Unbounded operatorIn mathematics, more specifically functional analysis and operator theory, the notion of unbounded operator provides an abstract framework for dealing with differential operators, unbounded observables in quantum mechanics, and other cases. The term "unbounded operator" can be misleading, since "unbounded" should sometimes be understood as "not necessarily bounded"; "operator" should be understood as "linear operator" (as in the case of "bounded operator"); the domain of the operator is a linear subspace, not necessarily the whole space; this linear subspace is not necessarily closed; often (but not always) it is assumed to be dense; in the special case of a bounded operator, still, the domain is usually assumed to be the whole space.
Arcuate nucleusThe arcuate nucleus of the hypothalamus (also known as ARH, ARC, or infundibular nucleus) is an aggregation of neurons in the mediobasal hypothalamus, adjacent to the third ventricle and the median eminence. The arcuate nucleus includes several important and diverse populations of neurons that help mediate different neuroendocrine and physiological functions, including neuroendocrine neurons, centrally projecting neurons, and astrocytes.
Compact operatorIn functional analysis, a branch of mathematics, a compact operator is a linear operator , where are normed vector spaces, with the property that maps bounded subsets of to relatively compact subsets of (subsets with compact closure in ). Such an operator is necessarily a bounded operator, and so continuous. Some authors require that are Banach, but the definition can be extended to more general spaces. Any bounded operator that has finite rank is a compact operator; indeed, the class of compact operators is a natural generalization of the class of finite-rank operators in an infinite-dimensional setting.
Brain simulationBrain simulation is the concept of creating a functioning computer model of a brain or part of a brain. Brain simulation projects intend to contribute to a complete understanding of the brain, and eventually also assist the process of treating and diagnosing brain diseases. Various simulations from around the world have been fully or partially released as open source software, such as C. elegans, and the Blue Brain Project Showcase.
DNA profilingDNA profiling (also called DNA fingerprinting and genetic fingerprinting) is the process of determining an individual's deoxyribonucleic acid (DNA) characteristics. DNA analysis intended to identify a species, rather than an individual, is called DNA barcoding. DNA profiling is a forensic technique in criminal investigations, comparing criminal suspects' profiles to DNA evidence so as to assess the likelihood of their involvement in the crime. It is also used in paternity testing, to establish immigration eligibility, and in genealogical and medical research.
Agouti-related peptideAgouti-related protein (AgRP), also called agouti-related peptide, is a neuropeptide produced in the brain by the AgRP/NPY neuron. It is synthesized in neuropeptide Y (NPY)-containing cell bodies located in the ventromedial part of the arcuate nucleus in the hypothalamus. AgRP is co-expressed with NPY and acts to increase appetite and decrease metabolism and energy expenditure. It is one of the most potent and long-lasting of appetite stimulators. In humans, the agouti-related peptide is encoded by the AGRP gene.
Bounded operatorIn functional analysis and operator theory, a bounded linear operator is a linear transformation between topological vector spaces (TVSs) and that maps bounded subsets of to bounded subsets of If and are normed vector spaces (a special type of TVS), then is bounded if and only if there exists some such that for all The smallest such is called the operator norm of and denoted by A bounded operator between normed spaces is continuous and vice versa. The concept of a bounded linear operator has been extended from normed spaces to all topological vector spaces.
Cross-correlationIn signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recognition, single particle analysis, electron tomography, averaging, cryptanalysis, and neurophysiology. The cross-correlation is similar in nature to the convolution of two functions.
Brain damageNeurotrauma, brain damage or brain injury (BI) is the destruction or degeneration of brain cells. Brain injuries occur due to a wide range of internal and external factors. In general, brain damage refers to significant, undiscriminating trauma-induced damage. A common category with the greatest number of injuries is traumatic brain injury (TBI) following physical trauma or head injury from an outside source, and the term acquired brain injury (ABI) is used in appropriate circles to differentiate brain injuries occurring after birth from injury, from a genetic disorder (GBI), or from a congenital disorder (CBI).
Lateralization of brain functionThe lateralization of brain function (or hemispheric dominance/ latralisation ) is the tendency for some neural functions or cognitive processes to be specialized to one side of the brain or the other. The median longitudinal fissure separates the human brain into two distinct cerebral hemispheres, connected by the corpus callosum. Although the macrostructure of the two hemispheres appears to be almost identical, different composition of neuronal networks allows for specialized function that is different in each hemisphere.
Brain tumorA brain tumor occurs when abnormal cells form within the brain. There are two main types of tumors: malignant tumors and benign (non-cancerous) tumors. These can be further classified as primary tumors, which start within the brain, and secondary tumors, which most commonly have spread from tumors located outside the brain, known as brain metastasis tumors. All types of brain tumors may produce symptoms that vary depending on the size of the tumor and the part of the brain that is involved.
Electrical engineeringElectrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the latter half of the 19th century after the commercialization of the electric telegraph, the telephone, and electrical power generation, distribution, and use.
