HIERARCHAL INDUCTIVE PROCESS MODELING AND ANALYSIS ...

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25 20 ● P Z D N F ● ● ● Median Activation Values 15 10 ● ● 5 ● ● 0 ● ● ● 0.2 0.4 0.6 0.8 1.0 ReMSE cutoff Figure 8: Mean Activation Values by different Cutoffs. The lower the median activation value the more discriminatory powers that entity holds at that particular cutoff. Between 0.4 and 1, Zooplankton consistently has the lowest median activation value. phytoplankton and detritus are concerned, they seem to have similar behavior with high activations values. We are to note that for cutoffs less than 0.4 no one entity seems to have greater discriminatory power. Based on this graph alone it would seem that zooplankton is the one entity that yields the most information when it comes to model selection and therefore would be the entity worth collecting in the field. That said, Table 4 also reveals a worrisome amount of data constraints combinations which yield no models with reMSE less than one. A example of that being 29
experiment 22, yielding no good fit models under 1 reMSE cutoff. Another case that is cause for worry is the one where time-series are given to all 5 entities which we would expect to have at least one model selected in between the 0.1 to 1 range of reMSE cutoff. This observation raises the question that there may be an underlying issue with the model selection process. Incidentally, all of the combinations that yield no models under the 1 reMSE cutoff are experiments to which we gave Z a time-series constraint, which may say something about the processes that drive zooplankton; the library may be in need of improvements. 3.3 Summary This result analysis allows us to make the following observations: • In most cases, increasing the number of time-series constraints up to 3 seemed to reduce the number of good fit models under a 0.5 cutoff. If we consider experiments 1 through 25, there was only one case (experiment 20) for which the number of good fit models increased and six cases for which the number of good fit models went to zero (experiment 12, 16,17,18, 22, 23) which can been interpreted as a deficiency in the library. Overall, this result is due to the fact that the reMSE is an average of the fit of all the state variables for which we have time-series. • The decision as to which data to collect next should take into consideration the previously acquired time-series. Recommendations may differ based on state variables previously measured and used with HIPM in the model selection process. The reason for this is once again the way the reMSE is calculated. Indeed, depending on how well the previously included time-series fitted a particular model will determine whether or not the addition of another timeseries will throw the said model in or out of the pool of good fit models. 30
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 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: different restriction powers based
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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