LEADER 03933nam 22005895 450 001 996418276203316 005 20200706091701.0 010 $a3-030-38852-2 024 7 $a10.1007/978-3-030-38852-2 035 $a(CKB)4100000010672605 035 $a(DE-He213)978-3-030-38852-2 035 $a(MiAaPQ)EBC6138232 035 $a(PPN)243226306 035 $a(EXLCZ)994100000010672605 100 $a20200316d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aModeling Information Diffusion in Online Social Networks with Partial Differential Equations$b[electronic resource] /$fby Haiyan Wang, Feng Wang, Kuai Xu 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (XIII, 144 p. 39 illus., 29 illus. in color.) 225 1 $aSurveys and Tutorials in the Applied Mathematical Sciences,$x2199-4765 ;$v7 311 $a3-030-38850-6 327 $aOrdinary Differential Equation Models on Social Networks -- Spatio-temporal Patterns of Information Diffusion -- Clustering of Online Social Network Graphs -- Partial Differential Equation Models -- Modeling Complex Interactions -- Mathematical Analysis -- Applications. 330 $aThe book lies at the interface of mathematics, social media analysis, and data science. Its authors aim to introduce a new dynamic modeling approach to the use of partial differential equations for describing information diffusion over online social networks. The eigenvalues and eigenvectors of the Laplacian matrix for the underlying social network are used to find communities (clusters) of online users. Once these clusters are embedded in a Euclidean space, the mathematical models, which are reaction-diffusion equations, are developed based on intuitive social distances between clusters within the Euclidean space. The models are validated with data from major social media such as Twitter. In addition, mathematical analysis of these models is applied, revealing insights into information flow on social media. Two applications with geocoded Twitter data are included in the book: one describing the social movement in Twitter during the Egyptian revolution in 2011 and another predicting influenza prevalence. The new approach advocates a paradigm shift for modeling information diffusion in online social networks and lays the theoretical groundwork for many spatio-temporal modeling problems in the big-data era. 410 0$aSurveys and Tutorials in the Applied Mathematical Sciences,$x2199-4765 ;$v7 606 $aPartial differential equations 606 $aApplication software 606 $aCommunication 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aComputer Appl. in Social and Behavioral Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/I23028 606 $aCommunication Studies$3https://scigraph.springernature.com/ontologies/product-market-codes/X28000 615 0$aPartial differential equations. 615 0$aApplication software. 615 0$aCommunication. 615 14$aPartial Differential Equations. 615 24$aComputer Appl. in Social and Behavioral Sciences. 615 24$aCommunication Studies. 676 $a515.353 700 $aWang$b Haiyan$4aut$4http://id.loc.gov/vocabulary/relators/aut$0899993 702 $aWang$b Feng$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aXu$b Kuai$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418276203316 996 $aModeling Information Diffusion in Online Social Networks with Partial Differential Equations$92368775 997 $aUNISA LEADER 04423nam 2200637 450 001 9910542869103321 005 20230809230443.0 010 $a3-11-038340-3 010 $a3-11-035178-1 024 7 $a10.1515/9783110351781 035 $a(CKB)3850000000001206 035 $a(MiAaPQ)EBC4851863 035 $a(DE-B1597)276799 035 $a(OCoLC)986030583 035 $a(OCoLC)987927213 035 $a(DE-B1597)9783110351781 035 $a(Au-PeEL)EBL4851863 035 $a(CaPaEBR)ebr11380709 035 $a(CaONFJC)MIL1008620 035 $a(EXLCZ)993850000000001206 100 $a20170519h20172017 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 00$aMetric theories of gravity $eperturbations and conservation laws /$fAlexander N. Petrov, [and three others] 210 1$aBerlin, [Germany] ;$aBoston, [Massachusetts] :$cDe Gruyter,$d2017. 210 4$dİ2017 215 $a1 online resource (622 pages) 225 1 $aDe Gruyter Studies in Mathematical Physics ;$vVolume 38 311 $a3-11-035173-0 320 $aIncludes bibliographical references. 327 $tFrontmatter -- $tPreface -- $tContents -- $tList of Figures -- $tPrimary notations -- $t1. Conservation laws in theoretical physics: A brief introduction -- $t2. Field-theoretical formulation of general relativity: The theory -- $t3. Asymptotically flat spacetime in the field-theoretical formulation -- $t4. Exact solutions of general relativity in the field-theoretical formalism -- $t5. Field-theoretical derivation of cosmological perturbations -- $t6. Currents and superpotentials on arbitrary backgrounds: Three approaches -- $t7. Conservation laws in an arbitrary multi-dimensional metric theory -- $t8. Conserved quantities in the Einstein-Gauss-Bonnet gravity -- $t9. Generic gravity: Particle content, weak field limits, conserved charges -- $t10. Conservation laws in covariant field theories with gauge symmetries -- $tAppendix A: Tensor quantities and tensor operations -- $tAppendix B: Retarded functions -- $tBibliography -- $tIndex 330 $aBy focusing on the mostly used variational methods, this monograph aspires to give a unified description and comparison of various ways of constructing conserved quantities for perturbations and to study symmetries in general relativity and modified theories of gravity. The main emphasis lies on the field-theoretical covariant formulation of perturbations, the canonical Noether approach and the Belinfante procedure of symmetrisation. The general formalism is applied to build the gauge-invariant cosmological perturbation theory, conserved currents and superpotentials to describe physically important solutions of gravity theories. Meticulous attention is given to the construction of conserved quantities in asymptotically-flat spacetimes as well as in asymptotically constant curvature spacetimes such as the Anti-de Sitter space. Significant part of the book can be used in graduate courses on conservation laws in general relativity. THE SERIES: DE GRUYTER STUDIES IN MATHEMATICAL PHYSICS The series is devoted to the publication of monographs and high-level texts in mathematical physics. They cover topics and methods in fields of current interest, with an emphasis on didactical presentation. The series will enable readers to understand, apply, and develop further, with sufficient rigor, mathematical methods to given problems in physics. The works in this series are aimed at advanced students and researchers in mathematical and theoretical physics. They can also serve as secondary reading for lectures and seminars at advanced levels. 410 0$aDe Gruyter studies in mathematical physics ;$vVolume 38. 606 $aGravity 606 $aGravity anomalies 606 $aGravitational waves 606 $aGeneral relativity (Physics) 606 $aForce and energy 615 0$aGravity. 615 0$aGravity anomalies. 615 0$aGravitational waves. 615 0$aGeneral relativity (Physics) 615 0$aForce and energy. 676 $a531/.1401 700 $aPetrov$b Alexander N., $01117787 702 $aPetrov$b Alexander N. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910542869103321 996 $aMetric theories of gravity$92645540 997 $aUNINA