MULTIPLE INTERSECTIONS OF SPACE-TIME ANISOTROPIC GAUSSIAN FIELDS

Let X={X(t)∈R^(d),t∈R^(N)}be a centered space-time anisotropic Gaussian field with indices H=(H_(1),…,H_(N))∈(0,1)~N,where the components X_(i)(i=1,…,d)of X are independent,and the canonical metric√(E(X_(i)(t)-X_(i)(s))^(2))^(1/2)(i=1,…,d)is commensurate with■for s=(s_(1),…,s_(N)),t=(t_(1),…,t_(N))∈R~N,α_(i)∈(0,1],and with the continuous functionγ(·)satisfying certain conditions.First,the upper and lower bounds of the hitting probabilities of X can be derived from the corresponding generalized Hausdorff measure and capacity,which are based on the kernel functions depending explicitly onγ(·).Furthermore,the multiple intersections of the sample paths of two independent centered space-time anisotropic Gaussian fields with different distributions are considered.Our results extend the corresponding results for anisotropic Gaussian fields to a large class of space-time anisotropic Gaussian fields.

A Mean-Field Game for a Forward-Backward Stochastic System With Partial Observation and Common Noise

This paper considers a linear-quadratic(LQ) meanfield game governed by a forward-backward stochastic system with partial observation and common noise,where a coupling structure enters state equations,cost functionals and observation equations.Firstly,to reduce the complexity of solving the meanfield game,a limiting control problem is introduced.By virtue of the decomposition approach,an admissible control set is proposed.Applying a filter technique and dimensional-expansion technique,a decentralized control strategy and a consistency condition system are derived,and the related solvability is also addressed.Secondly,we discuss an approximate Nash equilibrium property of the decentralized control strategy.Finally,we work out a financial problem with some numerical simulations.

A New Two-Parameter Family of Nonlinear Conjugate Gradient Method Without Line Search for Unconstrained Optimization Problem

This paper puts forward a two-parameter family of nonlinear conjugate gradient(CG)method without line search for solving unconstrained optimization problem.The main feature of this method is that it does not rely on any line search and only requires a simple step size formula to always generate a sufficient descent direction.Under certain assumptions,the proposed method is proved to possess global convergence.Finally,our method is compared with other potential methods.A large number of numerical experiments show that our method is more competitive and effective.

Tree: Reducing the use of restrictive practices on psychiatric wards through virtual reality immersive technology training

BACKGROUND Restrictive practices(RPs)are defined by measures linked to physical and chemical restraints to reduce the movement or control behaviours during any emergency.Seclusion is an equal part of RPs intended to isolate and reduce the sensory stimulation to safeguard the patient and those within the vicinity.Using interventions by way of virtual reality(VR)could assist with reducing the need for RPs as it could help reduce anxiety or agitation by way of placing users into realistic and immersive environments.This could also aid staff to and change current RPs.AIM To assess the feasibility and effectiveness of using a VR platform to provide reduction in RP training.METHODS A randomised controlled feasibility study,accompanied by evaluations at 1 month and 6 months,was conducted within inpatient psychiatric wards at Southern Health National Health Service Foundation Trust,United Kingdom.Virti VR scenarios were used on VR headsets to provide training on reducing RPs in 3 inpatient psychiatric wards.Outcome measures included general self-efficacy scale,generalised anxiety disorder assessment 7(GAD-7),Burnout Assessment Tool 12,the Everyday Discrimination Scale,and the Compassionate Engagement and Action Scale.RESULTS Findings revealed statistically significant differences between the VR and treatment as usual groups,in the Everyday Discrimination Scale items Q8 and Q9:P=0.023 and P=0.040 respectively,indicating higher levels of perceived discrimination in the VR group.There were no significant differences between groups in terms of general self-efficacy,generalised anxiety disorder assessment 9,and Burnout Assessment Tool 12 scores.A significant difference was observed within the VR group for compassionate engagement from others(P=0.005)over time.Most respondents recorded System Usability Scale scores above 70,with an average score of 71.79.There was a significant reduction in rates of RPs in the VR group vs treatment as usual group with a fluctuating variability observed in the VR group likely due to external factors not captured in the study.CONCLUSION Ongoing advancement of VR technology enables the possibility of creating scenarios and simulations tailored to healthcare environments that empower staff by providing more comprehensive and effective training for handling situations.

