Normalization Model
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Normalization Model
The normalization model is an influential model of responses of neurons in primary visual cortex. David Heeger developed the model in the early 1990s, and later refined it together with Matteo Carandini and J. Anthony Movshon. The model involves a divisive stage. In the numerator is the output of the classical receptive field. In the denominator, a constant plus a measure of local stimulus contrast. Although the normalization model was initially developed to explain responses in the primary visual cortex, normalization is now thought to operate throughout the visual system, and in many other sensory modalities and brain regions, including the representation of odors in the olfactory bulb, the modulatory effects of visual attention, the encoding of value, and the integration of multisensory information. It has also been observed at subthreshold potentials in the hippocampus. Its presence in such a diversity of neural systems in multiple species, from invertebrates to mammals, sugg ...
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Neurons
A neuron, neurone, or nerve cell is an electrically excitable cell that communicates with other cells via specialized connections called synapses. The neuron is the main component of nervous tissue in all animals except sponges and placozoa. Non-animals like plants and fungi do not have nerve cells. Neurons are typically classified into three types based on their function. Sensory neurons respond to stimuli such as touch, sound, or light that affect the cells of the sensory organs, and they send signals to the spinal cord or brain. Motor neurons receive signals from the brain and spinal cord to control everything from muscle contractions to glandular output. Interneurons connect neurons to other neurons within the same region of the brain or spinal cord. When multiple neurons are connected together, they form what is called a neural circuit. A typical neuron consists of a cell body (soma), dendrites, and a single axon. The soma is a compact structure, and the axon and dend ...
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Primary Visual Cortex
The visual cortex of the brain is the area of the cerebral cortex that processes visual information. It is located in the occipital lobe. Sensory input originating from the eyes travels through the lateral geniculate nucleus in the thalamus and then reaches the visual cortex. The area of the visual cortex that receives the sensory input from the lateral geniculate nucleus is the primary visual cortex, also known as visual area 1 ( V1), Brodmann area 17, or the striate cortex. The extrastriate areas consist of visual areas 2, 3, 4, and 5 (also known as V2, V3, V4, and V5, or Brodmann area 18 and all Brodmann area 19). Both hemispheres of the brain include a visual cortex; the visual cortex in the left hemisphere receives signals from the right visual field, and the visual cortex in the right hemisphere receives signals from the left visual field. Introduction The primary visual cortex (V1) is located in and around the calcarine fissure in the occipital lobe. Each hemisphere's V1 ...
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David Heeger
David J. Heeger (born 1961) is an American neuroscientist, psychologist, computer scientist, data scientist, and entrepreneur. He is a professor at New York University, Chief Scientific Officer oStatespace Labs and Chief Scientific Officer and co-founder oEpistemic AI Research Heeger's academic research spans a cross-section of engineering, psychology, and neuroscience. In the fields of perceptual psychology, systems neuroscience, cognitive neuroscience, and computational neuroscience, Heeger has developed computational theories of neuronal processing in the visual system, and he has performed psychophysics (perceptual psychology) and neuroimaging (functional magnetic resonance imaging, fMRI) experiments on human vision. His primary contribution to computational neuroscience is a theory of neural processing called the normalization model. His experimental research has contributed to our understanding of the topographic organization of visual cortex (retinotopy), visual awarene ...
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Matteo Carandini
Matteo Carandini (born 1967) is a neuroscientist who studies the visual system. He is currently a professor at University College London, where he co-directs thCortical Processing Laboratorywith Kenneth D Harris. He studies the visual cortex at the level of individual neurons and populations of neurons, their intercommunication within the visual cortex, with a particular interest in the functions of the eye, thalamus, and the early visual areas of the cerebral cortex. Carandini conducts his research with the goal of contributing to the knowledge of how the brain processes visual information in the human brain and he works primarily with mice. His grandfather was ambassador Nicolo Carandini, and his uncle is archaeologist Andrea Carandini. Achievements In the 1990s, working with David Heeger and J. Anthony Movshon he refined and provided evidence for Heeger's normalization model of V1 responses. Together with David Ferster he characterized the relationship between synapti ...
