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Models Of Neural Computation
Models of neural computation are attempts to elucidate, in an abstract and mathematical fashion, the core principles that underlie information processing in biological nervous systems, or functional components thereof. This article aims to provide an overview of the most definitive models of neuro-biological computation as well as the tools commonly used to construct and analyze them. Introduction Due to the complexity of nervous system behavior, the associated experimental error bounds are ill-defined, but the relative merit of the different models of a particular subsystem can be compared according to how closely they reproduce real-world behaviors or respond to specific input signals. In the closely related field of computational neuroethology, the practice is to include the environment in the model in such a way that the loop is closed. In the cases where competing models are unavailable, or where only gross responses have been measured or quantified, a clearly formulated model ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientific Model
Scientific modelling is a scientific activity, the aim of which is to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate by referencing it to existing and usually commonly accepted knowledge. It requires selecting and identifying relevant aspects of a situation in the real world and then developing a model to replicate a system with those features. Different types of models may be used for different purposes, such as conceptual models to better understand, operational models to operationalize, mathematical models to quantify, computational models to simulate, and graphical models to visualize the subject. Modelling is an essential and inseparable part of many scientific disciplines, each of which has its own ideas about specific types of modelling. The following was said by John von Neumann. There is also an increasing attention to scientific modelling in fields such as science education, philosophy of science, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Levenberg–Marquardt Algorithm
In mathematics and computing, the Levenberg–Marquardt algorithm (LMA or just LM), also known as the damped least-squares (DLS) method, is used to solve non-linear least squares problems. These minimization problems arise especially in least squares curve fitting. The LMA interpolates between the Gauss–Newton algorithm (GNA) and the method of gradient descent. The LMA is more robust than the GNA, which means that in many cases it finds a solution even if it starts very far off the final minimum. For well-behaved functions and reasonable starting parameters, the LMA tends to be slower than the GNA. LMA can also be viewed as Gauss–Newton using a trust region approach. The algorithm was first published in 1944 by Kenneth Levenberg, while working at the Frankford Army Arsenal. It was rediscovered in 1963 by Donald Marquardt, who worked as a statistician at DuPont, and independently by Girard, Wynne and Morrison. The LMA is used in many software applications for solving gen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axon
An axon (from Greek ἄξων ''áxōn'', axis), or nerve fiber (or nerve fibre: see spelling differences), is a long, slender projection of a nerve cell, or neuron, in vertebrates, that typically conducts electrical impulses known as action potentials away from the nerve cell body. The function of the axon is to transmit information to different neurons, muscles, and glands. In certain sensory neurons ( pseudounipolar neurons), such as those for touch and warmth, the axons are called afferent nerve fibers and the electrical impulse travels along these from the periphery to the cell body and from the cell body to the spinal cord along another branch of the same axon. Axon dysfunction can be the cause of many inherited and acquired neurological disorders that affect both the peripheral and central neurons. Nerve fibers are classed into three types group A nerve fibers, group B nerve fibers, and group C nerve fibers. Groups A and B are myelinated, and group C are unmyelinated. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soliton
In mathematics and physics, a soliton or solitary wave is a self-reinforcing wave packet that maintains its shape while it propagates at a constant velocity. Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium. (Dispersive effects are a property of certain systems where the speed of a wave depends on its frequency.) Solitons are the solutions of a widespread class of weakly nonlinear dispersive partial differential equations describing physical systems. The soliton phenomenon was first described in 1834 by John Scott Russell (1808–1882) who observed a solitary wave in the Union Canal in Scotland. He reproduced the phenomenon in a wave tank and named it the " Wave of Translation". Definition A single, consensus definition of a soliton is difficult to find. ascribe three properties to solitons: # They are of permanent form; # They are localized within a region; # They can interact with other solitons, and emerge from the collision unchan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematically, density is defined as mass divided by volume: : \rho = \frac where ''ρ'' is the density, ''m'' is the mass, and ''V'' is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume, although this is scientifically inaccurate – this quantity is more specifically called specific weight. For a pure substance the density has the same numerical value as its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity and packaging. Osmium and iridium are the densest known elements at standard conditions for temperature and pressure. To simplify comparisons of density across different s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sound
In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the brain. Only acoustic waves that have frequencies lying between about 20 Hz and 20 kHz, the audio frequency range, elicit an auditory percept in humans. In air at atmospheric pressure, these represent sound waves with wavelengths of to . Sound waves above 20 kHz are known as ultrasound and are not audible to humans. Sound waves below 20 Hz are known as infrasound. Different animal species have varying hearing ranges. Acoustics Acoustics is the interdisciplinary science that deals with the study of mechanical waves in gasses, liquids, and solids including vibration, sound, ultrasound, and infrasound. A scientist who works in the field of acoustics is an ''acoustician'', while someone working in the field of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solitary Wave (water Waves)
