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Bicoherence
In mathematics and statistical analysis, bicoherence (also known as bispectral coherency) is a squared normalised version of the bispectrum. The bicoherence takes values bounded between 0 and 1, which make it a convenient measure for quantifying the extent of phase coupling in a signal. The prefix ''bi-'' in ''bispectrum'' and ''bicoherence'' refers not to two time series ''x''''t'', ''y''''t'' but rather to two frequencies of a single signal. The ''bispectrum'' is a statistic used to search for nonlinear interactions. The Fourier transform of the second-order cumulant, i.e., the autocorrelation function, is the traditional power spectrum. The Fourier transform of C3(t1,t2) (third-order cumulant) is called bispectrum or bispectral density. They fall in the category of ''Higher Order Spectra'', or ''Polyspectra'' and provide supplementary information to the power spectrum. The third order polyspectrum (bispectrum) is the easiest to compute, and hence the most popular. The differen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coherence (signal Processing)
In signal processing, the coherence is a statistic that can be used to examine the relation between two signals or data sets. It is commonly used to estimate the power transfer between input and output of a linear system. If the signals are ergodic, and the system function is linear, it can be used to estimate the causality between the input and output. Definition and formulation The coherence (sometimes called magnitude-squared coherence) between two signals x(t) and y(t) is a real-valued function that is defined as: ::C_(f) = \frac where Gxy(f) is the Cross-spectral density between x and y, and Gxx(f) and Gyy(f) the auto spectral density of x and y respectively. The magnitude of the spectral density is denoted as , G, . Given the restrictions noted above (ergodicity, linearity) the coherence function estimates the extent to which y(t) may be predicted from x(t) by an optimum linear least squares function. Values of coherence will always satisfy 0\le C_(f)\le 1. For an ''ideal' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electroencephalography
Electroencephalography (EEG) is a method to record an electrogram of the spontaneous electrical activity of the brain. The biosignals detected by EEG have been shown to represent the postsynaptic potentials of pyramidal neurons in the neocortex and allocortex. It is typically non-invasive, with the EEG electrodes placed along the scalp (commonly called "scalp EEG") using the International 10-20 system, or variations of it. Electrocorticography, involving surgical placement of electrodes, is sometimes called " intracranial EEG". Clinical interpretation of EEG recordings is most often performed by visual inspection of the tracing or quantitative EEG analysis. Voltage fluctuations measured by the EEG bioamplifier and electrodes allow the evaluation of normal brain activity. As the electrical activity monitored by EEG originates in neurons in the underlying brain tissue, the recordings made by the electrodes on the surface of the scalp vary in accordance with their orientation and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates Function (mathematics), functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, applied mathematics; as well as in physics, including the branches of hydrodynamics, thermodynamics, and particularly quantum mechanics. By extension, use of complex analysis also has applications in engineering fields such as nuclear engineering, nuclear, aerospace engineering, aerospace, mechanical engineering, mechanical and electrical engineering. As a differentiable function of a complex variable is equal to its Taylor series (that is, it is Analyticity of holomorphic functions, analytic), complex analysis is particularly concerned with analytic functions of a complex variable (that is, holomorphic functions). History Complex analysis is one of the classical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monthly Notices Of The Royal Astronomical Society
''Monthly Notices of the Royal Astronomical Society'' (MNRAS) is a peer-reviewed scientific journal covering research in astronomy and astrophysics. It has been in continuous existence since 1827 and publishes letters and papers reporting original research in relevant fields. Despite the name, the journal is no longer monthly, nor does it carry the notices of the Royal Astronomical Society. History The first issue of MNRAS was published on 9 February 1827 as ''Monthly Notices of the Astronomical Society of London'' and it has been in continuous publication ever since. It took its current name from the second volume, after the Astronomical Society of London became the Royal Astronomical Society (RAS). Until 1960 it carried the monthly notices of the RAS, at which time these were transferred to the newly established ''Quarterly Journal of the Royal Astronomical Society'' (1960–1996) and then to its successor journal ''Astronomy & Geophysics'' (since 1997). Until 1965, MNRAS ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Seizures
An epileptic seizure, informally known as a seizure, is a period of symptoms due to abnormally excessive or neural oscillation, synchronous neuronal activity in the brain. Outward effects vary from uncontrolled shaking movements involving much of the body with loss of consciousness (tonic-clonic seizure), to shaking movements involving only part of the body with variable levels of consciousness (focal seizure), to a subtle momentary loss of awareness (absence seizure). Most of the time these episodes last less than two minutes and it takes some time to return to normal. Urinary incontinence, Loss of bladder control may occur. Seizures may be provoked and unprovoked. Provoked seizures are due to a temporary event such as low blood sugar, alcohol withdrawal, abusing alcohol together with prescription medication, low blood sodium, fever, brain infection, or concussion. Unprovoked seizures occur without a known or fixable cause such that ongoing seizures are likely. Unprovoked seizur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Awake
