Contributors |
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xv | |
Preface |
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xvii | |
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Section I Cellular Population Dynamics |
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1 Population Dynamics and Evolution of Cancer Cells |
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3 | (34) |
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Ignacio A. Rodriguez-Brenes |
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3 | (3) |
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2 Evolutionary Dynamics of Escape From Tissue Homeostasis |
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6 | (6) |
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2.1 Mathematical Models of Tissue Homeostasis |
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6 | (2) |
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2.2 Evolutionary Dynamics of Feedback Escape |
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8 | (2) |
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2.3 Feedback, Stem Cell Enrichment, and Drug Resistance |
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10 | (2) |
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3 Telomeres and the Evolutionary Potential of Cells |
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12 | (7) |
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3.1 Replicative Limits and Cellular Hierarchy |
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12 | (3) |
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3.2 Replicative Limits and Precancerous Mutations |
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15 | (2) |
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3.3 Replicative Limits in a Growing Cell Population |
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17 | (2) |
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4 Dynamics of Therapy Responses and Resistance Evolution |
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19 | (9) |
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4.1 Dynamics Underlying Chemoprevention With Aspirin |
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24 | (4) |
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28 | (1) |
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28 | (9) |
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2 Stochastic and Deterministic Modeling of Cell Migration |
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37 | (56) |
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38 | (4) |
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42 | (20) |
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2.1 Connecting Stochastic and Deterministic Models of Cell Movement |
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42 | (15) |
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57 | (2) |
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2.3 Higher Order Closure Approximations |
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59 | (3) |
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62 | (23) |
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63 | (5) |
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68 | (9) |
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77 | (5) |
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3.4 Persistence of Motion |
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82 | (3) |
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85 | (1) |
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86 | (7) |
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3 Data-Driven Mathematical Modeling of Microbial Community Dynamics |
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93 | (38) |
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93 | (1) |
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2 Microbial Community Profiling |
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94 | (2) |
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3 Mechanistic Modeling Approach |
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96 | (14) |
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3.1 Derivation of Specific LV Systems |
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98 | (2) |
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3.2 Generalized Lotka--Volterra Equations |
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100 | (2) |
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102 | (8) |
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110 | (16) |
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4.1 Attractor Reconstruction From Time-Series Data |
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112 | (14) |
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126 | (2) |
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128 | (1) |
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128 | (3) |
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4 Reaction--Diffusion Kinetics in Growing Domains |
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131 | (24) |
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132 | (1) |
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2 Diffusion on a Uniformly Growing Domain |
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133 | (8) |
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133 | (2) |
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2.2 Fokker--Planck Equation |
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135 | (6) |
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3 Encounter-Controlled Annihilation: Mean-Field Theory |
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141 | (3) |
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4 Exact Solution for Encounter-Controlled Annihilation |
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144 | (4) |
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5 Conclusions and Outlook |
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148 | (1) |
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149 | (1) |
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150 | (5) |
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Section II Insect Experiments to Human Demographic Theories |
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5 The Life Table Population Identity: Discovery, Formulations, Proof, Extensions, and Applications |
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155 | (32) |
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155 | (1) |
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156 | (2) |
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157 | (1) |
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2.2 Equality of Life-Lived and Life-Left Pyramids |
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157 | (1) |
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3 Discovery of Carey's Equality |
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158 | (9) |
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3.1 Background and Motivation |
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158 | (2) |
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160 | (1) |
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160 | (2) |
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3.4 Construction of a Heuristic Life Table |
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162 | (2) |
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164 | (3) |
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167 | (2) |
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4.1 Model 1: Equality of Age Structure and Death Distribution |
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167 | (1) |
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4.2 Model 2: Theorem of Life Lived and Life Left |
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167 | (2) |
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169 | (1) |
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170 | (4) |
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6.1 Death Cohort Equal Birth Cohort |
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170 | (2) |
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6.2 Equality in Stable Populations |
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172 | (1) |
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6.3 Nonstationary/Nonstable Populations |
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173 | (1) |
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7 Applications: Residual Demography in Medfly Populations |
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174 | (6) |
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7.1 Medfly Population Seasonal Trends in Mean Age |
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175 | (4) |
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7.2 Age-Structure Estimation |
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179 | (1) |
