The Hydrostatic Approximation for the Primitive Equations by the Scaled Navier-Stokes Equations under the No-Slip Boundary Condition

In this paper we justify the hydrostatic approximation of the primitive equations in the maximal $L^p$-$L^q$-setting in the three-dimensional layer domain \Omega = \Torus^2 \times (-1, 1) under the no-slip (Dirichlet) boundary condition in any time interval $(0, T)$ for $T>0$. We show that the solution to the scaled Navier-Stokes equations with Besov initial data $u_0 \in B^{s}_{q,p}(\Omega)$ for $s > 2 - 2/p + 1/ q$ converges to the solution to the primitive equations with the same initial data in $\mathbb{E}_1 (T) = W^{1, p}(0, T ; L^q (\Omega)) \cap L^p(0, T ; W^{2, q} (\Omega))$ with order $O(\epsilon)$ where $(p,q) \in (1,\infty)^2$ satisfies \frac{1}{p} \leq \min \bracket{ 1 - 1/q, 3/2 - 2/q }. The global well-posedness of the scaled Navier-Stokes equations in $\mathbb{E}_1 (T)$ is also proved for sufficiently small $\epsilon>0$. Note that $T = \infty$ is included.Comment: 24page

Hierarchical Neural Memory Network for Low Latency Event Processing

This paper proposes a low latency neural network architecture for event-based dense prediction tasks. Conventional architectures encode entire scene contents at a fixed rate regardless of their temporal characteristics. Instead, the proposed network encodes contents at a proper temporal scale depending on its movement speed. We achieve this by constructing temporal hierarchy using stacked latent memories that operate at different rates. Given low latency event steams, the multi-level memories gradually extract dynamic to static scene contents by propagating information from the fast to the slow memory modules. The architecture not only reduces the redundancy of conventional architectures but also exploits long-term dependencies. Furthermore, an attention-based event representation efficiently encodes sparse event streams into the memory cells. We conduct extensive evaluations on three event-based dense prediction tasks, where the proposed approach outperforms the existing methods on accuracy and latency, while demonstrating effective event and image fusion capabilities. The code is available at https://hamarh.github.io/hmnet/Comment: Accepted to CVPR 202

Microphase-separated Structure of Ultrathin Polyurethane Films

We firstly observed the effect of film thickness on a microphase-separated structure of polyurethane at the ultrathin states. The interdomain spacing of domains decreased with decreasing film thickness due simply to the reduction of the space for domains.Nagasaki Symposium on Nano-Dynamics 2008 (NSND2008) 平成20年1月29日(火)於長崎大学 Invited Lectur

[3H]9-Methyl-7-bromoeudistomin D, a caffeine-like powerful Ca2+ releaser, binds to caffeine-binding sites distinct from the ryanodine receptors in brain microsomes

Abstract[3H]9-Methyl-7-bromoeudistomin D ([3H]MBED), the most powerful Ca2+ releaser from sarcoplasmic reticulum, specifically bound to the brain microsomes. Caffeine competitively inhibited [3H]MBED binding. [3H]MBED binding was markedly blocked by procaine, whereas that was enhanced by adenosine-5′-(β,γ-methylene)triphosphate. The Bmax value was 170 times more than that of [3H]ryanodine binding. The profile of sucrose-density gradient centrifugation of solubilized microsomes indicated that [3H]MBED binding protein was different from [3H]ryanodine binding protein. These results suggest that there are MBED/caffeine-binding sites in brain that are distinct from the ryanodine receptor and that MBED becomes an essential molecular probe for characterizing caffeine-binding protein in the central nervous system

Growth suppression of ice crystal basal face in the presence of a moderate ice-binding protein does not confer hyperactivity

Ice-binding proteins (IBPs) affect ice crystal growth by attaching to crystal faces. We present the effects on the growth of an ice single crystal caused by an ice-binding protein from the sea ice microalga Fragilariopsis cylindrus (fcIBP) that is characterized by the widespread domain of unknown function 3494 (DUF3494) and known to cause a moderate freezing point depression (below 1 °C). By the application of interferometry, bright-field microscopy, and fluorescence microscopy, we observed that the fcIBP attaches to the basal faces of ice crystals, thereby inhibiting their growth in the c direction and resulting in an increase in the effective supercooling with increasing fcIBP concentration. In addition, we observed that the fcIBP attaches to prism faces and inhibits their growth. In the event that the effective supercooling is small and crystals are faceted, this process causes an emergence of prism faces and suppresses crystal growth in the a direction. When the effective supercooling is large and ice crystals have developed into a dendritic shape, the suppression of prism face growth results in thinner dendrite branches, and growth in the a direction is accelerated due to enhanced latent heat dissipation. Our observations clearly indicate that the fcIBP occupies a separate position in the classification of IBPs due to the fact that it suppresses the growth of basal faces, despite its moderate freezing point depression