pith. sign in

arxiv: 2606.18215 · v1 · pith:CRGYWV73new · submitted 2026-06-16 · 💻 cs.DB

A benchmark suite of intracellular Boolean model variants and multiscale simulations for computational biology

Pith reviewed 2026-06-26 21:42 UTC · model grok-4.3

classification 💻 cs.DB
keywords benchmark suiteBoolean regulatory networksmultiscale simulationssystems biologymodel variantsstochastic trajectoriesintracellular models
0
0 comments X

The pith

PhysiBench supplies 612 executable Boolean network variants and 120000 multiscale simulations as a benchmark for systems biology methods.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces PhysiBench, an open resource consisting of 612 executable intracellular Boolean regulatory network variants derived from seven published networks and a dataset of 120000 time-resolved multiscale stochastic simulations. These variants are generated through mutation-based model construction, online behavioral filtering, and offline sensitivity evaluation, and each simulation trajectory is linked to its model, parameters, seed, and outputs. The resource is positioned to support direct simulation, surrogate modeling, data-driven inference, simulation-based optimization, and comparative benchmarking, with technical validations covering file integrity, executability, graph-based structural diversity, and behavioral heterogeneity. A sympathetic reader would care because the suite supplies ready-to-use, diverse models and linked data that can standardize testing of computational approaches in cell-cycle, developmental, cancer, immune, and cell-fate contexts without requiring repeated custom construction from scratch.

Core claim

The central discovery is a benchmark suite of 612 executable Boolean model variants and 120000 linked multiscale simulation trajectories derived from seven source networks through mutation-based construction, behavioral filtering, and sensitivity evaluation, validated for structural diversity via graph analyses and for behavioral heterogeneity via multiscale outputs, enabling workflows including direct simulation in PhysiBoSS/PhysiCell, surrogate modeling, data-driven inference, simulation-based optimization, and comparative benchmarking.

What carries the argument

Mutation-based model construction combined with online behavioral filtering and offline sensitivity evaluation applied to seven published Boolean networks to generate executable variants.

If this is right

  • The models can be executed directly under systematically sampled stimulation protocols with fixed initial configurations in the PhysiBoSS/PhysiCell framework.
  • The linked dataset of 120000 trajectories enables development and testing of surrogate modeling and data-driven inference methods.
  • Comparative benchmarking of different computational methods is facilitated by the standardized model identifiers and output files.
  • Graph-based structural diversity analyses and behavioral heterogeneity assessments from multiscale outputs provide quantitative validation of the suite.
  • The resource supports simulation-based optimization tasks across cell-cycle control, developmental patterning, cancer signaling, immune response, and cell-fate decision networks.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The public availability of linked model and simulation files could reduce duplicated effort when researchers build test cases for new algorithms.
  • Community extensions might add further source networks or vary the simulation framework while retaining the same validation pipeline.
  • The format of model identifiers plus input-parameter and output files could be adopted as a de-facto standard for sharing multiscale Boolean simulation data.

Load-bearing premise

The mutation-based construction, filtering, and sensitivity steps applied to the seven source networks produce variants that are sufficiently diverse, executable, and representative to serve as an effective benchmark suite.

What would settle it

A finding that a substantial fraction of the 612 models fail executability checks or that graph analyses show low structural diversity and simulation outputs lack measurable behavioral heterogeneity would undermine the claim that the suite functions as a useful benchmark.

Figures

Figures reproduced from arXiv: 2606.18215 by Alessandro Savino, Marco Masera, Riccardo Smeriglio, Roberta Bardini, Stefano Di Carlo.

