Synchronization and Exponential Estimates of Complex Networks with Mixed Time-varying Coupling Delays

Exponential estimates and sufficient conditions for the exponential synchronization of complex dynamical networks with bounded time-varying delays are given in terms of linear matrix inequalities （LMIs）. A generalized complex networks model involving both neutral delays and retarded ones is presented. The exponential synchronization problem of the complex networks is converted equivalently into the exponential stability problem of a group of uncorrelated delay functional differential equations with mixed timevarying delays. By utilizing the free weighting matrix technique, a less conservative delay-dependent synchronization criterion is derived. An illustrative example is provided to demonstrate the effectiveness of the proposed method.

Improved results on state estimation for neural networks with time-varying delays

In this paper, some improved results on the state estimation problem for recurrent neural networks with both time-varying and distributed time-varying delays are presented. Through available output measurements, an improved delay-dependent criterion is established to estimate the neuron states such that the dynamics of the estimation error is globally exponentially stable, and the derivative of time-delay being less than 1 is removed, which generalize the existent methods. Finally, two illustrative examples are given to demonstrate the effectiveness of the proposed results.

Improved population mean estimator with exponential function under non-response

In this article,we consider a new family of exponential type estimators for estimating the unknown population mean of the study variable.We propose estimators taking advantage of the auxiliary variable information under the first and second non-response cases separately.The required theoretical comparisons are obtained and the numerical studies are conducted.In conclusion,the results show that the proposed family of estimators is the most efficient estimator with respect to the estimators in literature under the obtained conditions for both cases.

EXPONENTIAL ESTIMATES FOR STOCHASTIC DELAY HYBRID SYSTEMS WITH MARKOVIAN SWITCHING

This paper deals with the problem of norm bounds for the solutions of stochastic hybrid systems with Markovian switching and time delay. Based on Lyapunov-Krasovskii theory for functional differential equations and the linear matrix inequality （LMI） approach, mean square exponential estimates for the solutions of this class of linear stochastic hybrid systems are derived. Finally, An example is illustrated to show the applicability and effectiveness of our method.

Reliability analysis of extended generalized inverted exponential distribution with applications

A general version of the inverted exponential distribution is introduced, studied and analyzed. This generalization depends on the method of Marshall-Olkin to extend a family of distributions. Some statistical and reliability properties of this family are studied. In addition, numerical estimation of the maximum likelihood estimate（MLE） parameters are discussed in details. As an application, some real data sets are analyzed and it is observed that the presented family provides a better fit than some other known distributions.

GROWTH ESTIMATES FOR SINE-TYPE-FUNCTIONS AND APPLICATIONS TO RIESZ BASES OF EXPONENTIALS

We present explicit estimates for the growth of sine-type-functions as well as for the derivatives at their zero sets, thus obtaining explicit constants in a result of Levin. The estimates are then used to derive explicit lower bounds for exponential Riesz bases, as they arise in Avdonin's Theorem on 1/4 in the mean or in a Theorem, of Bogmtr, Horvath, Job and Seip. An application is discussed, where knowledge of explicit lower bounds of exponential Riese bases is desirable.

Modeling height–diameter relationship for Populus euphratica in the Tarim riparian forest ecosystem, Northwest China

Modeling height–diameter relationships is an important component in estimating and predicting forest development under different forest management scenarios. In this paper, ten widely used candidate height–diameter models were fitted to tree height and diameter at breast height（DBH）data for Populus euphratica Oliv. within a 100 ha permanent plots at Arghan Village in the lower reaches of the Tarim River, Xinjiang Uyghur Autonomous Region of China. Data from 4781 trees were used and split randomly into two sets：75 % of the data were used to estimate model parameters（model calibration）, and the remaining data（25 %） were reserved for model validation. All model performances were evaluated and compared by means of multiple model performance criteria such as asymptotic t-statistics of model parameters, standardized residuals against predicted height,root mean square error（RMSE）, Akaike’s informationcriterion（AIC）, mean prediction error（ME） and mean absolute error（MAE）. The estimated parameter a for model（6） was not statistically significant at a level of a = 0.05. RMSE and AIC test result for all models showed that exponential models（1）,（2）,（3） and（4） performed significantly better than others. All ten models had very small MEs and MAEs. Nearly all models underestimated tree heights except for model（6）. Comparing the MEs and MAEs of models, model（1） produced smaller MEs（0.0059） and MAEs（1.3754） than other models. To assess the predictive performance of models, we also calculated MEs by dividing the model validation data set into 10-cm DBH classes. This suggested that all models were likely to create higher mean prediction errors for tree DBH classes[20 cm. However, no clear trend was found among models.Model（6） generated significantly smaller mean prediction errors across all tree DBH classes. Considering all the aforementioned criteria, model（1）： TH ？ 1：3 t a= e1 t b？eàc？DBHT and model（6）： TH ？ 1：3 t DBH2= ea t b？DBH t c ？ DBH2T are recommended as suitable models for describing the height–diameter relationship of P. euphratica. The limitations of other models showing poor performance in predicting tree height are discussed. We provide explanations for these shortcomings.

