In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set. This exhibition of similar patterns at increasingly smaller scales is called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, the shape is called affine self-similar. Fractal geometry lies within the mathematical branch of measure theory.
A complex system is a system composed of many components which may interact with each other. Examples of complex systems are Earth's global climate, organisms, the human brain, infrastructure such as power grid, transportation or communication systems, complex software and electronic systems, social and economic organizations, an ecosystem, a living cell, and, ultimately, for some authors, the entire universe.
In mathematics, a fractal dimension is a term invoked in the science of geometry to provide a rational statistical index of complexity detail in a pattern. A fractal pattern changes with the scale at which it is measured. It is also a measure of the space-filling capacity of a pattern, and it tells how a fractal scales differently, in a fractal (non-integer) dimension.
A dopamine antagonist, also known as an anti-dopaminergic and a dopamine receptor antagonist (DRA), is a type of drug which blocks dopamine receptors by receptor antagonism. Most antipsychotics are dopamine antagonists, and as such they have found use in treating schizophrenia, bipolar disorder, and stimulant psychosis. Several other dopamine antagonists are antiemetics used in the treatment of nausea and vomiting.
Heart rate variability (HRV) is the physiological phenomenon of variation in the time interval between heartbeats. It is measured by the variation in the beat-to-beat interval.
Recurrence quantification analysis (RQA) is a method of nonlinear data analysis for the investigation of dynamical systems. It quantifies the number and duration of recurrences of a dynamical system presented by its phase space trajectory.
Research concerning the relationship between the thermodynamic quantity entropy and both the origin and evolution of life began around the turn of the 20th century. In 1910 American historian Henry Adams printed and distributed to university libraries and history professors the small volume A Letter to American Teachers of History proposing a theory of history based on the second law of thermodynamics and on the principle of entropy.
EEGLAB is a MATLAB toolbox distributed under the free BSD license for processing data from electroencephalography (EEG), magnetoencephalography (MEG), and other electrophysiological signals. Along with all the basic processing tools, EEGLAB implements independent component analysis (ICA), time/frequency analysis, artifact rejection, and several modes of data visualization. EEGLAB allows users to import their electrophysiological data in about 20 binary file formats, preprocess the data, visualize activity in single trials, and perform ICA. Artifactual ICA components may be subtracted from the data. Alternatively, ICA components representing brain activity may be further processed and analyzed. EEGLAB also allows users to group data from several subjects, and to cluster their independent components.
Fractal analysis is assessing fractal characteristics of data. It consists of several methods to assign a fractal dimension and other fractal characteristics to a dataset which may be a theoretical dataset, or a pattern or signal extracted from phenomena including topography, natural geometric objects, ecology and aquatic sciences, sound, market fluctuations, heart rates, frequency domain in electroencephalography signals, digital images, molecular motion, and data science. Fractal analysis is now widely used in all areas of science. An important limitation of fractal analysis is that arriving at an empirically determined fractal dimension does not necessarily prove that a pattern is fractal; rather, other essential characteristics have to be considered. Fractal analysis is valuable in expanding our knowledge of the structure and function of various systems, and as a potential tool to mathematically assess novel areas of study. Fractal calculus was formulated which is a generalization of ordinary calculus.
Marc Jeannerod was a neurologist, a neurophysiologist and an internationally recognized expert in cognitive neuroscience and experimental psychology. His research focuses on the cognitive and neurophysiological mechanisms underpinning motor control, motor cognition, the sense of agency, and more recently language and social cognition. Jeannerod's work bridges with elegance and rigor various levels of analysis, ranging from neuroscience to philosophy of mind, with clear implications for the understanding of a number of psychiatric and neurological disorders, especially schizophrenia.
Roxindole (EMD-49,980) is a dopaminergic and serotonergic drug which was originally developed by Merck KGaA for the treatment of schizophrenia. In clinical trials its antipsychotic efficacy was only modest but it was unexpectedly found to produce potent and rapid antidepressant and anxiolytic effects. As a result, roxindole was further researched for the treatment of depression instead. It has also been investigated as a therapy for Parkinson's disease and prolactinoma.