Figure 1
Figure 1. Figure 1: Overview of the resource, including a benchmark suite of 612 variant intracellular Boolean [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Overview of the pipeline. Starting from seven reference intracellular Boolean regulatory [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Pairwise structural distances computed on the Control Set used to validate the graph [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Pairwise structural distances across the curated Boolean model collection. Panels show [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
read the original abstract

We present PhysiBench, an open resource for developing and evaluating computational methods in systems biology including a benchmark suite of 612 executable intracellular Boolean regulatory network variants and a dataset of 120,000 time-resolved multiscale stochastic simulations. The benchmark models are derived from seven published Boolean networks spanning cell-cycle control, developmental patterning, cancer signaling, immune response, and cell-fate decisions, and are executable in the PhysiBoSS/PhysiCell multiscale simulation framework. Model variants are generated through mutation-based model construction, online behavioral filtering, and offline sensitivity evaluation. The simulation dataset is produced from 60 selected models under systematically sampled stimulation protocols and fixed model-level initial configurations. Each trajectory is linked to its model identifier, input-parameter file, stochastic seed, and cell-level output file. PhysiBench supports direct simulation, surrogate modeling, data-driven inference, simulation-based optimization, and comparative benchmarking. Technical validation includes file-integrity and executability checks, graph-based structural diversity analyses, and behavioral heterogeneity assessment from multiscale simulation outputs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 3 minor

Summary. The paper presents PhysiBench, an open resource consisting of a benchmark suite of 612 executable intracellular Boolean regulatory network variants derived from seven published networks (spanning cell-cycle, developmental, cancer, immune, and cell-fate processes) via mutation-based construction, online behavioral filtering, and offline sensitivity evaluation, together with a linked dataset of 120,000 time-resolved multiscale stochastic simulations produced from 60 selected models under sampled stimulation protocols. The models are executable in PhysiBoSS/PhysiCell; trajectories are linked to model identifiers, input files, seeds, and outputs. Technical validation comprises file-integrity and executability checks, graph-based structural diversity analyses, and behavioral heterogeneity assessment from simulation outputs. The resource is positioned to support direct simulation, surrogate modeling, data-driven inference, simulation-based optimization, and comparative benchmarking.

Significance. If the validation steps demonstrably establish sufficient structural and behavioral diversity together with executability, PhysiBench would constitute a useful standardized, open benchmark resource for computational systems biology. The explicit linkage of each trajectory to its originating model, parameters, and stochastic seed, combined with the multiscale simulation framework, would facilitate reproducible method development and comparative evaluation in an area that currently lacks such curated suites.

major comments (1)
  1. [Abstract] Abstract: the technical validation is described only at a high level (file-integrity checks, graph-based structural diversity analyses, behavioral heterogeneity assessment) with no quantitative results, specific metrics (e.g., ranges of graph distances or heterogeneity scores), or exclusion criteria reported. This information is load-bearing for the central claim that the 612 variants plus 120k trajectories form a usable, validated benchmark suite.
minor comments (3)
  1. A summary table listing the seven source networks, the number of variants generated per network, and the final counts after filtering would improve clarity and allow readers to assess coverage.
  2. The selection process for the 60 models used to generate the 120k trajectories should be stated explicitly (e.g., stratification criteria or sensitivity thresholds).
  3. All original publications for the seven source Boolean networks must be cited with full references.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of PhysiBench and the constructive comment on the abstract. We address the point below.

read point-by-point responses
  1. Referee: [Abstract] Abstract: the technical validation is described only at a high level (file-integrity checks, graph-based structural diversity analyses, behavioral heterogeneity assessment) with no quantitative results, specific metrics (e.g., ranges of graph distances or heterogeneity scores), or exclusion criteria reported. This information is load-bearing for the central claim that the 612 variants plus 120k trajectories form a usable, validated benchmark suite.