Prediction of Lung Cancer Stage Using Tumor Gene Expression Data

Lung cancer remains a significant global health challenge and identifying lung cancer at an early stage is essential for enhancing patient outcomes. The study focuses on developing and optimizing gene expression-based models for classifying cancer types using machine learning techniques. By applying Log2 normalization to gene expression data and conducting Wilcoxon rank sum tests, the researchers employed various classifiers and Incremental Feature Selection (IFS) strategies. The study culminated in two optimized models using the XGBoost classifier, comprising 10 and 74 genes respectively. The 10-gene model, due to its simplicity, is proposed for easier clinical implementation, whereas the 74-gene model exhibited superior performance in terms of Specificity, AUC (Area Under the Curve), and Precision. These models were evaluated based on their sensitivity, AUC, and specificity, aiming to achieve high sensitivity and AUC while maintaining reasonable specificity.

Exploration of the Impact Mechanism of Government Credibility Based on Variable Screening Method

Government credibility is an important asset of contemporary national governance, an important criterion for evaluating government legitimacy, and a key factor in measuring the effectiveness of government governance. In recent years, researchers’ research on government credibility has mostly focused on exploring theories and mechanisms, with little empirical research on this topic. This article intends to apply variable selection models in the field of social statistics to the issue of government credibility, in order to achieve empirical research on government credibility and explore its core influencing factors from a statistical perspective. Specifically, this article intends to use four regression-analysis-based methods and three random-forest-based methods to study the influencing factors of government credibility in various provinces in China, and compare the performance of these seven variable selection methods in different dimensions. The research results show that there are certain differences in simplicity, accuracy, and variable importance ranking among different variable selection methods, which present different importance in the study of government credibility issues. This study provides a methodological reference for variable selection models in the field of social science research, and also offers a multidimensional comparative perspective for analyzing the influencing factors of government credibility.

Recent advances of variational model in medical imaging and applications to computer aided surgery

In this paper, we review some mathematical models in medical image processing. Due to the superiority in modeling and computation, variational methods have been proven to be powerful techniques, which have been extremely popular and dramatically improved in the past two decades. On one hand, many models have been proposed for nearly all kinds of applications. On the other hand, a lot of models can be globally optimized and also many computation tools have been introduced. Under the variational framework, we focus on two basic problems in medical imaging： image restoration and segmentation, which are core components for kinds of specific tasks. For image restoration, we discuss some models on both additive and multiplicative noises. For image segmentation, we review some models on both whole image segmentation and specific target delineation, with the later being a key step in computer aided surgery. Additionally, we present some models on liver delineation and give their applications to living donor liver transplantation.

HITTING PROBABILITIES AND INTERSECTIONS OF TIME-SPACE ANISOTROPIC RANDOM FIELDS

Let X^(H)={X^(H)(s),s∈R^(N_(1))}and X^(K)={X^(K)(t),t∈R^(N_(2))}be two independent time-space anisotropic random fields with indices H∈(0,1)^(N_(1)) and K∈(0,1)^(N_(2)),which may not possess Gaussianity,and which take values in R^(d) with a space metric τ.Under certain general conditions with density functions defined on a bounded interval,we study problems regarding the hitting probabilities of time-space anisotropic random fields and the existence of intersections of the sample paths of random fields X^(H) and X^(K).More generally,for any Borel set F⊂R^(d),the conditions required for F to contain intersection points of X^(H) and X^(K) are established.As an application,we give an example of an anisotropic non-Gaussian random field to show that these results are applicable to the solutions of non-linear systems of stochastic fractional heat equations.

Precise large deviations for sums of random vectors in a multidimensional size-dependent renewal risk model

Consider a multidimensional renewal risk model, in which the claim sizes {Xk, k ≥1} form a sequence of independent and identically distributed random vectors with nonnegative components that are allowed to be dependent on each other. The univariate marginal distributions of these vectors have consistently varying tails and finite means. Suppose that the claim sizes and inter-arrival times correspondingly form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure. A precise large deviation for the multidimensional renewal risk model is obtained.

