Abstract-The recent expansion of pervasive computing technology has contributed with novel means to pursue human activities in urban space. The urban dynamics unveiled by these means generate an enormous amount of data. These data are mainly endowed by portable and radio-frequency devices, transportation systems, video surveillance, satellites, unmanned aerial vehicles, and social networking services. This has opened a new avenue of opportunities, to understand and predict urban dynamics in detail, and plan various real-time services and applications in response to that. Over the last decade, certain aspects of the crowd, e.g. mobility, sentimental, size estimation and behavioral, have been analyzed in detail and the outcomes have been reported. This article mainly conducted an extensive survey on various data sources used for different urban applications, the state-of-the-art on urban data generation techniques and associated processing methods in order to demonstrate their merits and capabilities. Then, a possible crowd event detection framework is discussed which fuses data from all the available pervasive technology sources. In addition, available open-access crowd datasets for urban event detection are provided along with relevant Application Programming Interfaces, and finally, some open challenges and promising research directions are outlined.Index Terms-Urban sensing, pervasive technology, crowd mobility and management, information fusion, decision support system, benchmark datasets.

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Matrix inversion is used in the least squares analysis of data to estimate parameters and their varianoea and covariances. When the data come from the analysis of variance, analysis of covariance, order statistics, or the fitting of response-surfaces, the matrix to be inverted usually falls into a structured pattern that simplifies its inversion.One class of patterned matrices is characterized by non-eingular symmetrical arrangemepts in which linear combinations of the first (r -1) rows provide the right-hand portion, starting with the elements on the principal diagonal, of the rth and remaining rows. That is: for r ;ai ~j, with v;; =v;; for all i ~j. The inverses of matrices of this clase contain a non-null principal diagonal, and immediately adjacent to the principal diagonal, (r -1) non-niJll superdiagonals and (r -1) non-null subdiagonals. All other elements are zero. These inverses are called diagonal matrices of type r. That is, a matrix is diagonal of type r if a;, ~o for I i -il ~rand a;; ~a# for all i ~j. When r ~2, the inverse is easily written in terms of BH and Vif· A general procedure for obtaining the inverse when r =3 is given.The results for r = 2 are illustrated by a problem in order statistics using the two-parameter exponential distribution.Patterned matrices also are amenable to partitioning and this is another convenient device to find the exact inverse quickly. In fitting a response-surface to data, for example, a complicated-looking matrix can be abbreviated and simplified by selective partitioning. When this has been done, the exact inverse can be found by equating the product of the matrix and its inverse to the elements of the identity matrix. This procedure is illustrated with some data from a problem in the fitting of a respon&e-surface.When the matrix has no special pattern, as in the usual regression problem, the recommended procedure for matrix inversion is the modified square root method.