Analytical Model for Enhanced Eigen-Mode Sensitivities in a Coupled Micro-Resonator Array for Ultra-Sensitive Mass Measurement

Resonant sensors using coupled micro-cantilever array have applications in a wide range of areas including ultrasensitive mass detection of bio-molecules and chemical analytes. A target mass deposited on one of the cantilevers can be detected by measuring shift in eigen-spectrum. Experimental observations indicate that eigenmodes are more sensitive to mass perturbation than resonant frequencies or eigenvalues. However, analytical works, available in literatures, are limited to only two and three cantilever array for eigenvalue sensitivity and only two cantilever array for eigenmode sensitivity. In the present work, an analytical foundation for estimation of eigenmode sensitivities for a general n-array micro-resonator sensor is developed using matrix perturbation theory. The formulation characterizes the modal spectrum and eigenmode sensitivities as a function of elastic interconnection stiffness parameter and unperturbed eigenmodes. Measurement of added mass is demonstrated for different analyte locations using numerically constructed frequency response function (FRF) curves. Error in measurement is also investigated as a function of interconnection stiffness ratio, position of analyte mass, and selection of particular eigenmode to be measured.

Measuring intrinsic significance of community structure

The significance of communities is an important inherent property of the community structure. It measures the degree of reliability of the community structure identified by the algorithm. Real networks obtained from complex systems always contain error links. Moreover, most of the community detecting algorithms usually involve random factors. Thus evaluating the significance of community structure is very important. In this paper, using the matrix perturbation theory, we propose a normalized index to efficiently evaluate the significance of community structure without detecting communities. Furthermore, we find that the peaks of this index can be used to determine the optimal number of communities and identify hierarchical community structure, which are two challenging problems in many community detecting algorithms. Lastly, the index is applied to 16 typical real networks, and we find that significant community structures exist in many social networks and in the C. elegans neural network. Comparatively insignificant community structures are identified in protein-interaction networks and metabolic networks. Our method can be generalized to broad clustering problems in data mining.

Clustering Based on Eigenvectors of the Adjacency Matrix

The paper presents a novel spectral algorithm EVSA (eigenvector structure analysis), which uses eigenvalues and eigenvectors of the adjacency matrix in order to discover clusters. Based on matrix perturbation theory and properties of graph spectra we show that the adjacency matrix can be more suitable for partitioning than other Laplacian matrices. The main problem concerning the use of the adjacency matrix is the selection of the appropriate eigenvectors. We thus propose an approach based on analysis of the adjacency matrix spectrum and eigenvector pairwise correlations. Formulated rules and heuristics allow choosing the right eigenvectors representing clusters, i.e., automatically establishing the number of groups. The algorithm requires only one parameter-the number of nearest neighbors. Unlike many other spectral methods, our solution does not need an additional clustering algorithm for final partitioning. We evaluate the proposed approach using real-world datasets of different sizes. Its performance is competitive to other both standard and new solutions, which require the number of clusters to be given as an input parameter.