Explores regular structures in graphs and contingency tables by spectral theory and statistical methods This book bridges the gap between graph theory and statistics by giving answers to the demanding questions which arise when statisticians are confronted with large weighted graphs or rectangular arrays. Classical and modern statistical methods applicable to biological, social, communication networks, or microarrays are presented together with the theoretical background and proofs. This book is suitable for a one-semester course for graduate students in data mining, multivariate statistics, or applied graph theory; but by skipping the proofs, the algorithms can also be used by specialists who just want to retrieve information from their data when analysing communication, social, or biological networks. Spectral Clustering and Biclustering: Provides a unified treatment for edge-weighted graphs and contingency tables via methods of multivariate statistical analysis (factoring, clustering, and biclustering). Uses spectral embedding and relaxation to estimate multiway cuts of edge-weighted graphs and bicuts of contingency tables. Goes beyond the expanders by describing the structure of dense graphs with a small spectral gap via the structural eigenvalues and eigen-subspaces of the normalized modularity matrix. Treats graphs like statistical data by combining methods of graph theory and statistics. Establishes a common outline structure for the contents of each algorithm, applicable to networks and microarrays, with unified notions and principles.
This book gives a brief survey of the theory of multidimensional (multivariate), weakly stationary time series, with emphasis on dimension reduction and prediction. Understanding the covered material requires a certain mathematical maturity, a degree of knowledge in probability theory, linear algebra, and also in real, complex and functional analysis. For this, the cited literature and the Appendix contain all necessary material. The main tools of the book include harmonic analysis, some abstract algebra, and state space methods: linear time-invariant filters, factorization of rational spectral densities, and methods that reduce the rank of the spectral density matrix. Serves to find analogies between classical results (Cramer, Wold, Kolmogorov, Wiener, Kálmán, Rozanov) and up-to-date methods for dimension reduction in multidimensional time series Provides a unified treatment for time and frequency domain inferences by using machinery of complex and harmonic analysis, spectral and Smith--McMillan decompositions. Establishes analogies between the time and frequency domain notions and calculations Discusses the Wold's decomposition and the Kolmogorov's classification together, by distinguishing between different types of singularities. Understanding the remote past helps us to characterize the ideal situation where there is a regular part at present. Examples and constructions are also given Establishes a common outline structure for the state space models, prediction, and innovation algorithms with unified notions and principles, which is applicable to real-life high frequency time series It is an ideal companion for graduate students studying the theory of multivariate time series and researchers working in this field.
Scholars and readers who are interested in eighteenth-century British literature are surely familiar with Hester Lynch Thrale Piozzi in the light she came to be known in her lifetime and after: first, as the “formidable hostess” of Streatham House, South London, and then as an outcast from respectable eighteenth-century society after she had married the Italian piano teacher of her daughter. As a writer, her importance has long been that of a footnote to Samuel Johnson and as a consequence, she has been part of the official British literary canon only as a character. This volume introduces Hester Lynch Thrale Piozzi as a whole, trying to link her fascinating and subversive biography to her development as a writer, emphasizing the innovative issues of her works, her style and her social and personal beliefs. Piozzi’s biography is an interesting example of the dynamic scene of the late eighteenth century, where she was both conservative and subversive: she was an eccentric, and although her decision to marry the Italian singer and composer Gabriele Piozzi disgraced her, it was through this act of subversion that Hester Thrale Piozzi could finally make her own entrance into the world as a public writer. Once she had transgressed the social codes of so-called “feminine” behaviour, she was also ready to move into the public sphere, publish her works and make money out of them, pioneering several traditional literary genres through her passionate search for professional independence in the literary canon of the eighteenth century.
This book focuses on literary multilingualism and specifically on the challenging condition of writing in Trieste, a key European borderland located at the intersection between the Latin, Germanic and Slav civilisations. By focusing on some of the most representative modern writers operating in the area, such as Italo Svevo, Boris Pahor, Claudio Magris and James Joyce, this work offers a wide-ranging discussion of multilingual practices deriving from the different language choices made by these writers. Along with the most common manifest strategies, such as code-switching and hybridisations, Deganutti highlights how Triestine writers found innovative latent practices to engage with multilingualism, such as writing in an analogical way or exploiting internal linguistic stratifications. Moreover, she shows how they provided answers to the several linguistic, cultural and even political challenges they were subjected to, with the result of redefining linguistic boundaries that clearly separate different tongues. This book will be of interest to graduate students, researchers and academics interested in literary multilingualism in the fields of sociolinguistics, borderland studies and comparative literature.
Explores regular structures in graphs and contingency tables by spectral theory and statistical methods This book bridges the gap between graph theory and statistics by giving answers to the demanding questions which arise when statisticians are confronted with large weighted graphs or rectangular arrays. Classical and modern statistical methods applicable to biological, social, communication networks, or microarrays are presented together with the theoretical background and proofs. This book is suitable for a one-semester course for graduate students in data mining, multivariate statistics, or applied graph theory; but by skipping the proofs, the algorithms can also be used by specialists who just want to retrieve information from their data when analysing communication, social, or biological networks. Spectral Clustering and Biclustering: Provides a unified treatment for edge-weighted graphs and contingency tables via methods of multivariate statistical analysis (factoring, clustering, and biclustering). Uses spectral embedding and relaxation to estimate multiway cuts of edge-weighted graphs and bicuts of contingency tables. Goes beyond the expanders by describing the structure of dense graphs with a small spectral gap via the structural eigenvalues and eigen-subspaces of the normalized modularity matrix. Treats graphs like statistical data by combining methods of graph theory and statistics. Establishes a common outline structure for the contents of each algorithm, applicable to networks and microarrays, with unified notions and principles.
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