion. For robotic grasping, the cluttered and self-occlusion scenarios bring new challenges to the this field. Currently, society uses CNNs to solve this problem. The CNN models will suffer high uncertainty caused by the environmental factors and the object itself. These models usually maintain a Gaussian distribution, which is not suitable for the underlying manifold structure of the pose. Many works decouple rotation from the translation and quantify rotational uncertainty. Only a few works pay attention to the uncertainty of the 6D pose. This work proposes a distribution that can capture the uncertainty of the 6D pose parameterized by the dual quaternions, meanwhile, the proposed distribution takes the periodic nature of the underlying structure into account. The presented results include the normalization constant computation and parameter estimation techniques of the distribution. This work shows the benefits of the proposed distribution, which provides a more realistic explanation for the uncertainty in the 6D pose and eliminates the drawback inherited from the planar rigid motion.

Normalization of D-instanton amplitudes

D-instanton amplitudes suffer from various infrared divergences associated with tachyonic or massless open string modes, leading to ambiguous contribution to string amplitudes. It has been shown previously that string field theory can resolve these ambiguities and lead to unambiguous expressions for D-instanton contributions to string amplitudes, except for an overall normalization constant that remains undetermined. In this paper we show that string field theory, together with the world-sheet description of the amplitudes, can also fix this normalization constant. We apply our analysis to the special case of two dimensional string theory, obtaining results in agreement with the matrix model results obtained by Balthazar, Rodriguez and Yin.

ON A RESCALED NONLOCAL DIFFUSION PROBLEM WITH NEUMANN BOUNDARY CONDITIONS

In this work, we consider the rescaled nonlocal diffusion problem with Neumann Boundary Conditions \[ \begin{cases} u_t^{\epsilon}(x,t)=\displaystyle\frac{1}{\epsilon^2} \int_{\Omega}J_{\epsilon}(x-y)(u^\epsilon(y,t)-u^\epsilon(x,t))dy\\ \qquad \qquad+\displaystyle\frac{1}{\epsilon}\int_{\partial \Omega}G_\epsilon(x-y)g(y,t)dS_y,\\ u^\epsilon(x,0)=u_0(x), \end{cases} \] where $\Omega\subset\mathbb{R}^{N}$ is a bounded, connected and smooth domain, $g$ a positive continuous function, $J_\epsilon(z)=C_1\frac{1}{\epsilon^N}J(\frac{z}{\epsilon}), G_\epsilon(x)=C_1\frac{1}{\epsilon^N}G(\frac{x}{\epsilon}),$ $J$ and $G$ well defined kernels, $C_1$ a normalization constant. The solutions of this model have been used without prove to approximate the solutions of a family of nonlocal diffusion problems to solutions of the respective analogous local problem. We prove existence and uniqueness of the solutions for this problem by using the Banach Fixed Point Theorem. Finally, some conclusions are given.

The Luminosity Function of Galaxies in Some Nearby Clusters

In the present work, the galaxy luminosity function (LF) has been studied for a sample of seven clusters in the redshift range (0.0 ≲ z ≲ 0.1), within Abell radius (1.5 h−1 Mpc), in the five SDSS passbands ugriz. In each case, the absolute magnitude distribution is found and then fitted with a Schechter function. The fitting is done, using the χ2 – minimization method to find the best values of Schechter parameters Ф* (normalization constant), M* (characteristic absolute magnitude), and α (faint-end slope). No remarkable changes are found in the values of M* and α, for any cluster, in any passband. Furthermore, the LF does not seem to vary with such cluster parameters as richness, velocity dispersion, and Bautz–Morgan morphology. Finally, it is found that M* becomes brighter toward redder bands, whereas almost no variation is seen in the value of α with passband, being around (−1.00).