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8 Relevance and Implications for Future Studies |
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180 | (3) |
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181 | (1) |
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8.2 Historical Demography |
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181 | (1) |
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8.3 Demographic Principles |
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182 | (1) |
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8.4 Replacement-Level Populations in the 21st Century |
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182 | (1) |
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183 | (1) |
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183 | (1) |
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183 | (1) |
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183 | (4) |
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6 Stochastic Modeling of Some Natural Phenomena: A Special Reference to Human Fertility |
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187 | (88) |
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187 | (4) |
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190 | (1) |
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1.2 The Qualities of a Model Builder |
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190 | (1) |
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1.3 Uses of Mathematical Models |
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191 | (1) |
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2 Models Based on Bernoulli Trials |
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191 | (27) |
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2.1 Bernoulli Trials and Related Distributions |
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191 | (1) |
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2.2 Binomial Distribution |
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192 | (1) |
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2.3 Geometric Distribution |
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192 | (1) |
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2.4 Negative Binomial Distribution |
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193 | (1) |
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2.5 Applications of Binomial, Geometric, and Negative Binomial Distributions in Human Reproduction Process |
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194 | (3) |
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2.6 Some Extended Distributions |
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197 | (7) |
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2.7 Stopping Rule and Sex Ratio at Birth |
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204 | (1) |
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2.8 Binomial Distribution as a Number of Male Births out of n Births: A Caution |
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205 | (3) |
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2.9 Sex Ratio at Birth Under Sex-Selective Abortions |
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208 | (3) |
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2.10 A Modified Form of Binomial Distribution |
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211 | (4) |
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2.11 A Probability Model for Time of First Conception/Birth |
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215 | (1) |
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2.12 Time Between Consecutive Births (Interlive Birth Interval or Closed Birth Interval) |
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216 | (1) |
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2.13 A Probability Model for Number of Births for Migrated Couples |
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217 | (1) |
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3 Poisson, Exponential, and Gamma Distributions as Continuous Analog of Binomial, Geometric, and Negative-Binomial Distributions |
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218 | (10) |
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218 | (3) |
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3.2 An Alternative Way for Finding pk(t): The Use of Gamma Distribution |
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221 | (1) |
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3.3 A Probability Model for Number of Complete Conceptions in Time Interval (0, T) |
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222 | (2) |
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3.4 Exponential Distribution as Continuous Analog of Geometric Distribution |
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224 | (1) |
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3.5 A Probability Model for Time of First Birth |
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224 | (1) |
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3.6 A Probability Model for Time of First Birth Accounting for Adolescent Sterility |
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225 | (1) |
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3.7 Menstruating Interval Under Nonuse of Contraception |
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225 | (3) |
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4 A Parity-Dependent Model for Number of Births and Its Application |
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228 | (12) |
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5 Equilibrium Birth Process |
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240 | (9) |
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6 Distribution Function and Its Use in Computation of Certain Parameters |
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249 | (3) |
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7 Use of [ 1 --- F(x)] in Computation of Certain Parameters of Interest |
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252 | (12) |
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7.1 Prevalence/Incidence Mean |
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252 | (2) |
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7.2 Estimation of Mean PPA Using Prevalence/Incidence Method |
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254 | (1) |
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7.3 Application for Computation of Mean Duration of Breastfeeding |
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255 | (1) |
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7.4 Estimation of Parity Progression Ratios and IPPR From Open and Closed Birth Interval Data |
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255 | (9) |
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8 Use of Mathematical Models: Some Examples |
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264 | (9) |
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264 | (1) |
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8.2 Getting Estimates of Parameters |
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265 | (1) |
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8.3 Testing Adequacy of Model |
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265 | (2) |
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8.4 Impact of Alternations in Parameters |
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267 | (1) |
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8.5 Explaining Apparent Inconsistencies |
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267 | (6) |
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273 | (1) |
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273 | (1) |
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274 | (1) |
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7 Two Decades of Drosophila Population Dynamics: Modeling, Experiments, and Implications |
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275 | (40) |
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276 | (3) |
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2 The Laboratory Ecology of Drosophila |
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279 | (1) |
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3 The Drosophila Model: The Importance of Larval and Adult Food Levels |
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280 | (2) |
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4 Larval vs Adult Food Levels and the Dynamics of Small Drosophila Populations |
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282 | (2) |
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5 Effects of Immigration on Small Population Constancy and Persistence |
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284 | (2) |
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6 Synchrony and Asynchrony in Metapopulations |
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286 | (6) |
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7 Stabilizing Small Populations |
