Reconstructing Images from Projections Using the Maximum-Entropy Method. Numerical Simulations of Low-Aspect Astrotomography

The reconstruction of images from a small number of projections using the maximum-entropy method (MEM) with the Shannon entropy is considered. MEM provides higher-quality image reconstruction for sources with extended components than the Hogbom CLEAN method, which is also used in low-aspect astrotomography. The quality of image reconstruction for sources with mixed structure containing bright, compact features embedded in a comparatively weak, extended base can be further improved using a difference-mapping method, which requires a generalization of MEM for the reconstruction of sign-variable functions.We draw conclusions based on the results of numerical simulations for a number of model radio sources with various morphologies.Comment: 11 pages, 9 figure

A Solution to the Problem of Phaseless Mapping for a High-Orbit Space-Ground Radio Interferometer

We consider the problem of mapping with ultra-high angular resolution using a space-ground radio interferometer with a space antenna in a high orbit,whose apogee height exceeds the radius of the Earth by a factor of ten. In this case, a multielement interferometer essentially degenerates into a two-element interferometer. The degeneracy of the close-phase relations prevents the use of standard methods for hybrid mapping and self-calibration for the correct reconstruction of images. We propose a new phaseless mapping method based on methods for the reconstruction of images in the complete absence of phase information, using only the amplitudes of the spatial-coherence function of the source. In connection with this problem, we propose a new method for the reliable solution of the phase problem, based on optimizing information-carrying nonlinear functionals, in particular, the Shannon entropy. Results of simulations of mapping radio sources with various structures with ultra-high angular resolution in the framework of the RADIOASTRON mission are presented.Comment: 15 pages, 7 figure

Invariant information and quantum state estimation

The invariant information introduced by Brukner and Zeilinger, Phys. Rev. Lett. 83, 3354 (1999), is reconsidered from the point of view of quantum state estimation. We show that it is directly related to the mean error of the standard reconstruction from the measurement of a complete set of mutually complementary observables. We give its generalization in terms of the Fisher information. Provided that the optimum reconstruction is adopted, the corresponding quantity loses its invariant character.Comment: 4 pages, no figure

Reconstruction of the spin state

System of 1/2 spin particles is observed repeatedly using Stern-Gerlach apparatuses with rotated orientations. Synthesis of such non-commuting observables is analyzed using maximum likelihood estimation as an example of quantum state reconstruction. Repeated incompatible observations represent a new generalized measurement. This idealized scheme will serve for analysis of future experiments in neutron and quantum optics.Comment: 4 pages, 1 figur

Unravelling the size distribution of social groups with information theory on complex networks

The minimization of Fisher's information (MFI) approach of Frieden et al. [Phys. Rev. E {\bf 60} 48 (1999)] is applied to the study of size distributions in social groups on the basis of a recently established analogy between scale invariant systems and classical gases [arXiv:0908.0504]. Going beyond the ideal gas scenario is seen to be tantamount to simulating the interactions taking place in a network's competitive cluster growth process. We find a scaling rule that allows to classify the final cluster-size distributions using only one parameter that we call the competitiveness. Empirical city-size distributions and electoral results can be thus reproduced and classified according to this competitiveness, which also allows to correctly predict well-established assessments such as the "six-degrees of separation", which is shown here to be a direct consequence of the maximum number of stable social relationships that one person can maintain, known as Dunbar's number. Finally, we show that scaled city-size distributions of large countries follow the same universal distribution

Configuration Complexities of Hydrogenic Atoms

The Fisher-Shannon and Cramer-Rao information measures, and the LMC-like or shape complexity (i.e., the disequilibrium times the Shannon entropic power) of hydrogenic stationary states are investigated in both position and momentum spaces. First, it is shown that not only the Fisher information and the variance (then, the Cramer-Rao measure) but also the disequilibrium associated to the quantum-mechanical probability density can be explicitly expressed in terms of the three quantum numbers (n, l, m) of the corresponding state. Second, the three composite measures mentioned above are analytically, numerically and physically discussed for both ground and excited states. It is observed, in particular, that these configuration complexities do not depend on the nuclear charge Z. Moreover, the Fisher-Shannon measure is shown to quadratically depend on the principal quantum number n. Finally, sharp upper bounds to the Fisher-Shannon measure and the shape complexity of a general hydrogenic orbital are given in terms of the quantum numbers.Comment: 22 pages, 7 figures, accepted i

Outcome measurement instruments for peripheral vascular malformations and an assessment of the measurement properties: a systematic review

