Contributors |
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xiii | |
Preface |
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xv | |
Section VI Agent Based Models, Capture-Recapture Methods and Multi-Species Mutualism |
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1 An Agent-Based Model of the Spatial Distribution and Density of the Santa Cruz Island Fox |
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3 | (30) |
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4 | (3) |
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2 Incorporating GIS Data into an ABM |
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7 | (4) |
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7 | (2) |
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2.2 Projections and Coordinate Systems for GIS Data |
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9 | (2) |
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11 | (12) |
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11 | (2) |
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13 | (4) |
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17 | (6) |
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23 | (6) |
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4.1 Results of Model Analysis Without Golden Eagle Predation |
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23 | (3) |
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4.2 Model Results with Golden Eagle Predation |
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26 | (3) |
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5 Conclusions and Discussion |
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29 | (1) |
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30 | (1) |
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30 | (1) |
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30 | (1) |
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30 | (3) |
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2 Capture-Recapture Methods and Models: Estimating Population Size |
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33 | (52) |
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33 | (3) |
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2 Closed Population Capture-Recapture Studies |
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36 | (15) |
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2.1 Simple Beginnings: Lincoln-Petersen Estimator |
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36 | (4) |
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2.2 Multiple Capture Occasions |
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40 | (11) |
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51 | (23) |
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3.1 Unobserved Heterogeneity |
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53 | (4) |
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3.2 Observed (Time-Invariant) Heterogeneity |
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57 | (6) |
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3.3 Time-Varying Observed Individual Heterogeneity |
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63 | (11) |
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74 | (3) |
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77 | (3) |
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80 | (5) |
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3 Mathematical Modeling of Multispecies Mutualism: From Particular Models Toward a Generalization of the Concept |
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85 | (48) |
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86 | (1) |
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2 Mutualism Within the Framework of a General Model |
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87 | (5) |
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2.1 Mechanisms Behind Mutualisms |
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87 | (1) |
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2.2 To Be or Not to Be Independent |
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88 | (1) |
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2.3 The Generalization Paradigm |
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89 | (3) |
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3 Modeling Considerations: From Specific Models to a More General Framework |
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92 | (7) |
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3.1 The Lotka-Volterra Legacy |
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92 | (2) |
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3.2 Saturating Functional Responses and More General Frameworks |
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94 | (2) |
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3.3 An Unlikely Marriage: Two-Sex Reproduction in the Mutualistic Framework |
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96 | (2) |
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3.4 Getting Away From the Logistic Growth: Allee Effects |
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98 | (1) |
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4 Two-Dimensional Models: A Stability Analysis |
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99 | (16) |
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4.1 Stability Results Using the LaSalle Invariance Principle |
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101 | (3) |
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4.2 Stability Results Using the Dulac Criterion: Threshold-Like Parameters |
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104 | (6) |
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110 | (5) |
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5 n-Dimensional Models: Boundedness and Unboundedness |
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115 | (12) |
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116 | (2) |
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5.2 Boundedness vs Unboundedness: A Tale of n Parameters |
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118 | (1) |
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5.3 Particular Growth Conditions: A Single Parameter to Rule Them All |
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119 | (2) |
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5.4 Mutualism as Reduction of Mortality for the Benefiting Species |
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121 | (2) |
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5.5 Mutualism as a Positive Contribution to the Fertility Rate of the Benefiting Species |
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123 | (2) |
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5.6 Which Species Is Responsible for Unboundedness? |
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125 | (2) |
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127 | (1) |
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128 | (1) |
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129 | (4) |
Section VII Stochastic Complexity and Structural Dynamics |
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4 Stochastic Models for Structured Populations |
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133 | (24) |
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133 | (2) |
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2 Introduction: Population Dynamics in a Constant Environment |
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135 | (2) |
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3 Structured Populations in Stochastic Environments |
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137 | (12) |
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137 | (2) |
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139 | (5) |
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3.3 Limiting Distributions |
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144 | (1) |
