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Maximally Informative Dimensions
Maximally informative dimensions is a dimensionality reduction technique used in the statistical analyses of neural responses. Specifically, it is a way of projecting a stimulus onto a low-dimensional subspace so that as much information as possible about the stimulus is preserved in the neural response. It is motivated by the fact that natural stimuli are typically confined by their statistics to a lower-dimensional space than that spanned by white noise but correctly identifying this subspace using traditional techniques is complicated by the correlations that exist within natural images. Within this subspace, stimulus-response functions may be either linear or nonlinear. The idea was originally developed by Tatyana Sharpee, Nicole C. Rust, and William Bialek in 2003. Mathematical formulation Neural stimulus-response functions are typically given as the probability of a neuron generating an action potential, or spike, in response to a stimulus \mathbf. The goal of maximally ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Dimensionality Reduction
Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally close to its intrinsic dimension. Working in high-dimensional spaces can be undesirable for many reasons; raw data are often sparse as a consequence of the curse of dimensionality, and analyzing the data is usually computationally intractable. Dimensionality reduction is common in fields that deal with large numbers of observations and/or large numbers of variables, such as signal processing, speech recognition, neuroinformatics, and bioinformatics. Methods are commonly divided into linear and nonlinear approaches. Linear approaches can be further divided into feature selection and feature extraction. Dimensionality reduction can be used for noise reduction, data visualization, cluster analysis, or as an intermediate step to facilitat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
William Bialek
William Samuel Bialek (born 14 August 1960) is a theoretical biophysicist and a professor at Princeton University and The Graduate Center, CUNY. Much of his work, which has ranged over a wide variety of theoretical problems at the interface of physics and biology, centers around whether various functions of living beings are optimal, and (if so) whether a precise quantification of their performance approaches limits set by basic physical principles. Best known among these is an influential series of studies applying the principles of information theory to the analysis of the neural encoding of information in the nervous system, showing that aspects of brain function can be described as essentially optimal strategies for adapting to the complex dynamics of the world, making the most of the available signals in the face of fundamental physical constraints and limitations. Bialek received his AB (1979) and PhD (1983) degrees in Biophysics from the University of California, Berkeley. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Spike-triggered Covariance
Spike-triggered covariance (STC) analysis is a tool for characterizing a neuron's response properties using the covariance of stimuli that elicit spikes from a neuron. STC is related to the spike-triggered average (STA), and provides a complementary tool for estimating linear filters in a linear-nonlinear-Poisson (LNP) cascade model. Unlike STA, the STC can be used to identify a multi-dimensional feature space in which a neuron computes its response. STC analysis identifies the stimulus features affecting a neuron's response via an eigenvector decomposition of the spike-triggered covariance matrix.Brenner, N., Bialek, W., & de Ruyter van Steveninck, R.R. (2000). Schwartz, O., Chichilnisky, E. J., & Simoncelli, E. P. (2002). Bialek, W. & de Ruyter van Steveninck, R. (2005). Arxiv preprint q-bio/0505003.Schwartz O., Pillow J. W., Rust N. C., & Simoncelli E. P. (2006). Spike-triggered neural characterization. ''Journal of Vision'' 6:484-507 Eigenvectors with eigenvalues significant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Normal Distribution
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f(x) = \frac e^\,. The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter \sigma^2 is the variance. The standard deviation of the distribution is (sigma). A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. Their importance is partly due to the central limit theorem. It states that, under some conditions, the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable—whose distribution c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Dirac Delta Function
In mathematical analysis, the Dirac delta function (or distribution), also known as the unit impulse, is a generalized function on the real numbers, whose value is zero everywhere except at zero, and whose integral over the entire real line is equal to one. Thus it can be Heuristic, represented heuristically as \delta (x) = \begin 0, & x \neq 0 \\ , & x = 0 \end such that \int_^ \delta(x) dx=1. Since there is no function having this property, modelling the delta "function" rigorously involves the use of limit (mathematics), limits or, as is common in mathematics, measure theory and the theory of distribution (mathematics), distributions. The delta function was introduced by physicist Paul Dirac, and has since been applied routinely in physics and engineering to model point masses and instantaneous impulses. It is called the delta function because it is a continuous analogue of the Kronecker delta function, which is usually defined on a discrete domain and takes values ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Mean
