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References

Source: vignettes/citations.Rmd
citations.Rmd

This page contains all references cited in the TSENAT package, organized by topic. For a complete list in BibTeX format, see the vignettes/TSENAT.bib file.

Information Theory & Entropy

Foundational Work

  • Shannon, C. E. (1948). “A mathematical theory of communication.” The Bell System Technical Journal, 27(3-4), 379-423.

  • Simpson, E. H. (1949). “Measurement of diversity.” Nature, 163, 688. doi: 10.1038/163688a0

  • Kullback, S., & Leibler, R. A. (1951). “On information and sufficiency.” Annals of Mathematical Statistics, 22(1), 79-86. doi: 10.1214/aoms/1177729694

Tsallis Entropy Theory

  • Tsallis, C. (2017). “On the foundations of statistical mechanics.” European Physical Journal Special Topics, 226, 1433-1443. doi: 10.1140/epjst/e2016-60252-2

  • Furuichi, S. (2006). “Information theoretical properties of Tsallis entropies.” Journal of Mathematical Physics, 47, 023302. doi: 10.1063/1.2165744

  • Anastasiadis, A. (2012). “Entropy properties and multiple Tsallis distributions.” Entropy, 14, 174-176. doi: 10.3390/e14020174

  • Alomani, G., & Kayid, M. (2023). “Further properties of Tsallis entropy and its application.” Entropy, 25(2), 199. doi: 10.3390/e25020199

Divergence & Diversity Measures

  • van Erven, T., & Harremoes, P. (2014). “Rényi divergence and Kullback-Leibler divergence.” IEEE Transactions on Information Theory, 60(7), 3797-3820. doi: 10.1109/TIT.2014.2320500

  • Jost, L. (2006). “Entropy and diversity.” Oikos, 113(2), 363-375. doi: 10.1111/j.2006.0030-1299.14714.x

  • Chao, A., Chiu, C.-H., & Jost, L. (2010). “Phylogenetic diversity measures based on Hill numbers.” Philosophical Transactions of the Royal Society B, 365(1558), 3599-3609. doi: 10.1098/rstb.2010.0272

  • Sason, I. (2022). “Divergence measures: Mathematical foundations and applications in information-theoretic and statistical problems.” Entropy, 24(5), 712. doi: 10.3390/e24050712

  • Sfetcu, R.-C., Sfetcu, S.-C., & Preda, V. (2022). “Some properties of weighted Tsallis and Kaniadakis divergences.” Entropy, 24(11), 1616. doi: 10.3390/e24111616

Applications in Biology

  • Yulmetyev, R. M., Emelyanova, N. A., & Gafarov, F. M. (2004). “Dynamical Shannon entropy and information Tsallis entropy in complex systems.” Physica A, 341, 649-676. doi: 10.1016/j.physa.2004.03.094

  • Bajić, D. (2022). “On quantization errors in approximate and sample entropy.” Entropy, 24(1), 73. doi: 10.3390/e24010073

  • Bajić, D. (2024). “Information theory, living systems, and communication engineering.” Entropy, 26(5), 430. doi: 10.3390/e26050430

  • Gao, X., Tsai, S.-B., Liu, F., Pan, L., & Deng, Y. (2019). “Uncertainty measure based on Tsallis entropy in evidence theory.” International Journal of Intelligent Systems, 34(6), 1626-1647. doi: 10.1002/int.22185

Statistical Methods & Hypothesis Testing

Multiple Testing Correction

  • Benjamini, Y., & Hochberg, Y. (1995). “Controlling the false discovery rate: a practical and powerful approach to multiple testing.” Journal of the Royal Statistical Society B, 57(1), 289-300.

  • Holm, S. (1979). “A simple sequentially rejective multiple test procedure.” Scandinavian Journal of Statistics, 6, 65-70.

Permutation & Non-Parametric Methods

  • Ernst, M. D. (2004). “Permutation methods: A basis for exact inference.” Statistical Science, 19(4), 676-685.

  • Meinshausen, N., Maathuis, M. H., & Bühlmann, P. (2012). “Asymptotic optimality of the Westfall-Young permutation procedure for multiple testing under dependence.” The Annals of Statistics, 39(6), 3369-3391. doi: 10.1214/11-AOS946

  • Saulsbury, J. G. (2020). “Permutation tests for comparative data.” bioRxiv. doi: 10.1101/2020.10.24.325472

  • Elkin, L. A., & Kay, M. (2023). “An aligned rank transform procedure for multifactor contrast tests.” Journal of Statistical Software (forthcoming).

