Optimal Markov Approximations and Generalized Embeddings

Based on information theory, we present a method to determine an optimal Markov approximation for modelling and prediction from time series data. The method finds a balance between minimal modelling errors by taking as much as possible memory into account and minimal statistical errors by working in embedding spaces of rather small dimension. A key ingredient is an estimate of the statistical error of entropy estimates. The method is illustrated with several examples and the consequences for prediction are evaluated by means of the root mean squard prediction error for point prediction.Comment: 12 pages, 6 figure

Precursors of extreme increments

We investigate precursors and predictability of extreme increments in a time series. The events we are focusing on consist in large increments within successive time steps. We are especially interested in understanding how the quality of the predictions depends on the strategy to choose precursors, on the size of the event and on the correlation strength. We study the prediction of extreme increments analytically in an AR(1) process, and numerically in wind speed recordings and long-range correlated ARMA data. We evaluate the success of predictions via receiver operator characteristics (ROC-curves). Furthermore, we observe an increase of the quality of predictions with increasing event size and with decreasing correlation in all examples. Both effects can be understood by using the likelihood ratio as a summary index for smooth ROC-curves

Elephant – Open-Source Tool for the Analysis of Electrophysiological Data Sets

The need for reproducible research has become a topic of intense discussion in the neurosciences. Reproducibility is based on building well-defined workflows leading to documented, traceable analysis steps. In recent years software tools (e.g., Neurotools [1], spykeutils [2], OpenElectrophy [3]) have been developed to analyze electrophysiological data. However, many tools tend to specialize in particular types of analysis and do not use a common data model, forcing the user to rely on multiple tools during an analysis. Often the code base of such tools is not written in a modular way, which complicates the combination and comparison of different analysis methods.Here we introduce the Electrophysiology Analysis Toolkit (Elephant) as a community-centered initiative (http://neuralensemble.org/elephant/). Elephant is an easy-to-use, open source Python toolkit, that offers a broad range of functions for analyzing multi-scale data of brain dynamics from experiments and brain simulations. The focus is the analysis of electrical activity, ranging from single unit or massively parallel spike train data to population signals such as the local field potentials. The scope of the library covers analysis methods for time series data (e.g., signal processing, spectral analysis), spike trains (e.g., spike train correlation, spike pattern analysis) and methods for relating both signal types (e.g., spike-triggered averaging). In the context of hypothesis testing, utility modules for the generation of realizations of stochastic processes and of surrogate signals are implemented.We chose to use Neo [4] as the underlying data model. This guarantees compatibility within the toolkit, but also provides access to various file I/O modules to access data in both open and proprietary formats. We demonstrate the usage of Elephant in the form of use cases, and outline how to parallelize analyses using the toolkit. In particular, we illustrate the use of Elephant and the task-system on the Unified Portal (UP) [5] of the Human Brain Project which will be the central platform for collaboration by managing complex analysis workflows in a provenance-tracked fashion. Using the web interface of the UP, neuroscientists can launch either generic analysis scripts made available to the community to analyze their data, or alternatively upload and run custom-tailored analysis programs based on Neo and Elephant. The collaborative nature of the portal will enable scientists to easily share and reproduce an analysis inside or even outside their collaborative groups on the UP. Elephant is released on the python package index PyPI [6], and documentation is available at [7]. Please feel free to contribute your analysis tools into Elephant![1] http://neuralensemble.org/NeuroTools/[2] http://spykeutils.readthedocs.org/en/0.4.1/[3] http://neuralensemble.org/OpenElectrophy/[4] Garcia et al. (2014) Front. Neuroinform 8:10, doi:10.3389/fninf.2014.00010[5] https://developer.humanbrainproject.eu/docs/Unified%20Portal/latest/[6] https://pypi.python.org/pypi/elephant[7] http://elephant.readthedocs.org/en/latest/index.ht

Elephant – Open-Source Tool for the Analysis of Electrophysiological Data Sets

The need for reproducible research has become a topic of intense discussion in theneurosciences. Reproducibility is based on building workflows and traceable analysissteps. In recent years software tools (e.g., Neurotools [1], spykeutils [2], OpenElectrophy[3]) have been developed to analyze electrophysiological data. However, many toolstend to specialize in particular types of analysis and do not use a common data model,forcing the user to rely on multiple tools during an analysis. Often the code base ofsuch tools is not written in a modular way, which complicates the combination andcomparison of different analysis methods.Here we introduce the Electrophysiology Analysis Toolkit (Elephant) as a community-centered initiative (http://neuralensemble.org/elephant/). Elephant is an easy-to-use,open-source Python library, that offers a broad range of functions for analyzing multi-scale data of brain dynamics from experiments and brain simulations. The focus is theanalysis of electrical activity, such as single unit or massively parallel spike train data andlocal field potentials (LFP). The scope of the library covers signal-based analysis (e.g.,signal processing, spectral analysis), spike-based analysis (e.g., spike train correlation,spike pattern analysis) and methods combining both signal types (e.g., spike-triggeredaveraging). In the context of hypothesis testing, utility modules for the generation ofrealizations of stochastic processes and of surrogate signals are implemented.We chose to use Neo [4] as the underlying data model. This guarantees compatibilitywithin the toolkit, but also provides access to various file I/O modules to access data inboth open and proprietary formats. We demonstrate the usage of Elephant in the formof use cases, and outline how to parallelize analyses within the library. In particular, weillustrate the use of Elephant within the Human Brain Project framework.References1 http://neuralensemble.org/NeuroTools/2 http://spykeutils.readthedocs.org/en/0.4.1/3 http://neuralensemble.org/OpenElectrophy/4 Garcia et al. (2014) Front. Neuroinform 8:10 doi:10.3389/fninf.2014.0001