EEG microstates are transient, patterned, quasi-stable states or patterns of an electroencephalogram. These tend to last anywhere from milliseconds to seconds and are hypothesized to be the most basic instantiations of human neurological tasks, and are thus nicknamed "the atoms of thought". Microstate estimation and analysis was originally done using alpha band activity, though broader bandwidth EEG bands are now typically used. The quasi-stability of microstates means that the "global [EEG] topography is fixed, but strength might vary and polarity invert."
Resting state fMRI is a method of functional magnetic resonance imaging (fMRI) that is used in brain mapping to evaluate regional interactions that occur in a resting or task-negative state, when an explicit task is not being performed. A number of resting-state brain networks have been identified, one of which is the default mode network. These brain networks are observed through changes in blood flow in the brain which creates what is referred to as a blood-oxygen-level dependent (BOLD) signal that can be measured using fMRI.
Transfer entropy is a non-parametric statistic measuring the amount of directed (time-asymmetric) transfer of information between two random processes. Transfer entropy from a process X to another process Y is the amount of uncertainty reduced in future values of Y by knowing the past values of X given past values of Y. More specifically, if and for denote two random processes and the amount of information is measured using Shannon's entropy, the transfer entropy can be written as:
The Neurophysiological Biomarker Toolbox (NBT) is an open source MATLAB toolbox for the computation and integration of neurophysiological biomarkers. The NBT toolbox has so far been used in seven peer-reviewed research articles, and has a broad user base of more than 1000 users. The NBT toolbox provides unique features for analysis of resting-state EEG or MEG recordings. NBT offers a pipeline from data storage to statistics including artifact rejection, signal visualization, biomarker computation, statistical testing, and biomarker databasing. NBT allows for easy implementation of new biomarkers, and incorporates an online wiki that aims at facilitating collaboration among NBT users including extensive help and tutorials. The standardised way of data storage and analysis that NBT proposes allow different research projects to merge, compare, or share their data and biomarker algorithms.
Chung-Kang Peng is the Director of the Center for Dynamical Biomarkers at Beth Israel Deaconess Medical Center / Harvard Medical School (BIDMC/HMS). Under his direction the Center for Dynamical Biomarkers researches fundamental theories and novel computational algorithms for characterizing physiological states in terms of their dynamical properties. He is also currently the K.-T. Li Visiting Chair Professor at National Central University (NCU), Visiting Chair Professor at National Chiao Tung University (NCTU) in Taiwan, and Visiting Professor at China Academy of Chinese Medical Sciences in China. During 2012–2014, he served as the founding Dean of the College of Health Sciences and Technology at NCU in Taiwan.
Ary Louis Goldberger is a physician-educator, whose collaborative research work is at the interface of biomedicine and complexity science. He holds a BA from Harvard College and an MD from Yale Medical School. He did his clinical training in internal medicine and cardiovascular disease at Yale–New Haven Hospital and at the University of California, San Diego, respectively. He currently serves as Professor of Medicine at Harvard Medical School and was one of the Core Founding Faculty (2010-2015) of the Wyss Institute for Biologically Inspired Engineering at Harvard University.
Felix Tretter is an Austrian psychologist and psychiatrist. From 1992 to 2014 he was head of the addiction department of the Isar-Amper-Klinikum München-Ost, formerly known as Bezirkskrankenhaus Haar, Bavaria, Germany. His scientific work has emphasis on modelling of psychophysical scenarios in schizophrenia and addiction research with methods of systems science.
NeuroKit ("nk") is an open source toolbox for physiological signal processing. The most recent version, NeuroKit2, is written in Python and is available from the PyPI package repository. As of June 2022, the software was used in 94 scientific publications. NeuroKit2 is presented as one of the most popular and contributor-friendly open-source software for neurophysiology based on the number of downloads, the number of contributors, and other GitHub metrics.
