Continuous Time Correlation Analysis Techniques For Spike Trains

ABSTRACT: Correlation is the most basic analysis tool for time series. To apply correlation to train of action potentials generated by neurons, the conventional method is to discretize the time. However, time binning is not optimal: time resolution is sacrificed, and it introduces the notorious problem of bin size sensitivity. Since spike trains can be considered as a realization of a point process, the signal has no amplitude and all information is embedded in the times of occurrence. Instead of time binning, we propose a set of methods based on kernel smoothing to analyze the correlations. Smoothing is done in continuous time so we do not lose the exact time of spikes while enabling interaction between spikes at a distance. We present three techniques derived from correlation: (1) spike train similarity measure, (2) synchrony detection mechanism, and (3) continuous cross correlogram.

Solid and transparent data analysis is the most important basis for reliable interpretation of experiments. The technique of parallel spike train recordings using multi-electrode arrangements has been available for many decades now, but only recently gained wide popularity among electro physiologists. Many traditional analysis methods are based on firing rates obtained by trial-averaging, and some of the assumptions for such procedures to work can be ignored without serious consequences. The situation is different for correlation analysis, the result of which may be considerably distorted if certain critical assumptions are violated. The focus of this book is on concepts and methods of correlation analysis (synchrony, patterns, rate covariance), combined with a solid introduction into approaches for single spike trains, which represent the basis of correlations analysis. The book also emphasizes pitfalls and potential wrong interpretations of data due to violations of critical assumptions.

Modern recording techniques such as multi-electrode arrays and 2-photon imaging are capable of simultaneously monitoring the activity of large neuronal ensembles at single cell resolution. This makes it possible to study the dynamics of neural populations of considerable size, and to gain insights into their computations and functional organization. The key challenge with multi-electrode recordings is their high-dimensional nature. Understanding this kind of data requires powerful statistical techniques for capturing the structure of the neural population responses and their relation with external stimuli or behavioral observations. Contributions to this Research Topic should advance statistical modeling of neural populations. Questions of particular interest include: 1. What classes of statistical methods are most useful for modeling population activity? 2. What are the main limitations of current approaches, and what can be done to overcome them? 3. How can statistical methods be used to empirically test existing models of (probabilistic) population coding? 4. What role can statistical methods play in formulating novel hypotheses about the principles of information processing in neural populations? This Research Topic is connected to a one day workshop at the Computational Neuroscience Meeting 2009 in Berlin (http://www.cnsorg.org/2009/workshops.shtml and http://www.kyb.tuebingen.mpg.de/bethge/workshops/cns2009/)

This solid introduction uses the principles of physics and the tools of mathematics to approach fundamental questions of neuroscience.

Signal Processing for Neuroscientists introduces analysis techniques primarily aimed at neuroscientists and biomedical engineering students with a reasonable but modest background in mathematics, physics, and computer programming. The focus of this text is on what can be considered the ‘golden trio’ in the signal processing field: averaging, Fourier analysis, and filtering. Techniques such as convolution, correlation, coherence, and wavelet analysis are considered in the context of time and frequency domain analysis. The whole spectrum of signal analysis is covered, ranging from data acquisition to data processing; and from the mathematical background of the analysis to the practical application of processing algorithms. Overall, the approach to the mathematics is informal with a focus on basic understanding of the methods and their interrelationships rather than detailed proofs or derivations. One of the principle goals is to provide the reader with the background required to understand the principles of commercially available analyses software, and to allow him/her to construct his/her own analysis tools in an environment such as MATLAB®. Multiple color illustrations are integrated in the text Includes an introduction to biomedical signals, noise characteristics, and recording techniques Basics and background for more advanced topics can be found in extensive notes and appendices A Companion Website hosts the MATLAB scripts and several data files: http://www.elsevierdirect.com/companion.jsp?ISBN=9780123708670

