Pattern Matching Experiments



In [1]:

    
from DSGRN import *

Networks

We give two sets of networks. One of them allows for all parameters. The other is identical except it only uses essential parameters.



In [2]:

    
network_strings = [ 
["SWI4 : (NDD1)(~YOX1)", "HCM1 : SWI4", "NDD1 : HCM1", "YOX1 : SWI4"],
["SWI4 : (NDD1)(~YOX1)", "HCM1 : SWI4", "NDD1 : HCM1", "YOX1 : (SWI4)(HCM1)"],
["SWI4 : (NDD1)(~YOX1)", "HCM1 : SWI4", "NDD1 : HCM1", "YOX1 : (SWI4)(~HCM1)"],
["SWI4 : (NDD1)(~YOX1)", "HCM1 : SWI4", "NDD1 : HCM1", "YOX1 : (SWI4)(NDD1)"],
["SWI4 : (NDD1)(~YOX1)", "HCM1 : SWI4", "NDD1 : HCM1", "YOX1 : (SWI4)(~NDD1)"],
["SWI4 : (NDD1)(~YOX1)", "HCM1 : (SWI4)(YOX1)", "NDD1 : HCM1", "YOX1 : SWI4"],
["SWI4 : (NDD1)(~YOX1)", "HCM1 : (SWI4)(~YOX1)", "NDD1 : HCM1", "YOX1 : SWI4"],
["SWI4 : (NDD1)(~YOX1)", "HCM1 : SWI4", "NDD1 : (HCM1)(YOX1)", "YOX1 : SWI4"],
["SWI4 : (NDD1)(~YOX1)", "HCM1 : SWI4", "NDD1 : (HCM1)(~YOX1)", "YOX1 : SWI4"] ]

Full Networks



In [3]:

    
networks = [Network() for i in range(0,9)]
for i,network in enumerate(networks):
    network.assign('\n'.join(network_strings[i]))

Essential Networks



In [4]:

    
essential_network_strings = [ [ line + " : E" for line in network_string ] for network_string in network_strings]
essential_networks = [Network() for i in range(0,9)]
for i,network in enumerate(essential_networks):
    network.assign('\n'.join(essential_network_strings[i]))

Path match analysis

We give two functions for path match analysis. One looks at the entire domain graph. The other only checks for path matches in stable Morse sets.

Analysis on entire domain graph



In [5]:

    
def Analyze(network, events, event_ordering):
    poe = PosetOfExtrema(network, events, event_ordering )
    pattern_graph = PatternGraph(poe)
    parameter_graph = ParameterGraph(network)
    result = []
    for parameter_index in range(0, parameter_graph.size()):
        parameter = parameter_graph.parameter(parameter_index)
        search_graph = SearchGraph(DomainGraph(parameter))
        matching_graph = MatchingGraph(search_graph, pattern_graph);
        if PathMatch(matching_graph):
            result.append(parameter_index)
    return [result,  parameter_graph.size()]

Analysis on stable Morse set only



In [6]:

    
def AnalyzeOnStable(network, events, event_ordering):
    poe = PosetOfExtrema(network, events, event_ordering )
    pattern_graph = PatternGraph(poe)
    parameter_graph = ParameterGraph(network)
    results = []
    for parameter_index in range(0, parameter_graph.size()):
        parameter = parameter_graph.parameter(parameter_index)
        domain_graph = DomainGraph(parameter)
        morse_decomposition = MorseDecomposition(domain_graph.digraph())
        morse_graph = MorseGraph()
        morse_graph.assign(domain_graph, morse_decomposition)
        MorseNodes = range(0, morse_graph.poset().size())
        isStable = lambda node : len(morse_graph.poset().children(node)) == 0
        isStableFC = lambda node : morse_graph.annotation(node)[0] == 'FC' and isStable(node)
        hasStableFC = any( isStableFC(node) for node in MorseNodes)
        StableNodes = [ node for node in MorseNodes if isStable(node) ]
        subresult = []
        for node in StableNodes:
            search_graph = SearchGraph(domain_graph, node)
            matching_graph = MatchingGraph(search_graph, pattern_graph)
            path_match = PathMatch(matching_graph)
            if path_match:
                subresult.append([parameter_index, node])
        results.append([subresult, 1 if hasStableFC else 0])
    return [results, parameter_graph.size()]

Poset of Extrema

We study two poset of extrema. The first poset comes from looking at times [10,60] and assuming SWI4 happens before the other minima at the beginning and thus can be excluded. The other comes from including all extrema.