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3.4 A Key Limit: Stochastic Growth Rate |
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145 | (4) |
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4 Stochastic Growth Rate: Small-Noise Approximation |
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149 | (2) |
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5 Stochastic Growth Rate: Derivatives |
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151 | (2) |
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5.1 Derivatives With Respect to Vital Rates |
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152 | (1) |
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5.2 Derivatives With Respect to Transition Matrix Elements |
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153 | (1) |
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153 | (1) |
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154 | (3) |
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5 Studying Complexity and Risk Through Stochastic Population Dynamics: Persistence, Resonance, and Extinction in Ecosystems |
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157 | (38) |
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157 | (8) |
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160 | (2) |
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1.2 Examples of Basic Stochastic Processes |
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162 | (3) |
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2 Persistence in Stochastic Models |
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165 | (10) |
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2.1 Stochastic Logistic Growth Model for a Single Population Species |
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166 | (1) |
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2.2 Quasi-Stationarity (QSD) of a Birth-Death Process |
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167 | (2) |
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2.3 Stochastic Model for Interacting Population Species: Native and Invading Species |
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169 | (2) |
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2.4 Stochastic Model for Heterogeneity in Population of a Single Type of Cells |
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171 | (4) |
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3 Types of Stochasticity and Extinction in Stochastic Models |
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175 | (5) |
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3.1 Time to Extinction of a Birth-Death Process |
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175 | (1) |
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3.2 The Role of Stochasticity and Heterogeneity on Extinction Risk |
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176 | (4) |
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4 Oscillations and Resonance in the Stochastic Models |
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180 | (5) |
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4.1 Sustained Oscillations via Coherence Resonance |
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180 | (2) |
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4.2 Sustained Oscillations via Stochastic Resonance |
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182 | (3) |
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5 Computational Stochastic Approaches |
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185 | (5) |
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5.1 Agent-Based Models and Parameter Estimation as Emergent Behavior |
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185 | (3) |
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5.2 Algorithms for Simulating Stochastic Models |
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188 | (2) |
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190 | (1) |
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190 | (5) |
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6 Analyzing Variety of Birth Intervals: A Stochastic Approach |
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195 | (92) |
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195 | (5) |
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1.1 Heterogeneity and Selection |
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198 | (1) |
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1.2 Variety of Birth Intervals |
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198 | (2) |
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2 Impact of Heterogeneity on Distributions of Duration Variables |
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200 | (15) |
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2.1 Selection Bias in Postpartum Amenorrhea Period From Follow-Up Studies and Its Adjustment |
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200 | (8) |
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2.2 Estimating Birth Interval Characteristic of Women |
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208 | (4) |
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2.3 Impact of Heterogeneity on Time of First Conception |
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212 | (3) |
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3 Sampling Frame as a Determinant of Duration Variable |
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215 | (58) |
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3.1 Usual Closed Birth Interval vs Most Recent Closed Birth Interval |
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215 | (27) |
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3.2 Most Recent Closed Birth Interval Assuming ith Order Births to Be Uniformly Distributed Over Time |
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242 | (8) |
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3.3 Closed Birth Interval vs Straddling Birth Interval |
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250 | (4) |
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254 | (11) |
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3.5 Forward Birth Interval |
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265 | (7) |
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3.6 Interior Birth Interval |
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272 | (1) |
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4 Analyzing Consecutive Closed Birth Intervals: A Correlation Analysis |
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273 | (7) |
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4.1 Consecutive Closed Birth Intervals |
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273 | (3) |
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4.2 Application of the Analysis on NFHS-2 Data |
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276 | (4) |
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280 | (7) |
Section VIII GWAS, Species Divergence and Bayesian Item Response Theory |
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7 Detection of Quantitative Trait Loci From Genome-Wide Association Studies |
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287 | (68) |
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287 | (1) |
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2 SNP Data and Data Preparation |
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288 | (13) |
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2.1 Description of the Data |
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288 | (1) |
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289 | (12) |
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301 | (1) |
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4 Nontree-Based Methods of GWAS Analysis |
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301 | (14) |
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4.1 Single-Marker Association |
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302 | (5) |