Moisture Control Methods in Silk Reeling Process of Tobacco Based on the Random Forest Regression

The moisture control of materials in silk reeling technology of tobacco is regarded as the key factor influencing the inner quality of cigarette. In this paper, according to the statistical data of the silk reeling production line of Yunyan (Ruanzhen brand) of Qujing cigarette factory from June 2013 to May 2014, it is feasible to apply the random forest regression model to study the problem of moisture control theoretically. In the perfuming stage of silk reeling, a random forest regression model is established to describe the change of moisture content of finished cut tobacco in the export link of perfuming stage, aroused by several factors including incoming water content and different environment. According to the model, good moisture control in the export link of perfuming stage (accordance with the technological standards) can be realized by adjusting the regulating reference value of incoming moisture under specific workshop environments. In the drying stage of silk reeling, the most effective method of moisture control is to adjust the cylinder wall temperature by means of analyzing the correlation coefficients among variables which influence the moisture content of cut tobacco in the export link of drying stage and then establishing another random forest regression model. And this method is consistent with the traditional production experiences. In conclusion, these methods referred above provide strong theoretical basis for stable moisture control in the export link of perfuming stage.

Stability and boundedness in terms of two measures for nonlinear impulsive control systems

In this paper we study stability and boundedness in terms of two measures for impulsive control systems. By using variational Lyapunov method, a new variational comparison principle and some criteria on stability and boundedness are obtained. An example is presented to illustrate the efficiency of proposed result.

A Hierarchy of Nonlinear Lattice Soliton Equations and Its Darboux Transformation

A hierarchy of nonlinear lattice soliton equations is derived from a new discrete spectral problem. The Hamiltonian structure of the resulting hierarchy is constructed by using a trace identity formula. Moreover, a Darboux transformation is established with the help of gauge transformations of Lax pairs for the typical lattice soliton equations. The exact solutions are given by applying the Darboux transformation.

Global and Bifurcation Analysis of an HIV Pathogenesis Model with Saturated Reverse Function

In this paper,an HIV dynamics model with the proliferation of CD4 T cells is proposed.The authors consider nonnegativity,boundedness,global asymptotic stability of the solutions and bifurcation properties of the steady states.It is proved that the virus is cleared from the host under some conditions if the basic reproduction number R0 is less than unity.Meanwhile,the model exhibits the phenomenon of backward bifurcation.We also obtain one equilibrium is semi-stable by using center manifold theory.It is proved that the endemic equilibrium is globally asymptotically stable under some conditions if R0 is greater than unity.It also is proved that the model undergoes Hopf bifurcation from the endemic equilibrium under some conditions.It is novelty that the model exhibits two famous bifurcations,backward bifurcation and Hopf bifurcation.The model is extended to incorporate the specific Cytotoxic T Lymphocytes(CTLs)immune response.Stabilities of equilibria and Hopf bifurcation are considered accordingly.In addition,some numerical simulations for justifying the theoretical analysis results are also given in paper.

CENTRAL LIMIT THEOREM AND MODERATE DEVIATIONS FOR A CLASS OF SEMILINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

In this paper we prove a central limit theorem and a moderate deviation principle for a class of semilinear stochastic partial differential equations, which contain the stochastic Burgers’ equation and the stochastic reaction-diffusion equation. The weak convergence method plays an important role.

A Criterion for Stability of Synchronization and Application to Coupled Chua's Systems

We investigate synchronization in an array network of nearest-neighbor coupled chaotic oscillators. By using of the Lyapunov stability theory and matrix theory, a criterion for stability of complete synchronization is deduced. Meanwhile, an estimate of the critical coupling strength is obtained to ensure achieving chaos synchronization. As an example application, a model of coupled Chua＇s circuits with linearly bidirectional coupling is studied to verify the validity of the criterion.

EXTINCTION OF POPULATION-SIZE-DEPENDENT BRANCHING CHAINS IN RANDOM ENVIRONMENTS

We consider a population-size-dependent branching chain in a general random environment.We give suffcident conditions for certain extinction and for non-certain extinction.The chain exhibits different asymptotic according to supk,θmk,θ1, mk,θn→1 as k →∞, n→∞, infk,θmk,θ1.