Wakefulness is a daily recurring brain state and state of consciousness in which an individual is conscious and engages in coherent cognitive and behavioral responses to the external world. Being awake is the opposite of being asleep, in which most external inputs to the brain are excluded from neural processing. Effects upon the brain The longer the brain has been awake, the greater the synchronous firing rates of cerebral cortex neurons. After sustained periods of sleep, both the speed and synchronicity of the neurons firing are shown to decrease. Another effect of wakefulness is the reduction of glycogen held in the astrocytes, which supply energy to the neurons. Studies have shown that one of sleep's underlying functions is to replenish this glycogen energy source. Maintenance by the brain Wakefulness is produced by a complex interaction between multiple neurotransmitter systems arising in the brainstem and ascending through the midbrain, hypothalamus, thalamus and basa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sleep
Sleep is a sedentary state of mind and body. It is characterized by altered consciousness, relatively inhibited sensory activity, reduced muscle activity and reduced interactions with surroundings. It is distinguished from wakefulness by a decreased ability to react to stimuli, but more reactive than a coma or disorders of consciousness, with sleep displaying different, active brain patterns. Sleep occurs in repeating periods, in which the body alternates between two distinct modes: REM sleep and non-REM sleep. Although REM stands for "rapid eye movement", this mode of sleep has many other aspects, including virtual paralysis of the body. Dreams are a succession of images, ideas, emotions, and sensations that usually occur involuntarily in the mind during certain stages of sleep. During sleep, most of the body's systems are in an anabolic state, helping to restore the immune, nervous, skeletal, and muscular systems; these are vital processes that maintain mood, memory, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Signals (biology)
In biology, cell signaling (cell signalling in British English) or cell communication is the ability of a cell to receive, process, and transmit signals with its environment and with itself. Cell signaling is a fundamental property of all cellular life in prokaryotes and eukaryotes. Signals that originate from outside a cell (or extracellular signals) can be physical agents like mechanical pressure, voltage, temperature, light, or chemical signals (e.g., small molecules, peptides, or gas). Cell signaling can occur over short or long distances, and as a result can be classified as autocrine, juxtacrine, intracrine, paracrine, or endocrine. Signaling molecules can be synthesized from various biosynthetic pathways and released through passive or active transports, or even from cell damage. Receptors play a key role in cell signaling as they are able to detect chemical signals or physical stimuli. Receptors are generally proteins located on the cell surface or within the interior ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravitational Waves
Gravitational waves are waves of the intensity of gravity generated by the accelerated masses of an orbital binary system that Wave propagation, propagate as waves outward from their source at the speed of light. They were first proposed by Oliver Heaviside in 1893 and then later by Henri Poincaré in 1905 as waves similar to Electromagnetic radiation, electromagnetic waves but the gravitational equivalent. Gravitational waves were later #History, predicted in 1916 by Albert Einstein on the basis of his General relativity, general theory of relativity as ripples in spacetime. Later he refused to accept gravitational waves. Gravitational waves transport energy as gravitational radiation, a form of radiant energy similar to electromagnetic radiation. Newton's law of universal gravitation, part of classical mechanics, does not provide for their existence, since that law is predicated on the assumption that Speed of gravity, physical interactions propagate instantaneously (at infinite ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Analysis
Statistical inference is the process of using data analysis to infer properties of an underlying distribution of probability.Upton, G., Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP. . Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population. Inferential statistics can be contrasted with descriptive statistics. Descriptive statistics is solely concerned with properties of the observed data, and it does not rest on the assumption that the data come from a larger population. In machine learning, the term ''inference'' is sometimes used instead to mean "make a prediction, by evaluating an already trained model"; in this context inferring properties of the model is referred to as ''training'' or ''learning'' (rather than ''inference''), and using a model for prediction is referred to as ''inference'' (instead of ''prediction''); ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plasma Physics
Plasma ()πλάσμα , Henry George Liddell, Robert Scott, ''A Greek English Lexicon'', on Perseus is one of the . It contains a significant portion of charged particles – s and/or s. The presence of these charged particles is what primarily sets plasma apart from the other fundamental states of matter. It is the most abundant form of |