Original Poset of Extrema



In [7]:

    
original_events = [("HCM1", "min"), ("NDD1", "min"), ("YOX1", "min"), 
          ("SWI4", "max"), ("HCM1", "max"), ("YOX1", "max"), 
          ("NDD1", "max"),
          ("SWI4","min")]
original_event_ordering = [ (i,j) for i in [0,1,2] for j in [3,4,5] ] + \
                 [ (i,j) for i in [3,4,5] for j in [6] ] + \
                 [ (i,j) for i in [6] for j in [7] ]



In [8]:

    
DrawGraph(PosetOfExtrema(networks[0], original_events, original_event_ordering ))









    Out[8]:

Alternative Poset of Extrema



In [9]:

    
all_events = [("SWI4", "min"), ("HCM1", "min"), ("NDD1", "min"), ("YOX1", "min"), 
          ("SWI4", "max"), ("HCM1", "max"), ("YOX1", "max"), 
          ("NDD1", "max"),
          ("SWI4","min"),
          ("YOX1", "min"), ("HCM1","min"),
          ("NDD1", "min"),
          ("SWI4", "max"), ("HCM1", "max"), ("YOX1", "max"),
          ("NDD1", "max")]
all_event_ordering = [ (i,j) for i in [0,1,2,3] for j in [4,5,6] ] + \
                 [ (i,j) for i in [4,5,6] for j in [7] ] + \
                 [ (i,j) for i in [7] for j in [8] ] + \
                 [ (i,j) for i in [8] for j in [9,10] ] + \
                 [ (i,j) for i in [9,10] for j in [11,12,13,14] ] + \
                 [ (11,15) ]



In [10]:

    
DrawGraph(PosetOfExtrema(networks[0], all_events, all_event_ordering ))









    Out[10]:

Experiments

There are 8 experiements corresponding to 3 binary choices:

Full networks vs Essential networks
Path matching in entire domain graph vs path matching in stable Morse sets
Original poset of extrema vs Alternative poset of extrema



In [11]:

    
def DisplayExperiment(results, title):
    markdown_string = "# " + title + "\n\n"
    markdown_string += "| network | # parameters | # parameters with path match |\n"
    markdown_string += "| ------- |------------ | ---------------------------- |\n"
    for i, item in enumerate(results):
        [parameters_with_path_match, pgsize] = item
        markdown_string += ("|" + str(i) + "|" + str(pgsize) + "|" + str(len(parameters_with_path_match)) + "|\n")
    from IPython.display import display, Markdown, Latex
    display(Markdown(markdown_string))
def DisplayStableExperiment(results, title):
    markdown_string = "# " + title + "\n\n"
    markdown_string += "| network | # parameters | # parameters with stable FC | # parameters with path match |\n"
    markdown_string += "| ------- |------------ | ---------------------------- | ---------------------------- |\n"
    for i, item in enumerate(results):
        [results, pgsize] = item
        parameters_with_path_match = sum([ 1 if pair[0] else 0 for pair in results])
        parameters_with_stable_fc = sum([ 1 if pair[1] else 0 for pair in results])
        markdown_string += ("|" + str(i) + "|" + str(pgsize) + "|" +str(parameters_with_stable_fc) +"|"+str(parameters_with_path_match) + "|\n")
    from IPython.display import display, Markdown, Latex
    display(Markdown(markdown_string))



In [12]:

    
%%time
experiment = lambda network : Analyze(network, original_events, original_event_ordering)
experimental_results_1 = [ experiment(network) for network in networks ]
DisplayExperiment(experimental_results_1, "Experiment 1: All parameters, original poset of extrema")









    




Experiment 1: All parameters, original poset of extrema


network
# parameters
# parameters with path match




0
1080
22


1
8640
316


2
8640
180


3
8640
226


4
8640
280


5
8640
176


6
8640
270


7
8640
176


8
8640
176










    



CPU times: user 12.9 s, sys: 63.4 ms, total: 13 s
Wall time: 13.1 s



In [13]:

    
%%time
experiment = lambda network : Analyze(network, original_events, original_event_ordering)
experimental_results_2 = [ experiment(network) for network in essential_networks ]
DisplayExperiment(experimental_results_2, "Experiment 2: Essential parameters, original poset of extrema")









    




Experiment 2: Essential parameters, original poset of extrema


network
# parameters
# parameters with path match




0
14
8


1
56
38


2
56
18


3
56
25


4
56
28


5
56
16


6
56
30


7
56
24


8
56
24










    



