Orbit Determination with the two-body Integrals

We investigate a method to compute a finite set of preliminary orbits for solar system bodies using the first integrals of the Kepler problem. This method is thought for the applications to the modern sets of astrometric observations, where often the information contained in the observations allows only to compute, by interpolation, two angular positions of the observed body and their time derivatives at a given epoch; we call this set of data attributable. Given two attributables of the same body at two different epochs we can use the energy and angular momentum integrals of the two-body problem to write a system of polynomial equations for the topocentric distance and the radial velocity at the two epochs. We define two different algorithms for the computation of the solutions, based on different ways to perform elimination of variables and obtain a univariate polynomial. Moreover we use the redundancy of the data to test the hypothesis that two attributables belong to the same body (linkage problem). It is also possible to compute a covariance matrix, describing the uncertainty of the preliminary orbits which results from the observation error statistics. The performance of this method has been investigated by using a large set of simulated observations of the Pan-STARRS project.Comment: 23 pages, 1 figur

Efficient intra- and inter-night linking of asteroid detections using kd-trees

The Panoramic Survey Telescope And Rapid Response System (Pan-STARRS) under development at the University of Hawaii's Institute for Astronomy is creating the first fully automated end-to-end Moving Object Processing System (MOPS) in the world. It will be capable of identifying detections of moving objects in our solar system and linking those detections within and between nights, attributing those detections to known objects, calculating initial and differentially-corrected orbits for linked detections, precovering detections when they exist, and orbit identification. Here we describe new kd-tree and variable-tree algorithms that allow fast, efficient, scalable linking of intra and inter-night detections. Using a pseudo-realistic simulation of the Pan-STARRS survey strategy incorporating weather, astrometric accuracy and false detections we have achieved nearly 100% efficiency and accuracy for intra-night linking and nearly 100% efficiency for inter-night linking within a lunation. At realistic sky-plane densities for both real and false detections the intra-night linking of detections into `tracks' currently has an accuracy of 0.3%. Successful tests of the MOPS on real source detections from the Spacewatch asteroid survey indicate that the MOPS is capable of identifying asteroids in real data.Comment: Accepted to Icaru

(WP 2021-05) Heterogeneity in Individual Expectations, Sentiment, and Constant-Gain Learning

This paper uses adaptive learning to understand the heterogeneity of individual-level expectations. We exploit individual Survey of Professional Forecasters data on output and inflation forecasts. We endow all forecasters with the same information set that they would have as economic agents in a benchmark New Keynesian model. Forecasters are, however, allowed to differ in the constant gain values that they use to update their beliefs and in their sentiments. The latter are defined as the degrees of excess optimism or pessimism about the economy that cannot be justified by the learning model. Our results highlight the heterogeneity in the gain coefficients adopted by forecasters. The median values of the gain coefficients occasionally jump to higher values in the 1970-80s, and stabilize in the 1990s and 2000s. Individual sentiment is also persistent and heterogeneous. Differences in sentiment, however, do not simply cancel out in the aggregate: the majority of forecasters exhibit excess optimism, or excess pessimism, at the same time

(WP 2020-04) Heterogeneity in Individual Expectations, Sentiment, and Constant-Gain Learning

The adaptive learning approach has been fruitfully employed to model the formation of aggregate expectations at the macroeconomic level, as an alternative to rational expectations. This paper uses adaptive learning to understand, instead, the formation of expectations at the micro-level, by focusing on individual expectations and, in particular, trying to account for their heterogeneity. We exploit survey data on output and inflation expectations by individual professional forecasters. We link micro and macro by endowing forecasters with the same information set that they would have as economic agents in a benchmark New Keynesian model. Forecasters are, however, allowed to differ in the constant gain values that they use to update their beliefs. We estimate the best-fitting constant gain for each forecaster. We also extract individual measures of sentiment, defined as the degrees of excess optimism and pessimism that cannot be justified by the near-rational learning model, given the state of the economy and the updated beliefs. Our results highlight the heterogeneity in the gain coefficients adopted by forecasters, which is particularly pronounced at the beginning of the sample. The median values are consistent with those typically estimated using aggregate data, and display some moderate time variation: they occasionally jump to higher values in the 1970-80s, and stabilize in the 1990s and 2000s. Individual sentiment is persistent and heterogeneous. Differences in sentiment, however, don\u27t simply cancel out in the aggregate: the majority of forecasters exhibit excess optimism, or excess pessimism, at the same time

Symmetric Periodic Solutions of the Anisotropic Manev Problem

We consider the Manev Potential in an anisotropic space, i.e., such that the force acts differently in each direction. Using a generalization of the Poincare' continuation method we study the existence of periodic solutions for weak anisotropy. In particular we find that the symmetric periodic orbits of the Manev system are perturbed to periodic orbits in the anisotropic problem.Comment: Late

An automatic and fast procedure for the numerical analysis of curved masonry structures

A fast and innovative discrete model approach coupled with homogenization procedure is here presented. The method is able to comply with the main features required for an accurate simulation of masonry curved elements, such as the orthotropy and the typical in- and-out-of-plane coupled behavior exhibited by masonry vaults. Furthermore, homogenization techniques directly implemented in the method allows reducing consistently the number of variables, leading to a fair combination of accuracy and reasonable computational time. The discrete model is an assembly of elastic units joint by non-linear interfaces. These latter are modeled with 3D linear brick elements and Concrete Damage Plasticity (CDP) is used for modeling the non-linear mechanical properties coming from the homogenization step. In order to overcome potential difficulties during the preparation of the model, the discretized mesh is obtained automatically by means of an ad-hoc script implemented by the Authors. The proposed approach is validated taking advantage of numerical data already available on a cloister vault. The numerical comparison shows the reliability of the method and its efficacy in the simulation of both global behavior and crack pattern, requiring a low computational effort.(undefined

Explicit Complex Solutions to the Fresnel Coefficients

Global Navigation Satellite System Reflectometry (GNSS-R) is a microwave remote sensing technique which can be used to derive information about the composition or the properties of ground surfaces. The received power of the GPS signals reflected by the ground is proportional to the magnitude of the reflection Fresnel coefficients In particular, it depends on the incidence angle $\theta$ and on the ground's permittivity $\epsilon$. The knowledge of $\epsilon$ is important for determining various conditions and characteristics of the surface (e.g., soil moisture, salinity, freeze-thaw transitions). The value of $\epsilon$ can be found from the Fresnel reflection coefficients, for a given incidence angle $\theta$. For dispersive media, $\epsilon$ is a complex quantity; we present explicit formulas, which express both $\Re(\varepsilon)$ and $\Im(\varepsilon)$ as a function of the incident angle $\theta$ and of the magnitude of the linearly polarized Fresnel reflection coefficients