Stochastic Resonance
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Stochastic Resonance
Stochastic resonance (SR) is a phenomenon in which a signal that is normally too weak to be detected by a sensor, can be boosted by adding white noise to the signal, which contains a wide spectrum of frequencies. The frequencies in the white noise corresponding to the original signal's frequencies will resonate with each other, amplifying the original signal while not amplifying the rest of the white noise – thereby increasing the signal-to-noise ratio, which makes the original signal more prominent. Further, the added white noise can be enough to be detectable by the sensor, which can then filter it out to effectively detect the original, previously undetectable signal. This phenomenon of boosting undetectable signals by resonating with added white noise extends to many other systems – whether electromagnetic, physical or biological – and is an active area of research. Stochastic resonance was first proposed by the Italian physicists Roberto Benzi, Alfonso Sutera and Ang ...
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White Noise
In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density. The term is used, with this or similar meanings, in many scientific and technical disciplines, including physics, acoustical engineering, telecommunications, and statistical forecasting. White noise refers to a statistical model for signals and signal sources, rather than to any specific signal. White noise draws its name from white light, although light that appears white generally does not have a flat power spectral density over the visible band. In discrete time, white noise is a discrete signal whose samples are regarded as a sequence of serially uncorrelated random variables with zero mean and finite variance; a single realization of white noise is a random shock. Depending on the context, one may also require that the samples be independent and have identical probability distribution (in other words independent and iden ...
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Signal Processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as audio signal processing, sound, image processing, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, Data storage, digital storage efficiency, correcting distorted signals, subjective video quality and to also detect or pinpoint components of interest in a measured signal. History According to Alan V. Oppenheim and Ronald W. Schafer, the principles of signal processing can be found in the classical numerical analysis techniques of the 17th century. They further state that the digital refinement of these techniques can be found in the digital control systems of the 1940s and 1950s. In 1948, Claude Shannon wrote the influential paper "A Mathematical Theory of Communication" which was published in the Bell System Technical Journal. The paper laid the groundwork for later development of information c ...
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Signal Detection Theory
Detection theory or signal detection theory is a means to measure the ability to differentiate between information-bearing patterns (called stimulus in living organisms, signal in machines) and random patterns that distract from the information (called noise, consisting of background stimuli and random activity of the detection machine and of the nervous system of the operator). In the field of electronics, signal recovery is the separation of such patterns from a disguising background. According to the theory, there are a number of determiners of how a detecting system will detect a signal, and where its threshold levels will be. The theory can explain how changing the threshold will affect the ability to discern, often exposing how adapted the system is to the task, purpose or goal at which it is aimed. When the detecting system is a human being, characteristics such as experience, expectations, physiological state (e.g., fatigue) and other factors can affect the threshold app ...
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Mutual Coherence (linear Algebra)
In linear algebra, the coherence or mutual coherence of a matrix ''A'' is defined as the maximum absolute value of the cross-correlations between the columns of ''A''. Formally, let a_1, \ldots, a_m\in ^d be the columns of the matrix ''A'', which are assumed to be normalized such that a_i^H a_i = 1. The mutual coherence of ''A'' is then defined as :M = \max_ \left, a_i^H a_j \. A lower bound is : M\ge \sqrt A deterministic matrix with the mutual coherence almost meeting the lower bound can be constructed by Weil's theorem. This concept was reintroduced by David Donoho and Michael Elad in the context of sparse representations. A special case of this definition for the two-ortho case appeared earlier in the paper by Donoho and Huo. The mutual coherence has since been used extensively in the field of sparse representations of signals. In particular, it is used as a measure of the ability of suboptimal algorithms such as matching pursuit and basis pursuit to correctly identif ...
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Gaussian Noise
Gaussian noise, named after Carl Friedrich Gauss, is a term from signal processing theory denoting a kind of signal noise that has a probability density function (pdf) equal to that of the normal distribution (which is also known as the Gaussian distribution). In other words, the values that the noise can take are Gaussian-distributed. The probability density function p of a Gaussian random variable z is given by: : p_G(z) = \frac e^ where z represents the grey level, \mu the mean grey value and \sigma its standard deviation. A special case is ''White Gaussian noise'', in which the values at any pair of times are identically distributed and statistically independent (and hence uncorrelated). In communication channel testing and modelling, Gaussian noise is used as additive white noise to generate additive white Gaussian noise. In telecommunications and computer networking, communication channels can be affected by wideband Gaussian noise coming from many natural sources, su ...
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Analog-to-digital Converter
In electronics, an analog-to-digital converter (ADC, A/D, or A-to-D) is a system that converts an analog signal, such as a sound picked up by a microphone or light entering a digital camera, into a digital signal. An ADC may also provide an isolated measurement such as an electronic device that converts an analog input voltage or current to a digital number representing the magnitude of the voltage or current. Typically the digital output is a two's complement binary number that is proportional to the input, but there are other possibilities. There are several ADC architectures. Due to the complexity and the need for precisely matched components, all but the most specialized ADCs are implemented as integrated circuits (ICs). These typically take the form of metal–oxide–semiconductor (MOS) mixed-signal integrated circuit chips that integrate both analog and digital circuits. A digital-to-analog converter (DAC) performs the reverse function; it converts a digital signa ...
