The local stability of a nonlinear dynamical system at an equilibrium point with a pair of purely imaginary eigenvalues can be assessed through the computation of a cubic Hopf normal form coefficient, assuming the remaining eigenvalues have negative real parts. In this paper, a modal decomposition of the Hopf coefficient is proved. The decomposition provides a new methodology for analyzing the ...

This paper proposes a blind watermarking algorithm based on maximum wavelet coefficient quantization for copyright protection. The wavelet coefficients are grouped into different block size and blocks are randomly selected from different subbands. We add different energies to the maximum wavelet coefficient under the constraint that the maximum wavelet coefficient is always maximum in a block. ...

ZHAOWEI HUA: Bayesian Analysis of Varying Coefficient Models and Applications. (Under the direction of Hongtu Zhu and David B. Dunson.) The varying coefficient models have been very important analytic tools to study the dynamic pattern in biomedicine fields. Since nonparametric varying coefficient models make few assumptions on the specification of the model, the ‘curse of dimensionality’ is an...

Tunnelling probabilities in field emission processes are usually calculated assuming flat emitting surfaces. This corresponds to consider the electric field as a constant along the potential barrier. Previous work have shown the importance of taking into account image effects but neglecting local field variations. Even when the local field has been taken into account, a proper three dimensional...

This paper considers statistical inference for the heteroscedastic varying coefficient model. We propose an efficient estimator for coefficient functions that is more efficient than the conventional local-linear estimator. We establish asymptotic normality for the proposed estimator and conduct some simulation to illustrate the performance of the proposed method.

We propose in this work a generalization of the functional linear model in which an additional real variable influences smoothly the functional coefficient. This leads us to build a varying-coefficient regressionmodel for functional data. We propose two estimators based respectively on conditional functional principal regression and on local penalized regression splines and prove their pointwis...

This paper constructs a local generalized finite element basis for elliptic problems with heterogeneous and highly varying diffusion coefficient. The basis functions are solutions to local problems on vertex patches. The error of the corresponding generalized finite element method decays exponentially with respect to the number of layers of elements in the patches. Hence, on a uniform mesh of s...

We propose an extended local-world evolving network model including a triad formation step. In the process of network evolution, random fluctuation in the number of new edges is involved. We derive analytical expressions for degree distribution, clustering coefficient and average path length. Our model can unify the generic properties of real-life networks: scale-free degree distribution, high ...

Probabilistic networks display a wide range of high average clustering coefficients independent of the number of nodes in the network. In particular, the local clustering coefficient decreases with the degree of the subtending node in a complicated manner not explained by any current models. While a number of hypotheses have been proposed to explain some of these observed properties, there are ...