© 2019, The Author(s). Purpose: The Outcome measures for vascular malformation (OVAMA) group reached consensus on the core outcome domains for the core outcome set (COS) for peripheral vascular malformations (venous, lymphatic and arteriovenous malformations). However, it is unclear which instruments should be used to measure these domains. Therefore, our aims were to identify all outcome measurement instruments available for vascular malformations, and to evaluate their measurement properties. Methods: With the first literature search, we identified outcomes and instruments previously used in prospective studies on vascular malformations. A second search yielded studies on measurement properties of patient- and physician-reported instruments that were either developed for vascular malformations, or used in prospective studies. If the latter instruments were not specifically validated for vascular malformations, we performed a third search for studies on measurement properties in clinically similar diseases (vascular or lymphatic diseases and benign tumors). We assessed the methodological quality of these studies following the Consensus-based Standards for the selection of health Measurement Instruments methodology, and evaluated the quality of the measurement properties. Results: The first search yielded 27 studies, none using disease-specific instruments. The second and third search included 22 development and/or validation studies, concerning six instruments. Only the Lymphatic Malformation Function Instrument was developed specifically for vascular malformations. Other instruments were generic QoL instruments developed and/or partly validated for clinically similar diseases. Conclusions: Additional research on measurement properties is needed to assess which instruments may be included in the COS. This review informs the instrument selection and/or the development of new instruments. Systematic review registration: PROSPERO, 42017056242

China\u27s hegemonic intentions and trajectory: Will it opt for benevolent, coercive, or Dutch‐style hegemony?

China\u27s unprecedented economic growth led some scholars to conclude that it will replace the United States as the future global hegemon. However, China\u27s intentions in exercising future global leadership are yet unknown and difficult to extrapolate from its often contradictory behaviour. A preliminary overview of China\u27s island building in the South China Sea reveals its potentially coercive intentions. This inference is consistent with the analysis of those who prognosticate China\u27s violent rise. Conversely and simultaneously, China\u27s participation in peacekeeping operations and its global investments evince its benevolent hegemonic intentions, which are congruent with the argument of those who predict China\u27s peaceful hegemonic ascent. Confronted with these divergent tendencies in China\u27s recent international relations, and assuming its continued rise, it is, thus, essential to examine China\u27s strategic intentions and how these may ultimately project its violent or peaceful hegemonic rise. This article argues that the “Third Way” or “Dutch‐style” hegemony is highly instructive in this context and, thus, should be examined and added to the existing debate on China\u27s rise as either a benevolent or coercive hegemon. We argue that Dutch‐style hegemony may be the most viable way for China to proceed in its global hegemonic ascendancy

Induced measures in the space of mixed quantum states

We analyze several product measures in the space of mixed quantum states. In particular we study measures induced by the operation of partial tracing. The natural, rotationally invariant measure on the set of all pure states of a N x K composite system, induces a unique measure in the space of N x N mixed states (or in the space of K x K mixed states, if the reduction takes place with respect to the first subsystem). For K=N the induced measure is equal to the Hilbert-Schmidt measure, which is shown to coincide with the measure induced by singular values of non-Hermitian random Gaussian matrices pertaining to the Ginibre ensemble. We compute several averages with respect to this measure and show that the mean entanglement of $N \times N$ pure states behaves as lnN-1/2.Comment: 12 latex pages, 2 figures in epsf, submited to J. Phys. A. ver.3, some improvements and a few references adde

Apolipoprotein E4 has extensive conformational heterogeneity in lipid-free and lipid-bound forms

The ε4-allele variant of apolipoprotein E (ApoE4) is the strongest genetic risk factor for Alzheimer\u27s disease, although it only differs from its neutral counterpart ApoE3 by a single amino acid substitution. While ApoE4 influences the formation of plaques and neurofibrillary tangles, the structural determinants of pathogenicity remain undetermined due to limited structural information. Previous studies have led to conflicting models of the C-terminal region positioning with respect to the N-terminal domain across isoforms largely because the data are potentially confounded by the presence of heterogeneous oligomers. Here, we apply a combination of single-molecule spectroscopy and molecular dynamics simulations to construct an atomically detailed model of monomeric ApoE4 and probe the effect of lipid association. Importantly, our approach overcomes previous limitations by allowing us to work at picomolar concentrations where only the monomer is present. Our data reveal that ApoE4 is far more disordered and extended than previously thought and retains significant conformational heterogeneity after binding lipids. Comparing the proximity of the N- and C-terminal domains across the three major isoforms (ApoE4, ApoE3, and ApoE2) suggests that all maintain heterogeneous conformations in their monomeric form, with ApoE2 adopting a slightly more compact ensemble. Overall, these data provide a foundation for understanding how ApoE4 differs from nonpathogenic and protective variants of the protein