Linear formIn mathematics, a linear form (also known as a linear functional, a one-form, or a covector) is a linear map from a vector space to its field of scalars (often, the real numbers or the complex numbers). If V is a vector space over a field k, the set of all linear functionals from V to k is itself a vector space over k with addition and scalar multiplication defined pointwise. This space is called the dual space of V, or sometimes the algebraic dual space, when a topological dual space is also considered.
Linear independenceIn the theory of vector spaces, a set of vectors is said to be if there exists no nontrivial linear combination of the vectors that equals the zero vector. If such a linear combination exists, then the vectors are said to be . These concepts are central to the definition of dimension. A vector space can be of finite dimension or infinite dimension depending on the maximum number of linearly independent vectors. The definition of linear dependence and the ability to determine whether a subset of vectors in a vector space is linearly dependent are central to determining the dimension of a vector space.
Linear mapIn mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of modules over a ring; see Module homomorphism. If a linear map is a bijection then it is called a .
Stimulus (physiology)In physiology, a stimulus is a detectable change in the physical or chemical structure of an organism's internal or external environment. The ability of an organism or organ to detect external stimuli, so that an appropriate reaction can be made, is called sensitivity (excitability). Sensory receptors can receive information from outside the body, as in touch receptors found in the skin or light receptors in the eye, as well as from inside the body, as in chemoreceptors and mechanoreceptors.
Retinal detachmentRetinal detachment is a disorder of the eye in which the retina peels away from its underlying layer of support tissue. Initial detachment may be localized, but without rapid treatment the entire retina may detach, leading to vision loss and blindness. It is a surgical emergency. The retina is a thin layer of light-sensitive tissue on the back wall of the eye. The optical system of the eye focuses light on the retina much like light is focused on the film in a camera.
MicrosaccadeMicrosaccades are a kind of fixational eye movement. They are small, jerk-like, involuntary eye movements, similar to miniature versions of voluntary saccades. They typically occur during prolonged visual fixation (of at least several seconds), not only in humans, but also in animals with foveal vision (primates, cats, dogs etc.). Microsaccade amplitudes vary from 2 to 120 arcminutes. The first empirical evidence for their existence was provided by Robert Darwin, the father of Charles Darwin.
LinearityIn mathematics, the term linear is used in two distinct senses for two different properties: linearity of a function (or mapping ); linearity of a polynomial. An example of a linear function is the function defined by that maps the real line to a line in the Euclidean plane R2 that passes through the origin. An example of a linear polynomial in the variables and is Linearity of a mapping is closely related to proportionality. Examples in physics include the linear relationship of voltage and current in an electrical conductor (Ohm's law), and the relationship of mass and weight.
Retinal ganglion cellA retinal ganglion cell (RGC) is a type of neuron located near the inner surface (the ganglion cell layer) of the retina of the eye. It receives visual information from photoreceptors via two intermediate neuron types: bipolar cells and retina amacrine cells. Retina amacrine cells, particularly narrow field cells, are important for creating functional subunits within the ganglion cell layer and making it so that ganglion cells can observe a small dot moving a small distance.
SaccadeA saccade (səˈkɑːd , French for jerk) is a quick, simultaneous movement of both eyes between two or more phases of fixation in the same direction. In contrast, in smooth pursuit movements, the eyes move smoothly instead of in jumps. The phenomenon can be associated with a shift in frequency of an emitted signal or a movement of a body part or device. Controlled cortically by the frontal eye fields (FEF), or subcortically by the superior colliculus, saccades serve as a mechanism for fixation, rapid eye movement, and the fast phase of optokinetic nystagmus.
Continuous linear operatorIn functional analysis and related areas of mathematics, a continuous linear operator or continuous linear mapping is a continuous linear transformation between topological vector spaces. An operator between two normed spaces is a bounded linear operator if and only if it is a continuous linear operator. Continuous function (topology) and Discontinuous linear map Bounded operator Suppose that is a linear operator between two topological vector spaces (TVSs). The following are equivalent: is continuous.
EyeEyes are organs of the visual system. They provide living organisms with vision, the ability to receive and process visual detail, as well as enabling several photo response functions that are independent of vision. Eyes detect light and convert it into electro-chemical impulses in neurons (neurones).
Nonlinear systemIn mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists since most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems.
LearningLearning is the process of acquiring new understanding, knowledge, behaviors, skills, values, attitudes, and preferences. The ability to learn is possessed by humans, animals, and some machines; there is also evidence for some kind of learning in certain plants. Some learning is immediate, induced by a single event (e.g. being burned by a hot stove), but much skill and knowledge accumulate from repeated experiences. The changes induced by learning often last a lifetime, and it is hard to distinguish learned material that seems to be "lost" from that which cannot be retrieved.
Human eyeThe human eye is a sensory organ, part of the sensory nervous system, that reacts to visible light and allows humans to use visual information for various purposes including seeing things, keeping balance, and maintaining circadian rhythm. The eye can be considered as a living optical device. It is approximately spherical in shape, with its outer layers, such as the outermost, white part of the eye (the sclera) and one of its inner layers (the pigmented choroid) keeping the eye essentially light tight except on the eye's optic axis.
RhodopsinRhodopsin, also known as visual purple, is a protein encoded by the RHO gene and a G-protein-coupled receptor (GPCR). It is the opsin of the rod cells in the retina and a light-sensitive receptor protein that triggers visual phototransduction in rods. Rhodopsin mediates dim light vision and thus is extremely sensitive to light. When rhodopsin is exposed to light, it immediately photobleaches. In humans, it is regenerated fully in about 30 minutes, after which the rods are more sensitive.
TremorA tremor is an involuntary, somewhat rhythmic, muscle contraction and relaxation involving oscillations or twitching movements of one or more body parts. It is the most common of all involuntary movements and can affect the hands, arms, eyes, face, head, vocal folds, trunk, and legs. Most tremors occur in the hands. In some people, a tremor is a symptom of another neurological disorder. Tremor is most commonly classified by clinical features and cause or origin.
Visual field testA visual field test is an eye examination that can detect dysfunction in central and peripheral vision which may be caused by various medical conditions such as glaucoma, stroke, pituitary disease, brain tumours or other neurological deficits. Visual field testing can be performed clinically by keeping the subject's gaze fixed while presenting objects at various places within their visual field. Simple manual equipment can be used such as in the tangent screen test or the Amsler grid.
Linear programmingLinear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints.
Linear combinationIn mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants). The concept of linear combinations is central to linear algebra and related fields of mathematics. Most of this article deals with linear combinations in the context of a vector space over a field, with some generalizations given at the end of the article.
Eye surgeryEye surgery, also known as ophthalmic surgery or ocular surgery, is surgery performed on the eye or its adnexa. Eye surgery is part of ophthalmology and is performed by an ophthalmologist or eye surgeon. The eye is a fragile organ, and requires due care before, during, and after a surgical procedure to minimize or prevent further damage. An eye surgeon is responsible for selecting the appropriate surgical procedure for the patient, and for taking the necessary safety precautions.
