Compact 99-Point Finite Difference Methods with High Accuracy Order and/or MM-Matrix Property for Elliptic Cross-Interface Problems

In this paper we develop finite difference schemes for elliptic problems with piecewise continuous coefficients that have (possibly huge) jumps across fixed internal interfaces. In contrast with such problems involving one smooth non-intersecting interface, that have been extensively studied, there are very few papers addressing elliptic interface problems with intersecting interfaces of coefficient jumps. It is well known that if the values of the permeability in the four subregions around a point of intersection of two such internal interfaces are all different, the solution has a point singularity that significantly affects the accuracy of the approximation in the vicinity of the intersection point. In the present paper we propose a fourth-order $9$-point finite difference scheme on uniform Cartesian meshes for an elliptic problem whose coefficient is piecewise constant in four rectangular subdomains of the overall two-dimensional rectangular domain. Moreover, for the special case when the intersecting point of the two lines of coefficient jumps is a grid point, such a compact scheme, involving relatively simple formulas for computation of the stencil coefficients, can even reach sixth order of accuracy. Furthermore, we show that the resulting linear system for the special case has an $M$-matrix, and prove the theoretical sixth order convergence rate using the discrete maximum principle. Our numerical experiments demonstrate the fourth (for the general case) and sixth (for the special case) accuracy orders of the proposed schemes. In the general case, we derive a compact third-order finite difference scheme, also yielding a linear system with an $M$-matrix. In addition, using the discrete maximum principle, we prove the third order convergence rate of the scheme for the general elliptic cross-interface problem.Comment: 25 pages, 13 figure

緑内障患者の房水に含まれる変化した代謝物がヒトの線維柱帯細胞の性質に及ぼす影響

要約のみTohoku University中澤徹課

Sixth-Order Hybrid FDMs and/or the M-Matrix Property for Elliptic Interface Problems with Mixed Boundary Conditions

In this paper, we develop sixth-order hybrid finite difference methods (FDMs) for the elliptic interface problem $-\nabla \cdot( a\nabla u)=f$ in $\Omega\backslash \Gamma$, where $\Gamma$ is a smooth interface inside $\Omega$. The variable scalar coefficient $a>0$ and source $f$ are possibly discontinuous across $\Gamma$. The hybrid FDMs utilize a 9-point compact stencil at any interior regular point of the grid and a 13-point stencil at irregular points near $\Gamma$. For interior regular points away from $\Gamma$, we obtain a sixth-order 9-point compact FDM satisfying the M-matrix property. Consequently, for the elliptic problem without interface (i.e., $\Gamma$ is empty), our compact FDM satisfies the discrete maximum principle, which guarantees the theoretical sixth-order convergence. We also derive sixth-order compact (4-point for corners and 6-point for edges) FDMs having the M-matrix property at any boundary point subject to (mixed) Dirichlet/Neumann/Robin boundary conditions. For irregular points near $\Gamma$, we propose fifth-order 13-point FDMs, whose stencil coefficients can be effectively calculated by recursively solving several small linear systems. Theoretically, the proposed high order FDMs use high order (partial) derivatives of the coefficient $a$, the source term $f$, the interface curve $\Gamma$, the two jump functions along $\Gamma$, and the functions on $\partial \Omega$. Numerically, we always use function values to approximate all required high order (partial) derivatives in our hybrid FDMs without losing accuracy. Our proposed FDMs are independent of the choice representing $\Gamma$ and are also applicable if the jump conditions on $\Gamma$ only depend on the geometry (e.g., curvature) of the curve $\Gamma$. Our numerical experiments confirm the sixth-order convergence in the $l_{\infty}$ norm of the proposed hybrid FDMs for the elliptic interface problem

Erdosteine prevents contrast-induced renal oxidative stress damage in mice

Purpose: To investigate the protective effect of erdosteine on contrast-induced renal oxidative stress in mice. Methods: C57BL/6 mice were injected intraperitoneally with contrast medium to establish an acute kidney injury model (AKI). Renal function, blood urea nitrogen (BUN) and serum creatinine (SCr) were determined. Also, oxidative stress, lactate dehydrogenase (LDH), malondialdehyde (MDA), superoxide dismutase (SOD) and reduced glutathione (GSH) were evaluated. And the renal tissue structure was examined by light microscopy, while Western blot (WB) and Real-time polymerase chain reaction (RT-PCR) were used to determine the expressions of senescence-related factor, Nrf-2 and downstream antioxidant factor. Results: Erdosteine improved the renal structure of mice and significantly decreased serum BUN and SCr levels. In addition, erdosteine promoted the expression of antioxidant enzymes SOD1, SOD2, GPX1 and GPX3 in renal tissues, decreased the content of ROS, and inhibited the content of LDH and MDA in serum. Also, WB and RT-PCR results showed that erdosteine activated Nrf2 pathway, thereby alleviating contrast-induced renal injury. Conclusion: Erdosteine inhibits contrast-induced renal oxidative stress in mice and delays cell senescence by activating Nrf2 pathway. This will be of great significance in the treatment of contrast-induced nephropathy

Fast Color-guided Depth Denoising for RGB-D Images by Graph Filtering

Depth images captured by off-the-shelf RGB-D cameras suffer from much stronger noise than color images. In this paper, we propose a method to denoise the depth images in RGB-D images by color-guided graph filtering. Our iterative method contains two components: color-guided similarity graph construction, and graph filtering on the depth signal. Implemented in graph vertex domain, filtering is accelerated as computation only occurs among neighboring vertices. Experimental results show that our method outperforms state-of-art depth image denoising methods significantly both on quality and efficiency.Comment: 5 pages, 4 figure