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4.2 Haplotype Association Mapping |
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307 | (7) |
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4.3 Regression-Based Methods of QTL Detection |
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314 | (1) |
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5 Tree-Based Methods for Phased Data |
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315 | (27) |
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5.1 Perfect Phylogeny Construction |
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315 | (4) |
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319 | (3) |
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5.3 Models of Allele Substitution |
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322 | (3) |
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5.4 Likelihood Score Approach |
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325 | (11) |
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5.5 Bayesian SNP Detection |
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336 | (6) |
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6 Tree-Based GWAS Analysis From Unphased Genetic Data |
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342 | (5) |
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6.1 Local Semiperfect Phylogeny Construction |
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343 | (2) |
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6.2 Determination of Significance |
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345 | (2) |
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347 | (1) |
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348 | (5) |
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353 | (2) |
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8 Bayesian Item Response Theory for Cancer Biomarker Discovery |
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355 | (50) |
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Katabathula Ramachandra Murthy |
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356 | (2) |
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358 | (10) |
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358 | (1) |
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359 | (3) |
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362 | (6) |
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3 Biomarker Information Function |
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368 | (8) |
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3.1 One Parameter Logistic |
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369 | (1) |
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3.2 Two Parameter Logistic |
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369 | (1) |
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3.3 Three Parameter Logistic |
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369 | (1) |
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3.4 Graded Response Model |
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370 | (2) |
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372 | (2) |
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374 | (2) |
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4 Bayesian Frame Work for IRT models |
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376 | (3) |
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4.1 Markov Chain Monte Carlo Methods (MCMC) |
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377 | (1) |
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378 | (1) |
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379 | (18) |
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379 | (1) |
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379 | (12) |
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5.3 Applications of IRT in Cancer Research |
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391 | (6) |
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6 Future Developments of IRT in Biological Modelling |
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397 | (1) |
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7 Stan Codes for IRT Models |
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398 | (1) |
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398 | (1) |
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399 | (2) |
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401 | (4) |
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9 Effects of Phenotypic Plasticity and Unpredictability of Selection Environment on Niche Separation and Species Divergence |
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405 | (30) |
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406 | (4) |
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410 | (8) |
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410 | (2) |
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412 | (4) |
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416 | (2) |
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418 | (7) |
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3.1 Haploid Population With Single Gaussian Food Supply |
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418 | (3) |
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3.2 Haploid Population With Double Gaussian Food Supply |
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421 | (2) |
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3.3 Diploid Population Having Additive Allelic Effect Gene Interaction and Double Food Supply |
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423 | (2) |
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425 | (4) |
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429 | (2) |
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431 | (4) |
Section IX Aging and Age-Structured Population Dynamics |
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10 Theory and Applications of Backward Probabilities and Prevalences in Cross-Longitudinal Surveys |
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435 | (52) |
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1 Backward Probabilities Estimated From Chained Labor Force Surveys |
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437 | (20) |
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1.1 Probability or Forward Probability |
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437 | (2) |
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439 | (3) |
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1.3 Markov Chains and Strong Ergodicity |
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442 | (10) |
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452 | (2) |
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1.5 Backward Prevalence of a Specific Cohort |
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454 | (3) |
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1.6 Forward Prevalence of a Specific Cohort |
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457 | (1) |
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2 Backward Probabilities With Transient States and an Absorbing State |
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457 | (27) |
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2.1 Chaining Forward for a Specific Cohort |
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460 | (6) |
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2.2 Chaining Backward for a Specific Cohort |
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466 | (12) |
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2.3 Some Estimations of Backward Prevalences |
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478 | (4) |
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2.4 Limitations Concerning the Estimation of Forward and Backward Prevalences |
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482 | (1) |
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2.5 Perspectives Concerning the Estimation of Backward Prevalences |