    Authors: We agree that the abstract describes the technical validation at a high level without quantitative metrics or explicit exclusion criteria. The full manuscript reports these details in the Technical Validation section, including graph-based structural analyses and behavioral heterogeneity from the multiscale outputs. To address the concern, we will revise the abstract to include representative quantitative results (e.g., observed ranges for structural diversity metrics and heterogeneity scores) and note the key filtering criteria used to select the final set of 612 variants. This change will make the abstract self-contained while preserving its length constraints. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper constructs and releases an explicit benchmark resource (612 model variants + 120k trajectories) via a described pipeline of mutation-based generation, online filtering, and offline sensitivity evaluation, followed by matching technical validation steps (file integrity, graph metrics, behavioral heterogeneity). No equations, fitted parameters, or first-principles predictions are claimed whose outputs reduce by construction to the inputs; the central claim is simply the existence and executability of the constructed suite, which is supported directly by the construction and validation process without self-referential reduction or load-bearing self-citation chains.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The central claim is the existence and utility of the released benchmark resource; it rests on the executability of the generated models in the cited framework and the linkage of simulation metadata, with no free parameters, domain axioms, or invented entities required beyond the standard Boolean network formalism.

pith-pipeline@v0.9.1-grok · 5717 in / 1273 out tokens · 36738 ms · 2026-06-26T21:42:43.964756+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

52 extracted references · 24 canonical work pages

  1. [1]

    Machine and deep learning for longitudinal biomedical data: a review of methods and applications.Artificial Intelligence Review, 56(Suppl 2):1711–1771 (2023)

    Cascarano, A., Mur-Petit, J., Hernandez-Gonzalez, J., Camacho, M., de Toro Eadie, N., Gkontra, P., Chadeau-Hyam, M., Vitria, J., and Lekadir, K. Machine and deep learning for longitudinal biomedical data: a review of methods and applications.Artificial Intelligence Review, 56(Suppl 2):1711–1771 (2023). https://doi.org/10.1007/s10462-023-10561-w

  2. [2]

    Mgod: Multi-granular outlier detection with 44 clustlier analysis

    Abrate, M. P., Smeriglio, R., Bardini, R., Savino, A., and Di Carlo, S. Fast and accu- rate LSTM meta-modeling of TNF-induced tumor resistancein vitro. InProceedings of the 2024 IEEE International Conference on Bioinformatics and Biomedicine (BIBM), 6194–6201 (2024). https://doi.org/10.1109/BIBM62325.2024.10822769

  3. [3]

    Advances in surrogate modeling for biological agent-based simulations: trends, challenges, and future prospects,

    K. A. Norton, D. Bergman, H. V. Jain, and T. Jackson, “Advances in surrogate modeling for biological agent-based simulations: trends, challenges, and future prospects,”Journal of Mathematical Biology, vol. 92, no. 1, p. 6, 2026

  4. [4]

    Optimizing dosage-specific treatments in a multiscale model of tumor growth.Frontiers in Molecular Biosciences, 9:836794 (2022)

    Ponce-de-Le´ on, M., Montagud, A., Akasiadis, C., Schreiber, J., Ntiniakou, T., and Valencia, A. Optimizing dosage-specific treatments in a multiscale model of tumor growth.Frontiers in Molecular Biosciences, 9:836794 (2022). https://doi.org/10.3389/fmolb.2022.836794

  5. [5]

    and Di Carlo, S

    Bardini, R. and Di Carlo, S. Computational methods for biofabrication in tissue engineering and regenerative medicine—a literature review.Computational and Structural Biotechnology Journal, 23:601–616 (2024). https://doi.org/10.1016/j.csbj.2023.12.035

  6. [6]

    A methodology combining rein- forcement learning and simulation to optimize the in silico culture of epithelial sheets.Journal of Computational Science, 76:102226 (2024)

    Castrignano, A., Bardini, R., Savino, A., and Di Carlo, S. A methodology combining rein- forcement learning and simulation to optimize the in silico culture of epithelial sheets.Journal of Computational Science, 76:102226 (2024). https://doi.org/10.1016/j.jocs.2024.102226

  7. [7]

    A methodology for co-simulation- based optimization of biofabrication protocols

    Giannantoni, L., Bardini, R., and Di Carlo, S. A methodology for co-simulation- based optimization of biofabrication protocols. InProceedings of the International Work- Conference on Bioinformatics and Biomedical Engineering, pp. 179–192 (2022). Springer. https://doi.org/10.1007/978-3-031-07802-6 17