Railway Traffic Accident Forecast Based on an Optimized Deep Auto-encoder

Safety is the key point of railway transportation, and railway traffic accident prediction is the main content of safety management. There are complex nonlinear relationships between an accident and its relevant indexes. For this reason, triangular gray relational analysis (TGRA) is used for obtaining the indexes related to the accident and the deep auto-encoder (DAE) for finding out the complex relationships between them and then predicting the accident. In addition, a nonlinear weight changing particle swarm optimization algorithm, which has better convergence and global searching ability, is proposed to obtain better DAE structure and parameters, including the number of hidden layers, the number of neurons at each hidden layer and learning rates. The model was used to forecast railway traffic accidents at Shenyang Railway Bureau, Guangzhou Railway Corporation, and Nanchang Railway Bureau. The results of the experiments show that the proposed model achieves the best performance for predicting railway traffic accidents

Building Marginal Pattern Library with Unbiased Training Dataset for Enhancing Model-Free Load-ED Mapping

Input-output mapping for a given power system problem, such as loads versus economic dispatch (ED) results, has been demonstrated to be learnable through artificial intelligence (AI) techniques, including neural networks. However, the process of identifying and constructing a comprehensive dataset for the training of such input-output mapping remains a challenge to be solved. Conventionally, load samples are generated by a pre-defined distribution, and then ED is solved based on those load samples to form training datasets, but this paper demonstrates that such dataset generation is biased regarding load-ED mapping. The marginal unit and line congestion (i.e., marginal pattern) exhibit a unique characteristic called step change in which the marginal pattern changes when the load goes from one critical loading level (CLL) to another, and there is no change of marginal units within the interval of the two adjacent CLLs. Those loading intervals differ significantly in size. The randomly generated training dataset overfills intervals with large sizes and underfits intervals with small sizes, so it is biased. In this paper, three algorithms are proposed to construct a marginal pattern library to examine this bias according to different computational needs, and an enhancement algorithm is proposed to eliminate the bias for the load-ED dataset generation. Three illustrative test cases demonstrate the proposed algorithms, and comparative studies are constructed to show the superiority of the enhanced, unbiased dataset

Developmental Context Determines Latency of MYC-Induced Tumorigenesis

One of the enigmas in tumor biology is that different types of cancers are prevalent in different age groups. One possible explanation is that the ability of a specific oncogene to cause tumorigenesis in a particular cell type depends on epigenetic parameters such as the developmental context. To address this hypothesis, we have used the tetracycline regulatory system to generate transgenic mice in which the expression of a c-MYC human transgene can be conditionally regulated in murine hepatocytes. MYC's ability to induce tumorigenesis was dependent upon developmental context. In embryonic and neonatal mice, MYC overexpression in the liver induced marked cell proliferation and immediate onset of neoplasia. In contrast, in adult mice MYC overexpression induced cell growth and DNA replication without mitotic cell division, and mice succumbed to neoplasia only after a prolonged latency. In adult hepatocytes, MYC activation failed to induce cell division, which was at least in part mediated through the activation of p53. Surprisingly, apoptosis is not a barrier to MYC inducing tumorigenesis. The ability of oncogenes to induce tumorigenesis may be generally restrained by developmentally specific mechanisms. Adult somatic cells have evolved mechanisms to prevent individual oncogenes from initiating cellular growth, DNA replication, and mitotic cellular division alone, thereby preventing any single genetic event from inducing tumorigenesis

Hollow-Core Negative Curvature Fiber with High Birefringence for Low Refractive Index Sensing Based on Surface Plasmon Resonance Effect

In this paper, a hollow-core negative curvature fiber (HC-NCF) with high birefringence is proposed for low refractive index (RI) sensing based on surface plasmon resonance effect. In the design, the cladding region of the HC-NCF is composed of only one ring of eight silica tubes, and two of them are selectively filled with the gold wires. The influences of the gold wires-filled HC-NCF structure parameters on the propagation characteristic are investigated by the finite element method. Moreover, the sensing performances in the low RI range of 1.20–1.34 are evaluated by the traditional confinement loss method and novel birefringence analysis method, respectively. The simulation results show that for the confinement loss method, the obtained maximum sensitivity, resolution, and figure of merit of the gold wires-filled HC-NCF-based sensor are −5700 nm/RIU, 2.63 × 10−5 RIU, and 317 RIU−1, respectively. For the birefringence analysis method, the obtained maximum sensitivity, resolution, and birefringence of the gold wires-filled HC-NCF-based sensor are −6100 nm/RIU, 2.56 × 10−5 RIU, and 1.72 × 10−3, respectively. It is believed that the proposed gold wires-filled HC-NCF-based low RI sensor has important applications in the fields of biochemistry and medicine

Allocating the fixed cost:an approach based on data envelopment analysis and cooperative game

Allocating the fixed cost among a set of users in a fair way is an important issue both in management and economic research. Recently, Du et al. (Eur J Oper Res 235(1): 206–214, 2014) proposed a novel approach for allocating the fixed cost based on the game cross-efficiency method by taking the game relations among users in efficiency evaluation. This paper proves that the novel approach of Du et al. (Eur J Oper Res 235(1): 206–214, 2014) is equivalent to the efficiency maximization approach of Li et al. (Omega 41(1): 55–60, 2013), and may exist multiple optimal cost allocation plans. Taking into account the game relations in the allocation process, this paper proposes a cooperative game approach, and uses the nucleolus as a solution to the proposed cooperative game. The proposed approach in this paper is illustrated with a dataset from the prior literature and a real dataset of a steel and iron enterprise in China