Numerical methods for partial differential equationsNumerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs). In principle, specialized methods for hyperbolic, parabolic or elliptic partial differential equations exist. Finite difference method In this method, functions are represented by their values at certain grid points and derivatives are approximated through differences in these values.
Numerical methods for linear least squaresNumerical methods for linear least squares entails the numerical analysis of linear least squares problems. A general approach to the least squares problem can be described as follows. Suppose that we can find an n by m matrix S such that XS is an orthogonal projection onto the image of X. Then a solution to our minimization problem is given by simply because is exactly a sought for orthogonal projection of onto an image of X (see the picture below and note that as explained in the next section the image of X is just a subspace generated by column vectors of X).
Probabilistic numericsProbabilistic numerics is an active field of study at the intersection of applied mathematics, statistics, and machine learning centering on the concept of uncertainty in computation. In probabilistic numerics, tasks in numerical analysis such as finding numerical solutions for integration, linear algebra, optimization and simulation and differential equations are seen as problems of statistical, probabilistic, or Bayesian inference.
Human brainThe human brain is the central organ of the human nervous system, and with the spinal cord makes up the central nervous system. The brain consists of the cerebrum, the brainstem and the cerebellum. It controls most of the activities of the body, processing, integrating, and coordinating the information it receives from the sense organs, and making decisions as to the instructions sent to the rest of the body. The brain is contained in, and protected by, the skull bones of the head.
Optical fiberAn optical fiber, or optical fibre in Commonwealth English, is a flexible, transparent fiber made by drawing glass (silica) or plastic to a diameter slightly thicker than that of a human hair. Optical fibers are used most often as a means to transmit light between the two ends of the fiber and find wide usage in fiber-optic communications, where they permit transmission over longer distances and at higher bandwidths (data transfer rates) than electrical cables.
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.
Orbitofrontal cortexThe orbitofrontal cortex (OFC) is a prefrontal cortex region in the frontal lobes of the brain which is involved in the cognitive process of decision-making. In non-human primates it consists of the association cortex areas Brodmann area 11, 12 and 13; in humans it consists of Brodmann area 10, 11 and 47. The OFC is functionally related to the ventromedial prefrontal cortex. Therefore, the region is distinguished due to the distinct neural connections and the distinct functions it performs.
Entorhinal cortexThe entorhinal cortex (EC) is an area of the brain's allocortex, located in the medial temporal lobe, whose functions include being a widespread network hub for memory, navigation, and the perception of time. The EC is the main interface between the hippocampus and neocortex. The EC-hippocampus system plays an important role in declarative (autobiographical/episodic/semantic) memories and in particular spatial memories including memory formation, memory consolidation, and memory optimization in sleep.
Optical phenomenonOptical phenomena are any observable events that result from the interaction of light and matter. All optical phenomena coincide with quantum phenomena. Common optical phenomena are often due to the interaction of light from the Sun or Moon with the atmosphere, clouds, water, dust, and other particulates. One common example is the rainbow, when light from the Sun is reflected and refracted by water droplets. Some phenomena, such as the green ray, are so rare they are sometimes thought to be mythical.
Anatomical terms of locationStandard anatomical terms of location are used to unambiguously describe the anatomy of animals, including humans. The terms, typically derived from Latin or Greek roots, describe something in its standard anatomical position. This position provides a definition of what is at the front ("anterior"), behind ("posterior") and so on. As part of defining and describing terms, the body is described through the use of anatomical planes and anatomical axes. The meaning of terms that are used can change depending on whether an organism is bipedal or quadrupedal.
