Spatial cognitionSpatial cognition is the acquisition, organization, utilization, and revision of knowledge about spatial environments. It is most about how animals including humans behave within space and the knowledge they built around it, rather than space itself. These capabilities enable individuals to manage basic and high-level cognitive tasks in everyday life. Numerous disciplines (such as cognitive psychology, neuroscience, artificial intelligence, geographic information science, cartography, etc.
Gap junctionFirst photographed around 1952 it wasn't until 1969 that gap junctions were referred to as "gap junctions". Named after the 2-4 nm gap they bridged between cell membranes, they had been characterised in more detail by 1967. Gap junctions are one of four broad categories of intercellular connections that form between a multitude of animal cell types. Within a gap junction reside protein complexes, referred initially to as "globules", observed to connect one cell to another and also vesicles within a cell to the outer cell membrane.
Spatial memoryIn cognitive psychology and neuroscience, spatial memory is a form of memory responsible for the recording and recovery of information needed to plan a course to a location and to recall the location of an object or the occurrence of an event. Spatial memory is necessary for orientation in space. Spatial memory can also be divided into egocentric and allocentric spatial memory. A person's spatial memory is required to navigate around a familiar city. A rat's spatial memory is needed to learn the location of food at the end of a maze.
BrainA brain is an organ that serves as the center of the nervous system in all vertebrate and most invertebrate animals. It is located in the head, usually close to the sensory organs for senses such as vision. It is the most complex organ in a vertebrate's body. In a human, the cerebral cortex contains approximately 14–16 billion neurons, and the estimated number of neurons in the cerebellum is 55–70 billion. Each neuron is connected by synapses to several thousand other neurons.
AstrocyteAstrocytes (from Ancient Greek ἄστρον, ástron, "star" + κύτος, kútos, "cavity", "cell"), also known collectively as astroglia, are characteristic star-shaped glial cells in the brain and spinal cord. They perform many functions, including biochemical control of endothelial cells that form the blood–brain barrier, provision of nutrients to the nervous tissue, maintenance of extracellular ion balance, regulation of cerebral blood flow, and a role in the repair and scarring process of the brain and spinal cord following infection and traumatic injuries.
Excitatory synapseAn excitatory synapse is a synapse in which an action potential in a presynaptic neuron increases the probability of an action potential occurring in a postsynaptic cell. Neurons form networks through which nerve impulses travels, each neuron often making numerous connections with other cells of neurons. These electrical signals may be excitatory or inhibitory, and, if the total of excitatory influences exceeds that of the inhibitory influences, the neuron will generate a new action potential at its axon hillock, thus transmitting the information to yet another cell.
Numerical methods for ordinary differential equationsNumerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.
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.
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).