  8. [8]

    & Niepert, M.PDEBench: An Extensive Benchmark for Scientific Machine Learning

    Takamoto, M., Praditia, T., Leiteritz, R., MacKinlay, D., Alesiani, F., Pfl¨ uger, D. & Niepert, M.PDEBench: An Extensive Benchmark for Scientific Machine Learning. In: Advances in Neural Information Processing Systems 36 (NeurIPS 2022), Datasets and Bench- marks Track. Available at:https://papers.neurips.cc/paper_files/paper/2022/file/ 0a9747136d411fb83f...

  9. [9]

    GitHub repository

    PDEBench Project.PDEBench: An Extensive Benchmark for Scientific Machine Learning. GitHub repository. Available at:https://github.com/pdebench/PDEBenchAccessed: 24 March 2026

  10. [10]

    & Niepert, M.PDEBench Datasets

    Takamoto, M., Praditia, T., Leiteritz, R., MacKinlay, D., Alesiani, F., Pfl¨ uger, D. & Niepert, M.PDEBench Datasets. DaRUS dataset. doi:10.18419/DARUS-2986. Available at:https:// darus.uni-stuttgart.de/dataset.xhtml?persistentId=doi:10.18419/darus-2986Ac- cessed: 24 March 2026

  11. [11]

    and Scher, Sebastian and Weyn, Jonathan A

    Rasp, S., D¨ uben, P. D., Scher, S., Weyn, J. A., Mouatadid, S. & Thuerey, N.Weather- Bench: A Benchmark Data Set for Data-Driven Weather Forecasting.Journal of Advances in Modeling Earth Systems12, e2020MS002203 (2020). doi:10.1029/2020MS002203. Available at:https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2020MS002203Accessed: 24 March 2026

  12. [12]

    GitHub repository

    Pangeo Data.WeatherBench: A benchmark dataset for data-driven weather forecasting. GitHub repository. Available at:https://github.com/pangeo-data/WeatherBenchAc- cessed: 24 March 2026. 17

  13. [13]

    GitHub repository

    Google Research.WeatherBench 2: A benchmark for the next generation of data-driven global weather models. GitHub repository. Available at:https://github.com/google-research/ weatherbench2Accessed: 24 March 2026

  14. [14]

    The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learning.Advances in Neural Information Processing Systems37, 44989–45037 (2024)

    Ohana, R.et al. The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learning.Advances in Neural Information Processing Systems37, 44989–45037 (2024). Available at:https://openreview.net/forum?id=00Sx577BT3Accessed: 24 March 2026

  15. [15]

    GitHub repository

    Polymathic AI.The Well: 15TB of Physics Simulations. GitHub repository. Available at: https://github.com/PolymathicAI/the_wellAccessed: 24 March 2026

  16. [16]

    A., Al Sawaftah, N

    Alsalloum, G. A., Al Sawaftah, N. M., Percival, K. M., and Husseini, G. A. Digital twins of biological systems: A narrative review.IEEE Open Journal of Engineering in Medicine and Biology(2024). https://doi.org/10.1109/OJEMB.2024.3426916

  17. [17]

    Multi-level and hybrid modeling ap- proaches for systems biology.Computational and Structural Biotechnology Journal, 15:396–402 (2017)

    Bardini, R., Politano, G., Benso, A., and Di Carlo, S. Multi-level and hybrid modeling ap- proaches for systems biology.Computational and Structural Biotechnology Journal, 15:396–402 (2017). https://doi.org/10.1016/j.csbj.2017.05.001

  18. [18]

    https://doi.org/10.1093/bioinformatics/btx123

    Stoll, G., Caron, B., Viara, E., Dugourd, A., Zinovyev, A., Naldi, A.,et al.MaBoSS 2.0: an environment for stochastic Boolean modeling.Bioinformatics, 33(14):2226–2228 (2017). https://doi.org/10.1093/bioinformatics/btx123

