Well-posedness of mild solutions to the drift-diffusion and the vorticity equations in amalgam spaces

We consider the Cauchy problem of the drift-diffusion and the vorticity equations. Both equations involve the Poisson equation and a nonlocal effect of the Green's function influences the solution to the problem. In this paper, we study the well-posedness of the drift-diffusion and the vorticity equations by using amalgam spaces of Lebesgue spaces. Moreover, we show the unconditional uniqueness of mild solutions to the drift-diffusion equation in amalgam spaces

Convergence rate of Tsallis entropic regularized optimal transport

In this paper, we consider Tsallis entropic regularized optimal transport and discuss the convergence rate as the regularization parameter $\varepsilon$ goes to $0$. In particular, we establish the convergence rate of the Tsallis entropic regularized optimal transport using the quantization and shadow arguments developed by Eckstein--Nutz. We compare this to the convergence rate of the entropic regularized optimal transport with Kullback--Leibler (KL) divergence and show that KL is the fastest convergence rate in terms of Tsallis relative entropy.Comment: 21 page

Maximal regularity of the heat evolution equation on spatial local spaces and application to a singular limit problem of the Keller–Segel system

We consider the singular limit problem for the Cauchy problem of the (Patlak–) Keller–Segel system of parabolic-parabolic type. The problem is considered in the uniformly local Lebesgue spaces and the singular limit problem as the relaxation parameter $$tau$$ goes to infinity, the solution to the Keller–Segel equation converges to a solution to the drift-diffusion system in the strong uniformly local topology. For the proof, we follow the former result due to Kurokiba–Ogawa [20–22] and we establish maximal regularity for the heat equation over the uniformly local Lebesgue and Morrey spaces which are non-UMD Banach spaces and apply it for the strong convergence of the singular limit problem in the scaling critical local spaces

Finite time blow up and concentration phenomena for a solution to drift-diffusion equations in higher dimensions

We show the finite time blow up of a solution to the Cauchy problem of a drift-diffusion equation of a parabolic-elliptic type in higher space dimensions. If the initial data satisfies a certain condition involving the entropy functional, then the corresponding solution to the equation does not exist globally in time and blows up in a finite time for the scaling critical space. Besides there exists a concentration point such that the solution exhibits the concentration in the critical norm. This type of blow up was observed in the scaling critical two dimensions. The proof is based on the profile decomposition and the Shannon inequality in the weighted space

函数解析的方法による移流拡散方程式の特異極限問題と解の漸近挙動について

要約のみTohoku University小川卓克課

Dynamic optimization of multicast active probing path to locate lossy links for OpenFlow networks

To maintain a high quality of service in managed networks, detecting and locating high loss-rate links (i.e., lossy links that are likely congested or physically unstable) in a fast and efficient manner is required. In our previous work, we proposed a centrally-managed network-assisted framework of locating lossy links on OpenFlow networks. In the framework, the OpenFlow controller builds a multicast measurement route; a measurement host launches a series of multicast probe packets traversing all full-duplex links along the measurement route; and then the controller collects statistical information (flow-stats) on the arrival of those probe packets at different input ports on selected switches and compares them to narrow down and identify the locations of high loss-rate links. The number of accesses to switches in collecting the flow-stats until locating all lossy links should be as small as possible for fast and efficient measurement. However, it strongly depends on not only the collection order of the flow-stats but also the topological locations of lossy links in the multicast measurement route; the former one was investigated in the previous work but the latter has not been well explored. Therefore, in this paper, we develop a new dynamic scheme of building the multicast measurement route and controlling the collection order of flow-stats from switches, which leverages lossy link locations obtained in the recent past measurements in a repeated-measurement setting. The results of numerical simulation on real-world large-scale network topologies suggest the effectiveness and also the issues of the proposed lossy link location scheme.The 34th International Conference on Information Networking (ICOIN 2020), January 7-10, 2020, Barcelona, Spai

Anti-hypercholesterolemic Effects and a Good Safety Profile of SCM-198 in Animals: From ApoE Knockout Mice to Rhesus Monkeys

Although several lipid-lowering agents have been introduced for the treatment of atherosclerosis (AS), currently marketed medications have not solved the problem completely. This study aims to investigate the effects of leonurine (SCM-198) on dyslipidemia in mammals with ApoE knockout (ApoE-/-) mice, New Zealand white rabbits and senile Rhesus monkeys fed with high fat diet were dosed daily with leonurine or atorvastatin. The serum total cholesterol (TC), triglyceride (TG), low density lipoprotein (LDL), and high-density lipoprotein (HDL) were determined. Moreover, in Rhesus monkeys, bodyweight, arterial ultrasound of right common carotid artery, Apolipoprotein A1 (ApoA1) and ApoB levels, hematologic and toxicological examinations were detected. Serum TC and TG in both mice and rabbits were significantly reduced by SCM-198 and atorvastatin. In the 10 mg/kg SCM-198 group of monkeys, maximum TC reduction of 24.05% was achieved at day 150, while 13.16% LDL reduction achieved at day 60, without arterial morphologic changes or adverse events. Atorvastatin (1.2 mg/kg) showed similar effects as SCM-198 in improving lipid profiles in monkeys, yet its long-term use could induce tolerance. Furthermore, leonurine suppressed genes expression of fatty acid synthesis, such as fatty acid synthase (FASN), stearoyl-CoA desaturase (SCD-1), sterol regulatory element-binding protein (SREBF) in liver in high fat diet feeding ApoE-/- mice. SCM-198, with a reliable safety profile, is of high value in improving lipid profiles in mammals, providing an alternative to a substantial population who are statin-intolerant