Nonlocal elliptic and parabolic equations with general stable operators in weighted Sobolev spaces

We study nonlocal elliptic and parabolic equations on $C^{1,\tau}$ open sets in weighted Sobolev spaces, where $\tau\in (0,1)$. The operators we consider are infinitesimal generators of symmetric stable L\'evy processes, whose L\'evy measures are allowed to be very singular. Additionally, for parabolic equations, the measures are assumed to be merely measurable in the time variable.Comment: 38 page

Efficacy and safety of rapid intermittent bolus compared with slow continuous infusion in patients with severe hypernatremia (SALSA II trial): a study protocol for a randomized controlled trial

Background Hypernatremia is a common electrolyte disorder in children and elderly people and has high short-term mortality. However, no high-quality studies have examined the correction rate of hypernatremia and the amount of fluid required for correction. Therefore, in this study, we will compare the efficacy and safety of rapid intermittent bolus (RIB) and slow continuous infusion (SCI) of electrolyte-free solution in hypernatremia treatment. Methods This is a prospective, investigator-initiated, multicenter, open-label, randomized controlled study with two experimental groups. A total of 166 participants with severe hypernatremia will be enrolled and divided into two randomized groups; both the RIB and SCI groups will be managed with electrolyte-free water. We plan to infuse the same amount of fluid to both groups, for 1 hour in the RIB group and continuously in the SCI group. The primary outcome is a rapid decrease in serum sodium levels within 24 hours. The secondary outcomes will further compare the efficacy and safety of the two treatment protocols. Conclusion This is the first randomized controlled trial to evaluate the efficacy and safety of RIB correction compared with SCI in adult patients with severe hypernatremia

FlashPage: A read cache for low-latency SSDs in web proxy servers

The paper introduces FlashPage, a high-speed SSD caching system designed for ultra-fast media, with the goal of enhancing web page delivery in proxy servers. Traditional SSD caching schemes, designed primarily for slow HDD-based primary storage, encounter difficulties when applied to capacity-class SSDs as primary storage. This limits the high-performance capabilities of caching media. To address this issue, FlashPage operates within the Linux virtual filesystem layer, shortening the hit-handling path and minimizing lookup overhead. It incorporates a compact radix tree to fast locate cached data. These approaches reduce the software overhead for a 4kB read hit by over 5 times. FlashPage also employs novel admission and eviction policies to minimize flash wear while maintaining a high hit rate. As a second-level storage cache, FlashPage predicts the hotness of potential demotion candidates in the first-level storage cache (i.e., page cache), achieving a 10.1% higher hit rate and reducing write traffic by 10.4% compared to LRU. Evaluations using Varnish and Squid HTTP caches show its effectiveness, with up to 29.6% and 38.2% faster web request processing compared to Bcache and DM-Cache, state-of-the-art caching schemes in mainline Linux kernels

A Sobolev space theory for the Stochastic Partial Differential Equations with space-time non-local operators

We deal with the Sobolev space theory for the stochastic partial differential equation (SPDE) driven by Wiener processes $$\partial_{t}^{\alpha}u=\left( \phi(\Delta) u +f(u) \right) + \partial_t^\beta \sum_{k=1}^\infty \int_0^t g^k(u)\,dw_s^k, \quad t>0, x\in \mathbb{R}^d; \,\,\, u(0,\cdot)=u_0$$ as well as the SPDE driven by space-time white noise $$\partial^{\alpha}_{t}u=\phi(\Delta)u + f(u) + \partial^{\beta-1}_{t}h(u) \dot{W}, \quad t>0,x\in \mathbb{R}^d; \quad u(0,\cdot)=u_{0}.$$ Here, $\alpha\in (0,1), \beta\in (-\infty, \alpha+1/2)$, $\{w_t^k : k=1,2,\cdots\}$ is a family of independent one-dimensional Wiener processes, and $\dot{W}$ is a space-time white noise defined on $[0,\infty)\times \mathbb{R}^d$. The time non-local operator $\partial_{t}^{\gamma}$ denotes the Caputo fractional derivative if $\gamma>0$ and the Riemann-Liouville fractional integral if $\gamma\leq0$. The the spatial non-local operator $\phi(\Delta)$ is a type of integro-differential operator whose symbol is $-\phi(|\xi|^2)$, where $\phi$ is a Bernstein function satisfying \begin{equation*} \kappa_0\left(\frac{R}{r}\right)^{\delta_{0}} \leq \frac{\phi(R)}{\phi(r)}, \qquad \forall\,\, 0<r<R<\infty \end{equation*} with some constants $\kappa_0>0$ and $\delta_0\in (0,1]$. We prove the uniqueness and existence results in Sobolev spaces, and obtain the maximal regularity results of solutions.Comment: 50 page

Sobolev regularity theory for the non-local elliptic and parabolic equations on C1,1C^{1,1} open sets

We study the zero exterior problem for the elliptic equation $$\Delta^{\alpha/2}u-\lambda u=f, \quad x\in D\,; \quad u|_{D^c}=0$$ as well as for the parabolic equation $$u_t=\Delta^{\alpha/2}u+f, \quad t>0,\, x\in D \,; \quad u(0,\cdot)|_D=u_0, \,u|_{[0,T]\times D^c}=0.$$ Here, $\alpha\in (0,2)$, $\lambda \geq 0$ and $D$ is a $C^{1,1}$ open set. We prove uniqueness and existence of solutions in weighted Sobolev spaces, and obtain global Sobolev and H\"older estimates of solutions and their arbitrary order derivatives. We measure the Sobolev and H\"older regularities of solutions and their arbitrary derivatives using a system of weights consisting of appropriate powers of the distance to the boundary. The range of admissible powers of the distance to the boundary is sharp.Comment: 42 pages; Title changed; The paper has been accepted for publication in "Discrete and Continuous Dynamical Systems (DCDS)

시계열 데이터 영상화를 통한 아웃라이어 데이터의 라벨 노이즈 감소

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ClusterFetch: A lightweight prefetcher that responds to intensive disk read patterns

Application launch and loading times are important determinants of user experience in the personal computing environment. Since these delays largely depend on the performance of secondary storage, they can be reduced by prefetching disk blocks. However, existing prefetching schemes for general workloads incur a significant overhead in analyzing correlations between blocks so as to choose the blocks to prefetch, and, more significantly, these analyses lack accuracy. We propose a lightweight prefetcher called ClusterFetch which records the sequences of I/O requests that are triggered by file requests during launch and loading. When the same application is run again, the disk blocks that correspond to the stored sequences of I/O requests are prefetched when the related files are opened. Experimental results show that ClusterFetch can reduce application launch times by up to 30.9%, and loading times by up to 15.9%

TOWARD ENERGY-EFFICIENT ERROR CONTROL IN 3G BROADCAST VIDEO

Energy use is a key issue in battery-operated mobile devices. In order to extend battery life, mobiles showing video often allow a controlled drop in quality, which is tolerable when the shortcomings of a small screen are combined with the imperfections of visual perception. Both energy consumption and video quality are affected by the Reed-Solomon codes and interleaving levels used in 3G video broadcast services. We explore the effect of these elements of MAC-layer error control, and show how they can be manipulated to save energy while maintaining acceptable video quality through a controlled reduction in the number of parity symbols in the Reed-Solomon code and the level of interleaving. © 2002-2012 IEEE.