  19. [19]

    PhysiBoSS: a multiscale agent-based modeling framework inte- grating physical dimension and cell signalling.Bioinformatics, 35(7):1188–1196 (2019)

    Letort, G., Montagud, A., Stoll, G., Heiland, R., Barillot, E., Macklin, P.,et al., and Calzone, L. PhysiBoSS: a multiscale agent-based modeling framework inte- grating physical dimension and cell signalling.Bioinformatics, 35(7):1188–1196 (2019). https://doi.org/10.1093/bioinformatics/bty766

  20. [20]

    Calzone, L., No¨ el, V., Barillot, E., Kroemer, G., and Stoll, G. modeling signaling pathways in biology with MaBoSS: From one single cell to a dynamic population of heterogeneous interacting cells.Computational and Structural Biotechnology Journal, 20:5661–5671 (2022). https://doi.org/10.1016/j.csbj.2022.09.034

  21. [21]

    NeKo: a tool for automatic network construction from prior knowledge.PLOS Computational Biology, 21(9):e1013300 (2025)

    Ruscone, M., Tsirvouli, E., Checcoli, A., Turei, D., Barillot, E., Saez-Rodriguez, J.,et al. NeKo: a tool for automatic network construction from prior knowledge.PLOS Computational Biology, 21(9):e1013300 (2025). https://doi.org/10.1371/journal.pcbi.1013300

  22. [22]

    Z., Guillaume, H., Shaffer, S

    Ouellet, M., Kim, J. Z., Guillaume, H., Shaffer, S. M., Bassett, L. C., and Bassett, D. S. Break- ing reflection symmetry: evolving long dynamical cycles in Boolean systems.New Journal of Physics, 26(2):023006 (2024). https://doi.org/10.1088/1367-2630/ad1b5a

  23. [23]

    S., Glont, M., Nguyen, T

    Malik-Sheriff, R. S., Glont, M., Nguyen, T. V., Tiwari, K., Roberts, M. G., Xavier, A.,et al., and Hermjakob, H. BioModels—15 years of sharing computational models in life science. Nucleic Acids Research, 48(D1):D407–D415 (2020). https://doi.org/10.1093/nar/gkz1055

  24. [24]

    From quantitative SBML models to Boolean networks.Applied Network Science, 7(1):73 (2022)

    Vaginay, A., Boukhobza, T., and Sma¨ ıl-Tabbone, M. From quantitative SBML models to Boolean networks.Applied Network Science, 7(1):73 (2022). https://doi.org/10.1007/s41109- 022-00473-8

  25. [25]

    P., Vasilescu, D., Marupilla, G., Wilson, M., Agmon, E., Agnew, H., Andrews, S

    Shaikh, B., Smith, L. P., Vasilescu, D., Marupilla, G., Wilson, M., Agmon, E., Agnew, H., Andrews, S. S., Anwar, A., Beber, M. E., et al. BioSimulators: a central registry of simulation engines and services for recommending specific tools.Nucleic Acids Research, 50(W1):W108– W114 (2022). https://doi.org/10.1093/nar/gkac231

  26. [26]

    PhysiBoSS-Models: A database for multiscale models.arXiv preprint arXiv:2508.05550(2025)

    Noel, V., Ruscone, M., Heiland, R., Montagud, A., Valencia, A., Barillot, E., Macklin, P., and Calzone, L. PhysiBoSS-Models: A database for multiscale models.arXiv preprint arXiv:2508.05550(2025). https://arxiv.org/abs/2508.05550

  27. [27]

    & Henzinger, T.Repository of logically consis- tent real-world Boolean network models

    Pastva, S., ˇSafr´ anek, D., Beneˇ s, N., Brim, L. & Henzinger, T.Repository of logically consis- tent real-world Boolean network models. bioRxiv. Available at:https://www.biorxiv.org/ content/10.1101/2023.06.12.544361v1.fullAccessed: 24 March 2026. 18

