Cerebral cortexThe cerebral cortex, also known as the cerebral mantle, is the outer layer of neural tissue of the cerebrum of the brain in humans and other mammals. The cerebral cortex mostly consists of the six-layered neocortex, with just 10% consisting of allocortex. It is separated into two cortices, by the longitudinal fissure that divides the cerebrum into the left and right cerebral hemispheres. The two hemispheres are joined beneath the cortex by the corpus callosum. The cerebral cortex is the largest site of neural integration in the central nervous system.
Motor cortexThe motor cortex is the region of the cerebral cortex involved in the planning, control, and execution of voluntary movements. The motor cortex is an area of the frontal lobe located in the posterior precentral gyrus immediately anterior to the central sulcus. The motor cortex can be divided into three areas: 1. The primary motor cortex is the main contributor to generating neural impulses that pass down to the spinal cord and control the execution of movement. However, some of the other motor areas in the brain also play a role in this function.
Visual cortexThe 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.
Receptive fieldThe 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.
Cortical homunculusA cortical homunculus () is a distorted representation of the human body, based on a neurological "map" of the areas and proportions of the human brain dedicated to processing motor functions, or sensory functions, for different parts of the body. Nerve fibresconducting somatosensory information from all over the bodyterminate in various areas of the parietal lobe in the cerebral cortex, forming a representational map of the body. Findings from the 2010s and early 2020s began to call this interpretation into question, and research is ongoing in this field.
CorrelationIn statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are linearly related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve.
Cortical columnA cortical column is a group of neurons forming a cylindrical structure through the cerebral cortex of the brain perpendicular to the cortical surface. The structure was first identified by Mountcastle in 1957. He later identified minicolumns as the basic units of the neocortex which were arranged into columns. Each contains the same types of neurons, connectivity, and firing properties. Columns are also called hypercolumn, macrocolumn, functional column or sometimes cortical module.
Linear differential equationIn mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a0(x), ..., an(x) and b(x) are arbitrary differentiable functions that do not need to be linear, and y′, ..., y(n) are the successive derivatives of an unknown function y of the variable x. Such an equation is an ordinary differential equation (ODE).
Differential equationIn mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
Visual systemThe visual system comprises the sensory organ (the eye) and parts of the central nervous system (the retina containing photoreceptor cells, the optic nerve, the optic tract and the visual cortex) which gives organisms the sense of sight (the ability to detect and process visible light) as well as enabling the formation of several non-image photo response functions. It detects and interprets information from the optical spectrum perceptible to that species to "build a representation" of the surrounding environment.
Cortical stimulation mappingCortical stimulation mapping (CSM) is a type of electrocorticography that involves a physically invasive procedure and aims to localize the function of specific brain regions through direct electrical stimulation of the cerebral cortex. It remains one of the earliest methods of analyzing the brain and has allowed researchers to study the relationship between cortical structure and systemic function.
Ordinary differential equationIn mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. The term "ordinary" is used in contrast with partial differential equations which may be with respect to one independent variable. A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a_0(x), .
Topographic map (neuroanatomy)A topographic map is the ordered projection of a sensory surface, like the retina or the skin, or an effector system, like the musculature, to one or more structures of the central nervous system. Topographic maps can be found in all sensory systems and in many motor systems. Retinotopy The visual system refers to the part of the central nervous system that allows an organism to see. It interprets information from visible light to build a representation of the world.
Auditory cortexThe auditory cortex is the part of the temporal lobe that processes auditory information in humans and many other vertebrates. It is a part of the auditory system, performing basic and higher functions in hearing, such as possible relations to language switching. It is located bilaterally, roughly at the upper sides of the temporal lobes – in humans, curving down and onto the medial surface, on the superior temporal plane, within the lateral sulcus and comprising parts of the transverse temporal gyri, and the superior temporal gyrus, including the planum polare and planum temporale (roughly Brodmann areas 41 and 42, and partially 22).
Homogeneous differential equationA differential equation can be homogeneous in either of two respects. A first order differential equation is said to be homogeneous if it may be written where f and g are homogeneous functions of the same degree of x and y. In this case, the change of variable y = ux leads to an equation of the form which is easy to solve by integration of the two members. Otherwise, a differential equation is homogeneous if it is a homogeneous function of the unknown function and its derivatives.
Delay differential equationIn mathematics, delay differential equations (DDEs) are a type of differential equation in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times. DDEs are also called time-delay systems, systems with aftereffect or dead-time, hereditary systems, equations with deviating argument, or differential-difference equations. They belong to the class of systems with the functional state, i.e.
Partial differential equationIn mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similar to how x is thought of as an unknown number to be solved for in an algebraic equation like x2 − 3x + 2 = 0. However, it is usually impossible to write down explicit formulas for solutions of partial differential equations.
Hermite polynomialsIn mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence. The polynomials arise in: signal processing as Hermitian wavelets for wavelet transform analysis probability, such as the Edgeworth series, as well as in connection with Brownian motion; combinatorics, as an example of an Appell sequence, obeying the umbral calculus; numerical analysis as Gaussian quadrature; physics, where they give rise to the eigenstates of the quantum harmonic oscillator; and they also occur in some cases of the heat equation (when the term is present); systems theory in connection with nonlinear operations on Gaussian noise.
Correlation functionA correlation function is a function that gives the statistical correlation between random variables, contingent on the spatial or temporal distance between those variables. If one considers the correlation function between random variables representing the same quantity measured at two different points, then this is often referred to as an autocorrelation function, which is made up of autocorrelations.
Bernoulli differential equationIn mathematics, an ordinary differential equation is called a Bernoulli differential equation if it is of the form where is a real number. Some authors allow any real , whereas others require that not be 0 or 1. The equation was first discussed in a work of 1695 by Jacob Bernoulli, after whom it is named. The earliest solution, however, was offered by Gottfried Leibniz, who published his result in the same year and whose method is the one still used today.