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Receptive Field
The receptive field, or sensory space, is a delimited medium where some physiological stimuli can evoke a sensory neuronal response in specific organisms. Complexity of the receptive field ranges from the unidimensional chemical structure of odorants to the multidimensional spacetime of human visual field, through the bidimensional skin surface, being a receptive field for touch perception. Receptive fields can positively or negatively alter the membrane potential with or without affecting the rate of action potentials. A sensory space can be dependent of an animal's location. For a particular sound wave traveling in an appropriate transmission medium, by means of sound localization, an auditory space would amount to a reference system that continuously shifts as the animal moves (taking into consideration the space inside the ears as well). Conversely, receptive fields can be largely independent of the animal's location, as in the case of place cells. A sensory space can also m ...
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Contrast (vision)
Contrast is the contradiction in luminance or colour that makes an object (or its representation in an image or display) distinguishable. In visual perception of the real world, contrast is determined by the difference in the colour and brightness of the object and other objects within the same field of view. The human visual system is more sensitive to contrast than absolute luminance; we can perceive the world similarly regardless of the huge changes in illumination over the day or from place to place. The maximum ''contrast'' of an image is the contrast ratio or dynamic range. Images with a contrast ratio close to their medium's maximum possible contrast ratio experience a ''conservation of contrast'', wherein any increase in contrast in some parts of the image must necessarily result in a decrease in contrast elsewhere. Brightening an image will increase contrast in dark areas but decrease contrast in bright areas, while darkening the image will have the opposite effect. B ...
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Efficient Coding Hypothesis
The efficient coding hypothesis was proposed by Horace Barlow in 1961 as a theoretical model of sensory coding in the brain. Within the brain, neurons communicate with one another by sending electrical impulses referred to as action potentials or spikes. One goal of sensory neuroscience is to decipher the meaning of these spikes in order to understand how the brain represents and processes information about the outside world. Barlow hypothesized that the spikes in the sensory system formed a neural code for efficiently representing sensory information. By efficient Barlow meant that the code minimized the number of spikes needed to transmit a given signal. This is somewhat analogous to transmitting information across the internet, where different file formats can be used to transmit a given image. Different file formats require different number of bits for representing the same image at given distortion level, and some are better suited for representing certain classes of images ...
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Infomax
Infomax is an optimization principle for artificial neural networks and other information processing systems. It prescribes that a function that maps a set of input values ''I'' to a set of output values ''O'' should be chosen or learned so as to maximize the average Shannon mutual information between ''I'' and ''O'', subject to a set of specified constraints and/or noise processes. Infomax algorithms are learning algorithms that perform this optimization process. The principle was described by Linsker in 1988. Infomax, in its zero-noise limit, is related to the principle of redundancy reduction proposed for biological sensory processing by Horace Barlow in 1961, and applied quantitatively to retinal processing by Atick and Redlich. One of the applications of infomax has been to an independent component analysis algorithm that finds independent signals by maximizing entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly a ...
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Multivariate Pareto Distribution
In statistics, a multivariate Pareto distribution is a multivariate extension of a univariate Pareto distribution The Pareto distribution, named after the Italian civil engineer, economist, and sociologist Vilfredo Pareto ( ), is a power-law probability distribution that is used in description of social, quality control, scientific, geophysical, actua .... There are several different types of univariate Pareto distributions including Pareto Types I−IV and Feller−Pareto. Chapter 3. Multivariate Pareto distributions have been defined for many of these types. Bivariate Pareto distributions Bivariate Pareto distribution of the first kind Mardia (1962) defined a bivariate distribution with cumulative distribution function (CDF) given by : F(x_1, x_2) = 1 -\sum_^2\left(\frac\right)^+ \left(\sum_^2 \frac - 1\right)^, \qquad x_i > \theta_i > 0, i=1,2; a>0, and joint density function : f(x_1, x_2) = (a+1)a(\theta_1 \theta_2)^(\theta_2x_1 + \theta_1x_2 - \theta_1 \theta_ ...
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