A New Method of Multi-Focus Image Fusion Using Laplacian Operator and Region Optimization

Considering the continuous advancement in the field of imaging sensor, a host of other new issues have emerged. A major problem is how to find focus areas more accurately for multi-focus image fusion. The multi-focus image fusion extracts the focused information from the source images to construct a global in-focus image which includes more information than any of the source images. In this paper, a novel multi-focus image fusion based on Laplacian operator and region optimization is proposed. The evaluation of image saliency based on Laplacian operator can easily distinguish the focus region and out of focus region. And the decision map obtained by Laplacian operator processing has less the residual information than other methods. For getting precise decision map, focus area and edge optimization based on regional connectivity and edge detection have been taken. Finally, the original images are fused through the decision map. Experimental results indicate that the proposed algorithm outperforms the other series of algorithms in terms of both subjective and objective evaluations.

Dynamics and data fitting of a time-delayed SIRS hepatitis B model with psychological inhibition factor and limited medical resources

Hepatitis B is an infectious disease worthy of attention.Considering the incubation period,psychological inhibition factor,vaccine,limited medical resources and horizontal transmission,an SIRS model is proposed to describe hepatitis B transmission dynamics.In order to describe the behavior changes caused by people's psychological changes,the non-monotonic incidence rate is adopted in the model.We use the saturated treatment rate to describe the limited medical resources.Mathematical analysis shows the existence conditions of the equilibria,forward or backward bifurcation,Hopf bifurcation and the Bogdanov-Takens bifurcation.During the observation of the case data of hepatitis B in China,it is found that there are mainly three features,periodic outbreaks,aperiodic outbreaks,and periodic outbreaks turns to aperiodic outbreaks.According to the above features,we select three different representative regions,Jiangxi,Zhejiang province and Beijing,and then use our model to fit the actual monthly hepatitis B case data.The basic reproduction numbers that we estimated are 1.7712,1.4805 and 1.4132,respectively.The results of data fitting are consistent with those of theoretical analysis.According to the sensitivity analysis of Ro,we conclude that reducing contact,increasing treatment rate,strengthening vaccination and revaccinating can effectively prevent and control the prevalence of hepatitis B.

Travelling solitary wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order

In this paper, the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied. By using the first integral method, which is based on the divisor theorem, some exact explicit travelling solitary wave solutions for the above equation are obtained. As a result, some minor errors and some known results in the previousl literature are clarified and improved.

Stability of GM(1,1) power model on vector transformation

The morbidity problem of the GM（1,1） power model in parameter identification is discussed by using multiple and rotation transformation of vectors. Firstly we consider the morbidity problem of the special matrix and prove that the condition number of the coefficient matrix is determined by the ratio of lengths and the included angle of the column vector, which could be adjusted by multiple and rotation transformation to turn the matrix to a well-conditioned one. Then partition the corresponding matrix of the GM（1,1） power model in accordance with the column vector and regulate the matrix to a well-conditioned one by multiple and rotation transformation of vectors, which completely solve the instability problem of the GM（1,1） power model. Numerical results show that vector transformation is a new method in studying the stability problem of the GM（1,1） power model.

THE OSCILLATION OF THE POISSON SEMIGROUP ASSOCIATED TO PARABOLIC HERMITE OPERATOR

Let O（PτL be the oscillation of the Possion semigroup associated with the parabolic Hermite operator = t-△＋｜x｜2. We show that O（PτL） is bounded from LP （Rn＋1） into itself for 1 〈 p 〈 ∞, bounded from L1（Rn＋l） into weak-L1（Rn＋1） and bounded from Lc∞（Rn＋1） into BMO（Rn＋1）. In the case p = ∞ we show that the range of the image of the operator O（PτL） is strictly smaller than the range of a general singular operator.

Outer Synchronization of Complex Networks by Impulse

This paper investigates outer synchronization of complex networks,especially,outer complete synchronizationand outer anti-synchronization between the driving network and the response network.Employing the impulsivecontrol method which is uncontinuous,simple,efficient,low-cost and easy to implement in practical applications,weobtain some sufficient conditions of outer complete synchronization and outer anti-synchronization between two complexnetworks.Numerical simulations demonstrate the effectiveness of the proposed impulsive control scheme.

REGULARITY OF P-HARMONIC MAPPINGS INTO NPC SPACES

Let M be a C^(2)-smooth Riemannian manifold with boundary and X be a metric space with non-positive curvature in the sense of Alexandrov.Let u:M→X be a Sobolev mapping in the sense of Korevaar and Schoen.In this short note,we introduce a notion of p-energy for u which is slightly different from the original definition of Korevaar and Schoen.We show that each minimizing p-harmonic mapping(p≥2)associated to our notion of p-energy is locally Holder continuous whenever its image lies in a compact subset of X.