EXPONENTIAL ESTIMATE OF SOLUTION TO STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

In this paper, by the Burkholder-Davis-Gundy inequality and It? formula, the exponential estimate of the solution to stochastic functional differential equations with infinite delay is established in the phase space BC((-∞,0];Rd). Furthermore, the sample Lyapunov exponent of the solution is obtained, which is less than a positive constant 2√K + 65K. Moreover, a pth moment of the solution is studied.

AN EXPONENTIAL WAVE INTEGRATOR PSEUDOSPECTRAL METHOD FOR THE SYMMETRIC REGULARIZED-LONG-WAVE EQUATION

An efficient and accurate exponential wave integrator Fourier pseudospectral （EWI-FP） method is proposed and analyzed for solving the symmetric regularized-long-wave （SRLW） equation, which is used for modeling the weakly nonlinear ion acoustic and space-charge waves. The numerical method here is based on a Gautschi-type exponential wave integrator for temporal approximation and the Fourier pseudospectral method for spatial discretization. The scheme is fully explicit and efficient due to the fast Fourier transform. Numerical analysis of the proposed EWI-FP method is carried out and rigorous error estimates are established without CFL-type condition by means of the mathematical induction. The error bound shows that EWI-FP has second order accuracy in time and spectral accuracy in space. Numerical results are reported to confirm the theoretical studies and indicate that the error bound here is optimal.

EXPONENTIAL ESTIMATES FOR STOCHASTIC DELAY EQUATIONS WITH NORM-BOUNDED UNCERTAINTIES

This paper presents the sufficient conditions for the exponential stability of linear or semi-linear stochastic delay equations with time-varying norm bounded parameter uncertainties.Exponen-tial estimates for the solutions are also obtained by using a modified Lyapunov-Krasovski functional.These conditions can be tested numerically using interior point algorithms.

Partial Collapsing Degeneration of Floer Trajectories and Adiabatic Gluing

In the present paper,we study partial collapsing degeneration of Hamiltonian-perturbed Floer trajectories for an adiabatic ε-family and its reversal adiabatic gluing,as the prototype of the partial collapsing degeneration of 2-dimensional(perturbed)J-holomorphic maps to 1-dimensional gradient segments.We consider the case when the Floer equations are S^(1)-invariant on parts of their domains whose adiabatic limit has positive length as ε→0,which we call thimble-flow-thimble configurations.The main gluing theorem we prove also applies to the case with Lagrangian boundaries such as in the problem of recovering holomorphic disks out of pearly configuration.In particular,our gluing theorem gives rise to a new direct proof of the chain isomorphism property between the Morse-Bott version of Lagrangian intersection Floer complex of L by Fukaya-Oh-Ohta-Ono and the pearly complex of L Lalonde and Biran-Cornea.It also provides another proof of the present authors’earlier proof of the isomorphism property of the PSS map without involving the target rescaling and the scale-dependent gluing.

STABILITY OF TIME VARYING SINGULAR DIFFERENTIAL SYSTEMS WITH DELAY

In this paper, stability of time varying singular differential systems with delay is considered. Based on variation formula and Gronwall-Bellman integral inequality, we obtain the exponential estimation of the solution and the sufficient conditions under which the considered system is stable and exponentially asymptotically stable. These results will be very useful to further research on Roust stability and control design of uncertain singular control systems with delay.

Exit problems for nonlinear stochastic evolution equations on Hilbert spaces

This paper extends exit theorems of Da Prato and Zabczyk to nonconstant diffusion coefficients.It uses extensively general, exponential estimates due to Peszat.

Virtual neighborhood technique for moduli spaces of holomorphic curves

We use the technique of Ruan(1999)and Li and Ruan(2001)to construct the virtual neighborhoods and show that the Gromov-Witten invariants can be defined as integrals over the top strata of the virtual neighborhoods.We prove that the invariants defined in this way satisfy all the axioms of Gromov-Witten invariants summarized by Kontsevich and Manin(1994).

A note on testing conditional independence for social network analysis

In social network analysis, logistic regression models have been widely used to establish the relationship between the response variable and covariates. However, such models often require the network relationships to be mutually independent, after controlling for a set of covariates. To assess the validity of this assumption,we propose test statistics, under the logistic regression setting, for three important social network drivers. They are, respectively, reciprocity, centrality, and transitivity. The asymptotic distributions of those test statistics are obtained. Extensive simulation studies are also presented to demonstrate their finite sample performance and usefulness.