  28. [28]

    GitHub repository

    Sybila.Biodivine Boolean Models (BBM) Benchmark Dataset. GitHub repository. Available at:https://github.com/sybila/biodivine-boolean-modelsAccessed: 24 March 2026

  29. [29]

    L.Parameter Sensitivity in Tumor Models: Dataset from PhysiCell Simulations

    Rocha, H. L.Parameter Sensitivity in Tumor Models: Dataset from PhysiCell Simulations. Zenodo dataset. doi:10.5281/zenodo.14590312. Available at:https://zenodo.org/records/ 14590312Accessed: 24 March 2026

  30. [30]

    Dynamical analysis of a generic Boolean model for the control of the mammalian cell cycle.Bioinformatics22(14), e124–e131 (2006)

    Faur´ e, A., Naldi, A., Chaouiya, C., and Thieffry, D. Dynamical analysis of a generic Boolean model for the control of the mammalian cell cycle.Bioinformatics22(14), e124–e131 (2006). https://doi.org/10.1093/bioinformatics/btl210

  31. [31]

    Gene Interaction Network simulation (GINsim) Model Repository

    Faur´ e, A.Restriction point control of the mammalian cell cycle. Gene Interaction Network simulation (GINsim) Model Repository. Available at:https://ginsim.github.io/models/ 2006-mammal-cell-cycle/Accessed: 23 March 2026

  32. [32]

    and Othmer, H

    Albert, R. and Othmer, H. G. The topology of the regulatory interactions predicts the expres- sion pattern of the segment polarity genes inDrosophila melanogaster.Journal of Theoretical Biology223(1), 1–18 (2003)

  33. [33]

    Stabilizing patterning in the Drosophilasegment polarity network by selecting modelsin silico.Biosystems102(1), 3–10 (2010)

    Stoll, G., Bischofberger, M., Rougemont, J., and Naef, F. Stabilizing patterning in the Drosophilasegment polarity network by selecting modelsin silico.Biosystems102(1), 3–10 (2010)

  34. [34]

    MaBoSS model repository

    MaBoSS Project.Drosophila Patterning. MaBoSS model repository. Available at:https: //maboss.curie.fr/Accessed: 23 March 2026

  35. [35]

    M., Naldi, A., Van Iersel, M

    Chaouiya, C., B´ erenguier, D., Keating, S. M., Naldi, A., Van Iersel, M. P., Rodriguez, N., et al.SBML qualitative models: a model representation format and infrastructure to foster interactions between qualitative modeling formalisms and tools.BMC Systems Biology7(1), 135 (2013)

  36. [36]

    BioMod- els Database, BIOMD0000000562

    BioModels.Chaouiya2013 - EGF and TNFalpha mediated signalling pathway. BioMod- els Database, BIOMD0000000562. Available at:https://www.ebi.ac.uk/biomodels/ BIOMD0000000562Accessed: 23 March 2026

  37. [37]

    Discovery of drug synergies in gastric cancer cells predicted by logical modeling.PLoS Computational Biology11(8), e1004426 (2015)

    Flobak, ˚A., Baudot, A., Remy, E., Thommesen, L., Thieffry, D., Kuiper, M., and Lægreid, A. Discovery of drug synergies in gastric cancer cells predicted by logical modeling.PLoS Computational Biology11(8), e1004426 (2015)

  38. [38]

    PhysiBoSS boolean-models repository

    PhysiBoSS.gastric cancer. PhysiBoSS boolean-models repository. Available at:https:// github.com/PhysiBoSS/boolean-models/tree/main/gastric_cancerAccessed: 23 March 2026

  39. [39]

    E.,et al., and the COVID-19 Disease Map Community

    Niarakis, A., Ostaszewski, M., Mazein, A., Kuperstein, I., Kutmon, M., Gillespie, M. E.,et al., and the COVID-19 Disease Map Community. Drug-target identification in COVID-19 dis- ease mechanisms using computational systems biology approaches.Frontiers in Immunology, 14:1282859 (2024). https://doi.org/10.3389/fimmu.2023.1282859

