HIERARCHAL INDUCTIVE PROCESS MODELING AND ANALYSIS ...

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modeling. It makes for an easier construction of systems of equations by building in fragments. Table 1: In this table we are first giving an example of generic entity definition with its variables and parameters followed by an example of an instantiated entity, more specifically Phytoplankton - P, to which the variable “conc” is given a time series and the other variables initial values. pe = lib.add_generic_entity("P", { "conc":"sum", "growth_rate":"prod", "growth_lim":"min"}, { "max_growth": (0.4,0.8), "exude_rate": (0.001,0.2), "death_rate": (0.02,0.04), "Ek_max":(1,100), "sinking_rate":(0.0001,0.25), "biomin":(0.02,0.04), "PhotoInhib":(200,1500),}); p1 = entity_instance (pe, "phyto", { "conc": ("system", "PHA_c", (0,600)), "growth_rate": ("system", 0, (0,1)), "growth_lim": ("system", 1, (0,1))}, { "max_growth":0.59, "exude_rate":0.19, "death_rate":0.025, "Ek_max":30, "biomin":0.025, "PhotoInhib":200 } ); 15
Table 2: Defining a process - Growth lib.add_generic_process( "growth", "", [("P",[pe],1,1), ("N",[no3,fe],1,100), ("D",[de],1,1), ("E",[ee],1,1)], [("limited_growth", ["P","N","E"], 0), ("exudation",["P"],1), ("nutrient_uptake",["P","N"],0)], {}, {}, {"P.conc": "P.growth_rate * P.conc"} ); To sum it up, HIPM’s power resides in its knowledge of the modeled domain as well as its ability to estimate parameters (Bridewell et al. 2007). 2.2 Experiment Design Having now established how HIPM works let us consider the problem at hand. Though in theory HIPM is an extremely powerful tool which permits a search through a wide structure and parameter space, previous research has demonstrated that a more thorough investigation of HIPM’s output is necessary to evaluate its potential and usefulness to biologist. In our example of the Ross Sea ecosystem with the process-entity library set up as described, the search space represents 1120 possible models; each model can take on a wide variety of parameters set depending on the constraints given to the software. The Phytoplankton dynamic models of the Ross Sea have five variables: Phytoplankton (P ), Zooplankton (Z), Detritus (D), Nitrate (N) and Iron (F ). In previous research, real-life time series about Phyto- 16
Page 1 and 2: HIERARCHAL INDUCTIVE PROCESS MODELI
Page 3 and 4: APPENDIX . . . . . . . . . . . . .
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: fitted such as for “conc”, with
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 and 80:
[9] Dzeroski, S. and Todorovski, L.
Page 81 and 82:
APPENDIX A. Sample CIAO data - 1997
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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