Linearized Asymptotic Stability for Fractional Differential Equations

We prove the theorem of linearized asymptotic stability for fractional differential equations. More precisely, we show that an equilibrium of a nonlinear Caputo fractional differential equation is asymptotically stable if its linearization at the equilibrium is asymptotically stable. As a consequence we extend Lyapunov's first method to fractional differential equations by proving that if the spectrum of the linearization is contained in the sector \{\lambda \in \C : |\arg \lambda| > \frac{\alpha \pi}{2}\} where $\alpha > 0$ denotes the order of the fractional differential equation, then the equilibrium of the nonlinear fractional differential equation is asymptotically stable

APMEC: An Automated Provisioning Framework for Multi-access Edge Computing

Novel use cases and verticals such as connected cars and human-robot cooperation in the areas of 5G and Tactile Internet can significantly benefit from the flexibility and reduced latency provided by Network Function Virtualization (NFV) and Multi-Access Edge Computing (MEC). Existing frameworks managing and orchestrating MEC and NFV are either tightly coupled or completely separated. The former design is inflexible and increases the complexity of one framework. Whereas, the latter leads to inefficient use of computation resources because information are not shared. We introduce APMEC, a dedicated framework for MEC while enabling the collaboration with the management and orchestration (MANO) frameworks for NFV. The new design allows to reuse allocated network services, thus maximizing resource utilization. Measurement results have shown that APMEC can allocate up to 60% more number of network services. Being developed on top of OpenStack, APMEC is an open source project, available for collaboration and facilitating further research activities

The spindle of oocytes observed by polarized light microscope can predict embryo quality

Background: The aim is to evaluate spindle position of metaphase II oocyte and the development of embryos originated from oocytes with spindle and without spindle.Methods: Cross-sectional analysis Research: 250 MII oocytes were analyzed with polarized microscope in Military Institute of Clinical Embryology and Histology, Vietnam Military Medical University.Results: Spindles were detected in 170 (77.98%) of 218 metaphase II oocytes, 115 spindles (67.65%) of MII oocytes is beneath or adjacent to the first polar body, 55 oocytes had the spindle located between 300 and 1800 away from the first polar body. Fertilization rate and the rate of good quality embryos in oocytes with a visible spindle (77.98% and 61.02%) were higher than those in oocytes without a visible spindle (22.02% and 36.84%), the difference was statistically significant with p <0.001 and p <0.05.Conclusions: The spindle position of metaphase II oocytes is not always beneath or adjacent to the first polar body. Fertilization rate and the rate of good quality embryos in oocytes with a visible spindle were higher than those in oocytes without a visible spindle

HD101584: Circumstellar characteristics and evolutionary status

We have performed a study of the characteristics of the circumstellar environment of the binary object HD101584, that provides information on a likely evolutionary scenario. We have obtained and analysed ALMA observations, complemented with observations using APEX, of a large number of molecular lines. An analysis of the spectral energy distribution has also been performed. Emissions from 12 molecular species (not counting isotopologues) have been observed, and most of them mapped with angular resolutions in the range 0.1" to 0.6". Four circumstellar components are identified: i) a central compact source of size 0.15", ii) an expanding equatorial density enhancement (a flattened density distribution in the plane of the orbit) of size 3", iii) a bipolar high-velocity outflow (150 km/s), and iv) an hourglass structure. The outflow is directed almost along the line of sight. There is evidence of a second bipolar outflow. The mass of the circumstellar gas is 0.5[D/1 kpc]^2 Msun, about half of it lies in the equatorial density enhancement. The dust mass is 0.01[D/1 kpc]^2 Msun, and a substantial fraction of this is in the form of large-sized, up to 1 mm, grains. The estimated kinetic age of the outflow is 770[D/1 kpc] yr. The kinetic energy and the scalar momentum of the accelerated gas are estimated to be 7x10^(45)[D/1 kpc]^2 erg and 10^(39)[D/1 kpc]^2 g cm/s, respectively. We provide good evidence that the binary system HD101584 is in a post-common-envelope-evolution phase, that ended before a stellar merger. Isotope ratios combined with stellar mass estimates suggest that the primary star's evolution was terminated already on the first red giant branch (RGB). Most of the energy required to drive the outflowing gas was probably released when material fell towards the companion.Comment: Accepted for publication in A&

Semi-Automatic 3-D Segmentation of Anatomical Structures of Brain MRI Volumes using Graph Cuts

We present a semi-automatic segmentation technique of the anatomical structures of the brain: cerebrum, cerebellum, and brain stem. The method uses graph cuts segmentation with an anatomic template for initialization. First, a skull stripping procedure is applied to remove non-brain tissues. Then, the segmentation is done hierarchically by first, extracting first the cerebrum from the brain, and then from the remaining volume the cerebellum and the brain stem are separated. This method is fast and can separate different anatomical structures of the brain in spite of weak boundaries. We describe our approach and present experimental results demonstrating its usefulness