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483 | (1) |
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484 | (1) |
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485 | (1) |
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485 | (2) |
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11 Behavior of Stationary Population Identity in Two-Dimensions: Age and Proportion of Population Truncated in Follow-up |
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487 | (14) |
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487 | (2) |
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2 Structure of the Two-Dimensional Captive Cohort |
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489 | (2) |
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3 Truncation of the Follow-up Data of Captive Cohorts |
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491 | (1) |
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4 Captive Population Age Structure, Truncation, and Partition Functions |
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492 | (6) |
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4.1 Time Left for a Captive Cohort and Right Truncation |
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493 | (5) |
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498 | (1) |
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499 | (1) |
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499 | (1) |
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500 | (1) |
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12 Demographic Situation of Manipur, India |
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501 | (50) |
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Moirangthem Hemanta Meitei |
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501 | (12) |
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1.1 The Origin of Communities in Manipur |
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507 | (1) |
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508 | (5) |
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2 Demographic Composition of Manipur |
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513 | (26) |
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2.1 Demographic Indicators |
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524 | (1) |
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2.2 Mortality Situation in Manipur |
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524 | (7) |
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531 | (5) |
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536 | (3) |
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539 | (7) |
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3.1 Future Trajectory of Population |
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541 | (5) |
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546 | (1) |
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547 | (4) |
Section X Collective Behaviors in Ecology |
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13 Deriving Mesoscopic Models of Collective Behavior for Finite Populations |
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551 | (44) |
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552 | (1) |
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552 | (1) |
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553 | (4) |
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3 Mesoscopic Description of a Pairwise Binary-Choice Model |
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557 | (13) |
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557 | (2) |
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3.2 Constructing Mesoscopic SDEs |
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559 | (7) |
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3.3 Characterizing Mesoscopic Dynamics |
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566 | (3) |
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3.4 Results for the Pairwise Pairwise Interaction Model |
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569 | (1) |
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4 Ternary Interaction Model for Binary Choice |
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570 | (7) |
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4.1 Constructing a Mesoscopic SDE for the Ternary Interaction Model |
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571 | (3) |
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4.2 Characterizing Mesoscopic Dynamics |
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574 | (1) |
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4.3 Results for the Ternary Interaction Model |
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574 | (3) |
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577 | (4) |
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5.1 Comparison of System-Size Expansion With Chemical Langevin Approach |
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577 | (1) |
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5.2 Multiplicative Noise at Mesoscopic Scales |
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578 | (1) |
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5.3 Extensions and Concluding Remarks |
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579 | (2) |
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581 | (1) |
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581 | (1) |
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581 | (9) |
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Appendix A The Chemical Langevin Equation |
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581 | (3) |
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Appendix B Pairwise Interaction Model in Two Spatial Dimensions |
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584 | (1) |
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B.1 van Kampen's System-Size Expansion of Transition Rates |
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584 | (1) |
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B.2 Chemical Langevin Approach |
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586 | (4) |
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590 | (5) |
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14 Collective Behavior and Ecology |
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595 | (32) |
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595 | (1) |
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2 Individual-Based Models |
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596 | (5) |
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597 | (1) |
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598 | (3) |
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601 | (1) |
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3 Collective Behavior (Using IBMs) |
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601 | (1) |
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601 | (1) |
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602 | (8) |
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603 | (3) |
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606 | (4) |
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5 Collective Behavior (Using FP) |
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610 | (4) |
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6 Collective Behavior and Ecology |
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614 | (11) |
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615 | (3) |
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618 | (7) |
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625 | (1) |
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626 | (1) |
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626 | (1) |
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626 | (1) |
Index |
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627 | |