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292 | (5) |
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7.1 Stabilizing Spatially Unstructured Populations |
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293 | (3) |
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7.2 Stabilizing Spatially Structured Populations |
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296 | (1) |
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8 The Devil in the Details |
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297 | (1) |
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9 Life History, Competitive Ability, and the Evolution of Population Stability |
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298 | (6) |
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304 | (11) |
Acknowledgments |
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306 | (1) |
References |
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306 | (309) |
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Section III Complex Environmental and Biogeochemical Dynamics |
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8 The Environmental Kuznets Curve Fails in a Globalized Socio-Ecological Metapopulation: A Sustainability Game Theory Approach |
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315 | (28) |
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316 | (3) |
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319 | (8) |
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319 | (6) |
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2.2 Ecosystem Services Impacts and the Cost of Abatement |
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325 | (2) |
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327 | (1) |
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327 | (8) |
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327 | (3) |
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330 | (1) |
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3.3 Intrinsic--Extrinsic Problem |
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330 | (3) |
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333 | (2) |
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335 | (1) |
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336 | (1) |
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336 | (7) |
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9 Integrated Approach for Modeling Coastal Lagoons: A Case for Chilka Lake, India |
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343 | (62) |
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S.R.V. Prasad Bhuvanagiri |
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344 | (1) |
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345 | (2) |
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3 Sampling Methods and Analysis |
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347 | (13) |
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347 | (1) |
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3.2 Salinity Measurements and Local Weather Data |
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347 | (1) |
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348 | (1) |
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348 | (12) |
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360 | (1) |
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5 3D Description of Chilka Lagoon |
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361 | (20) |
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363 | (1) |
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5.2 Algorithm Implementation |
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363 | (3) |
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5.3 Inferences From 3D Visualization |
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366 | (2) |
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5.4 Hydro-Environmental Findings |
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368 | (4) |
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5.5 Water and Salt Budgets for Chilka |
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372 | (9) |
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6 Dissolved Oxygen Dynamics |
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381 | (14) |
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6.1 Abstract Mathematical Model for DO Dynamics |
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384 | (1) |
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6.2 Development of Biogeochemical Model for DO in Lake Chilka |
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385 | (6) |
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391 | (1) |
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6.4 Model Calibration and Validation |
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392 | (1) |
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6.5 Influence of Individual Plankton Groups on the DO Dynamics |
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393 | (2) |
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395 | (1) |
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396 | (1) |
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396 | (4) |
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400 | (5) |
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Section IV Measures of Mortality and Stochastics |
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10 Measures and Models of Mortality |
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405 | (38) |
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405 | (11) |
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406 | (1) |
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1.2 Life Expectancy: Period vs Cohort |
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407 | (3) |
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1.3 Period-Cohort Measures: CAL and TCAL |
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410 | (3) |
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1.4 Mean, Median, Modal, and Maximum Ages at Death |
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413 | (1) |
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1.5 Variability of Age at Death |
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414 | (2) |
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416 | (18) |
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417 | (3) |
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420 | (3) |
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423 | (2) |
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2.4 (Generalized) Extreme-Value |
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425 | (2) |
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427 | (2) |
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429 | (4) |
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2.7 Heligman--Pollard Model |
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433 | (1) |
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434 | (6) |
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440 | (3) |
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11 Stochastic Population Models |
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443 | (38) |
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443 | (2) |
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2 Markov Population Models |
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445 | (16) |
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2.1 Definition and Representations |
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445 | (9) |
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2.2 Numerical Methods and Large-Sample Approximations |
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454 | (7) |
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3 Inference for Well-Mixed Population Processes |
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461 | (5) |
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3.1 Inference for Directly Observed Population Processes |
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461 | (1) |
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3.2 Inference for Discrete-Time Observations With Measurement Error |
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462 | (1) |
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3.3 Example: Simulated Birth--Death Process |
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463 | (3) |
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4 Spatial Population Processes |
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466 | (11) |
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4.1 Large-N Limits of Spatial Birth--Death Processes |
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468 | (1) |
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4.2 Spatial Diffusion From Spatial Birth--Death Processes |
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469 | (2) |