Impulsive synchronization of a nonlinear coupled complex network with a delay node

We investigate the impulsive synchronization of a nonlinear coupled complex network with a delay node. Both delay coupling and non-delay coupling, as well as the symmetrical coupling matrix and the asymmetrical coupling matrix are considered. Based on the comparison theorem of an impulsive differential system, some novel synchronization criteria are derived. Finally, numerical simulations demonstrate the effectiveness of the proposed synchronization criteria.

Recoverability analysis of block-sparse representation

Recoverability of block-sparse signals by convex relaxation methods is considered for the underdetermined linear model. In previous works, some explicit but pessimistic recoverability results which were associated with the dictionary were presented. This paper shows the recoverability of block-sparse signals are associated with the block structure when a random dictionary is given. Several probability inequalities are obtained to show how the recoverability changes along with the block structure parameters, such as the number of nonzero blocks, the block length, the dimension of the measurements and the dimension of the block-sparse representation signal. Also, this paper concludes that if the block-sparse structure can be considered, the recoverability of the signals wil be improved. Numerical examples are given to il ustrate the availability of the presented theoretical results.

Synchronization of impulsively coupled complex networks

We investigate the synchronization of complex networks,which are impulsively coupled only at discrete instants.Based on the comparison theory of impulsive differential systems,a distributed impulsive control scheme is proposed for complex dynamical networks to achieve synchronization.The proposed scheme not only takes into account the influence of all nodes to network synchronization,which depends on the weight of each node in the network,but also provides us with a flexible method to select the synchronized state of the network.In addition,it is unnecessary for the impulsive coupling matrix to be symmetrical.Finally,the proposed control scheme is applied to a chaotic Lorenz network and Chua＇s circuit network.Numerical simulations are used to illustrate the validity of this control scheme.

Petrology Characters of Conglomerates in Baikouquan Formation, Mahu Sag, Junggar Basin

Mahu Sag, one of the most oil and gas bearing sags in Junggar basin, is in the northwestern margin of the basin. On gentle slope region of the sag, a serial of large scale coarse fan delta deposits were developed in Triassic Baikouquan Formation. In order to understand the petrology characters of conglomerates in Baikouquan Formation, based on lots of cores, grain size analysis, normal thin sections, casting thin sections, scanning electron photomicrographs, mineral composition identifications, clay mineral and bulk composition identifications of X-ray diffraction, were comparatively studied for Xiazijie and Huangyangquan fan-delta in Mahu Sag. Mineral composition of conglomerates is main tuff, while eurite, dacite, rhyolite, andesite and granite are common. However, more tuff and granite, less eurite and andesite in Xiazijie fan-delta, there is no rhyolite in Huangyangquan fan-delta. Kaolinization and chloritization of conglomerates are ubiquitous in the formation. The content of chlorite and kaolinite is higher in Xiazijie fan-delta, with lower illite-smectite and illite. There is less feldspar of clastic and more calcite of cement in Xiazijie fan-delta.

Forecast for peak infections in the second wave of the Omicron after the adjustment of zero-COVID policy in the mainland of China

On December 7,2022,the Chinese government optimized the current epidemic prevention and control policy,and no longer adopted the zero-COVID policy and mandatory quarantine measures.Based on the above policy changes,this paper establishes a compartment dynamics model considering age distribution,home isolation and vaccinations.Parameter estimation was performed using improved least squares and Nelder-Mead simplex algorithms combined with modified case data.Then,using the estimated parameter values to predict a second wave of the outbreak,the peak of severe cases will reach on 8 May 2023,the number of severe cases will reach 206,000.Next,it is proposed that with the extension of the effective time of antibodies obtained after infection,the peak of severe cases in the second wave of the epidemic will be delayed,and the final scale of the disease will be reduced.When the effectiveness of antibodies is 6 months,the severe cases of the second wave will peak on July 5,2023,the number of severe cases is 194,000.Finally,the importance of vaccination rates is demonstrated,when the vaccination rate of susceptible people under 60 years old reaches 98%,and the vaccination rate of susceptible people over 60 years old reaches 96%,the peak of severe cases in the second wave of the epidemic will be reached on 13 July 2023,when the number of severe cases is 166,000.

Ⅰ型左删失下Topp-Leone分布的参数及可靠度函数的估计

Firstly, the maximum likelihood estimate and asymptotic confidence interval of the unkown parameter for the Topp-Leone distribution are obtained under Type-I left censored samples, furthermore, the asymptotic confidence interval of reliability function is obtained based on monotonicity. Secondly, under different loss functions, the Bayesian estimates of the unkown parameter and reliability function are obtained, and the expected mean square errors of Bayesian estimates are calculated. Monte-Carlo method is used to calculate the mean values and relative errors of the estimates. Finally, an example of life data is analyzed by using the statistical method in this paper.

