Mathematical economicsMathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, or other computational methods. Proponents of this approach claim that it allows the formulation of theoretical relationships with rigor, generality, and simplicity.
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.
Mathematical psychologyMathematical psychology is an approach to psychological research that is based on mathematical modeling of perceptual, thought, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior (in practice often constituted by task performance). The mathematical approach is used with the goal of deriving hypotheses that are more exact and thus yield stricter empirical validations.
Biological neuron modelBiological neuron models, also known as a spiking neuron models, are mathematical descriptions of the properties of certain cells in the nervous system that generate sharp electrical potentials across their cell membrane, roughly one millisecond in duration, called action potentials or spikes (Fig. 2). Since spikes are transmitted along the axon and synapses from the sending neuron to many other neurons, spiking neurons are considered to be a major information processing unit of the nervous system.
Single-unit recordingIn neuroscience, single-unit recordings (also, single-neuron recordings) provide a method of measuring the electro-physiological responses of a single neuron using a microelectrode system. When a neuron generates an action potential, the signal propagates down the neuron as a current which flows in and out of the cell through excitable membrane regions in the soma and axon. A microelectrode is inserted into the brain, where it can record the rate of change in voltage with respect to time.
ElectrophysiologyElectrophysiology (from Greek ἥλεκτ, ēlektron, "amber" [see the etymology of "electron"]; φύσις, physis, "nature, origin"; and -λογία, -logia) is the branch of physiology that studies the electrical properties of biological cells and tissues. It involves measurements of voltage changes or electric current or manipulations on a wide variety of scales from single ion channel proteins to whole organs like the heart. In neuroscience, it includes measurements of the electrical activity of neurons, and, in particular, action potential activity.
Patch clampThe patch clamp technique is a laboratory technique in electrophysiology used to study ionic currents in individual isolated living cells, tissue sections, or patches of cell membrane. The technique is especially useful in the study of excitable cells such as neurons, cardiomyocytes, muscle fibers, and pancreatic beta cells, and can also be applied to the study of bacterial ion channels in specially prepared giant spheroplasts. Patch clamping can be performed using the voltage clamp technique.
MicroelectrodeA microelectrode is an electrode used in electrophysiology either for recording neural signals or for the electrical stimulation of nervous tissue (they were first developed by Ida Hyde in 1921). Pulled glass pipettes with tip diameters of 0.5 μm or less are usually filled with 3 molars potassium chloride solution as the electrical conductor. When the tip penetrates a cell membrane the lipids in the membrane seal onto the glass, providing an excellent electrical connection between the tip and the interior of the cell, which is apparent because the microelectrode becomes electrically negative compared to the extracellular solution.
Place cellA place cell is a kind of pyramidal neuron in the hippocampus that becomes active when an animal enters a particular place in its environment, which is known as the place field. Place cells are thought to act collectively as a cognitive representation of a specific location in space, known as a cognitive map. Place cells work with other types of neurons in the hippocampus and surrounding regions to perform this kind of spatial processing. They have been found in a variety of animals, including rodents, bats, monkeys and humans.
Visual cortexThe visual cortex of the brain is the area of the cerebral cortex that processes visual information. It is located in the occipital lobe. Sensory input originating from the eyes travels through the lateral geniculate nucleus in the thalamus and then reaches the visual cortex. The area of the visual cortex that receives the sensory input from the lateral geniculate nucleus is the primary visual cortex, also known as visual area 1 (V1), Brodmann area 17, or the striate cortex.
Bayesian approaches to brain functionBayesian approaches to brain function investigate the capacity of the nervous system to operate in situations of uncertainty in a fashion that is close to the optimal prescribed by Bayesian statistics. This term is used in behavioural sciences and neuroscience and studies associated with this term often strive to explain the brain's cognitive abilities based on statistical principles. It is frequently assumed that the nervous system maintains internal probabilistic models that are updated by neural processing of sensory information using methods approximating those of Bayesian probability.
Prefrontal cortexIn mammalian brain anatomy, the prefrontal cortex (PFC) covers the front part of the frontal lobe of the cerebral cortex. The PFC contains the Brodmann areas BA8, BA9, BA10, BA11, BA12, BA13, BA14, BA24, BA25, BA32, BA44, BA45, BA46, and BA47. The basic activity of this brain region is considered to be orchestration of thoughts and actions in accordance with internal goals. Many authors have indicated an integral link between a person's will to live, personality, and the functions of the prefrontal cortex.
