Stability of weighted spectral distribution in a pseudo tree-like network model

The comparison of networks with different orders strongly depends on the stability analysis of graph features in evolving systems. In this paper, we rigorously investigate the stability of the weighted spectral distribution（i.e., a spectral graph feature） as the network order increases. First, we use deterministic scale-free networks generated by a pseudo treelike model to derive the precise formula of the spectral feature, and then analyze the stability of the spectral feature based on the precise formula. Except for the scale-free feature, the pseudo tree-like model exhibits the hierarchical and small-world structures of complex networks. The stability analysis is useful for the classification of networks with different orders and the similarity analysis of networks that may belong to the same evolving system.

Scaling of weighted spectral distribution in weighted small-world networks

Many real-world systems can be modeled by weighted small-world networks with high clustering coefficients. Recent studies for rigorously analyzing the weighted spectral distribution（W SD） have focused on unweighted networks with low clustering coefficients. In this paper, we rigorously analyze the W SD in a deterministic weighted scale-free small-world network model and find that the W SD grows sublinearly with increasing network order（i.e., the number of nodes） and provides a sensitive discrimination for each input of this model. This study demonstrates that the scaling feature of the W SD exists in the weighted network model which has high and order-independent clustering coefficients and reasonable power-law exponents.

Weighted spectral correlation angle target detection method for land‑based hyperspectral imaging

In land-based spectral imaging,the spectra of ground objects are inevitably afected by the imaging conditions(weather conditions,atmospheric conditions,light conditions,zenith and azimuth angle conditions)and spatial distribution of targets,leading to uncertainties featured by“same object diferent spectrum”.That is,the spectrum of a ground object may change within a certain range under diferent imaging conditions.Traditional target detection(TD)methods are mainly based on similarity measurements and do not fully account for the spectral uncertainties.These detection methods are prone to false detections or missed detections.Therefore,reducing the impact of spectral uncertainties on TD is an important research topic in hyperspectral imaging.In this paper,we frst review traditional TD methods and compare their principles and characteristics.It is found that the spectral correlation angle(SCA)method has good adaptability in land-based imaging.The shortcoming of the SCA method that it cannot refect the local spectrum characteristics,is also analyzed.As the efect of spectral uncertainties cannot be completely overcome by the SCA method,a new similarity measurement method,the weighted spectral correlation angle(WSCA)method,is proposed.It can reduce the infuence of spectral uncertainties on TD by increasing the weight of particular bands.Finally,we use two sets of experiments to analyze the efect of the WSCA method on TD.Its performance in overcoming spectral uncertainties caused by variations in imaging conditions or uneven spatial distributions of targets is tested.The results show that the WSCA method can efectively reduce the infuence of spectral uncertainties and obtain a good detection result.

Spectral clustering based on matrix perturbation theory

This paper exposes some intrlnsic chsracterlstlca of the spectral clustering method by using the tools from the mstrlx perturbation theory. We construct s welght mstrix of s graph and study Its elgenvalues and elgenvectors. It shows that the number of clusters Is equal to the number of elgenvslues that are larger than 1, and the number of polnts In each of the clusters can be spproxlmsted by the associated elgenvslue. It also shows that the elgenvector of the weight rnatrlx can be used dlrectly to perform clusterlng; that Is, the dlrectlonsl angle between the two-row vectors of the mstrlx derlved from the elgenvectors Is s sultable distance measure for clustsrlng. As s result, an unsupervised spectral clusterlng slgorlthm based on welght mstrlx （USCAWM） Is developed. The experlmental results on s number of srtlficisl and real-world data sets show the correctness of the theoretical analysis.

A Weighted Multi-Domain Spectral Penalty Method with Inhomogeneous Grid for Supersonic Injective Cavity Flows

In[J.Comput.Phys.192(1),pp.325-354(2003)],we have developed a multidomain spectral method with stable and conservative penalty interface conditions for the numerical simulation of supersonic reactive recessed cavity flows with homogeneous grid.In this work,the previously developed methodology is generalized to inhomogeneous grid to simulate the two dimensional supersonic injector-cavity system.Non-physical modes in the solution generated at the domain interfaces due to the spatial grid inhomogeneity are minimized using the new weighted multi-domain spectral penalty method.The proposed method yields accurate and stable solutions of the injector-cavity system which agree well with experiments qualitatively.Through the direct numerical simulation of the injector-cavity system using the weighted method,the geometric effect of the cavity wall on pressure fluctuations is investigated.It is shown that the recessed slanted cavity attenuates pressure fluctuations inside cavity enabling the cavity to act potentially as a stable flameholder for scramjet engine.

Spectral Decomposition of Weighted Shift Operators

The reseearch on the relation between weighted shift operators on Hilbert spaces and other important class of operators attracted the attention of some mathematicians. For example, the relation between weighted shift operators and subnormal operators has been thoroughly studied by J. Stampfli, R. Gellar and D. A. Herrero, etc. (see reference [1]) But the decomposability of weighted shift operators has not yet attracted enough attention up to now. We made initial research