HIERARCHAL INDUCTIVE PROCESS MODELING AND ANALYSIS ...

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TABLE OF CONTENTS ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii DEDICATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . v LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii LIST OF SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 METHOD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1 HIPM Description . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1.1 Measure of Fit . . . . . . . . . . . . . . . . . . . . . 12 2.1.2 Entities specification and model library . . . . . . . . 13 2.2 Experiment Design . . . . . . . . . . . . . . . . . . . . . . . . 16 3 COMPUTATIONAL RESULTS . . . . . . . . . . . . . . . . . . . . . 20 3.1 Increase in number of time-series input . . . . . . . . . . . . . 24 3.2 Value of Information . . . . . . . . . . . . . . . . . . . . . . . 28 3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 4 ANALYTICAL <strong>ANALYSIS</strong> . . . . . . . . . . . . . . . . . . . . . . . 33 4.1 Most recurrent models . . . . . . . . . . . . . . . . . . . . . . 33 4.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.3 Model A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.4 Model B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.5 Model C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.6 Effects of increasing the number of constraints . . . . . . . . . 63 5 CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 ii
APPENDIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 A. Sample CIAO data - 1997 . . . . . . . . . . . . . . . . . . . . . . . 72 B. Full entity specification file . . . . . . . . . . . . . . . . . . . . . . 73 C. Full ross Sea generic model library . . . . . . . . . . . . . . . . . . 75 D. Models selected in both experiment 8 and 19 . . . . . . . . . . . . 87 E. Models selected in both experiment 8 and 21 . . . . . . . . . . . . 89 iii
Page 1: HIERARCHAL INDUCTIVE PROCESS MODELI
Page 5 and 6: DEDICATION This Thesis is dedicated
Page 7 and 8: LIST OF TABLES 1 Example of entity
Page 9 and 10: LIST OF SYMBOLS P = Amount of Phyto
Page 11 and 12: models of natural systems are non-u
Page 13 and 14: Figure 1: This schematic represent
Page 15 and 16: specifying the space of possible eq
Page 17 and 18: phytoplankton productivity and comm
Page 19 and 20: 2 METHOD The method employed in thi
Page 21 and 22: set of values that respect the cons
Page 23 and 24: fitted such as for “conc”, with
Page 25 and 26: Table 2: Defining a process - Growt
Page 27 and 28: upon whether certain time-series ar
Page 29 and 30: 3 COMPUTATIONAL RESULTS The main to
Page 31 and 32: ● ● ● 2.0 ● [D,N] ●●●
Page 33 and 34: 3.1 Increase in number of time-seri
Page 35 and 36: Table 4: This table represents each
Page 37 and 38: different restriction powers based
Page 39 and 40: experiment 22, yielding no good fit
Page 41 and 42: not taken into consideration which
Page 43 and 44: Table 5: This table summarizes all
Page 45 and 46: Table 6: This table summarizes all
Page 47 and 48: 4.2 Preliminaries Both Models A and
Page 49 and 50: In addition to these 2 Lemmas, let
Page 51 and 52: When t → ∞ we get the following
Page 53 and 54:
For the Zooplankton not to go to ze
Page 55 and 56:
( ∴ P 0 + a ) 13 α − δ Z 0 e
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4.4 Model B Shifting our focus to M
Page 59 and 60:
Using the exogenous variables time-
Page 61 and 62:
Then finding an lower bound, dD l d
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Thus, using Proposition 1 we get, d
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∴ a 23 = 4.5.10 −4 ≤ F (t)
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Model C Where, dP dt dZ dt dD dt dN
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Next we turn our attention to P (t)
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We can rewrite D u (t) as, D u (t)
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his research on the Ross Sea Phytop
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zooplankton to be properly fitted m
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eally well (Atanasova et al. 2007).
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[9] Dzeroski, S. and Todorovski, L.
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APPENDIX A. Sample CIAO data - 1997
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"death_rate":0.02, "respiration_rat
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"death_rate": (0.02,0.04), "Ek_max"
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# --- GROWTH --- lib.add_generic_pr
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"arrigoetal1998", "light_lim", [("P
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lib.add_generic_process( "death_exp
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lib.add_generic_process( "holling_t
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[], {"max_mixing_rate":(0.000001,1)
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Model E [ dP [ ] dt = (1 − E ice
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Model G [ dP [ ] ( dt = (1 − E ic
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BIOGRAPHICAL SKETCH I was born and
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