This paper studied the dynamic complexity of a class of discrete population model by computer simulation. The autonomous predator-prey system model is established through theoretical derivation, which has Allee effect and Holling II functional effect. The growth states of discrete-time populations are simulated to explore the influence of the parameters’changes to its population size by MATLAB. It also illustrated the importance of Allee effect and Holling II functional in the model of interaction among populations. The research results show that the larger the processing time, the bigger parameter region for stable coexistence population when the processing time is within the effective range. The introduction of Allee effect makes dynamic behavior of the population more complicated, thus increase the extinction risk of predator population. The population appears bifurcation in advance when predator-prey system strongly affected by Allee effect. It will lead to population extinction, if Allee effect increasingly raises. The strong Allee effect is more prone to population extinction. The conclusion of this paper not only enriches the theory of ecology, but also puts forward important basis of conservation ecology.

BS algorithm is one of the classical algorithms for multiple change-points detection,
it may bring about too many misjudgments and a high time complexity due to the procedure of global
CUSUM statistic. On one hand, the BS algorithm is an o?-line sequential method, therefore the data
timing information is not fully utilized. On the other hand, the principle of the BS algorithm to detect
the change-points is to maximize the CUSUM statistic, which does not consider the morphological
characteristics of the statistical constituent sequence. In view of these, the paper proposes an improved
BS algorithm, named Shape-based BS algorithm, which is based on local shape recognition. Basing
on the local pattern recognition of statistic sequence not only decreases the computational complexity,
but also avoids mutual interference among change-points, and it could also promote the robustness in
discerning change points. At last, this paper uses Shape-based BS algorithm to reduce the scenarios of
electric power, and achieves satisfactory practical results.

Classical penalized regression model is inadequate of adaptivity for fitting complex data because that the spatial heterogeneity of observation data is not considered by the penalized term. According to the geometric meaning of radial basis, the local penalization vector based on the ranges of the data around each knot is constructed and added into the penalized term of the model. This new adaptive penalized spline regression model via radial basis gives less penalization to fitted curve where the observation data is volatile and more penalization to fitted curve where the observation data is flat, which makes the model adaptive to the local characterization of the sample points. Simulations and application show the fitting effect based on new model outperforms classical penalized spline regression model.

Due to the high segmentation accuracy and robustness, the multi-atlas based image segmentation method is currently a hot topic. It consists of two main components which are the image registration and the label fusion. The most of current multi-atlas based image segmentation methods consider the situation that the atlas images and the target image have the same resolution. But, we will always obtain the low-resolution target images because of the restriction on the acquisition time and collecting equipment. On the other hand, the atlases are generated before the target images, and we often use high-resolution images to obtain high-resolution atlases. Since the registration from high-resolution atlases to the low-resolution target image may not obtain the exact results, the accuracy of the multi-atlas based image segmentation methods will be reduced when applied to segment the low-resolution target images. In order to solve this problem, we present an accurate and robust image segmentation method for low-resolution target images by combining the advantages of the image super-resolution method and the multi-atlas segmentation method. The experiment results show that the proposed method significantly improves the accuracy of the original multi-atlas based image segmentation method.

In epidemiological studies, incidence of a disease is an important index which reflects the degree of the onset of a certain disease in the particular crowd. As a result, the structure of the confidence interval of it has important medical significance in judging disease extent. For some chronic diseases (such as cancer or cardiovascular, etc.), due to their long onset period and low incidence, Poisson sampling is in accord with the facts more than binomial sampling and inverse sampling. Four methods were used to study the construction of confidence interval for the incidence of chronic diseases under poisson distribution, and the performance properties of the four methods were compared through monte carlo simulation. Simulation results show that when higher incidence, pivot method did very well in both coverage and the interval length. When rates are relatively lower, pivot method is slightly inferior to Wald statistic method and the method of scoring on the interval length, but it did the best on the coverage. As a result, the overall performance of pivot method is very good.

With the help of rearrangement, this paper finds one class of functions in $H^p(\mathbf{R}^n)(0<p\leq 1)$ whose $H^p$-norms and $L^p$-norms are equivalent. More precisely, for each $f\in L^p(\mathbf{R}^n)$, there exists a function $g\in H^p(\mathbf{R}^n)$ satisfying $d_f=d_g$ and $\Vert g\Vert_{L^p}\leq\Vert g\Vert_{H^p}\leq C_p\Vert g\Vert_{L^p}$. Moreover, this paper also introduces a method to construct an $L^\infty$-atom of $H^p(\mathbf{R}^n)$.

