Maximum entropy image reconstruction-a practical non-information-theoretic approach

The maximum entropy method (MEM) of image reconstructtion is discussed in the context of incomplete Fourier information (as in aperture synthesis). Several current viewpoints on the conceptual foundation of the method are analysed and found to be unsatisfactory. It is concluded that the MEM is a form of model-fitting, the model being a non-linear transform of a band-limited function. A whole family of ’entropies’ can be constructed to give reconstructions which (a) are individually unique, (b) have sharpened peaks and (c) have flattened baselines. The widely discussed 1nB and - B1nB forms of the entropy are particular cases and lead to Lorentzian and Gaussian shaped peaks respectively. However, they hardly exhaust the possibilities-for example, B^1/2 is equally good. The two essential features of peak sharpening and baseline flattening are shown to depend on a parameter which can be controlled by adding a suitable constant to the zero spacing correlation ρ₀₀. This process, called FLOATing, effectively tames much of the unphysical behaviour noted in earlier studies of the MEM. A numerical scheme for obtaining the MEM reconstruction is described. This incorporates the FLOAT feature and uses the fast Fourier transform (FFT), requiring about a hundred FFTs for convergence. Using a model brightness distribution, the MEM reconstructions obtained for different entropies and different values of the resolution parameter are compared. The results substantiate the theoretically deduced properties of the MEM. To allow for noise in the data, the least-squares approach has been widely used. It is shown that this method is biased since it leads to deterministic residuals which do not have a Gaussian distribution. It is suggested that fitting the noisy data exactly has the advantage of being unbiased even though the noise appears in the final map. A comparison of the strengths and weaknesses of the MEM and CLEAN suggests that the MEM already has a useful role to play in image reconstruction.     

Plenty of nothing: Black hole entropy in induced gravity

We demonstrate how Sakharov's idea of induced gravity allows one to explain the statistical-mechanical origin of the entropy of a black hole. According to this idea, gravity becomes dynamical as the result of quantum effects in the system of heavy constituents of the underlying theory.The black hole entropy is related to the properties of the vacuum in the induced gravity in the presence of the horizon. We obtain the Bekenstein-Hawking entropy by direct counting the states of the constituents.     

Investigating the partonic entanglement entropy at low Bjorken-x within Gluon saturation approach

In this work, the entanglement entropy is examined within the context of deep inelastic scattering in $ep$ collisions. The calculation is based on a formalism where the partonic state at small- $x$ is maximally entangled, consisting of a large number of micro-states occurring with equal probabilities. Analytical expressions for the number of gluons, $N_{\text{gluon}}$, are considered, derived from gluon saturation models for dipole-target amplitudes within the framework of the Quantum Chromodynamics (QCD) color dipole picture. A comparison of the entanglement entropy with thermodynamic entropy measured in $pp$ and $ep$ collisions at high energies is done.     

Generalized Lyapunov characteristic indicators and corresponding Kolmogorov like entropy of the standard mapping

Lyapunov characteristic indicators are currently defined as the mean, i.e. the first moment, of the distribution of the local variations of the tangent vector to the flow. Higher moments of the distribution give further informations about the fluctuations around the average.     

Suprathermal particle distributions in space physics: Kappa distributions and entropy

The energization of a charged test-particle of mass m in contact with a large ensemble of charged particles of mass M at equilibrium is studied with the Fokker-Planck equation for Coulomb collisions and a quasi-linear diffusion operator for wave-particle interactions. The features of the nonequilibrium steady state velocity distribution of the test-particle system is studied as a function of the mass ratio m/M, and the relative strengths of the wave-particle interactions and Coulomb collisions. It is shown that the steady distribution function is not necessarily a Kappa distribution. The temperature of heavy minor ions given by the model is shown to vary linearly with the mass ratio as observed in the solar wind. The time evolution of the distribution function with and without the energization by wave-particle interactions is calculated and it is demonstrated that the Kullback relative entropy rather than the Tsallis nonextensive entropy rationalizes the results obtained.     

网络环境下的情报工作

从情报学的学科目标、信息网络目前的工作状况,科研对情报的要要求等方面论述了网络环境下的情报工作的重要意义。提出了情报队伍建设的重要性。并对信息服务与情报服务的不同进行了详细论证。     

天文文献情报工程概述

本文主要介绍中国科学院天文系统文献情报自动化建设、文献工程建设、数据工程建设、资源共享与计算机共享网建设。由于其牵涉到1984年以来的一系列工程建设呐容繁多,所以仅从文献情报现代化建设、资源共享建设出发,从整体上对各有关内容作一概述。     

紫金山天文台图书资料的国际交流及其展望

对紫金山天文台图书资料“国际交换”的过去、现状加以回顾 ,以及对未来“国际交换”及其发展加以探讨     

分形和混沌理论在天体物理中的应用

本文对当前应用日益广泛的非线性科学的两个重要分支──分形和混沌动力系统理论──作概述性的介绍，并简介了这两种非线性方法在天体物理中应用的重要结果，特别强调一些天体物理中典型的分形和混沌现象，诸如星系大尺度结构（分形）和星系动力学（混沌）。     

Floods on Mars released from groundwater by impact

On Earth, large earthquakes commonly cause saturated soils to liquefy and streamflow to increase. We suggest that meteoritic impacts on Mars may have repeatedly caused similar liquefaction to enable violent eruption of groundwater. The amount of erupted water may be comparable to that required to produce catastrophic floods and to form outflow channels.     