Effect Size & Interpretation

  • Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.

  • Kraemer, H. C., & Kupfer, D. J. (2005). “Size of treatment effects and their importance to clinical research and practice.” Biological Psychiatry, 59(11), 990-996. doi: 10.1016/j.biopsych.2005.09.014

  • Cliff, N. D. (1993). Dominance statistics: Ordinal analyses for ordinal data. JASS Monograph Series.

  • Kerby, D. S. (2014). “The simple difference formula: An approach to teaching nonparametric correlation.” Comprehensive Psychology, 3, 11.IT.3.1.

Linear & Generalized Additive Models

Linear Models & Mixed Effects

  • Hoff, P. D. (2023). Classical theory of linear statistical models (2nd ed.). Springer.

  • Demidenko, E. (2013). Mixed models: Theory and applications with R (2nd ed.). Wiley Series in Probability and Statistics.

Generalized Additive Models

  • Chapman, P. (2017). Generalized additive models: An introduction with R (4th ed.). CRC Press.

  • Goude, Y. (2024). “Forecasting at EDF: Generalized additive models for time series.” EDF R&D, EDF Lab Saclay.

  • Correia, H. E., & Abebe, A. (2021). “Regularised rank quasi-likelihood estimation for generalised additive models.” Journal of Nonparametric Statistics, 33(1), 101-117. doi: 10.1080/10485252.2021.1921176

Generalized Estimating Equations

  • Liang, K.-Y., & Zeger, S. L. (1986). “Longitudinal data analysis using generalized linear models.” Biometrika, 73(1), 13-22.

  • Hardin, J. W., & Hilbe, J. M. (2013). “Generalized estimating equations.” Encyclopedia of Biostatistics, 4, 2057-2066.

  • Pan, W. (2001). “Akaike’s information criterion in generalized estimating equations.” Biometrics, 57, 120-125.

Correlated & Longitudinal Data

  • Song, P. X. (2007). Correlated data analysis: Modeling, analytics, and applications. Springer Series in Statistics.

Bootstrap & Resampling Methods

  • Efron, B. (2010). Large-scale inference: Empirical Bayes methods for estimation, testing, and prediction. Cambridge University Press.

  • Efron, B., & Tibshirani, R. J. (1993). An introduction to the bootstrap. Chapman and Hall.

  • Jordá Muñoz, R. (2018). Métodos de remuestreo: Jackknife y Bootstrap. Master’s thesis, Universidad de Murcia, Facultad de Matemáticas.

Bayesian Methods

  • Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis (3rd ed.). Chapman and Hall/CRC.

  • Erhard, F., Hense, B., Jafari, M., Siebourg-Polster, J., Dölken, L., & Zimmer, R. (2018). “Improved Ribo-seq puromycin target reliability using Bayesian nonparametrics.” Bioinformatics, 34(12), 2096-2102.

Time Series Analysis

  • Chakraborty, T. (2019). Introductory time series analysis. Indian Statistical Institute, Kolkata.

  • Hyndman, R. J., & Athanasopoulos, G. (2018). Forecasting: Principles and practice (2nd ed.). Retrieved from https://otexts.com/fpp2/

  • Jose, J., & Lal, P. S. (2013). “Application of ARIMA(1,1,0) model for predicting time delay of search engine crawlers.” Informatica Economică, 17(4), 26-39. doi: 10.12948/issn14531305/17.4.2013.03

Transcriptomics & Gene Expression Applications

Single-Cell & Isoform Analysis

  • Cao, J., Packer, J. S., Ramani, V., Cusanovich, D. A., Huynh, C., Daza, R., …, Shendure, J. (2017). “Comprehensive single-cell transcriptional profiling of a multicellular organism.” Science, 357, 661-667. doi: 10.1126/science.aam8940

  • Gandrillon, O., Gaillard, M., Espinasse, T., Garnier, N. B., Dussiau, C., Kosmiker, O., & Sujobert, P. (2021). “Entropy as a measure of variability and stemness in single-cell transcriptomics.” Entropy, 21(5), 450.