  40. [40]

    pb4covid19 repository

    PhysiBoSS-COVID.boolean network. pb4covid19 repository. Available at: https://gitlab.lcsb.uni.lu/computational-modeling-and-simulation/pb4covid19/ -/tree/master/data/boolean_networkAccessed: 23 March 2026

  41. [41]

    Montagud, A., B´ eal, J., Tobalina, L., Traynard, P., Subramanian, V., Szalai, B.,et al.Patient- specific Boolean models of signalling networks guide personalised treatments.eLife11, e72626 (2022)

  42. [42]

    PhysiBoSS boolean-models repository

    PhysiBoSS.prostate cancer. PhysiBoSS boolean-models repository. Available at:https: //github.com/PhysiBoSS/boolean-models/tree/main/prostate_cancerAccessed: 23 March 2026. 19

  43. [43]

    Mathematical modeling of cell-fate decision in response to death receptor engage- ment.PLoS Computational Biology6(3), e1000702 (2010)

    Calzone, L., Tournier, L., Fourquet, S., Thieffry, D., Zhivotovsky, B., Barillot, E., and Zi- novyev, A. Mathematical modeling of cell-fate decision in response to death receptor engage- ment.PLoS Computational Biology6(3), e1000702 (2010)

  44. [44]

    PhysiBoSS boolean-models repository

    PhysiBoSS.tnf cell fate. PhysiBoSS boolean-models repository. Available at:https:// github.com/PhysiBoSS/boolean-models/tree/main/tnf_cell_fateAccessed: 23 March 2026

  45. [45]

    1997.Modelling Extremal Events for Insurance and Finance

    Benesty, J., Chen, J., Huang, Y., and Cohen, I. Pearson correlation coefficient. InNoise Reduction in Speech Processing, pp. 1–4 (2009). Springer. https://doi.org/10.1007/978-3-642- 00296-0 5

  46. [46]

    A., Yang, C

    McCabe, S., Torres, L., LaRock, T., Haque, S. A., Yang, C. H., Hartle, H., and Klein, B.netrd: A library for network reconstruction and graph distances.arXiv preprintarXiv:2010.16019 (2020)

  47. [47]

    J., and Schult, D

    Hagberg, A., Swart, P. J., and Schult, D. A. Exploring network structure, dynamics, and function usingNetworkX. Los Alamos National Laboratory Technical Report LA-UR-08-05495 (2008)

  48. [48]

    T., and Faloutsos, C

    Koutra, D., Vogelstein, J. T., and Faloutsos, C. DeltaCon: A principled massive-graph simi- larity function. InProceedings of the 2013 SIAM International Conference on Data Mining, 162–170 (2013)

  49. [49]

    Biological network comparison via Ipsen–Mikhailov distance

    Jurman, G., Riccadonna, S., Visintainer, R., and Furlanello, C. Biological network comparison via Ipsen–Mikhailov distance. arXiv preprint arXiv:1109.0220 (2011)

  50. [50]

    On a variational definition for the Jensen–Shannon symmetriza- tion of distances based on the information radius.Entropy23(4), 464 (2021)

    Nielsen, F. On a variational definition for the Jensen–Shannon symmetriza- tion of distances based on the information radius.Entropy23(4), 464 (2021). https://doi.org/10.3390/e21050485

  51. [51]

    PhysiBench resource

    Masera, M., Smeriglio, R., Bardini, R., Savino, A., Di Carlo, S.PhysiBench. PhysiBench resource. Available at:https://drive.cloud.polito.it/index.php/s/pefzfJpnZZiRMWY Accessed: 16 June 2026

  52. [52]

    GitHub repository

    PhysiBench GitHub repository.PhysiBench GitHub repository. GitHub repository. Available at:https://github.com/smilies-polito/PhysiBenchAccessed: 16 June 2026. 20