Global optimizationGlobal optimization is a branch of applied mathematics and numerical analysis that attempts to find the global minima or maxima of a function or a set of functions on a given set. It is usually described as a minimization problem because the maximization of the real-valued function is equivalent to the minimization of the function . Given a possibly nonlinear and non-convex continuous function with the global minima and the set of all global minimizers in , the standard minimization problem can be given as that is, finding and a global minimizer in ; where is a (not necessarily convex) compact set defined by inequalities .
Mathematical optimizationMathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.
Nervous tissueNervous tissue, also called neural tissue, is the main tissue component of the nervous system. The nervous system regulates and controls body functions and activity. It consists of two parts: the central nervous system (CNS) comprising the brain and spinal cord, and the peripheral nervous system (PNS) comprising the branching peripheral nerves. It is composed of neurons, also known as nerve cells, which receive and transmit impulses, and neuroglia, also known as glial cells or glia, which assist the propagation of the nerve impulse as well as provide nutrients to the neurons.
Convex optimizationConvex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard.
Fractional anisotropyFractional anisotropy (FA) is a scalar value between zero and one that describes the degree of anisotropy of a diffusion process. A value of zero means that diffusion is isotropic, i.e. it is unrestricted (or equally restricted) in all directions. A value of one means that diffusion occurs only along one axis and is fully restricted along all other directions. FA is a measure often used in diffusion imaging where it is thought to reflect fiber density, axonal diameter, and myelination in white matter.
Neuromyelitis optica spectrum disorderNeuromyelitis optica spectrum disorders (NMOSD), including neuromyelitis optica (NMO), are autoimmune diseases characterized by acute inflammation of the optic nerve (optic neuritis, ON) and the spinal cord (myelitis). Episodes of ON and myelitis can be simultaneous or successive. A relapsing disease course is common, especially in untreated patients. In more than 80% of cases, NMO is caused by immunoglobulin G autoantibodies to aquaporin 4 (anti-AQP4), the most abundant water channel protein in the central nervous system.
Nerve injuryNerve injury is an injury to nervous tissue. There is no single classification system that can describe all the many variations of nerve injuries. In 1941, Seddon introduced a classification of nerve injuries based on three main types of nerve fiber injury and whether there is continuity of the nerve. Usually, however, peripheral nerve injuries are classified in five stages, based on the extent of damage to both the nerve and the surrounding connective tissue, since supporting glial cells may be involved.
Pathophysiology of multiple sclerosisMultiple sclerosis is an inflammatory demyelinating disease of the CNS in which activated immune cells invade the central nervous system and cause inflammation, neurodegeneration, and tissue damage. The underlying cause is currently unknown. Current research in neuropathology, neuroimmunology, neurobiology, and neuroimaging, together with clinical neurology, provide support for the notion that MS is not a single disease but rather a spectrum.
Genetic algorithmIn computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algorithms are commonly used to generate high-quality solutions to optimization and search problems by relying on biologically inspired operators such as mutation, crossover and selection. Some examples of GA applications include optimizing decision trees for better performance, solving sudoku puzzles, hyperparameter optimization, causal inference, etc.
Multidisciplinary design optimizationMulti-disciplinary design optimization (MDO) is a field of engineering that uses optimization methods to solve design problems incorporating a number of disciplines. It is also known as multidisciplinary system design optimization (MSDO), and Multidisciplinary Design Analysis and Optimization (MDAO). MDO allows designers to incorporate all relevant disciplines simultaneously. The optimum of the simultaneous problem is superior to the design found by optimizing each discipline sequentially, since it can exploit the interactions between the disciplines.