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4.3 Inference on Spatial Birth Death Process Parameters |
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471 | (2) |
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4.4 Example: Simulated Spatial Population Process |
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473 | (4) |
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477 | (1) |
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478 | (3) |
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12 Survival Probabilities From 5-Year Cumulative Life Table Survival Ratios (Tx+5/Tx): Some Innovative Methodological Investigations |
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481 | (64) |
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482 | (18) |
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1.1 Some Preliminary Concepts and Definitions |
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482 | (1) |
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483 | (1) |
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1.3 Needs, Importance, and Uses of Life Tables |
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484 | (6) |
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1.4 Life Table Based on Age-Return Only |
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490 | (7) |
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497 | (2) |
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499 | (1) |
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1.7 Recent Contributions of Arni S. R. Srinivasa Rao and James R. Carey on Stationary Population and Other Related Issues |
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500 | (1) |
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2 A New Methodology for Life Table Construction at Ages 5 and Above From 5-Year Cumulative Life Table Survival Ratios (Tx+5/Tx) by Lahiri |
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500 | (19) |
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500 | (2) |
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2.2 Methodology: Analytical Approaches |
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502 | (17) |
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3 Summary and Conclusions |
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519 | (3) |
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3.1 Some Specific Observations and Direction for Future Research |
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521 | (1) |
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522 | (1) |
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Appendix A Analytical Justification for the Algebraic Chain Relationship (Formula 3 or 4 in the Text) Between the Two Consecutive spx's Under Conventional Approximation for 5LX From lx |
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522 | (1) |
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Appendix B Some Issues Related to the Fixation of T(i)w and Invariant Properties of 5S(i)(w--5)+, 5E(i)w--5, and 5p(i)w--5 Over Iterations Under Approach-II for Life Table Construction |
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523 | (1) |
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Invariant Properties of 5S(i)(w--5)+, 5E(i)w--5, and 5p(i)w--5 Over Iterations |
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524 | (1) |
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Appendix C Mathematical Proof of Convergence of the Iterative Procedure for Constructing Adult Abridged Mortality or Life Table From Cumulative Life Table Survival Ratios |
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525 | (6) |
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Appendix D Tabular Calculations |
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531 | (8) |
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539 | (3) |
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542 | (3) |
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Section V Human Inequality Measures and Well Being |
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13 Methods of Measuring Human Well-being and Human Development |
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545 | (32) |
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546 | (1) |
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2 Identifying the Statistical Problem |
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546 | (1) |
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3 Recent Developments in the Search for Innovations |
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547 | (1) |
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4 Unsupported Assumptions About the Existing Metric |
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548 | (1) |
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5 The Linkage of Process Data With Subjectivity |
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548 | (1) |
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6 Innovations in the Human Development Index System |
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549 | (2) |
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7 Subjective/Processual Breakthrough in the GNH System |
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551 | (1) |
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8 Introduction to Flinders University Innovation |
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552 | (1) |
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9 Quantifying Human Development: The Case of Timor-Leste 2016-17 |
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553 | (1) |
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10 Calculation of HDI and GDI |
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554 | (1) |
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554 | (1) |
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11 Calculation of HDI and GDI and Their Components for the Total Population |
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555 | (9) |
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555 | (7) |
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11.2 HDI and Gender Development Index for the Youth (Population Aged 15-34 Years) |
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562 | (2) |
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12 Gender Development Index for the Youth |
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564 | (1) |
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13 Quantifying Human Well-being: The Case of Assam Well-being Survey 2015 |
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565 | (1) |
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14 What Would a Well-being Index Do? |
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566 | (1) |
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15 How Is "Well-being" Defined in a Well-being Index? |
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566 | (1) |
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16 The Dimensions of Well-being Are Interconnected |
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567 | (1) |
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17 Key Steps in Preparing a Well-being Index |
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567 | (1) |
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18 Measuring Human Well-being in Assam, India |
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568 | (3) |
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19 What Are the Main Uses of a Well-being Index? |
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571 | (1) |
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Appendix: Methodology of Measuring Subjective Well-being |
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571 | (3) |
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574 | (1) |
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575 | (2) |
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14 A Bio-Demographic Perspective on Inequality and Life Expectancy: An Analysis of 159 Countries for the Periods 1970-90 and 1990-2010 |
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577 | (38) |
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578 | (3) |
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581 | (3) |
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584 | (3) |
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3.1 Changes in Life Expectancy and Differences Among the SES Quartiles |
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584 | (3) |
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587 | (1) |
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587 | (4) |
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591 | (2) |
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593 | (18) |
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611 | (2) |
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613 | (2) |
Index |
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615 | |