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

Genome of the pitcher plant <i>Cephalotus </i>reveals genetic changes associated with carnivory

Carnivorous plants exploit animals as a nutritional source and have inspired long-standing questions about the origin and evolution of carnivory-related traits. To investigate the molecular bases of carnivory, we sequenced the genome of the heterophyllous pitcher plant Cephalotus follicularis, in which we succeeded in regulating the developmental switch between carnivorous and non-carnivorous leaves. Transcriptome comparison of the two leaf types and gene repertoire analysis identified genetic changes associated with prey attraction, capture, digestion and nutrient absorption. Analysis of digestive fluid proteins from C. follicularis and three other carnivorous plants with independent carnivorous origins revealed repeated co-options of stress-responsive protein lineages coupled with convergent amino acid substitutions to acquire digestive physiology. These results imply constraints on the available routes to evolve plant carnivory

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