John Scott Russell FRSE FRS FRSA (9 May 1808, Parkhead, Glasgow – 8 June 1882, Ventnor, Isle of Wight) was a Scottish civil engineer, naval architect and shipbuilder who built '' Great Eastern'' in collaboration with Isambard Kingdom Brunel. He made the discovery of the wave of translation that gave birth to the modern study of solitons, and developed the wave-line system of ship construction. Russell was a promoter of the Great Exhibition of 1851. Early life John Russell was born on 9 May 1808 in Parkhead, Glasgow, the son of Reverend David Russell and Agnes Clark Scott. He spent one year at the University of St. Andrews before transferring to the University of Glasgow. It was while at the University of Glasgow that he added his mother's maiden name, Scott, to his own, to become John Scott Russell. He graduated from Glasgow University in 1825 at the age of 17 and moved to Edinburgh where he taught mathematics and science at the Leith Mechanics' Institute, achieving the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Action Potentials
An action potential occurs when the membrane potential of a specific cell location rapidly rises and falls. This depolarization then causes adjacent locations to similarly depolarize. Action potentials occur in several types of animal cells, called excitable cells, which include neurons, muscle cells, and in some plant cells. Certain endocrine cells such as pancreatic beta cells, and certain cells of the anterior pituitary gland are also excitable cells. In neurons, action potentials play a central role in cell-cell communication by providing for—or with regard to saltatory conduction, assisting—the propagation of signals along the neuron's axon toward synaptic boutons situated at the ends of an axon; these signals can then connect with other neurons at synapses, or to motor cells or glands. In other types of cells, their main function is to activate intracellular processes. In muscle cells, for example, an action potential is the first step in the chain of event ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hodgkin–Huxley Model
The Hodgkin–Huxley model, or conductance-based model, is a mathematical model that describes how action potentials in neurons are initiated and propagated. It is a set of nonlinear differential equations that approximates the electrical characteristics of excitable cells such as neurons and muscle cells. It is a continuous-time dynamical system. Alan Hodgkin and Andrew Huxley described the model in 1952 to explain the ionic mechanisms underlying the initiation and propagation of action potentials in the squid giant axon. They received the 1963 Nobel Prize in Physiology or Medicine for this work. Basic components The typical Hodgkin–Huxley model treats each component of an excitable cell as an electrical element (as shown in the figure). The lipid bilayer is represented as a capacitance (Cm). Voltage-gated ion channels are represented by electrical conductances (''g''''n'', where ''n'' is the specific ion channel) that depend on both voltage and time. Leak channels ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soliton Model In Neuroscience
The soliton hypothesis in neuroscience is a model that claims to explain how action potentials are initiated and conducted along axons based on a thermodynamic theory of nerve pulse propagation. It proposes that the signals travel along the cell's membrane in the form of certain kinds of solitary sound (or density) pulses that can be modeled as solitons. The model is proposed as an alternative to the Hodgkin–Huxley model in which action potentials: voltage-gated ion channels in the membrane open and allow sodium ions to enter the cell (inward current). The resulting decrease in membrane potential opens nearby voltage-gated sodium channels, thus propagating the action potential. The transmembrane potential is restored by delayed opening of potassium channels. Soliton hypothesis proponents assert that energy is mainly conserved during propagation except dissipation losses; Measured temperature changes are completely inconsistent with the Hodgkin-Huxley model. The soliton mode ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Central Pattern Generator
Central pattern generators (CPGs) are self-organizing biological neural circuits that produce rhythmic outputs in the absence of rhythmic input. They are the source of the tightly-coupled patterns of neural activity that drive rhythmic and stereotyped motor behaviors like walking, swimming, breathing, or chewing. The ability to function without input from higher brain areas still requires modulatory inputs, and their outputs are not fixed. Flexibility in response to sensory input is a fundamental quality of CPG-driven behavior. To be classified as a rhythmic generator, a CPG requires: # "two or more processes that interact such that each process sequentially increases and decreases, and # that, as a result of this interaction, the system repeatedly returns to its starting condition." CPGs have been found in invertebrates, and practically all vertebrate species investigated, including humans. General anatomy and physiology Intrinsic properties of CPG neurons CPG neurons can h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hindmarsh–Rose Model
The Hindmarsh–Rose model of neuronal activity is aimed to study the spiking-bursting behavior of the membrane potential observed in experiments made with a single neuron. The relevant variable is the membrane potential, ''x''(''t''), which is written in dimensionless units. There are two more variables, ''y''(''t'') and ''z''(''t''), which take into account the transport of ions across the membrane through the ion channels. The transport of sodium and potassium ions is made through fast ion channels and its rate is measured by ''y''(''t''), which is called the spiking variable. ''z''(''t'') corresponds to an adaptation current, which is incremented at every spike, leading to a decrease in the firing rate. Then, the Hindmarsh–Rose model has the mathematical form of a system of three nonlinear ordinary differential equations on the dimensionless dynamical variables ''x''(''t''), ''y''(''t''), and ''z''(''t''). They read: : \begin \frac &= y+\phi(x)-z+I, \\ \frac &= \psi(x)-y ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
