#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#
# Author: Ovidiu Parvu
# Contact: ovidiu.parvu@gmail.com
#
# Copyright Ovidiu Parvu 2014
#
# Remarks: 
#   1. Any line starting with the "#" character is interpreted as a comment.
#   2. Any line starting with the "P" character introduces a new logic 
#      statement.
#
#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++


#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#
# Natural language description:
# 
# The probability is greater than 0.9 that whenever the concentration of CDK1
# reaches very high levels (in our case >96% of its maximum value) all cells 
# will divide. To match the structure of PBLMSTL statements this can be 
# rewritten as the probability is greater than 0.9 that when the concentration 
# (denoted in PBLMSTL as density) of CDK1 (corresponding to scale and subsystem 
# Intracellular.CDK1) increases above 0.96 then all cells will divide i.e. the 
# sum of the (densities x areas) of all regions covered by cells (corresponding 
# to scale and subsystem Cellular.Embryo) will increase.
# 
#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

P > 0.9 [
    G [0, 100] (
        (
            (
                count(density(filter(regions, scaleAndSubsystem = Intracellular.CDK1 ^ density < 0.96))) = 
                count(density(filter(regions, scaleAndSubsystem = Intracellular.CDK1))) 
            ) ^ (
                X (
                    count(density(filter(regions, scaleAndSubsystem = Intracellular.CDK1 ^ density > 0.96))) = 
                    count(density(filter(regions, scaleAndSubsystem = Intracellular.CDK1))) 
                )
            )
        ) => (
            d(
                sum(
                    multiply(
                        area(filter(regions, scaleAndSubsystem = Cellular.Embryo)),
                        density(filter(regions, scaleAndSubsystem = Cellular.Embryo))
                    )
                )
            ) > 0
        )
    )
]


#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#
# Natural language description:
#
# The probability is greater than 0.9 that whenever the average concentration 
# of APC increases and reaches its local maximum value no cell will divide. To 
# match the structure of PBLMSTL statements this can be rewritten as the 
# probability is greater than 0.9 that if the average concentration 
# (represented in PBLMSTL as density) of APC (corresponding to scale and 
# subsystem Intracellular.APC) reaches a local maximum value i.e. increases and 
# then decreases, then no cell will divide i.e. the sum of the (densities x 
# areas) of all regions covered by cells (corresponding to scale and subsystem 
# Cellular.Embryo) will remain constant. 
#
#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

P > 0.9 [
    G [0, 100] (
        (
            (d(avg(density(filter(regions, scaleAndSubsystem = Intracellular.APC)))) > 0) ^
            (
                X (d(avg(density(filter(regions, scaleAndSubsystem = Intracellular.APC)))) < 0)
            )
        ) => (
            X (
                d(
                    sum(
                        multiply(
                            area(filter(regions, scaleAndSubsystem = Cellular.Embryo)),
                            density(filter(regions, scaleAndSubsystem = Cellular.Embryo))
                        )
                    )
                ) = 0
            )
        )
    )
]


#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#
# Natural language description:
# 
# The probability is greater than 0.9 that the average concentrations of CDK1, 
# Plk1 and APC increase and then decrease (i.e. oscillate) over time at least 
# three times. To match the structure of PBLMSTL statements this can be 
# rewritten as the average concentrations (represented in PBLMSTL as densities) 
# of CDK1, Plk1 and APC (corresponding to scale and subsystem 
# Intracellular.CDK1, Intracellular.Plk1, respectively Intracellular.APC) 
# increase and then decrease over time at least three times.
#
#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

P > 0.9 [
    (
        F [0, 100] (
            (d(avg(density(filter(regions, scaleAndSubsystem = Intracellular.CDK1)))) > 0) ^
            (
                F [0, 100] (
                    (d(avg(density(filter(regions, scaleAndSubsystem = Intracellular.CDK1)))) < 0) ^
                    (
                        F [0, 100] (
                            (d(avg(density(filter(regions, scaleAndSubsystem = Intracellular.CDK1)))) > 0) ^
                            (
                                F [0, 100] (
                                    (d(avg(density(filter(regions, scaleAndSubsystem = Intracellular.CDK1)))) < 0) ^
                                    (
                                        F [0, 100] (
                                            (d(avg(density(filter(regions, scaleAndSubsystem = Intracellular.CDK1)))) > 0) ^
                                            (
                                                F [0, 100] (
                                                    (d(avg(density(filter(regions, scaleAndSubsystem = Intracellular.CDK1)))) < 0)
                                                )
                                            )
                                        )
                                    )
                                )
                            )
                        )
                    )    
                )
            )
        )
    ) ^ (
        F [0, 100] (
            (d(avg(density(filter(regions, scaleAndSubsystem = Intracellular.Plk1)))) > 0) ^
            (
                F [0, 100] (
                    (d(avg(density(filter(regions, scaleAndSubsystem = Intracellular.Plk1)))) < 0) ^
                    (
                        F [0, 100] (
                            (d(avg(density(filter(regions, scaleAndSubsystem = Intracellular.Plk1)))) > 0) ^
                            (
                                F [0, 100] (
                                    (d(avg(density(filter(regions, scaleAndSubsystem = Intracellular.Plk1)))) < 0) ^
                                    (
                                        F [0, 100] (
                                            (d(avg(density(filter(regions, scaleAndSubsystem = Intracellular.Plk1)))) > 0) ^
                                            (
                                                F [0, 100] (
                                                    (d(avg(density(filter(regions, scaleAndSubsystem = Intracellular.Plk1)))) < 0) 
                                                )
                                            )
                                        )
                                    )
                                )
                            )
                        )
                    )
                )
            )
        )
    ) ^ (
        F [0, 100] (
            (d(avg(density(filter(regions, scaleAndSubsystem = Intracellular.APC)))) > 0) ^
            (
                F [0, 100] (
                    (d(avg(density(filter(regions, scaleAndSubsystem = Intracellular.APC)))) < 0) ^
                    (
                        F [0, 100] (
                            (d(avg(density(filter(regions, scaleAndSubsystem = Intracellular.APC)))) > 0) ^
                            (
                                F [0, 100] (
                                    (d(avg(density(filter(regions, scaleAndSubsystem = Intracellular.APC)))) < 0) ^
                                    (
                                        F [0, 100] (
                                            (d(avg(density(filter(regions, scaleAndSubsystem = Intracellular.APC)))) > 0) ^
                                            (
                                                F [0, 100] (
                                                    (d(avg(density(filter(regions, scaleAndSubsystem = Intracellular.APC)))) < 0) 
                                                )
                                            )
                                        )
                                    )
                                )
                            )
                        )
                    )
                )
            )
        )
    )
]