HIERARCHAL INDUCTIVE PROCESS MODELING AND ANALYSIS ...

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we will refer to the relative mean squared error as reMSE. The biggest asset to this rescaling is the ability to compare values across data sets. Typically, an ReMSE of 1.0 or above signifies that the model performs poorly and inversely, the lower the reMSE, the better the fit. 2.1.2 Entities specification and model library Each entity of a system is defined by a combination of variables and parameters which makes them actors but also receivers of action in the model. A distinction is to be made between generic entity and instantiated entity. Indeed, a formal generic entity has a name and a set of properties which can include both variables and parameters. In a given model the parameters of the instantiated entity will not change whereas the variables do. Every variable in the entity has a name and a rule that determines how multiple processes and their subprocesses are combined (e.g. summed, minimum, product, etc...). For the parameters there is a name and a range that constrains their possible values. On the other hand, instantiated entities have their variables associated with either time-series or they are given initial values and the parameters have been assigned real values. A field is also included to indicate the parent generic entity (Borrett et al. 2007). One given generic entity can be instantiated multiple times, the generic entity can be thought of as a blue print for the instantiated entities. For example in our system we defined the entity phytoplankton as presented in Table 1. Here our entity’s name is “P”; it contains the variables “conc”, “growth rate” and “growth lim” with the rules determining how they will be aggregated with other processes; the next part of the entity definition is the list of parameters that are of concern for this entity such as “max growth’ with possible values in the (0,600) range. Following the definition of a generic entity in Table 1 is an instantiated entity, “pe” which refers to the parent generic entity. The variables are then either given the name of a time-series to which the model will be 13
fitted such as for “conc”, with the “PHA c” referring to the phytoplankton column of the CIAO data set, or an initial value such as 0 for “growth rate”, indicating that this particular state variable won’t be fitted to a time-series. The mention “system” as opposed to “exogenous” simply states that this variable is dependent on the system as opposed to being independent like variables such as solar radiation or water temperature. The full instantiated entity library can be found in Appendix B and the generic entity library in Appendix C. For HIPM to be fully functional there needs to be a library of processes. Processes are the physical, chemical, or biological actions that drive change in dynamic models. Just as we made a distinction between generic entity and instantiated entity, we make a distinction between generic processes and instantiated processes. All generic processes are defined by a name by which entities can tie into the process, the subprocesses that are tied to that one process and one or multiple equations. The generic process can also include a set of Bolean conditions that determine if the process is active, making the process dynamic by turning the process on and off depending on whether the conditions are satisfied (Borrett et al. 2007). For instance we could set the photosynthetic process to only occur if a set environment light variable is greater than zero. We have an example of generic process in Table 2, it is named “growth”, and any of the following entities “P, N, D, E”can take a role in the process, then there is a list of the subprocesses, with the entities that can take a role in the subprocess, that are linked to this process and finally the equation that defined this process; this equation calls onto the “conc” and “growth rate’ variables that all entities must have. The instantiated process will take on a specific name and will be bound to a specific instantiated entity, one of P, N, D or E. The instantiated entity will take it’s role in the equation of the instantiated process. All the instantiated processes will be aggregated according to the rule defined in the generic entity. It is this organization in terms of entity and process that drives inductive process 14
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: set of values that respect the cons
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 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
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"arrigoetal1998", "light_lim", [("P
Page 91 and 92:
lib.add_generic_process( "death_exp
Page 93 and 94:
lib.add_generic_process( "holling_t
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[], {"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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