Technology Importation and Domestic Technology Acquisition in China from the Perspective of Innovation

Foreign and domestic technologies play different roles in a country's innovation. In recent years, Chinese firms have spent less on importing foreign technology and more on acquiring domestic technology. Based on the panel data model, state space model(SSM) and the Bayesian vector autoregressive model, this paper finds that the purchase of domestic technology plays a critical role in the innovation of high-tech firms with an elasticity coefficient higher than that of technology importation before 2010. China's high-tech firms can effectively absorb purchased domestic technology, which also brings about an increase in their independent R&D input and contributes more to innovation output than imported technology. Performance of technology importation is lackluster but shows an improving trend. Technology importation is not correlated with innovation output and has a substitutive effect with independent R&D input. China is yet to enhance its absorption of imported technology. Elasticity coefficient of technology importation turned positive in 2007 and increased year by year. China should promote synergy between technology importation and domestic technology acquisition.

Statistical Inference in Generalized Linear Mixed Models by Joint Modelling Mean and Covariance of Non-Normal Random Effects

Generalized linear mixed models (GLMMs) are typically constructed by incorporating random effects into the linear predictor. The random effects are usually assumed to be normally distributed with mean zero and variance-covariance identity matrix. In this paper, we propose to release random effects to non-normal distributions and discuss how to model the mean and covariance structures in GLMMs simultaneously. Parameter estimation is solved by using Quasi-Monte Carlo (QMC) method through iterative Newton-Raphson (NR) algorithm very well in terms of accuracy and stabilization, which is demonstrated by real binary salamander mating data analysis and simulation studies.

Research on Smart Growth of Sustainable Cities Based on Information Entropy and Super-Efficiency DEA Model

Since the “smart growth” was put forward in the late 90s, it has become an accepted design idea and concept in the field of urban design in the world, and has been deeply studied and applied. In order to better promote “smart grown”, we set up an evaluation system, which consists of eleven indicators. In this paper, Oxford City and Fengzhen City are used as the objects of the study. Then smart growth evaluation model is established. The weight of the index is calculated by the entropy method. We use the model to evaluate the development plans of the two cities, from which to calculate the contribution of the indicators on the level of smart growth. Finally, we use the super-efficient data envelopment analysis model (DEA) to rank the importance of the indicators to the smart growth. The results show that the level of smart growth in Oxford is higher than that in Fengzhen. And “Multifunctional Building Density in Central City”, “The Density of Public Area in Central City” two indicators account for more than 36% weight. The contribution of the two indicators is also located in the top two indicators. Two cities focus on the direction of smart growth is also different. In summary, the differences between China and Western countries in urban planning are mainly focused on housing and public resources.

Risk Assessment and Change Monitoring of Soil and Water Loss in Ruijin City Based on RS and GIS

The land use information extraction technology for the high-resolution remote sensing images of the Gaofen No. 1 satellite was construc-ted. According to the spectral, band, texture and shape attributes, land use types were divided, and the changing laws of land use types were ana- lyzed. Aftewards,according to the Table of Grading Standard of Sooil Erosion Intensity（SL190-96）,as well as vegetation coverage index NDVI slope, the risks of soil and water loss were assessed. Meanwhile, the level, scale, location and scope of changes in the risks of soil and water loss were monitored by using spatial visualization and spatial statistical techniques. The results showed that the area of areas without soil erosion and moderate soil erosion areas decreased obviously from 2015 to 2017, and the decreases were up to 22.929 3 and 13.626 3 km2 respectively. The ar-ea of mild soil erosion areas increased fast, and the increase reached 31.140 0 km2. The area of extremely strong soil erosion areas increased by 7.267 4 km2. In the city, moderate and strong soil erosion areas reduced, while extremely strong soil erosion patches increased fast, which was mainly related to road construction and construction and development of orchards. The extremely strong soil erosion areas were distributed in the shape of a banded loop, surrounded the suburbs of the city, and shrank towards the center of Ruijin City. The constructed technology to monitor the changes in land use and soil and water loss, as well as the changing laws of land use and soil and water loss provide the theoretical basis and plan-ning basis of soil and water conservation for urban planning departments and soil and water conservation departments.