A combined finite element and multiscale finite element method for the multiscale elliptic problems

The oversampling multiscale finite element method (MsFEM) is one of the most popular methods for simulating composite materials and flows in porous media which may have many scales. But the method may be inapplicable or inefficient in some portions of the computational domain, e.g., near the domain boundary or near long narrow channels inside the domain due to the lack of permeability information outside of the domain or the fact that the high-conductivity features cannot be localized within a coarse-grid block. In this paper we develop a combined finite element and multiscale finite element method (FE-MsFEM), which deals with such portions by using the standard finite element method on a fine mesh and the other portions by the oversampling MsFEM. The transmission conditions across the FE-MSFE interface is treated by the penalty technique. A rigorous convergence analysis for this special FE-MsFEM is given under the assumption that the diffusion coefficient is periodic. Numerical experiments are carried out for the elliptic equations with periodic and random highly oscillating coefficients, as well as multiscale problems with high contrast channels, to demonstrate the accuracy and efficiency of the proposed method

OTIS Layouts of De Bruijn Digraphs

The Optical Transpose Interconnection System (OTIS) was proposed by Marsden et al. [Opt. Lett 18 (1993) 1083--1085] to implement very dense one-to-one interconnection between processors in a free space of optical interconnections. The system which allows one-to-one optical communications from p groups of q transmitters to q groups of p receivers, using electronic intragroup communications for each group of consecutive d processors, is denoted by OTIS(p,q,d). H(p,q,d) is the digraph which characterizes the underlying topology of the optical interconnection implemented by OTIS(p,q,d). A digraph has an OTIS(p,q,d) layout if it is isomorphic to H(p,q,d). Based on results of Coudert et al. [Networks 40 (2002) 155--164], we characterize all OTIS(p,q,d) layouts of De Bruijn digraph B(d,n) where both p and q are powers of d. Coudert et al. posed the conjecture that if B(d,n) has an OTIS(p,q,d) layout, then both p and q are powers of d. As an effort to prove this conjecture, we prove that H(p,q,d) is a line digraph if and only if both p and q are multiples of d.Comment: Submitted to Network

Efficacy of a carbon monoxide gas cartridge against field rodents

Efficacy data of a gas cartridge are reported. The gas cartridge contains 50 g of potassium nitrate (27.5 g, 55%) mixed with sawdust (22.5 g, 45%). When ignited, it generates large amounts of carbon monoxide (avg. 23.46%) and carbon dioxide (avg. 26.26%). A mimic field trial was carried out on a winter day. The air temperature averaged 1.2°C, ranging from -3.3°C to +5°C. Sixteen adult albino rats were killed within 3 minutes exposure in a man-made burrow system, 200 cm long, with an inside diameter of 8 cm. Field trials were conducted in different parts of China, and there were no survivors in the 108 burrows treated. Upon excavation 144 dead rodents were recovered. The first test was carried out in Zhengding, Hebei Province. (The site was along a sunning ground where cereals are dried.) Each of 53 burrows was treated with a 50-g gas cartridge. When the burrow systems were excavated, 81 dead rodents were found: Cricetulus barabensis, 38 (46.9%); C. triton, 28 (34.6%); Mus musculus, 14 (17.3%); and Apodemus agrarius, 1 (1.2%). The second trial was carried out in a sugarcane field near a ditch in Zhangjiang, Guangdong Province. Fifty-five dead rodents were dug out of the 50 burrows treated: Rattus flavipectus, 26 (47.3%); Bandicota indica, 18 (32.7%); R. losea, 7 (12.7%); and Suncus murinus (Insectivore), 4 (7.3%). The third trial was conducted in a high mountain grassland pasture above 3500 m in Qinghae Province. Five marmot burrows were each treated with a dose of 600 g of gas cartridges per burrow. Eight dead Marmota hymalayana were found near the burrow entrance

Sparse Estimation of Multivariate Poisson Log-Normal Models from Count Data

Modeling data with multivariate count responses is a challenging problem due to the discrete nature of the responses. Existing methods for univariate count responses cannot be easily extended to the multivariate case since the dependency among multiple responses needs to be properly accommodated. In this paper, we propose a multivariate Poisson log-normal regression model for multivariate data with count responses. By simultaneously estimating the regression coefficients and inverse covariance matrix over the latent variables with an efficient Monte Carlo EM algorithm, the proposed regression model takes advantages of association among multiple count responses to improve the model prediction performance. Simulation studies and applications to real world data are conducted to systematically evaluate the performance of the proposed method in comparison with conventional methods