Frequency modified fourier transform and its application to asteroids

Recently a method has been suggested to analyze the chaotic behaviour of a conservative dynamical system by numerical analysis of the fundamental frequencies. Frequencies and amplitudes are determined step by step. As the frequencies are not generally orthogonal, a Gramm-Schmidt orthogonalization is made and for each new frequency the old amplitudes of previously determined frequencies are corrected. For a chaotic trajectory variations of the frequencies and amplitudes determined over different time periods are expected. The change of frequencies in such a calculation is a measure of the chaoticity of the trajectory. While amplitudes are corrected, the frequencies (once determined) are constant. We suggest here simple linear corrections of frequencies for the effect of other close frequencies. The improvement of frequency determination is demonstrated on a model case. This method is applied to the first fifty numbered asteroids.     

分形和混沌理论在太阳物理学中的应用

本文对非线性科学的两个重要分支－分形和混沌－在太阳物理学中的应用情况作了综述，主要内容包括：太阳活动混沌性的揭示；对太阳活动混沌性的可能解释－太阳非线性发电机理论；一些太阳现象的分形描述；耀斑的自组织临界行为研究。最后给出了作者对这一领域工作前景的展望。     

Origin of chaos in the Prometheus-Pandora system

We demonstrate that the chaotic orbits of Prometheus and Pandora are due to interactions associated with the 121:118 mean motion resonance. Differential precession splits this resonance into a quartet of components equally spaced in frequency. Libration widths of the individual components exceed the splitting, resulting in resonance overlap which causes the chaos. Mean motions of Prometheus and Pandora wander chaotically in zones of width 1.8 and 3.1 deg yr⁻¹, respectively. A model with 1.5 degrees of freedom captures the essential features of the chaotic dynamics. We use it to show that the Lyapunov exponent of 0.3 yr⁻¹ arises because the critical argument of the dominant member of the resonant quartet makes approximately two separatrix crossings every 6.2 year precessional cycle.     

Chaotic motions of prometheus and pandora

Recent HST images of the saturnian satellites Prometheus and Pandora show that their longitudes deviate from predictions of ephemerides based on Voyager images. Currently Prometheus is lagging and Pandora leading these predictions by somewhat more than 20°. We show that these discrepancies are fully accounted for by gravitational interactions between the two satellites. These peak every 24.8 days at conjunctions and excite chaotic perturbations. The Lyapunov exponent for the Prometheus-Pandora system is of order 0.3 year⁻¹ for satellite masses based on a nominal density of 0.63 g cm⁻³. Interactions are strongest when the orbits come closest together. This happens at intervals of 6.2 years when their apses are antialigned. In this context, we note the sudden changes of opposite signs in the mean motions of Prometheus and Pandora at the end of 2000 occurred around the time their apsidal lines were antialigned.     

Conditional Entropy

In this paper we show that the Conditional Entropy of nearby orbits may be a useful tool to explore the phase space associated to a given Hamiltonian. The arc length parameter along the orbits, instead of the time, is used as a random variable to compute the entropy. In the first part of this work we summarise the main analytical results to support this tool while, in the second part, we present numerical evidence that this technique is able to localise (stable) periodic and quasiperiodic orbits, 'aperiodic' orbits (chaotic motion) and unstable periodic orbits (the 'source' of chaotic motion). Besides, we show that this technique provides a measure of chaos which is similar to that given by the largest Lyapunov Characteristic Number. It is important to remark that this method is very simple to compute and does not require long time integrations, just realistic physical times. This revised version was published online in July 2006 with corrections to the Cover Date.     

Chaotic gravitational zones around a regularly shaped complex rotating body

In preparation for the Rosetta mission, the location and widths of gravitational resonances surrounding a regularly shaped and possibly complex rotating body are mapped following the second fundamental model of resonance. It is found that for uniaxial rotation of the central body, the surrounding resonances are widest for prograde orbits. If the figure axis is tilted with respect to the spin axis of the central body, an additional number of wide resonances appear with a preference for prograde and inclined orbits, and the occurrence of initial conditions which lie in the globally connected chaotic web is significantly increased. For larger rotational excitations, it is seen how these new additional resonances overlap internally at low eccentricity for very large semi-major axes. However, with exceptions for some excited short-axis rotational modes of the central body, it is argued that most resonances vanish for retrograde orbits lying in the plane normal to the body spin, and that resonant or non-resonant stability therefore can be expected for a wide range of mean orbit eccentricities.     

On the entropy of self-gravitating systems

Leningrad State University; Kursk Institute for Improvement of Teachers. Translated from Astrofizika, Vol. 29, No. 3, pp. 595–601, November–December, 1988.     

The entropy of a cratered surface

The definition of the entropy of a cratered surface is given by analogy with the entropy of the information theory. The saturation, defined as the ratio between the area covered by craters of diameterD and the total observed area, is adopted as a measure of the probability to find a portion of a planetary surface covered by craters of the given diameterD.The meaning of such a new function is discussed in comparison with statistical approaches to the study of the cratering. Applications to Mercury are discussed.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.