1,720,983 research outputs found
Isomonodromic Laplace transform with coalescing eigenvalues and confluence of Fuchsian singularities
Full text linkWe consider a Pfaffian system expressing isomonodromy of an irregular system of Okubo type, depending on complex deformation parameters u= (u1, ... , un) , which are eigenvalues of the leading matrix at the irregular singularity. At the same time, we consider a Pfaffian system of non-normalized Schlesinger-type expressing isomonodromy of a Fuchsian system, whose poles are the deformation parameters u1, ... , un. The parameters vary in a polydisc containing a coalescence locus for the eigenvalues of the leading matrix of the irregular system, corresponding to confluence of the Fuchsian singularities. We construct isomonodromic selected and singular vector solutions of the Fuchsian Pfaffian system together with their isomonodromic connection coefficients, so extending a result of Balser et al. (I SIAM J Math Anal 12(5): 691–721, 1981) and Guzzetti (Funkcial Ekvac 59(3): 383–433, 2016) to the isomonodromic case, including confluence of singularities. Then, we introduce an isomonodromic Laplace transform of the selected and singular vector solutions, allowing to obtain isomonodromic fundamental solutions for the irregular system, and their Stokes matrices expressed in terms of connection coefficients. These facts, in addition to extending (Balser et al. in I SIAM J Math Anal 12(5): 691–721, 1981; Guzzetti in Funkcial Ekvac 59(3): 383–433, 2016) to the isomonodromic case (with coalescences/confluences), allow to prove by means of Laplace transform the main result of Cotti et al. (Duke Math J arXiv:1706.04808, 2017), namely the analytic theory of non-generic isomonodromic deformations of the irregular system with coalescing eigenvalues
Notes on non-generic isomonodromy deformations
Full text linkSome of the main results of [Cotti G., Dubrovin B., Guzzetti D., Duke Math. J., to appear, arXiv:1706.04808], concerning non-generic isomonodromy deformations of a certain linear differential system with irregular singularity and coalescing eigenvalues, are reviewed from the point of view of Pfaffian systems, making a distinction between weak and strong isomonodromic deformations. Such distinction has a counterpart in the case of Fuchsian systems, which is well known as Schlesinger and non-Schlesinger deformations, reviewed in Appendix A
Deep Reinforcement Learning to Enhance Fly-Around Guidance for Uncooperative Space Objects Smart Imaging
No full textDriven by several potential applications, leading space agencies are increasingly investing in the gradual automation of space missions. Autonomous flight operations may be a key enabler for on-orbit servicing, assembly and manufacturing (OSAM) missions, carrying inherent benefits such as cost and risk reduction. Within the spectrum of proximity operations, this work focuses on autonomous path-planning for the reconstruction of geometry properties of an uncooperative target. The autonomous navigation problem is called active Simultaneous Localization and Mapping (SLAM) problem, and it has been largely studied within the field of robotics. Active SLAM problem may be formulated as a Partially Observable Markov Decision Process (POMDP). Previous works in astrodynamics have demonstrated that is possible to use Reinforcement Learning (RL) techniques to teach an agent that is moving along a pre-determined orbit when to collect measurements to optimize a given mapping goal. In this work, different RL methods are explored to develop an artificial intelligence agent capable of planning suboptimal paths for autonomous shape reconstruction of an unknown and uncooperative object via imaging. Proximity orbit dynamics are linearized and include orbit eccentricity. The geometry of the target object is rendered by a polyhedron shaped with a triangular mesh. Artificial intelligent agents are created using both the Deep Q-Network (DQN) and the Advantage Actor Critic (A2C) method. State-action value functions are approximated using Artificial Neural Networks (ANN) and trained according to RL principles. Training of the RL agent architecture occurs under fixed or random initial environment conditions. A large database of training tests has been collected. Trained agents show promising performance in achieving extended coverage of the target. Policy learning is demonstrated by displaying that RL agents, at minimum, have higher mapping performance than agents that behave randomly. Furthermore, RL agent may learn to maneuver the spacecraft to control target lighting conditions as a function of the Sun location. This work, therefore, preliminary demonstrates the applicability of RL to autonomous imaging of an uncooperative space object, thus setting a baseline for future works
Autonomous Small Body Gravimetry via A2C Path-Planning
