Human legThe human leg is the entire lower limb of the human body, including the foot, thigh or sometimes even the hip or buttock region. The major bones of the leg are the femur (thigh bone), tibia (shin bone), and adjacent fibula. The thigh is between the hip and knee, while the calf (rear) and shin (front) are between the knee and foot. Legs are used for standing, many forms of human movement, recreation such as dancing, and constitute a significant portion of a person's mass.
Primary somatosensory cortexIn neuroanatomy, the primary somatosensory cortex is located in the postcentral gyrus of the brain's parietal lobe, and is part of the somatosensory system. It was initially defined from surface stimulation studies of Wilder Penfield, and parallel surface potential studies of Bard, Woolsey, and Marshall. Although initially defined to be roughly the same as Brodmann areas 3, 1 and 2, more recent work by Kaas has suggested that for homogeny with other sensory fields only area 3 should be referred to as "primary somatosensory cortex", as it receives the bulk of the thalamocortical projections from the sensory input fields.
Somatosensory systemIn physiology, the somatosensory system is the network of neural structures in the brain and body that produce the perception of touch (haptic perception), as well as temperature (thermoception), body position (proprioception), and pain. It is a subset of the sensory nervous system, which also represents visual, auditory, olfactory, and gustatory stimuli. Somatosensation begins when mechano- and thermosensitive structures in the skin or internal organs sense physical stimuli such as pressure on the skin (see mechanotransduction, nociception).
Postcentral gyrusIn neuroanatomy, the postcentral gyrus is a prominent gyrus in the lateral parietal lobe of the human brain. It is the location of the primary somatosensory cortex, the main sensory receptive area for the sense of touch. Like other sensory areas, there is a map of sensory space in this location, called the sensory homunculus. The primary somatosensory cortex was initially defined from surface stimulation studies of Wilder Penfield, and parallel surface potential studies of Bard, Woolsey, and Marshall.
Upper limbThe upper limbs or upper extremities are the forelimbs of an upright-postured tetrapod vertebrate, extending from the scapulae and clavicles down to and including the digits, including all the musculatures and ligaments involved with the shoulder, elbow, wrist and knuckle joints. In humans, each upper limb is divided into the arm, forearm and hand, and is primarily used for climbing, lifting and manipulating objects. In formal usage, the term "arm" only refers to the structures from the shoulder to the elbow, explicitly excluding the forearm, and thus "upper limb" and "arm" are not synonymous.
Brodmann areaA Brodmann area is a region of the cerebral cortex, in the human or other primate brain, defined by its cytoarchitecture, or histological structure and organization of cells. The concept was first introduced by the German anatomist Korbinian Brodmann in the early 20th century. Brodmann mapped the human brain based on the varied cellular structure across the cortex and identified 52 distinct regions, which he numbered 1 to 52. These regions, or Brodmann areas, correspond with diverse functions including sensation, motor control, and cognition.
Representation theoryRepresentation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and their algebraic operations (for example, matrix addition, matrix multiplication).
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.
Limb (anatomy)A limb is a jointed, muscled appendage of a tetrapod vertebrate animal used for weight-bearing and terrestrial locomotion. The distalmost portion of a limb is known as its extremity. The limbs' bony endoskeleton, known as the appendicular skeleton, is homologous among all tetrapods, who use their limbs for walking, running and jumping, swimming, grasping and climbing. All tetrapods have four limbs that are organized into two bilaterally symmetrical pairs, with one pair at each end of the torso, which phylogenetrically correspond to the four paired fins (pectoral and pelvic fins) of their fish ancestors.
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.
Lie algebra representationIn the mathematical field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices (or endomorphisms of a vector space) in such a way that the Lie bracket is given by the commutator. In the language of physics, one looks for a vector space together with a collection of operators on satisfying some fixed set of commutation relations, such as the relations satisfied by the angular momentum operators.
Adjoint representationIn mathematics, the adjoint representation (or adjoint action) of a Lie group G is a way of representing the elements of the group as linear transformations of the group's Lie algebra, considered as a vector space. For example, if G is , the Lie group of real n-by-n invertible matrices, then the adjoint representation is the group homomorphism that sends an invertible n-by-n matrix to an endomorphism of the vector space of all linear transformations of defined by: . For any Lie group, this natural representation is obtained by linearizing (i.
LegA leg is a weight-bearing and locomotive anatomical structure, usually having a columnar shape. During locomotion, legs function as "extensible struts". The combination of movements at all joints can be modeled as a single, linear element capable of changing length and rotating about an omnidirectional "hip" joint. As an anatomical animal structure it is used for locomotion. The distal end is often modified to distribute force (such as a foot). Most animals have an even number of legs.
Algebra representationIn abstract algebra, a representation of an associative algebra is a module for that algebra. Here an associative algebra is a (not necessarily unital) ring. If the algebra is not unital, it may be made so in a standard way (see the adjoint functors page); there is no essential difference between modules for the resulting unital ring, in which the identity acts by the identity mapping, and representations of the algebra.
ProsthesisIn medicine, a prosthesis (: prostheses; from prósthesis), or a prosthetic implant, is an artificial device that replaces a missing body part, which may be lost through trauma, disease, or a condition present at birth (congenital disorder). Prostheses are intended to restore the normal functions of the missing body part. Amputee rehabilitation is primarily coordinated by a physiatrist as part of an inter-disciplinary team consisting of physiatrists, prosthetists, nurses, physical therapists, and occupational therapists.
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.
Group representationIn the mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space to itself (i.e. vector space automorphisms); in particular, they can be used to represent group elements as invertible matrices so that the group operation can be represented by matrix multiplication. In chemistry, a group representation can relate mathematical group elements to symmetric rotations and reflections of molecules.
Arthropod legThe arthropod leg is a form of jointed appendage of arthropods, usually used for walking. Many of the terms used for arthropod leg segments (called podomeres) are of Latin origin, and may be confused with terms for bones: coxa (meaning hip, plural coxae), trochanter, femur (plural femora), tibia (plural tibiae), tarsus (plural tarsi), ischium (plural ischia), metatarsus, carpus, dactylus (meaning finger), patella (plural patellae). Homologies of leg segments between groups are difficult to prove and are the source of much argument.
Brodmann area 32The Brodmann area 32, also known in the human brain as the dorsal anterior cingulate area 32, refers to a subdivision of the cytoarchitecturally defined cingulate cortex. In the human it forms an outer arc around the anterior cingulate gyrus. The cingulate sulcus defines approximately its inner boundary and the superior rostral sulcus (H) its ventral boundary; rostrally it extends almost to the margin of the frontal lobe.
Irreducible representationIn mathematics, specifically in the representation theory of groups and algebras, an irreducible representation or irrep of an algebraic structure is a nonzero representation that has no proper nontrivial subrepresentation , with closed under the action of . Every finite-dimensional unitary representation on a Hilbert space is the direct sum of irreducible representations. Irreducible representations are always indecomposable (i.e. cannot be decomposed further into a direct sum of representations), but the converse may not hold, e.