This is a uniquely comprehensive reference that summarizes the state of the art of signal processing theory and techniques for solving emerging problems in neuroscience, and which clearly presents new theory, algorithms, software and hardware tools that are specifically tailored to the nature of the neurobiological environment. It gives a broad overview of the basic principles, theories and methods in statistical signal processing for basic and applied neuroscience problems.Written by experts in the field, the book is an ideal reference for researchers working in the field of neural engineering, neural interface, computational neuroscience, neuroinformatics, neuropsychology and neural physiology. By giving a broad overview of the basic principles, theories and methods, it is also an ideal introduction to statistical signal processing in neuroscience. A comprehensive overview of the specific problems in neuroscience that require application of existing and development of new theory, techniques, and technology by the signal processing community Contains state-of-the-art signal processing, information theory, and machine learning algorithms and techniques for neuroscience research Presents quantitative and information-driven science that has been, or can be, applied to basic and translational neuroscience problems

Leon Cooper's somewhat peripatetic career has resulted in work in quantum field theory, superconductivity, the quantum theory of measurement as well as the mechanisms that underly learning and memory. He has written numerous essays on a variety of subjects as well as a highly regarded introduction to the ideas and methods of physics for non-physicists. Among the many accolades, he has received (some deserved) one he likes specially is the comment of an anonymous reviewer who characterized him as ?a nonsense physicist?.This compilation of papers presents the evolution of his thinking on mechanisms of learning, memory storage and higher brain function. The first half proceeds from early models of memory and synaptic plasticity to a concrete theory that has been put into detailed correspondence with experiment and leads to the very current exploration of the molecular basis for learning and memory storage. The second half outlines his efforts to investigate the properties of neural network systems and to explore to what extent they can be applied to real world problems.In all this collection, hopefully, provides a coherent, no-nonsense, account of a line of research that leads to present investigations into the biological basis for learning and memory storage and the information processing and classification properties of neural systems.

Intended for neurobiologists with an interest in mathematical analysis of neural data as well as the growing number of physicists and mathematicians interested in information processing by "real" nervous systems, Spikes provides a self-contained review of relevant concepts in information theory and statistical decision theory.

A practical guide to neural data analysis techniques that presents sample datasets and hands-on methods for analyzing the data. As neural data becomes increasingly complex, neuroscientists now require skills in computer programming, statistics, and data analysis. This book teaches practical neural data analysis techniques by presenting example datasets and developing techniques and tools for analyzing them. Each chapter begins with a specific example of neural data, which motivates mathematical and statistical analysis methods that are then applied to the data. This practical, hands-on approach is unique among data analysis textbooks and guides, and equips the reader with the tools necessary for real-world neural data analysis. The book begins with an introduction to MATLAB, the most common programming platform in neuroscience, which is used in the book. (Readers familiar with MATLAB can skip this chapter and might decide to focus on data type or method type.) The book goes on to cover neural field data and spike train data, spectral analysis, generalized linear models, coherence, and cross-frequency coupling. Each chapter offers a stand-alone case study that can be used separately as part of a targeted investigation. The book includes some mathematical discussion but does not focus on mathematical or statistical theory, emphasizing the practical instead. References are included for readers who want to explore the theoretical more deeply. The data and accompanying MATLAB code are freely available on the authors' website. The book can be used for upper-level undergraduate or graduate courses or as a professional reference. A version of this textbook with all of the examples in Python is available on the MIT Press website.

Great interest is now being shown in computational and mathematical neuroscience, fuelled in part by the rise in computing power, the ability to record large amounts of neurophysiological data, and advances in stochastic analysis. These techniques are leading to biophysically more realistic models. It has also become clear that both neuroscientists and mathematicians profit from collaborations in this exciting research area.Graduates and researchers in computational neuroscience and stochastic systems, and neuroscientists seeking to learn more about recent advances in the modelling and analysis of noisy neural systems, will benefit from this comprehensive overview. The series of self-contained chapters, each written by experts in their field, covers key topics such as: Markov chain models for ion channel release; stochastically forced single neurons and populations of neurons; statistical methods for parameterestimation; and the numerical approximation of these stochastic models.Each chapter gives an overview of a particular topic, including its history, important results in the area, and future challenges, and the text comes complete with a jargon-busting index of acronyms to allow readers to familiarize themselves with the language used.