No full textThe success of proximity operations near small bodies relies on proper characterization of the corresponding gravitational environment; the accuracy of the gravity field model is a critical element to plan safe spacecraft trajectories and constitutes a crucial aspect for the definition of the spacecraft dynamics. Currently, flight operations required for an accurate reconstruction of the gravity field are orchestrated by ground control personnel; however, automatizing such flight control processes may yield reduced operational costs and additional mission opportunities. The problem of autonomous gravity field reconstruction can be formulated as a Partially Observable Markov Decision Process; in this framework, a spacecraft moving in an unknown gravitational environment can be modeled as an agent that autonomously implements a guidance policy to obtain accurate grav-imetric measurements. Possibly compatible with limited on-board resources, advances in flight autonomy may be sought through the exploitation of novel techniques based on Reinforcement Learning (RL) and Artificial Neural Networks (ANN). The architecture proposed in this work employs a Hopfield Neural Network (HNN) for the reconstruction of the gravity field, which is represented as a spherical harmonics expansion, assuming an Exterior Gravity Field Model. The agent’s objective is to determine a trajectory around the target body that would allow the quick and precise estimation of the spherical harmonics coefficients via HNN. The algorithm adopted is the Advantage-Actor Critic (A2C), where the agent plays the roles of the Actor; such RL algorithm exploits two networks that work in parallel aiming to maximize the return, a scalar value that renders the accuracy of reconstruction of the gravity field. In particular, this works focuses on the reconstruction of the first zonal Stokes’ coefficient C2, testing the architecture on specific case studies, as well as on more generic environments. The ANN are updated using an Adam’s algorithm for the learning process, which is driven by a reward function designed to retrieve the expansion coefficient in a quick and safe manner. Results presented in this paper show that an agent with proper training performs better than one that follows random behavior, achieving the desired accuracy more often than in a random policy simulation, in a wide pool of scenarios (different initial conditions for the same asteroid and different asteroid); in addition, gravity coefficient reconstruction performance are improved if an expert-knowledge is infused into the training process. Such results allow to assess the feasibility of the method proposed, thus defining a promising starting point for further developments
The asymptotic behaviour of the Fourier transform of orthogonal polynomials II: Iterated Function Systems and Quantum Mechanics
No full textWe study measures generated by systems of linear iterated functions, their Fourier transforms, and those of their orthogonal polynomials. We characterize the asymptotic behaviours of their discrete and continuous averages.
Further related quantities are analyzed, and relevance of this analysis to quantum mechanics is briefly discussed
Periodic Orbit-Attitude Solutions Along Planar Orbits in a Perturbed Circular Restricted Three-Body Problem for the Earth-Moon System
No full textThe Earth-Moon system is nowadays attracting more and more interest as a well suited location for near and far future long term missions based on large structures. As a natural consequence, their design process has to go through a deep understanding of the orbital and attitude coupled motions which, although being significantly complex in a multi-attractors environment, may highlight interesting dynamical structures to be exploited for designing the vehicle passive guidance. Under the adoption of the Circular Restricted Three-Body Problem (CR3BP) model the understanding of either periodic or, at least, bounded behaviors for the rotational motion is still a young research field. The paper presents a systematic approach to search and identify the aforementioned structures, beneficial for naturally coupled stable motions of large structures located in the Earth-Moon system: firstly planar orbit-attitude periodic solutions are obtained and classified for rigid bodies travelling along known CR3BP periodic trajectories, disturbed by the gravity gradient effects only. The torque exerted by Solar Radiation Pressure (SRP) is, next, introduced into the model. The performed analysis highlighted that even with SRP torque included, rotational periodic behaviors still exist for specific resonance ratios between the solar apparent motion and the spacecraft orbit periods. The assumption of the Sun apparent orbit to be coplanar with the Earth-Moon motion is adopted and its effects assessed with respect to the Sun ephemerides exploitation; the reference path is initially kept fixed, and deviations due to SRP are then analyzed leading to nearly-periodic solution structures. A sensitivity analysis incorporating SRP investigates the uncertainties on some spacecraft parameters (e.g. reflectance/absorbance coefficients, position of the center of pressure, irradiated area) and their effects on the orbit-attitude nominal motion. As final step to refine the here presented model, the large structure flexibility has been inserted as perturbation, superimposed to a reference orbit-attitude rigid body motion: selected periodic solutions are assumed as reference and the modal and frequency analysis are performed, to detect excitation of the spacecraft structural modes and assess their effects with respect to the nominal rigid body solution. At the end, the presented model represents an effective tool to address and support the large structures in Earth-Moon system design, to preserve at the most a periodic nature of their coupled attitude-orbital dynamics. As a case study, the effectiveness of the proposed tool is discussed on a simplified extended space vehicle model
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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