The concept of meet C-continuity for posets is introduced. Properties and characterizations of meet C-continuity, as well as relationships of meet C-continuity with C-continuity and QC-continuity are given. Main results are: (1) A lattice which is also meet C-continuous must be distributive; (2) A bounded complete poset (bc-poset, for short) $L$ is meet C-continuous iff $\forall x\in L$ and every none-empty Scott closed set $S$ for which $\vee S$ exists, one has $x\wedge\vee S=\vee\{x\wedge s:s\in S\}$; (3) A complete lattice is a complete Heyting algebra iff it is meet continuous and meet C-continuous; (4) A bounded complete poset is C-continuous iff it is meet C-continuous and QC-continuous; (5) Some counterexamples are constructed to show that a distributive complete lattice needn’t be a meet C-continuous lattice and a meet C-continuous lattice needn’t be a meet continuous lattice.

In this paper, the author studies the $(\alpha,\beta)$-mixing sequences which are stochastically dominated. Some results on the strong stability for $(\alpha,\beta)$-mixing sequences are presented.

In 2012, Bang-Jensen and Huang (\emph{J. Combin. Theory Ser. B}. 2012, {\noindent\bf 102}: 701-714) proved that every $2$-arc-strong locally semicomplete digraph has two arc-disjoint strongly connected spanning subdigraphs, and conjectured that every $3$-strong local tournament has two arc-disjoint hamiltonian cycles. In this paper, the arc-disjoint hamiltonian paths and cycles in positive-round digraphs are discussed, and the following results are proved: every 3-arc-strong positive-round digraph contains two arc-disjoint hamiltonian cycles and every 4-arc-strong positive-round digraph contains one hamiltonian cycle and two hamiltonian paths, such that they are arc-disjoint pairwise. A round digraph must be positive-round, thus those conclusions on positive-round digraphs can be generalized to round digraphs. Since round digraphs form the subclass of local tournaments, Bang-Jensen and Huang's conjecture holds for round digraphs which is the subclass of local tournaments.

This paper considers the problem of variable selection in high-dimensional longitudinal linear regression models with monotone missing patterns. A new variable selection procedure is proposed based on the smooth-threshold inverse probability weighted generalized estimating equation. The proposed procedure avoids the convex optimization problem without using penalty functions. Besides, the proposed method can automatically eliminate inactive predictors by setting the corresponding parameters to be zero, and simultaneously estimate the nonzero regression coefficients. Under some regularity conditions, the variable selection procedure is proved to have Oracle property. Finally, some simulation studies are conducted to examine the finite sample property of the proposed variable selection procedure.

The deep learning method for pulmonary nodule detection is generally divided into
two stages: candidate nodule detection and false positive nodule elimination. Based on the two-stage
method, an incremental learning acceleration scheme is proposed that integrates new data to improve
the accuracy of the system. The training model of historical data screens new data and selects the
data with poor performance as an input for the continuous training of the two-stage model. The above
methods are tested on LUNA16 and TIANCHI17 two classic data sets. Using only half of the new
ones, the new model can achieve the same e?ect as the traditional two-stage method.

This paper introduces and characterizes rough continuity and topological continuity of maps between generalized approximation spaces. Properties and relationships of rough continuity and topological continuity are considered. It is proved that compositions of rough continuous maps are also rough continuous, and every rough continuous map is topological continuous. With these two continuities, concepts of rough homeomorphism properties and topological homeomorphism properties are defined. It is proved that every topological homeomorphism property is a rough homeomorphism property. Besides, some properties such as separation axioms, connectedness and compactness of generalized approximation spaces are shown to be rough or topological homeomorphism properties.

Corresponding to R-smash products of associative algebras, a kind of Poisson structure construction for relative semiclassical limits is constructed. Going a step further, Poisson structures with a kind of braiding of tensor products are given, which contain the results of Poisson polynomial extensions and double Poisson-Ore extensions.