CPU times: user 94.8 ms, sys: 3.15 ms, total: 97.9 ms
Wall time: 96.6 ms



In [14]:

    
%%time
experiment = lambda network : AnalyzeOnStable(network, original_events, original_event_ordering)
experimental_results_3 = [ experiment(network) for network in networks ]
DisplayStableExperiment(experimental_results_3, "Experiment 3: All parameters, original poset, stable only")









    




Experiment 3: All parameters, original poset, stable only


network
# parameters
# parameters with stable FC
# parameters with path match




0
1080
4
16


1
8640
56
224


2
8640
24
96


3
8640
132
166


4
8640
36
108


5
8640
56
128


6
8640
168
222


7
8640
48
118


8
8640
108
134










    



CPU times: user 8.8 s, sys: 25.5 ms, total: 8.82 s
Wall time: 8.83 s



In [15]:

    
%%time
experiment = lambda network : AnalyzeOnStable(network, original_events, original_event_ordering)
experimental_results_4 = [ experiment(network) for network in essential_networks ]
DisplayStableExperiment(experimental_results_4, "Experiment 4: Essential parameters, original poset, stable only")









    




Experiment 4: Essential parameters, original poset, stable only


network
# parameters
# parameters with stable FC
# parameters with path match




0
14
2
2


1
56
8
8


2
56
0
0


3
56
8
7


4
56
0
0


5
56
8
4


6
56
28
18


7
56
8
8


8
56
28
18










    



CPU times: user 93.6 ms, sys: 4.17 ms, total: 97.8 ms
Wall time: 95.9 ms



In [16]:

    
%%time
experiment = lambda network : Analyze(network, all_events, all_event_ordering)
experimental_results_5 = [ experiment(network) for network in networks ]
DisplayExperiment(experimental_results_5, "Experiment 5: All parameters, alternative poset of extrema")









    




Experiment 5: All parameters, alternative poset of extrema


network
# parameters
# parameters with path match




0
1080
22


1
8640
264


2
8640
176


3
8640
224


4
8640
278


5
8640
176


6
8640
268


7
8640
176


8
8640
176










    



CPU times: user 11 s, sys: 16.7 ms, total: 11 s
Wall time: 11 s



In [17]:

    
%%time
experiment = lambda network : Analyze(network, all_events, all_event_ordering)
experimental_results_6 = [ experiment(network) for network in essential_networks ]
DisplayExperiment(experimental_results_6, "Experiment 6: Essential parameters, alternative poset of extrema")









    




Experiment 6: Essential parameters, alternative poset of extrema


network
# parameters
# parameters with path match




0
14
8


1
56
32


2
56
16


3
56
24


4
56
28


5
56
16


6
56
28


7
56
24


8
56
24










    



CPU times: user 88.7 ms, sys: 3.88 ms, total: 92.6 ms
Wall time: 91.1 ms



In [18]:

    
%%time
experiment = lambda network : AnalyzeOnStable(network, all_events, all_event_ordering)
experimental_results_7 = [ experiment(network) for network in networks ]
DisplayStableExperiment(experimental_results_7, "Experiment 7: All parameters, alternative poset of extrema, stable only")









    




Experiment 7: All parameters, alternative poset of extrema, stable only


network
# parameters
# parameters with stable FC
# parameters with path match




0
1080
4
16


1
8640
56
192


2
8640
24
96


3
8640
132
164


4
8640
36
108


5
8640
56
128


6
8640
168
221


7
8640
48
118


8
8640
108
134










    



CPU times: user 9.23 s, sys: 33.6 ms, total: 9.26 s
Wall time: 9.27 s



In [19]:

    
%%time
experiment = lambda network : AnalyzeOnStable(network, all_events, all_event_ordering)
experimental_results_8 = [ experiment(network) for network in essential_networks ]
DisplayStableExperiment(experimental_results_8, "Experiment 8: Essential parameters, alternative poset of extrema, stable only")









    




Experiment 8: Essential parameters, alternative poset of extrema, stable only


network
# parameters
# parameters with stable FC
# parameters with path match




0
14
2
2


1
56
8
8


2
56
0
0


3
56
8
6


4
56
0
0


5
56
8
4


6
56
28
17


7
56
8
8


8
56
28
18










    



CPU times: user 104 ms, sys: 5.4 ms, total: 109 ms
Wall time: 108 ms



In [ ]:

network	# parameters	# parameters with path match
0	1080	22
1	8640	316
2	8640	180
3	8640	226
4	8640	280
5	8640	176
6	8640	270
7	8640	176
8	8640	176