Choreographic solution to the general relativistic three-body problem

We revisit the three-body problem in the framework of general relativity. The Newtonian N-body problem admits choreographic solutions, where a solution is called choreographic if every massive particles move periodically in a single closed orbit. One is a stable figure-eight orbit for a three-body system, which was found first by Moore (1993) and re-discovered with its existence proof by Chenciner and Montgomery (2000). In general relativity, however, the periastron shift prohibits a binary system from orbiting in a single closed curve. Therefore, it is unclear whether general relativistic effects admit a choreographic solution such as the figure eight. We carefully examine general relativistic corrections to initial conditions so that an orbit for a three-body system can be closed and a figure eight. This solution is still choreographic. This illustration suggests that the general relativistic N-body problem also may admit a certain class of choreographic solutions.Comment: 10 pages, 4 figures, text improved, accepted for publication in PR

Involvement of the Precuneus/Posterior Cingulate Cortex Is Significant for the Development of Alzheimer’s Disease: A PET (THK5351, PiB) and Resting fMRI Study

Background: Imaging studies in Alzheimer’s disease (AD) have yet to answer the underlying questions concerning the relationship among tau retention, neuroinflammation, network disruption and cognitive decline. We compared the spatial retention patterns of 18F-THK5351 and resting state network (RSN) disruption in patients with early AD and healthy controls.Methods: We enrolled 23 11C-Pittsburgh compound B (PiB)-positive patients with early AD and 24 11C-PiB-negative participants as healthy controls. All participants underwent resting state functional MRI and 18F-THK5351 PET scans. We used scaled subprofile modeling/principal component analysis (SSM/PCA) to reduce the complexity of multivariate data and to identify patterns that exhibited the largest statistical effects (variances) in THK5351 concentration in AD and healthy controls.Findings: SSM/PCA identified a significant spatial THK5351 pattern composed by mainly three clusters including precuneus/posterior cingulate cortex (PCC), right and left dorsolateral prefrontal cortex (DLPFC) which accounted for 23.6% of the total subject voxel variance of the data and had 82.6% sensitivity and 79.1% specificity in discriminating AD from healthy controls. There was a significant relationship between the intensity of the 18F-THK5351 covariation pattern and cognitive scores in AD. The spatial patterns of 18F-THK5351 uptake showed significant similarity with intrinsic functional connectivity, especially in the PCC network. Seed-based connectivity analysis from the PCC showed significant decrease in connectivity over widespread brain regions in AD patients. An evaluation of an autopsied AD patient with Braak V showed that 18F-THK5351 retention corresponded to tau deposition, monoamine oxidase-B (MAO-B) and astrogliosis in the precuneus/PCC.Interpretation: We identified an AD-specific spatial pattern of 18F-THK5351 retention in the precuneus/PCC, an important connectivity hub region in the brain. Disruption of the functional connections of this important network hub may play an important role in developing dementia in AD

Outage Analysis for Correlated Sources Coding over NOMA in Shadowed κ-µ Fading

We consider correlated sources coding over a up-link non-orthogonal multiple access shadowed κ-µ fading channel. The sufficient condition for lossless coding is determined by the intersection of the Slepian-Wolf region and multiple access channel region, assuming source-channel separation holds. The exact expression for the outage probability upper bound is derived by dividing the sufficient conditions into three cases. The accuracy of the analytical results is verified by the Monte-Carlo simulations. The analytical results indicate that more than 2nd order diversity gain can be achieved with a larger ratio of line-of-sight dominant component in single cluster or multiple clusters with non-line-of-sight component. It is also found that the shadowed κ-µ fading well represents one-sided Gaussian, Rayleigh, Rician, and Nakagami-m fading in calculating the outage probability. Furthermore, the ϵ-outage achievable rate is analyzed, which is found to be larger with higher source correlation and/or average signal-to-noise ratio

Performance analysis of one-source-with-one-helper transmission over shadowed κ-μ fading multiple access channels

The performance of correlated sources transmission over multiple access shadowed κ-μ fading channels is investigated, in which one of the correlated sources needs to be recovered at the destination, whereas the other serves as a helper. The sufficient condition for lossless coding is determined by the intersection of the modified Slepian–Wolf region and the multiple access channel region. The outage probability upper bounds are derived based on the sufficient condition, with the Gaussian codebook capacity and the constellation constrained capacity, respectively. The difference between the outage probabilities derived with the two kinds of capacities is found to be very minor, when the spectrum efficiency or source rate is low; however, with high spectrum efficiency or high source rate, such difference becomes significant. A closed-form outage approximation is also obtained at the high signal-to-noise ratio region. The accuracy of the analytical results is verified by the Monte-Carlo simulations. It is found that shadowing significantly affects the outage performance, however, it has no effect on the diversity gain. Furthermore, the power allocation between the source and the helper is studied to minimize the outage probability and it is found that generally more power should be allocated to the helper in the case with higher source-helper correlation