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Which reference is appropriate for the scalp ERP and EEG studies? This unsettled problem still inspires unceasing debate. The ideal reference should be the one with zero or constant potential but unfortunately it is well known that no point on the body fulfills this condition. Consequently, more than ten references are used in the present EEG-ERP studies. This diversity seriously undermines the reproducibility and comparability of results across laboratories. A comprehensive review accompanied by a brief communication with rigorous derivations and notable properties (Hu et al. Brain Topogr, 2019 . 10.1007/s10548-019-00706-y) is thus necessary to provide application-oriented principled recommendations. In this paper current popular references are classified into two categories: (1) unipolar references that construct a neutral reference, including both online unipolar references and offline re-references. Examples of unipolar references are the reference electrode standardization technique (REST), average reference (AR), and linked-mastoids/ears reference (LM); (2) non-unipolar references that include the bipolar reference and the Laplacian reference. We show that each reference is derived with a different assumption and serves different aims. We also note from (Hu et al. 2019 ) that there is a general form for the reference problem, the ‘no memory’ property of the unipolar references, and a unified estimator for the potentials at infinity termed as the regularized REST (rREST) which has more advantageous statistical evidence than AR. A thorough discussion of the advantages and limitations of references is provided with recommendations in the hope to clarify the role of each reference in the ERP and EEG practice.

Current high-throughput data acquisition technologies probe dynamical systems with different imaging modalities, generating massive data sets at different spatial and temporal resolutions posing challenging problems in multimodal data fusion. A case in point is the attempt to parse out the brain structures and networks that underpin human cognitive processes by analysis of different neuroimaging modalities (functional MRI, EEG, NIRS etc.). We emphasize that the multimodal, multi-scale nature of neuroimaging data is well reflected by a multi-way (tensor) structure where the underlying processes can be summarized by a relatively small number of components or "atoms". We introduce Markov-Penrose diagrams - an integration of Bayesian DAG and tensor network notation in order to analyze these models. These diagrams not only clarify matrix and tensor EEG and fMRI time/frequency analysis and inverse problems, but also help understand multimodal fusion via Multiway Partial Least Squares and Coupled Matrix-Tensor Factorization. We show here, for the first time, that Granger causal analysis of brain networks is a tensor regression problem, thus allowing the atomic decomposition of brain networks. Analysis of EEG and fMRI recordings shows the potential of the methods and suggests their use in other scientific domains.Comment: 23 pages, 15 figures, submitted to Proceedings of the IEE

This article reviews the contributions of the Cuban Neuroscience Center to the evolution of the statistical parametric mapping (SPM) of quantitative Multimodal Neuroimages (qMN), from its inception to more recent work. Attention is limited to methods that compare individual qMN to normative databases (n/qMN). This evolution is described in three successive stages: (a) the development of one variant of normative topographical quantitative EEG (n/qEEG-top) which carries out statistical comparison of individual EEG spectral topographies with regard to a normative database--as part of the now popular SPM of brain descriptive parameters; (b) the development of n/qEEG tomography (n/qEEG-TOM), which employs brain electrical tomography (BET) to calculate voxelwise SPM maps of source spectral features with respect to a norm; (c) the development of a more general n/qMN by substituting EEG parameters with other neuroimaging descriptive parameters to obtain SPM maps. The study also describes the creation of Cuban normative databases, starting with the Cuban EEG database obtained in the early 90s, and more recently, the Cuban Human Brain Mapping Project (CHBMP). This project has created a 240 subject database of the normal Cuban population, obtained from a population-based random sample, comprising clinical, neuropsychological, EEG, MRI and SPECT data for the same subjects. Examples of clinical studies using qMN are given and, more importantly, receiver operator characteristics (ROC) analyses of the different developments document a sustained effort to assess the clinical usefulness of the techniques.

In many situations, the gene expression signature is a unique marker of the biological state. We study the modification of the gene expression distribution function when the biological state of a system experiences a change. This change may be the result of a selective pressure, as in the Long Term Evolution Experiment with E. Coli populations, or the progression to Alzheimer disease in aged brains, or the progression from a normal tissue to the cancer state. The first two cases seem to belong to a class of transitions, where the initial and final states are relatively close to each other, and the distribution function for the differential expressions is short ranged, with a tail of only a few dozens of strongly varying genes. In the latter case, cancer, the initial and final states are far apart and separated by a low-fitness barrier. The distribution function shows a very heavy tail, with thousands of silenced and over-expressed genes. We characterize the biological states by means of their principal component representations, and the expression distribution functions by their maximal and minimal differential expression values and the exponents of the Pareto laws describing the tails.