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The benchmark problems

The problems are grouped after the type of model space and data that are used. An overview is shown in the following tables with links to more detailed descriptions and problem files. Parameter estimation problems (a fixed structure is assumed) are given in the last table, and all such problems starts by "pe_".

All problems can be downloaded as a zip-file.

Model space of chemical rate equations and simulated data

Source system/model Problem #var #exp #pts Noise Best error
simpleLin simpleLin1 3 3 13 0% 8
  simpleLin2   8 13 10% 140.2
simpleFb simpleFb1 3 4 7 0% 7
  simpleFb2   4 7 5% 42.14
  simpleFb3   1 7 0% 7
  simpleFb4   1 7 ~5%1 7.071
osc osc1 3 1 41 0% 6.149
  osc2   1 41 3% 87.34
metabol metabol1 5 12 7 0% 30
  metabol2   12 21 10% 751.6
  metabol3   12 21 20% 861.1
3genes 3genes1 8 16 21 0% 39
feedf feedf1 6 16 51 0% 1.760
  feedf2 6 16 51 5% 1958
inhosc inhosc1 4 4 51 0% 9.863
  inhosc2 4 4 51 5% 814.4
bifeedb bifeedb1 5 16 51 0% 8.444
  bifeedb2 5 16 51 5% 2933

S-system model space and simulated data

Source system/model Problem #var #exp #pts Noise Best error
ss_cascade ss_cascade1 3 8 41 0% 14
  ss_cascade2   4 41 0% 14
  ss_cascade3   8 41 5% 476.7
ss_branch ss_branch1 4 3 21 0% 17
  ss_branch2   6 51 0% 17
  ss_branch3   5 20 0% 17
  ss_branch4   4 20 0% 17
  ss_branch5   4 20 2.5% 142.1
  ss_branch6   5 31 0% 18
ss_5genes ss_5genes1 5 10 11 0% 23
  ss_5genes2   10 9 20% 211.0
  ss_5genes3   10 3 0% 23
  ss_5genes4   15 11 0% 23
  ss_5genes5   10 11 0% 23.00
  ss_5genes6   1 16 0% 23
  ss_5genes7   10 20 0% 23
  ss_5genes8   8 41 0% 28
ss_15genes ss_15genes1 15 10 11 0% 62
  ss_15genes2   20 11 10% 1783
ss_30genes ss_30genes1 30 15 11 0% 128
  ss_30genes2   20 11 10% 3628
  ss_30genes3   8 41 0% 128
ss_feedf ss_feedf1 6 16 51 0% 0.1969
  ss_feedf2 6 16 51 5% 1952
ss_inhosc ss_inhosc1 4 4 51 0% 0.1967
  ss_inhosc2 4 4 51 5% 371.2
ss_bifeedb ss_bifeedb1 5 16 51 0% 1.097
  ss_bifeedb2 5 16 51 5% 2491

GMA model space and simulated data

Source system/model Problem #var #exp #pts Noise Best error
gma_feedf gma_feedf1 6 16 51 0% 0.1777
  gma_feedf2 6 16 51 5% 1917
gma_inhosc gma_inhosc1 4 4 51 0% 0.2059
  gma_inhosc2 4 4 51 5% 371.4
gma_bifeedb gma_bifeedb1 5 16 51 0% 0.2546
  gma_bifeedb2 5 16 51 5% 2480

Various model spaces and data from real biological systems

Source system/model Problem #var #exp #pts Noise Best error
cytokine cytokine1 4 1 7 10%1 25.92
  cytokine2   1 7 10%1 42.17
ss_ethanolferm ss_ethanolferm1 4 3 11-19 ~30%1 127.4
  ss_ethanolferm2   2 11-15 ~30%1 1308
ss_sosrepair ss_sosrepair1 6 1 50 10%1 2642
  ss_sosrepair2   1 50 10%1 2823
ss_cadBA ss_cadBA1 4 1 25 <20%1 750.6
  ss_cadBA2   1 25 <20%1 709.1
ss_clock ss_clock1 7 1 12 ~10%1 928.4
  ss_clock2   1 12 ~10%1 814.5

Parameter estimation problems (the structure is fixed)

Source system/model Problem #var #exp #pts Noise Best error
3genes pe_3genes1 8 16 21 0% 0.0
  pe_3genes2f   16 21 3% 1286
  pe_3genes2   16 21 3% 1214
  pe_3genes3f   16 21 5% 3128
  pe_3genes3   16 21 5% 2309
4genes pe_4genes1 11 16 21 0% 0.0
5genes pe_5genes1 14 16 21 0% 0.0
6genes pe_6genes1 17 16 21 0% 0.0
pinene pe_pinene 5 1 9 5%1 9.936
ss_cascade pe_ss_cascade1 3 8 41 0% 0.0
ss_branch pe_ss_branch4 4 4 20 0% 0.0
ss_30genes pe_ss_30genes2f 30 20 11 10% 3240
  pe_ss_30genes2   20 11 10% 3004
pe_feedf pe_feedf1 6 16 51 0% 1.653
  pe_feedf2 6 16 51 5% 1856
pe_inhosc pe_inhosc1 4 4 51 0% 9.815
  pe_inhosc2 4 4 51 5% 799.6
pe_bifeedb pe_bifeedb1 5 16 51 0% 8.449
  pe_bifeedb2 5 16 51 5% 2814
pe_ss_feedf pe_ss_feedf1 6 16 51 0% 0.1004
  pe_ss_feedf2 6 16 51 5% 1825
pe_ss_inhosc pe_ss_inhosc1 4 4 51 0% 0.1259
  pe_ss_inhosc2 4 4 51 5% 338.7
pe_ss_bifeedb pe_ss_bifeedb1 5 16 51 0% 1.767
  pe_ss_bifeedb2 5 16 51 5% 2363
pe_gma_feedf pe_gma_feedf1 6 16 51 0% 0.01967
  pe_gma_feedf2 6 16 51 5% 1772
pe_gma_inhosc pe_gma_inhosc1 4 4 51 0% 0.1229
  pe_gma_inhosc2 4 4 51 5% 341.3
pe_gma_bifeedb pe_gma_bifeedb1 5 16 51 0% 1.506
  pe_gma_bifeedb2 5 16 51 5% 2386

#var = number of dependent variables, #exp = number of experimental conditions with different initial conditions and/or input functions, #pts = number of data-points per time-series. Noise is added from a Gaussian distribution with standard deviation given as a certain percentage (denoted Noise) of each experimental value. Problem names starting with ss_ correspond to S-systems.

1) Estimate from or assumption about data.