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Dither
Dither is an intentionally applied form of image noise, noise used to randomize quantization error, preventing large-scale patterns such as color banding in images. Dither is routinely used in processing of both digital audio and digital video, video data, and is often one of the last stages of Audio mastering, mastering audio to a compact disc, CD. A common use of dither is converting a grayscale image to Binary image, black and white, such that the density of black dots in the new image approximates the average gray level in the original. Etymology The term ''dither'' was published in books on analog computation and hydraulically controlled guns shortly after World War II. Though he did not use the term ''dither'', the concept of dithering to reduce quantization patterns was first applied by Lawrence G. Roberts in his 1961 MIT master's thesis and 1962 article. By 1964 dither was being used in the modern sense described in this article. The technique was in use at least ...
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James Collins (bioengineer)
James J. Collins (born June 26, 1965) is an American bioengineer, and the Termeer Professor of Medical Engineering & Science and Professor of Biological Engineering at MIT. He is one of the founders of the emerging field of synthetic biology, and has made multiple synthetic biology breakthroughs in biotechnology and biomedicine, including paper-based diagnostics for Zika & Ebola and programmable cells that serve as living diagnostics and living therapeutics to detect-and-treat infections, rare genetic metabolic disorders, and inflammatory bowel disease. Collins is also a pioneering researcher in systems biology, having made fundamental discoveries regarding the actions of antibiotics and the emergence of antibiotic resistance. Collins was elected a member of the National Academy of Engineering in 2011 for contributions to synthetic biology and engineered gene networks. Biography Collins received a bachelor's degree in physics (summa cum laude; class valedictorian) from the ...
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Synaptic Noise
Synaptic noise refers to the constant bombardment of synaptic activity in neurons. This occurs in the background of a cell when potentials are produced without the nerve stimulation of an action potential, and are due to the inherently random nature of synapses. These random potentials have similar time courses as excitatory postsynaptic potentials (EPSPs) and inhibitory postsynaptic potentials (IPSPs), yet they lead to variable neuronal responses. The variability is due to differences in the discharge times of action potentials. Causes Many types of noise exist in cells. First, there is intrinsic noise and extrinsic, or synaptic, noise. Within each category there are two further divisions of noise – voltage noise or temporal noise. Intrinsic voltage noise is due to random changes in the membrane potential of a cell, and intrinsic temporal noise is caused by variations in spike generation timing. The following sections give explanations about the causes of synaptic noise. Quanta ...
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Squid Giant Axon
The squid giant axon is the very large (up to 1.5 mm in diameter; typically around 0.5 mm) axon that controls part of the water jet propulsion system in squid. It was first described by L. W. Williams in 1909, but this discovery was forgotten until English zoologist and neurophysiologist J. Z. Young demonstrated the axon's function in the 1930s while working in the Stazione Zoologica in Naples, the Marine Biological Association in Plymouth and the Marine Biological Laboratory in Woods Hole. Squids use this system primarily for making brief but very fast movements through the water. On the underside of the squid's body, between the head and the mantle, is a siphon through which water can be rapidly expelled by the fast contractions of the body wall muscles of the animal. This contraction is initiated by action potentials in the giant axon. Action potentials travel faster in a larger axon than a smaller one, and squid have evolved the giant axon to improve the speed ...
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Purkinje Cells
Purkinje cells, or Purkinje neurons, are a class of GABAergic inhibitory neurons located in the cerebellum. They are named after their discoverer, Czech anatomist Jan Evangelista Purkyně, who characterized the cells in 1839. Structure These cells are some of the largest neurons in the human brain (Betz cells being the largest), with an intricately elaborate dendritic arbor, characterized by a large number of dendritic spines. Purkinje cells are found within the Purkinje layer in the cerebellum. Purkinje cells are aligned like dominos stacked one in front of the other. Their large dendritic arbors form nearly two-dimensional layers through which parallel fibers from the deeper-layers pass. These parallel fibers make relatively weaker excitatory (glutamatergic) synapses to spines in the Purkinje cell dendrite, whereas climbing fibers originating from the inferior olivary nucleus in the medulla provide very powerful excitatory input to the proximal dendrites and cell soma. P ...
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Gamma Wave
A gamma wave or gamma Rhythm is a pattern of neural oscillation in humans with a frequency between 25 and 140 Hz, the 40- Hz point being of particular interest. Gamma rhythms are correlated with large scale brain network activity and cognitive phenomena such as working memory, attention, and perceptual grouping, and can be increased in amplitude via meditation or neurostimulation. Altered gamma activity has been observed in many mood and cognitive disorders such as Alzheimer's disease, epilepsy, and schizophrenia. Discovery Gamma waves can be detected by electroencephalography or magnetoencephalography. One of the earliest reports of gamma wave activity was recorded from the visual cortex of awake monkeys. Subsequently, significant research activity has concentrated on gamma activity in visual cortex. Gamma activity has also been detected and studied across premotor, parietal, temporal, and frontal cortical regions Gamma waves constitute a common class of oscillatory ...
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