Positivity and boundedness preserving schemes for the fractional reaction-diffusion equation

In this paper, we design a semi-implicit scheme for the scalar time fractional reaction-diffusion equation. We theoretically prove that the numerical scheme is stable without the restriction on the ratio of the time and space stepsizes, and numerically show that the convergent orders are 1 %$2-\alpha$ in time and 2 in space. As a concrete model, the subdiffusive predator-prey system is discussed in detail. First, we prove that the analytical solution of the system is positive and bounded. Then we use the provided numerical scheme to solve the subdiffusive predator-prey system, and theoretically prove and numerically verify that the numerical scheme preserves the positivity and boundedness.Comment: 25 pages, 3 figure

Tempered Fractional Feynman-Kac Equation

Functionals of Brownian/non-Brownian motions have diverse applications and attracted a lot of interest of scientists. This paper focuses on deriving the forward and backward fractional Feynman-Kac equations describing the distribution of the functionals of the space and time tempered anomalous diffusion, belonging to the continuous time random walk class. Several examples of the functionals are explicitly treated, including the occupation time in half-space, the first passage time, the maximal displacement, the fluctuations of the occupation fraction, and the fluctuations of the time-averaged position.Comment: 17 pages, 6 figure

Fast predictor-corrector approach for the tempered fractional ordinary differential equations

The tempered evolution equation describes the trapped dynamics, widely appearing in nature, e.g., the motion of living particles in viscous liquid. This paper proposes the fast predictor-corrector approach for the tempered fractional ordinary differential equations by digging out the potential 'very' short memory principle. The algorithms basing on the idea of equidistributing are detailedly described; their effectiveness and low computation cost, being linearly increasing with time $t$, are numerically demonstrated.Comment: 23 pages,14 figure

Robust Image Segmentation Quality Assessment

Deep learning based image segmentation methods have achieved great success, even having human-level accuracy in some applications. However, due to the black box nature of deep learning, the best method may fail in some situations. Thus predicting segmentation quality without ground truth would be very crucial especially in clinical practice. Recently, people proposed to train neural networks to estimate the quality score by regression. Although it can achieve promising prediction accuracy, the network suffers robustness problem, e.g. it is vulnerable to adversarial attacks. In this paper, we propose to alleviate this problem by utilizing the difference between the input image and the reconstructed image, which is conditioned on the segmentation to be assessed, to lower the chance to overfit to the undesired image features from the original input image, and thus to increase the robustness. Results on ACDC17 dataset demonstrated our method is promising

Polynomial Spectral collocation Method for Space Fractional Advection-Diffusion Equation

This paper discusses the spectral collocation method for numerically solving nonlocal problems: one dimensional space fractional advection-diffusion equation; and two dimensional linear/nonlinear space fractional advection-diffusion equation. The differentiation matrixes of the left and right Riemann-Liouville and Caputo fractional derivatives are derived for any collocation points within any given interval. The stabilities of the one dimensional semi-discrete and full-discrete schemes are theoretically established. Several numerical examples with different boundary conditions are computed to testify the efficiency of the numerical schemes and confirm the exponential convergence; the physical simulations for L\'evy-Feller advection-diffusion equation are performed; and the eigenvalue distributions of the iterative matrix for a variety of systems are displayed to illustrate the stabilities of the numerical schemes in more general cases.Comment: 25 Pages, 22 figure

Bounds on some monotonic topological indices of bipartite graphs with a given number of cut edges

Let $I(G)$ be a topological index of a graph. If $I(G+e)<I(G)$ (or $I(G+e)>I(G)$, respectively) for each edge $e\not\in G$, then $I(G)$ is monotonically decreasing (or increasing, respectively) with the addition of edges. In this article, we present lower or upper bounds for some monotonic topological indices, including the Wiener index, the hyper-Wiener index, the Harary index, the connective eccentricity index, the eccentricity distance sum of bipartite graphs in terms of the number of cut edges, and characterize the corresponding extremal graphs, respectively