A mean is a quantity representing the "center" of a collection of numbers and is intermediate to the extreme values of the set of numbers. There are several kinds of means (or "measures of central tendency") in mathematics, especially in statistics. Each attempts to summarize or typify a given group of data, illustrating the magnitude and sign of the data set. Which of these measures is most illuminating depends on what is being measured, and on context and purpose. The ''arithmetic mean'', also known as "arithmetic average", is the sum of the values divided by the number of values. The arithmetic mean of a set of numbers ''x''1, ''x''2, ..., x''n'' is typically denoted using an overhead bar, \bar. If the numbers are from observing a sample of a larger group, the arithmetic mean is termed the '' sample mean'' (\bar) to distinguish it from the group mean (or expected value) of the underlying distribution, denoted \mu or \mu_x. Outside probability and statistics, a wide rang ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Bayes' Theorem
Bayes' theorem (alternatively Bayes' law or Bayes' rule, after Thomas Bayes) gives a mathematical rule for inverting Conditional probability, conditional probabilities, allowing one to find the probability of a cause given its effect. For example, if the risk of developing health problems is known to increase with age, Bayes' theorem allows the risk to someone of a known age to be assessed more accurately by conditioning it relative to their age, rather than assuming that the person is typical of the population as a whole. Based on Bayes' law, both the prevalence of a disease in a given population and the error rate of an infectious disease test must be taken into account to evaluate the meaning of a positive test result and avoid the ''base-rate fallacy''. One of Bayes' theorem's many applications is Bayesian inference, an approach to statistical inference, where it is used to invert the probability of Realization (probability), observations given a model configuration (i.e., th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Projection (mathematics)
In mathematics, a projection is an idempotent mapping of a set (or other mathematical structure) into a subset (or sub-structure). In this case, idempotent means that projecting twice is the same as projecting once. The restriction to a subspace of a projection is also called a ''projection'', even if the idempotence property is lost. An everyday example of a projection is the casting of shadows onto a plane (sheet of paper): the projection of a point is its shadow on the sheet of paper, and the projection (shadow) of a point on the sheet of paper is that point itself (idempotency). The shadow of a three-dimensional sphere is a disk. Originally, the notion of projection was introduced in Euclidean geometry to denote the projection of the three-dimensional Euclidean space onto a plane in it, like the shadow example. The two main projections of this kind are: * The projection from a point onto a plane or central projection: If is a point, called the center of projection, then t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Action Potential
An action potential (also known as a nerve impulse or "spike" when in a neuron) is a series of quick changes in voltage across a cell membrane. An action potential occurs when the membrane potential of a specific Cell (biology), cell rapidly rises and falls. This depolarization then causes adjacent locations to similarly depolarize. Action potentials occur in several types of Membrane potential#Cell excitability, excitable cells, which include animal cells like neurons and myocyte, muscle cells, as well as some plant cells. Certain endocrine cells such as pancreatic beta cells, and certain cells of the anterior pituitary gland are also excitable cells. In neurons, action potentials play a central role in cell–cell interaction, cell–cell communication by providing for—or with regard to saltatory conduction, assisting—the propagation of signals along the neuron's axon toward axon terminal, synaptic boutons situated at the ends of an axon; these signals can then connect wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Neuron
A neuron (American English), neurone (British English), or nerve cell, is an membrane potential#Cell excitability, excitable cell (biology), cell that fires electric signals called action potentials across a neural network (biology), neural network in the nervous system. They are located in the nervous system and help to receive and conduct impulses. Neurons communicate with other cells via synapses, which are specialized connections that commonly use minute amounts of chemical neurotransmitters to pass the electric signal from the presynaptic neuron to the target cell through the synaptic gap. Neurons are the main components of nervous tissue in all Animalia, animals except sponges and placozoans. Plants and fungi do not have nerve cells. Molecular evidence suggests that the ability to generate electric signals first appeared in evolution some 700 to 800 million years ago, during the Tonian period. Predecessors of neurons were the peptidergic secretory cells. They eventually ga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Nicole C
Nicole may refer to: People * Nicole (name) * Nicole (American singer) (born 1958), a contestant in season 3 of the American ''The X Factor'' * Nicole (Chilean singer) (born 1977) * Nicole (German singer) (born 1964), winner of the 1982 Eurovision Song Contest * Nicole, Countess of Penthièvre (c. 1424–after 1480) * Nicole, Duchess of Lorraine (1608–1657), French noblewoman * Nicole LaRoche, flutist in the band Brulé, releases solo albums as "Nicole" Storms * Tropical Storm Nicole, a number of named tropical and subtropical cyclones ** Tropical Storm Nicole (2010) ** Hurricane Nicole (2016) ** Hurricane Nicole (2022) Other uses * ''Nicole'' (film), a 1978 thriller * ''Nicole'' (video game), a visual novel style game * Nicole, Lot-et-Garonne, a town in France * “Nicole”, a song by Ween from the 1990 album '' GodWeenSatan: The Oneness'' * ''Nicole'' (album), an album by Indonesian singer NIKI See also * Nicolle * Nicoll Highway * Nichole * Nicholas (disa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