On the Application of Mean Value Analysis Without the Normalization Constant in the Closed Queuing Networks

An example of closed queue network could be view when patients arrive at a doctor’s office to update their medical records, then it’s off to the nurse’s station for various measurements like weight, blood pressure, and so on. The next stop is generally to queue (i.e., wait patiently) for one of the doctors to arrive and begin the consultation and examination. Perhaps it may be necessary to have some X-rays taken, an ultrasound may be called for, and so on. After these procedures have been completed, it may be necessary to talk with the doctor once again. The final center through which the patient must pass is always the billing office. In this work, multiple-node” system in which a customer requires service at more than one node, which may be viewed as a network of nodes, and each node is a service center having storage room for queues to form and perhaps with multiple servers to handle customer requests is investigated in order to provide some insight into the performance measure analysis. Our quest is to exempt the normalization constant in the computation of performance measure in the closed queueing network. The arrival properties and Little’s law are use with the help of some existing equations and formulas in queueing network. Performance measures, such as Mean number of customers, response time, throughput, and marginal probability distribution are obtained for central server and load dependent server closed queuing networks for nodes 4 and 5, and also for k = 3 and k = 10.

Homotopy Particle Filter and Data Assimilation

<p>A homotopy schedule is proposed, wherein from a known probability distribution the normalization constant for an improper probability density function can be found. An improper distribution is one for which the normalization is not known, but its functional form is. In the statistical mechanics constant this amounts to finding the canonical ensemble for the improper distribution. Along the way, the method will generate samples from the target distribution.</p><p>This homotopy schedule can be adopted to particle filters used for Bayesian estimation with the aim of improving estimates of the mean path and the uncertainty of a noisy dynamical system, for which noisy observations are available. The method is useful when the dynamics are highly nonlinear, especially if the observations that inform the likelihood have low uncertainty. In the context of data assimilation we require that the stochastic dynamics of the system have an asymptotic stationary distribution, which we use as a the known distribution in the homotopy procedure.</p><p>In this talk we present the methodology, apply it to the estimation of canonical ensembles and present numerical comparisons of the standard particle filter estimates with those of the homotopy data assimilation. </p><p> </p>

Intercomparison of aerosol measurements performed with multi-wavelength Raman lidars, automatic lidars and ceilometers in the framework of INTERACT-II campaign

Following the previous efforts of INTERACT (INTERcomparison of Aerosol and Cloud Tracking), the INTERACT-II campaign used multi-wavelength Raman lidar measurements to assess the performance of an automatic compact micro-pulse lidar (MiniMPL) and two ceilometers (CL51 and CS135) in providing reliable information about optical and geometric atmospheric aerosol properties. The campaign took place at the CNR-IMAA Atmospheric Observatory (760 ma.s.l.; 40.60∘ N, 15.72∘ E) in the framework of ACTRIS-2 (Aerosol Clouds Trace gases Research InfraStructure) H2020 project. Co-located simultaneous measurements involving a MiniMPL, two ceilometers and two EARLINET multi-wavelength Raman lidars were performed from July to December 2016. The intercomparison highlighted that the MiniMPL range-corrected signals (RCSs) show, on average, a fractional difference with respect to those of CNR-IMAA Atmospheric Observatory (CIAO) lidars ranging from 5 to 15 % below 2.0 km a.s.l. (above sea level), largely due to the use of an inaccurate overlap correction, and smaller than 5 % in the free troposphere. For the CL51, the attenuated backscatter values have an average fractional difference with respect to CIAO lidars < 20–30 % below 3 km and larger above. The variability of the CL51 calibration constant is within ±46 %. For the CS135, the performance is similar to the CL51 below 2.0 kma.s.l., while in the region above 3 kma.s.l. the differences are about ±40 %. The variability of the CS135 normalization constant is within ±47 %. Finally, additional tests performed during the campaign using the CHM15k ceilometer operated at CIAO showed the clear need to investigate the CHM15k historical dataset (2010–2016) to evaluate potential effects of ceilometer laser fluctuations on calibration stability. The number of laser pulses shows an average variability of 10 % with respect to the nominal power which conforms to the ceilometer specifications. Nevertheless, laser pulses variability follows seasonal behavior with an increase in the number of laser pulses in summer and a decrease in winter. This contributes to explain the dependency of the ceilometer calibration constant on the environmental temperature hypothesized during INTERACT.