**Developed as part of the COSMOS project:**

http://www.fi.isc.cnr.it/users/thomas.kreuz/Source-Code/cSPIKE.html References common for cSPIKE, SPIKY (see below) and PySpike (see below): [1] Kreuz T, Haas JS, Morelli A, Abarbanel HDI, Politi A: [2] Kreuz T, Chicharro D, Houghton C, Andrzejak RG, Mormann F: [3] Kreuz T, Mulansky M, Bozanic N: [4] Satuvuori E, Mulansky M, Bozanic N, Malvestio I, Zeldenrust F, Lenk K, Kreuz T: [5] Kreuz T, Satuvuori E, Pofahl M, Mulansky M: cSPIKE was developed by COSMOS ESR Eero Satuvuori (Project 9). |

We provide the Matlab source code to calculate the measure L first introduced in [1] with the improvements introduced in [2]. The nonlinear interdependence measure L allows for nonlinear coupling detection between two point processes. In particular, the nonlinear interdependence measure L is suited to be applied to spike trains from neurons. The approach is modular, for example different spike train distances [3] can be used to assess similarity. This modularity allows one to test for different manifestations of the coupling such as signatures in the event rate or event timing. For a detailed description of the source code see the document [1] Andrzejak RG, Kreuz T: “Characterizing unidirectional couplings between point processes and flows.” EPL, 96 (2011) 50012. [2] Malvestio I, Kreuz T, Andrzejak RG: “Robustness and versatility of a nonlinear interdependence method for directional coupling detection from spike trains.” Physical Review E, 96 (2017) 022203. [3] We use source code from cSPIKE (see above). This code was developed by COSMOS ESR Irene Malvestio (Project 10). |

Two libraries, both written in Rust. The first is for solving ODEs, the second is for performing Gram-Schmidt Orthonormalization: gram_schmidt: Gram-Schmidt Orthonormalization These libraries were developed by COSMOS ESR Janis Goldschmidt (Project 1). |

Name: Explosive Immunization.Author of the code: COSMOS ESR Pau ClusellaAuthors of the algorithm: Pau Clusella, Peter Grassberger, Francisco Pérez-Reche, Antonio PolitiShort description: A C-code performing the Explosive Immunization algorithm for fast network dismantling. Based on the concept of explosive percolation, the algorithm properly identifies the nodes whose removal minimizes the size of the largest component of a given network, thus preventing the spreading of epidemic processes. The method uses two different scores to quantify the blocking ability of each node. The first is used whenever the number of removed nodes is large enough to prevent the existence of a giant component, whereas the second is used when a giant component is unavoidable. For more information check the original paper [1].Download page: https://github.com/pclus/explosive-immunization[1] Clusella P., Grassberger P., Perez-Reche, F. J. and Politi A. “Immunization and targeted destruction of networks using explosive percolation”, Phys. Rev. Lett. 117, 208301 (2016) |

Features: https://github.com/maximelucas/AMCOS_booklet These LaTeX templates were developed by COSMOS ESRs Pau Clusella (Project 3) and Maxime Lucas (Project 6). |

**Developed by COSMOS groups related to the project:**

For a given dataset SPIKY calculates the measures of choice and allows the user to switch between different visualizations such as dissimilarity profiles, pairwise dissimilarity matrices, or hierarchical cluster trees. SPIKY also includes a spike train generator, an event detector (for continuous data) and complementary programs for the analysis of a large number of datasets and for evaluating the statistical significance of results. http://www.fi.isc.cnr.it/users/thomas.kreuz/Source-Code/SPIKY.html Links to the SPIKY Facebook group and SPIKY YouTube channel can be found here: Kreuz T, Mulansky M, Bozanic N: SPIKY was developed by Nebojsa Bozanic and COSMOS PI Thomas Kreuz. |

https://github.com/mariomulansky/PySpike Documentation for PySpike can be found here: http://mariomulansky.github.io/PySpike/ Mulansky M, Kreuz T: PySpike was developed by Mario Mulansky and COSMOS PI Thomas Kreuz. |

The Data Analysis with Models Of Coupled Oscillators (DAMOCO) toolbox is a collection of Matlab functions for multivariate data analysis, based on the coupled oscillators approach. It provides functions for computation of protophases (initial phase estimates) from time series via the Hilbert Transform, marker events, or via length of the trajectory in the state space. It allows a researcher to transform protophases into true phases and infer equations of phase dynamics of coupled oscillators. With DAMOCO you can easily compute synchronization and directionality indices as well as reveal a coupling structure of a network by means of pairwise or triplet analysis.http://www.stat.physik.uni-potsdam.de/~mros/damoco2.html DAMACO was developed by Björn Kralemann and COSMOS PIs Michael Rosenblum and Arkady Pikovsky. |

Detrended Fluctuation Analysis (DFA) is a classical approach to analyze long-range temporal and spatial correlations. This Matlab implementation provides an algorithm not only to quantify power-law scaling but first to test it against alternatives via (Bayesian) model comparison.Like in conventional DFA, after removing (linear or nonlinear) trends of a signal, mean squared fluctuations in consecutive intervals are determined. In contrast to DFA all values per interval are used to approximate the distribution of these mean squared fluctuations. This allows for estimating the corresponding log-likelihood as a function of interval size without presuming the fluctuations to be normally distributed. https://github.com/marlow17/FluctuationAnalysis.git Ton R, Daffertshofer A: Model selection for identifying power-law scaling. Neuroimage 136:215-26, 2016, doi:10.1016/j.neuroimage.2016.01.008 ‘Fluctuation Analysis’ was developed by COSMOS PI Andreas Daffertshofer. |

Other source codes from the Nonlinear Time Series Analysis Group at the Universitat Pompeu Fabra: These source codes were developed by COSMOS PI Ralph Andrzejak. |