  • Seweryn, M. T., Pietrzak, M., & Ma, Q. (2020). “Application of information theoretical approaches to assess diversity and similarity in single-cell transcriptomics.” Computational and Structural Biotechnology Journal, 18, 1830-1837. doi: 10.1016/j.csbj.2020.05.006

Information Theory in Genomics

  • Golomb, R., Yoles, M., Fishilevich, S., Cohen, B., Savariego Peled, S., Dahary, D., Gokhman, D., & Pilpel, Y. (2026). “An information content principle explains regulatory patterns of gene expression across human tissues.” bioRxiv. doi: 10.64898/2026.02.19.706555

  • Chanda, P., Costa, E., Hu, J., Sukumar, S., Van Hemert, J., & Walia, R. (2020). “Information theory in computational biology: Where we stand today.” Entropy, 22(6), 627. doi: 10.3390/e22060627

  • Adami, C. (2004). “Information theory in molecular biology.” Physics of Life Reviews, 1(1), 3-22. doi: 10.1016/j.plrev.2004.01.002

  • Hinostroza Fuentes, V. G., Toledo Tan, M. J., Kapetanaki, M., Rashidi, P., Huang, K., & Benos, P. V. (2026). “Information-theoretic methods in spatial transcriptomics.” TechRxiv. doi: 10.36227/techrxiv.177155947

  • Bartal, A., & Jagodnik, K. M. (2022). “Progress in and opportunities for applying information theory to computational biology and bioinformatics.” Entropy, 24(7), 925. doi: 10.3390/e24070925

Computational Approaches

  • Ramírez-Reyes, A., Hernández-Montoya, A. R., Herrera-Corral, G., & Domínguez-Jiménez, I. (2016). “Determining the entropic index q of Tsallis entropy in images through redundancy.” Entropy, 18(8), 299. doi: 10.3390/e18080299

  • Ré, M. A., & Azad, R. K. (2014). “Generalization of entropy based divergence measures for symbolic sequence analysis.” PLoS ONE, 9(4), e93532. doi: 10.1371/journal.pone.0093532

Cancer & Biological Systems

  • Tarabichi, M., Antoniou, A., Saiselet, M., Pita, J. M., Andry, G., Dumont, J. E., Detours, V., & Maenhaut, C. (2013). “Systems biology of cancer: entropy, disorder, and selection-driven evolution to independence, invasion and ‘swarm intelligence’.” Cancer Metastasis Reviews, 32, 403-421. doi: 10.1007/s10555-013-9431-y

  • Nijman, S. M. B. (2020). “Perturbation-driven entropy as a source of cancer cell heterogeneity.” Trends in Cancer, 6(6), 454-462. doi: 10.1016/j.trecan.2020.02.016

Complexity & Entropy in Physics

  • Shiner, J. S., Davison, M., & Landsberg, P. T. (2007). “Simple measures of complexity.” Physica A, 386, 101-118. doi: 10.1016/j.physa.2007.05.065

  • Shiner, J. S., & others. (2002). Entropy and entropy generation: Fundamentals and applications. Kluwer Academic Publishers.

Machine Learning & Control

  • Wang, Z., So, O., Gibson, J., Vlahov, B., Gandhi, M. S., Liu, G.-H., & Theodorou, E. A. (2021). “Variational inference model predictive control using Tsallis divergence.” arXiv preprint arXiv:2104.00241. doi: 10.48550/arXiv.2104.00241

  • Chernyshov, K. (2009). “Tsallis divergence of order 1/2 in system identification related problems.” Technical report, V. A. Trapeznikov Institute of Control Sciences, Moscow, Russia.

Validation & Quality Control

  • Tian, L., Dong, X., Sotero, S., Lucks, J. B., & Bustamante, C. D. (2019). “Benchmarking null models of transcription.” Genome Biology, 20, 104.

Documentation & Best Practices

  • Xie, Y., Allaire, J. J., & Grolemund, G. (2021). R markdown: The definitive guide (2nd ed.). CRC Press/Routledge.

  • Zhu, H. (2023). “Create awesome HTML table with kableExtra.” CRAN. Retrieved from https://haozhu233.github.io/kableExtra/

How to Cite TSENAT 

@Manual{TSENAT2026,
  title = {TSENAT: Tsallis Entropy Analysis Toolbox},
  author = {Cristobal Gallardo},
  year = {2026},
  note = {R package version 0.99.0},
  url = {https://github.com/gallardoalba/TSENAT}
}

Or in text: Gallardo, C. (2026). TSENAT: Tsallis Entropy Analysis Toolbox. R package version 0.99.0. https://github.com/gallardoalba/TSENAT