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.

By relaxing the hypothesis that the in°uence of independent variable in parametric
spatial lag model is a linear or nonlinear function of some known form, a nonparametric spatial lag
model with random independent variables is considered. The GMM estimation method of the model
is constructed, the asymptotic properties of the estimators are derived and the small sample perfor-
mances of the estimates are investigated by Monte Carlo simulation.In addition, the estimation methods
proposed are applied to estimate the growth rate of TFP of China's provinces and municipalities.

Bayesian analysis for joint mean and variance models is studied in this paper, in
which Gibbs sampler and Metropolis-Hastings algorithm are used to calculate Bayesian estimations of
unknown parameters and Bayesian case deletion diagnostic. Simulation studies and a real example are
used to illustrate the proposed methodology.

For two-stage series repairable system, a change-point control chart is used to monitor
the system to reveal state of the system, and then the corresponding maintenance policy is carried
out. Firstly, a change-point control chart is given to monitor the multistage system. Secondly, the
possible scenarios and the probability of occurrence of each scenario are analyzed, assuming that
assignable causes may occur in both two-stage, which follow general distribution; and the probability
of the corresponding maintenance policy is obtained based on the scenarios. Thirdly, a procedure
for calculating average revenue is presented according to renew-reward theory. Then, a numerical
example is given to illustrate the application of the proposed integrated model. The results show
that the integrated model outperforms the maintenance model in terms of average revenue earning.
Finally, using fractional factor design, a sensitivity analysis is conducted to develop insights into input
parameters that in°uence the integration e?orts.

Heavy-tailed distribution can well explain the economic, natural and social phenomena such as asset prices, income
distribution, hydro-geology, social media, etc.
Accurate estimation of extreme value index is a key technique for application of heavy-tailed
distribution. The Hill estimator, introduced in 1975, which opened a precedent of estimating extreme value index, is still
the focus of heavy-tailed modeling up to now. In order to overcome the shortcomings of the location variation and
asymptotic behavior of the existing estimators, borrowing the asymptotic expansion of statistic $M_{n}^{(\alpha)}(k_{0},k)$,
this paper proposes a new kind of location invariant extreme value index estimator (NLIE) and studies its asymptotic expansion under second order regular variation. The optimal choice of threshold is discussed as well. The NLIE is compared with the classical location invariant estimator $\hat{\gamma}_{n}^{H}(k_{0},k)$ by Monte-Carlo. The results show that NlIE behaves better than $\hat{\gamma}_{n}^{H}(k_{0},k)$.

Combining the conception of m dependent random variables with WOD random
variables, the conception of m-WOD random variables is given in this paper, which contains many
negative dependent random variables such as NA, m-NA, NSD, NOD, END, m-END and WOD. Based
on the m-WOD errors, the least squares (LS) estimator of nonlinear regression models is investigated
and some probability inequalities for the LS estimator are obtained. As an application, the complete
convergence and convergence in probability are presented under di?erent moment conditions, which
generalize the corresponding results.

The topic of the asymptotic distribution of the Wilcoxon two-sample statistic under
an associated sample is investigated in this paper. Using Hoeffding decomposition, it is shown that the
asymptotic distribution of the Wilcoxon two-sample statistic under an associated sample is the normal
distribution, which generalizes the existing asymptotic result of the Wilcoxon two-sample statistic under
a negatively associated sample.

A new method for solving nonlinear Schr?odinger equation with wave operator is
proposed. Fristly, the characteristics of the equilibrium solution of the transformed di?erential equation
are analyzed in the differential dynamical system. Secondly, the envelope periodic solutions in different
forms are obtained by combining Lame equation, a new Lame function and Jacobi elliptic function
expansion method. Finally, under extreme conditions, new solitary wave solutions and other forms of
solutions are presented.

By using the theory of variable exponent Sobolev spaces and the critical point theory,
periodic solutions for Kirchhoff-type p(t)-Laplacian systems are investigated. When the nonlinearity is
sublinear near zero or the nonlinearity is superlinear at infinity, the existence of infinitely many periodic
solutions for this system is obtained.

Fuzzy reasoning method has been successfully applied to fuzzy controller design, fuzzy
expert system integration and many other fields. As an improvement of the traditional fuzzy reasoning
method, Chinese scholars have proposed a symmetric inference method based on the triple I method.
The research on the nature, such as robustness of fuzzy reasoning method is an important direction
in the field of fuzzy logic. This paper discusses the robustness of the symmetric implication methods
based on the normalized Minkowski distance, the robustness of the four algorithms for several important
implication operators are given. Thus it provides a scientiˉc basis for the selection and applications of
fuzzy reasoning methods.

In this paper, the concept of the so called partial hyperbolic set is introduced, and
it is proved that a diffeomorphism on a compact Riemannian manifold
has the quasi-shadowing property in a neighborhood of the partially
hyperbolic set in the following sense: Let $f$ be a partially
hyperbolic diffeomorphism on a compact Riemannian manifold $M$, and
$\mathit\Lambda\subset M$ be a partially hyperbolic set of $f$.
There exists the neighborhood $O(\mathit\Lambda)$ of
$\mathit\Lambda$ such that for any $\varepsilon>0$ there exists
$\delta>0$ such that for any $\delta$-pseudo orbit
$\{x_{k}\}_{k\in\mathbb{Z}}\subset O(\mathit\Lambda)$ of $f$, there
exist a sequence of points $\{y_{k}\}_{k\in\mathbb{Z}}$ and a
sequence of center vectors $\{u_{k}\in
E_{x_{k}}^{c}\}_{k\in\mathbb{Z}}$ such that $d(x_{k},
y_{k})<\varepsilon$, where
$y_{k}=\exp_{x_{k}}(\exp^{-1}_{x_{k}}(f(y_{k-1}))+u_{k})$. As an
application, it is show that any diffeomorphism is topologically
quasi-stable under $C^{0}$-perturbation, if there exists an
invariant set in a neighborhood of the partially hyperbolic set.