With the help of $EQ^{rot}_1$ element and zero order Raviart-Thomas(R-T) elements, a new nonconforming mixed finite elements approximation scheme is proposed for the extended Fisher-Kolmogorov equation(EFK). Firstly, a priori estimate of approximation solutions is proved and the existence and uniqueness are also derived for semi-discrete scheme. Based on the high accuracy analysis of two elements and the priori estimate of the finite element solutions, the superclose properties of order $O(h^{2})$ for the primitive solution $u$ and the intermediate variable $v=-\Delta u~$in~$H^{1}$-norm and flux $\vec{p}=\nabla u$ in $(L^{2})^{2}$-norm are obtained without the boundedness of numerical solution $u_{h}$ in $L^{\infty}$-norm, respectively. Meanwhile, the global superconvergent error estimates for above variables of order $O(h^{2})$ are proved through interpolated postprocessing technique. Secondly, a new linearized backward Euler full-discrete scheme is established, the existence and uniqueness of approximation scheme are proved. On the other hand, the superclose properties of order $O(h^{2}+\tau)$ for variable $u,v$ in $H^{1}$-norm and $\vec{p}$ in $(L^{2})^{2}$-norm are obtained respectively through a new splitting technique for consistent error estimate and nonlinear term, which have never been considered in the previous literature. Furthermore, the global superconvergent estimates for above variables are deduced by interpolated postprocessing technique.~Here,~$h,~\tau$~are parameters of the subdivision in space and time step, respectively. Finally, numerical results are provided to confirm the theoretical analysis.

Under the mildly integrated and the mildly explosive cases, the asymptotic distributions of composite quantile estimation for moderate deviations from a unit root model with possibly infinite variance errors are obtained, respectively. Some simulation studies are also given to show that the composite quantile estimation has a good performance.

For functional clustering, similarity measure is one of the major approaches. However,
most researches measure the similarity of functional data from a single perspective, using either a
numerical distance approach or a curve shape approach. This paper proposes a new similarity measure
based on extreme point bias compensation. This new measure gives consideration to the numerical
distance and curve shape simultaneously. And the empirical results show the validity of the new
measure. Further, a multifunction clustering analysis method, the function entropy weight method, is
developed, which enriches the functional clustering analysis methods.

By using $k$-partition of matrices index set and the spectral radius for its sub-matrices, some new determinant conditions for generalized $H$-matrices under positive definite matrix conditions were presented. When a block matrix reduces a point matrix, these conditions then become the sufficient conditions for nonsingular $H$-matrices, and improve some recent related results. Numerical examples are given to show the effectiveness of the corresponding results.

By filling in the missing data of the life variable, the complete-data likelihood function of Weibull distribution with multiple change points for truncated and censored data is obtained. The full conditional distributions of change-point positions, shape parameters, and scale parameters are studied. Gibbs samples of the parameters are obtaines by MCMC method of Gibbs sampling together with Metropolis-Hastings algorithm, and the means of Gibbs samples are taken as Bayesian estimations of the parameters. The implementation steps of MCMC method are introduced in detail. The random simulation test results show that Bayesian estimations of the parameters are fairly accurate.

By using the moment inequality of negatively associated (NA, for short) random variables and the truncation method, the complete moment convergence for arrays of rowwise NA random variables are studied. Several sufficient conditions to prove the complete moment convergence for arrays of rowwise NA random variables are presented. The results obtained in this paper extend the corresponding ones for NA random variables.

A new method to construct two types of $\alpha$-curves based on C-B${\rm\acute{e}}$zier curve is given. The sufficient conditions for $\alpha$-curves of curvature monotony are deduced. The result shows that Quasi-Cubic B${\rm\acute{e}}$zier curve and quadratic B${\rm\acute{e}}$zier curve are special cases of $\alpha$-curves. The advantage of $\alpha$-curve is that it only has three control points and the shape of $\alpha$-curve can be adjusted by a shape parameter, therefore $\alpha$-curve is simpler and more powerful than C-B${\rm\acute{e}}$zier curve. The first type $\alpha$-curve has zero curvature at start point, and a pair of these $\alpha$-curves can be used in constructing S-shaped or C-shaped $G^{2}$ transition curves for separated circles, the ratio of two radii has no restriction. The second type $\alpha$-curve can be used in constructing a single transition curve with no curvature extreme for separated circles, and the endpoint curvature of this $\alpha$-curve degenerate to zero when specific shape parameter is selected. Test examples are given to show the effectiveness of these two types of $\alpha$-curves.