LEADER 05423nam 22006854a 450 001 9910144723003321 005 20170815122051.0 010 $a1-280-27839-0 010 $a9786610278398 010 $a0-470-35478-X 010 $a0-471-75472-2 010 $a0-471-75470-6 035 $a(CKB)1000000000377257 035 $a(EBL)239410 035 $a(OCoLC)61762097 035 $a(SSID)ssj0000157721 035 $a(PQKBManifestationID)11147173 035 $a(PQKBTitleCode)TC0000157721 035 $a(PQKBWorkID)10144536 035 $a(PQKB)10806848 035 $a(MiAaPQ)EBC239410 035 $a(EXLCZ)991000000000377257 100 $a20050427d2005 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFractal-based point processes$b[electronic resource] /$fSteven Bradley Lowen, Malvin Carl Teich 210 $aHoboken, N.J. $cWiley-Interscience$d2005 215 $a1 online resource (628 p.) 225 1 $aWiley Series in Probability and Statistics ;$vv.366 300 $aDescription based upon print version of record. 311 $a0-471-38376-7 320 $aIncludes bibliographical references (p. 513-565) and index. 327 $aFractal-Based Point Processes; Preface; Contents; List of Figures; List of Figures; List of Tables; List of Tables; Authors; 1 Introduction; 1.1 Fractals; 1.1 Coastline of Iceland at different scales; 1.2 Point Processes; 1.3 Fractal-Based Point Processes; 1.2 Vehicular-traffic point process; Problems; 1.1 Length of Icelandic coastline at different scales; 1.2 Polygon approximation for perimeter of circle; 2 Scaling, Fractals, and Chaos; 2.1 Dimension; 2.1 Representative objects: measurements and dimensions; 2.2 Scaling Functions; 2.3 Fractals; 2.4 Examples of Fractals 327 $a2.1 Cantor-set construction2.2 Realization of Brownian motion; 2.3 Fern: a nonrandom natural fractal; 2.4 Grand Canyon: a random natural fractal; 2.5 Examples of Nonfractals; 2.5 Realization of a homogeneous Poisson process; 2.6 Deterministic Chaos; 2.6 Nonchaotic system with nonfractal attractor: time course; 2.7 Chaotic system with nonfractal attractor: time course; 2.8 Chaotic system with fractal attractor; 2.9 Chaotic system with fractal attractor: time course; 2.10 Nonchaotic system with fractal attractor; 2.7 Origins of Fractal Behavior 327 $a2.11 Nonchaotic system with fractal attractor: time course2.8 Ubiquity of Fractal Behavior; Problems; 3 Point Processes: Definition and Measures; 3.1 Point Processes; 3.2 Representations; 3.1 Point-process representations; 3.3 Interval-Based Measures; 3.2 Rescaled-range analysis: pseudocode; 3.3 Rescaled-range analysis: illustration; 3.4 Detrended fluctuation analysis: pseudocode; 3.4 Count-Based Measures; 3.5 Detrended fluctuation analysis: illustration; 3.6 Construction of normalized variances; 3.5 Other Measures; Problems; 4 Point Processes: Examples; 4.1 Homogeneous Poisson Point Process 327 $a4.2 Renewal Point Processes4.3 Doubly Stochastic Poisson Point Processes; 4.1 Stochastic-rate point processes; 4.4 Integrate-and-Reset Point Processes; 4.5 Cascaded Point Processes; 4.2 Cascaded point process; 4.6 Branching Point Processes; 4.7 Le?vy-Dust Counterexample; Problems; 5 Fractal and Fractal-Rate Point Processes; 5.1 Measures of Fractal Behavior in Point Processes; 5.2 Ranges of Power-Law Exponents; 5.3 Relationships among Measures; 5.4 Examples of Fractal Behavior in Point Processes; 5.1 Representative rate spectra; 5.2 Representative normalized Haar-wavelet variances 327 $a5.5 Fractal-Based Point Processes5.3 Normalized Daubechies-wavelet variances; 5.4 Fractal and nonfractal point processes; 5.5 Fractal-rate and nonfractal point processes; Problems; 5.6 Estimated normalized-variance curves; 5.7 Representative interval spectra; 5.8 Representative interval wavelet variances; 5.9 Representative interevent-interval histograms; 5.10 Representative capacity dimensions; 5.11 Generalized dimensions for an exocytic point process; 6 Processes Based on Fractional Brownian Motion; 6.1 Fractional Brownian Motion; 6.1 Realizations of fractional Brownian motion 327 $a6.2 Fractional Gaussian Noise 330 $aAn integrated approach to fractals and point processesThis publication provides a complete and integrated presentation of the fields of fractals and point processes, from definitions and measures to analysis and estimation. The authors skillfully demonstrate how fractal-based point processes, established as the intersection of these two fields, are tremendously useful for representing and describing a wide variety of diverse phenomena in the physical and biological sciences. Topics range from information-packet arrivals on a computer network to action-potential occurrences in a neural 410 0$aWiley Series in Probability and Statistics 606 $aPoint processes 606 $aFractals 608 $aElectronic books. 615 0$aPoint processes. 615 0$aFractals. 676 $a514.742 676 $a519.2/3 676 $a519.23 700 $aLowen$b Steven Bradley$f1962-$0955849 701 $aTeich$b Malvin Carl$0302140 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910144723003321 996 $aFractal-based point processes$92163520 997 $aUNINA