On the Viability of Solutions to Conformable Stochastic Differential Equations

The viability of the conformable stochastic differential equations is studied.Some necessary and sufficient conditions in terms of the distance function to K are given.In addition,when the boundary of K is sufficiently smooth,our necessary and sufficient conditions can reduce to two relations just on the boundary of K.Lastly,an example is given to illustrate our main results.

The Non-inclusion Diagnosability of Hypercubes Under the PMC Model

Diagnosability of a multiprocessor system is an important measure of the reliability of interconnection networks.System-level diagnosis is a primary strategy to identify the faulty processors in a multiprocessor system.Based on a sound assumption proposed by Zhu et al.recently,we proposed a new diagnosability named non-inclusion diagnosability and showed that the non-inclusion diagnosability t_(N)(Q_(n))of the hypercube under the PMC model is 2n-2.That is,assume that if two vertex sets F_(1) and F_(2) are both consistent with a syndrome and F_(1)C F_(2),then F_(2) is not the faulty set which we are looking for;the faulty set F is 1-step diagnosable if|F|≤2n-2 in Q_(n) under the PMC model.

Basic reproduction number and predicted trends of coronavirus disease 2019 epidemic in the mainland of China

Background Coronavirus disease 2019(COVID-19)has caused a serious epidemic around the world,but it has been effectively controlled in the mainland of China.The Chinese government limited the migration of people almost from all walks of life.Medical workers have rushed into Hubei province to fight against the epidemic.Any activity that can increase infection is prohibited.The aim of this study was to confirm that timely lockdown,large-scale case-screening and other control measures proposed by the Chinese government were effective to contain the spread of the virus in the mainland of China.Methods Based on disease transmission-related parameters,this study was designed to predict the trend of COVID-19 epidemic in the mainland of China and provide theoretical basis for current prevention and control.An SEIQR epidemiological model incorporating asymptomatic transmission,short term immunity and imperfect isolation was constructed to evaluate the transmission dynamics of COVID-19 inside and outside of Hubei province.With COVID-19 cases confirmed by the National Health Commission(NHC),the optimal parameters of the model were set by calculating the minimum Chi-square value.Results Before the migration to and from Wuhan was cut off,the basic reproduction number in China was 5.6015.From 23 January to 26 January 2020,the basic reproduction number in China was 6.6037.From 27 January to 11 February 2020,the basic reproduction number outside Hubei province dropped below 1,but that in Hubei province remained 3.7732.Because of stricter controlling measures,especially after the initiation of the large-scale case-screening,the epidemic rampancy in Hubei has also been contained.The average basic reproduction number in Hubei province was 3.4094 as of 25 February 2020.We estimated the cumulative number of confirmed cases nationwide was 82186,and 69230 in Hubei province on 9 April 2020.Conclusions The lockdown of Hubei province significantly reduced the basic reproduction number.The large-scale case-screening also showed the effectiveness in the epidemic control.This study provided experiences that could be replicated in other countries suffering from the epidemic.Although the epidemic is subsiding in China,the controlling efforts should not be terminated before May.

Gravel Image Auto-Segmentation Based on an Improved Normalized Cuts Algorithm

The study of the grain-size distribution of gravels is always an important and challenging issue in stratigraphy and morphology, especially in the field of automated measurement. It largely reduces many manual processes and time consumption. Precise segmentation method plays a very important role in it. In this study, a digital image method using an improved normalized cuts algorithm is proposed for auto-segmentation of gravel image. It added grain-size estimation, and used the feature vector based on color. It has made great improvements in many respects, especially in accuracy of edge segmentation and automation. Compared with manual measurement methods and other image processing methods, the method studied in this paper is an efficient method for precisely segmenting gravel images.

Travelling Solitary Wave Solutions for Generalized Time-delayed Burgers-Fisher Equation

In this paper,travelling wave solutions for the generalized time-delayed Burgers-Fisher equation arestudied.By using the first-integral method,which is based on the ring theory of commutative algebra,we obtain aclass of travelling solitary wave solutions for the generalized time-delayed Burgers-Fisher equation.A minor error in theprevious article is clarified.

Gomory’s Method Based on the Objective Equivalent Face Technique

This paper discusses a re-examinatlon of dual methods based on Gomory＇s cutting plane for the solution of the integer programming problem, in which the increment of objection function is allowed as a pivot variable to decide the search direction and stepsize. Meanwhile, we adopt the current equivalent face technique so that lattices are found in the discrete integral face and stronger valid inequalities are acquired easily.