HIERARCHAL INDUCTIVE PROCESS MODELING AND ANALYSIS ...

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[18] Oreskes, N., K. Shrader-Frechette & K. Belitz.“Verification, validation, and confirmation of numerical models in the earth sciences. Science, vol. 263, pp. 641-646. [Reprinted in Transactions of the Computer Measurement Group, vol. 84, pp. 85-92].1994. [19] Oreskes, N. “Why believe a computer Models, measures, and meaning in the natural world, in The Earth Around Us: Maintaining a Livable Planet, edited by Jill S. Schneiderman (San Francisco: W.H. Freeman and Co.), pp. 70-82. 2000. [20] Tagliabue A. & K. R. Arrigo. “Anomalously Low Zooplankton Abundance in the Ross Sea: An Alternative Explanation, Limnology and Oceanography Vol. 48, No. 2, pp. 686-699. 2003. [21] Todorovski, L., Dzeroski, S., Kompare, B. “Modelling and prediction of phytoplankton growth with equation discovery.” Ecological Modelling 113, 7181. 1998. [22] Todorovski, L. “Using domain knowledge for automated modeling of dynamic systems with equation discovery”. Doctoral dissertation, Faculty of Computer and Information Science, University of Ljubljana. Ljubljana, Slovenia. 2003. [23] Todorovski, L., W. Bridewell, O. Shiran, & P. Langley. “Inducing hierarchical process models in dynamic domains”. Proceedings of the Twentieth National Conference on Artificial Intelligence, 892–897. 2005. 71
APPENDIX A. Sample CIAO data - 1997 JDAY TEMP DPML AI NITR PHOS SILC IRON_nm IRON_um PARL PHA PHA_c DIA DIA_c ZOO DET PURL TP 229 -1.842 68.86 0.87 31 2.1 75.97 0.5052 0.0005052 3.204 0.02518 2.2662 0.02518 1.7626 1.999 0.02289 1.678 4.0288 230 -1.842 79 0.84 31 2.1 75.86 0.505 0.000505 7.401 0.02518 2.2662 0.02518 1.7626 1.999 0.02289 3.891 4.0288 231 -1.844 83.75 0.82 31 2.1 75.73 0.5054 0.0005054 5.875 0.02518 2.2662 0.02518 1.7626 1.999 0.02289 3.166 4.0288 232 -1.848 84.19 0.84 31 2.1 75.7 0.5062 0.0005062 8.494 0.02518 2.2662 0.02518 1.7626 1.999 0.02289 4.425 4.0288 233 -1.838 112.1 0.83 31 2.1 75.7 0.5069 0.0005069 10.76 0.02518 2.2662 0.02518 1.7626 1.999 0.02289 5.595 4.0288 234 -1.832 114.4 0.86 31 2.1 75.64 0.5073 0.0005073 16.48 0.02518 2.2662 0.02518 1.7626 1.999 0.02289 8.723 4.0288 235 -1.84 103 0.9 31 2.1 75.54 0.5083 0.0005083 19.51 0.02518 2.2662 0.02518 1.7626 1.999 0.02289 10.33 4.0288 236 -1.844 92.1 0.88 31 2.1 75.44 0.5087 0.0005087 72
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HIERARCHAL INDUCTIVE PROCESS MODELI
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APPENDIX . . . . . . . . . . . . .
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DEDICATION This Thesis is dedicated
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LIST OF TABLES 1 Example of entity
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LIST OF SYMBOLS P = Amount of Phyto
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models of natural systems are non-u
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Figure 1: This schematic represent
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specifying the space of possible eq
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phytoplankton productivity and comm
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2 METHOD The method employed in thi
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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
Page 57 and 58: 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
Page 63 and 64: Thus, using Proposition 1 we get, d
Page 65 and 66: ∴ a 23 = 4.5.10 −4 ≤ F (t)
Page 67 and 68: Model C Where, dP dt dZ dt dD dt dN
Page 69 and 70: Next we turn our attention to P (t)
Page 71 and 72: We can rewrite D u (t) as, D u (t)
Page 73 and 74: his research on the Ross Sea Phytop
Page 75 and 76: zooplankton to be properly fitted m
Page 77 and 78: eally well (Atanasova et al. 2007).
Page 79: [9] Dzeroski, S. and Todorovski, L.
Page 83 and 84: "death_rate":0.02, "respiration_rat
Page 85 and 86: "death_rate": (0.02,0.04), "Ek_max"
Page 87 and 88: # --- GROWTH --- lib.add_generic_pr
Page 89 and 90: "arrigoetal1998", "light_lim", [("P
Page 91 and 92: lib.add_generic_process( "death_exp
Page 93 and 94: lib.add_generic_process( "holling_t
Page 95 and 96: [], {"max_mixing_rate":(0.000001,1)
Page 97 and 98: Model E [ dP [ ] dt = (1 − E ice
Page 99 and 100: Model G [ dP [ ] ( dt = (1 − E ic
Page 101: BIOGRAPHICAL SKETCH I was born and
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HIERARCHAL INDUCTIVE PROCESS MODELING AND ANALYSIS ...

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