Limit cycles in a Kolmogorov-type model

In this paper, a Kolmogorov-type model, which includes the Gause-type model (Kuang and Freedman, 1988), the general predator-prey model (Huang 1988, Huang and Merrill 1989), and many other specialized models, is studied. The stability of equilibrium points, the existence and uniqueness of limit cycles in the model are proved

Three-Tier Capacity and Traffic Allocation for Core, Edges, and Devices for Mobile Edge Computing

In order to satisfy the 5G requirements of ultra-low latency, mobile edge computing (MEC)-based architecture, composed of three-tier nodes, core, edges, and devices, is proposed. In MEC-based architecture, previous studies focused on the controlplane issue, i.e., how to allocate traffic to be processed at different nodes to meet this ultra-low latency requirement. Also important is how to allocate the capacity to different nodes in the management plane so as to establish a minimal-capacity network. The objectives of this paper is to solve two problems: 1) to allocate the capacity of all nodes in MEC-based architecture so as to provide a minimal-capacity network and 2) to allocate the traffic to satisfy the latency percentage constraint, i.e., at least a percentage of traffic satisfying the latency constraint. In order to achieve these objectives, a two-phase iterative optimization (TPIO) method is proposed to try to optimize capacity and traffic allocation in MEC-based architecture. TPIO iteratively uses two phases to adjust capacity and traffic allocation respectively because they are tightly coupled. In the first phase, using queuing theory calculates the optimal traffic allocation under fixed allocated capacity, while in the second phase, allocated capacity is further reduced under fixed traffic allocation to satisfy the latency percentage constraint. Simulation results show that MEC-based architecture can save about 20.7% of capacity of two-tier architecture. Further, an extra 12.2% capacity must be forfeited when the percentage of satisfying latency is 90%, compared to 50%.This work was supported in part by H2020 collaborative Europe/Taiwan research project 5G-CORAL (grant number 761586), and Ministry of Science and Technology, Taiwan for financially supporting this research under Contract No. MOST 106-2218-E-009-018

On the number of limit cycles of the Lienard equation

In this paper, we study a Lienard system of the form dot{x}=y-F(x), dot{y}=-x, where F(x) is an odd polynomial. We introduce a method that gives a sequence of algebraic approximations to the equation of each limit cycle of the system. This sequence seems to converge to the exact equation of each limit cycle. We obtain also a sequence of polynomials R_n(x) whose roots of odd multiplicity are related to the number and location of the limit cycles of the system.Comment: 10 pages, 5 figures. Submitted to Physical Review

Three Bianthraquinone Derivatives from the Mangrove Endophytic Fungus Alternaria sp. ZJ9-6B from the South China Sea

Three new bianthraquinone derivatives, alterporriol K (1), L (2) and M (3), along with six known compounds were obtained from extracts of the endophytic fungus Alternaria sp. ZJ9-6B, isolated from the mangrove Aegiceras corniculatum collected in the South China Sea. Their structures were elucidated by one- and two-dimensional NMR spectroscopy, MS data analysis and circular dichroism measurements. Compounds 1, 2 and 3 were first isolated alterporriols with a C-2–C-2′ linkage. The crystallographic data of tetrahydroaltersolanol B (7) was reported for the first time. In the primary bioassays, alterporriol K and L exhibited moderate cytotoxic activity towards MDA-MB-435 and MCF-7 cells with IC50 values ranging from 13.1 to 29.1 μM

Longitudinal Changes in Diffusion Tensor Imaging Following Mild Traumatic Brain Injury and Correlation With Outcome

The chronic consequences of traumatic brain injury (TBI) may contribute to the increased risk for early cognitive decline and dementia, primarily due to diffusion axonal injury. Previous studies in mild TBI (mTBI) have been controversial in describing the white matter tract integrity changes occurring at acute and subacute post-injury. In this prospective longitudinal study, we aim to investigate the longitudinal changes of white matter (WM) using diffusion tensor imaging (DTI) and their correlations with neuropsychological tests. Thirty-three patients with subacute mTBI and 31 matched healthy controls were studied with an extensive imaging and clinical battery. Neuroimaging was obtained within 7 days post-injury for acute scans and repeated at 1 and 3 months post-injury. Using a region-of-interest-based approach, tract-based spatial statistics was used to conduct voxel-wise analysis on diffusion changes in mTBI and was compared to those of healthy matched controls, scanned during the same time period and rescanned with an interval similar to that of patients. We found decreased fractional anisotropy (FA) values in the left anterior limb of internal capsule (ALIC) and right inferior fronto-occipital fasciculus (IFOF) during the 7 days post-injury, which showed longitudinal evidence of recovery following 1 month post-injury. Increased FA values in these two tracts at 1 month post-injury were positively associated with better performance on cognitive information processing speed at initial assessment. By contrast, there were also some tracts (right anterior corona radiata, forceps major, and body of corpus callosum) exhibiting the continuing loss of integrity sustaining even beyond 3 months, which can predict the persisting post-concussion syndromes. Continuing loss of structural integrity in some tracts may contribute to the persistent post-concussion syndromes in mTBI patients, suggesting certain tracts providing an objective biomarker for tracking the pathological recovery process following mTBI

Gray Matter Alterations in Post-Traumatic Stress Disorder, Obsessive-Compulsive Disorder, and Social Anxiety Disorder

Post-traumatic stress disorder (PTSD), obsessive-compulsive disorder (OCD) and social anxiety disorder (SAD) all bear the core symptom of anxiety and are separately classified in the new DSM-5 system. The aim of the present study is to obtain evidence for neuroanatomical difference for these disorders. We applied voxel-based morphometry (VBM) with Diffeomorphic Anatomic Registration Through Exponentiated Lie (DARTEL) to compare grey matter volume (GMV) in Magnetic Resonance (MR) images obtained for thirty patients with PTSD, twenty nine patients with OCD, twenty patients with SAD and thirty healthy controls. GMV across all four groups differed in left hypothalamus and left inferior parietal lobule and post hoc analyses revealed that this difference is primarily due to reduced GMV in the PTSD group relative to the other groups. Further analysis revealed that the PTSD group also showed reduced GMV in frontal lobe, temporal lobe and cerebellum compared to the OCD group, and reduced GMV in frontal lobes bilaterally compared to SAD group. A significant negative correlation with anxiety symptoms is observed for GMV in left hypothalamus in three disorder groups. We have thus found evidence for brain structure differences that in future could provide biomarkers to potentially support classification of these disorders using MRI