|
Quantitative Models Of The Action Potential
In neurophysiology, several mathematical models of the action potential have been developed, which fall into two basic types. The first type seeks to model the experimental data quantitatively, i.e., to reproduce the measurements of current and voltage exactly. The renowned Hodgkin–Huxley model of the axon from the ''Loligo'' squid exemplifies such models. Although qualitatively correct, the H-H model does not describe every type of excitable membrane accurately, since it considers only two ions (sodium and potassium), each with only one type of voltage-sensitive channel. However, other ions such as calcium may be important and there is a great diversity of channels for all ions. As an example, the cardiac action potential illustrates how differently shaped action potentials can be generated on membranes with voltage-sensitive calcium channels and different types of sodium/potassium channels. The second type of mathematical model is a simplification of the first type; the goal is no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neurophysiology
Neurophysiology is a branch of physiology and neuroscience that studies nervous system function rather than nervous system architecture. This area aids in the diagnosis and monitoring of neurological diseases. Historically, it has been dominated by electrophysiology—the electrical recording of neural activity ranging from the molar (the electroencephalogram, EEG) to the cellular (intracellular recording of the properties of single neurons), such as patch clamp, voltage clamp, extracellular single-unit recording and recording of local field potentials. However, since the neurone is an electrochemical machine, it is difficult to isolate electrical events from the metabolic and molecular processes that cause them. Thus, neurophysiologists currently utilise tools from chemistry (calcium imaging), physics (functional magnetic resonance imaging, Functional magnetic resonance imaging, fMRI), and molecular biology (site directed mutations) to examine brain activity. The word originates f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Excitatory Postsynaptic Potential
In neuroscience, an excitatory postsynaptic potential (EPSP) is a postsynaptic potential that makes the postsynaptic neuron more likely to fire an action potential. This temporary depolarization of postsynaptic membrane potential, caused by the flow of positively charged ions into the postsynaptic cell, is a result of opening ligand-gated ion channels. These are the opposite of inhibitory postsynaptic potentials (IPSPs), which usually result from the flow of ''negative'' ions into the cell or positive ions ''out'' of the cell. EPSPs can also result from a decrease in outgoing positive charges, while IPSPs are sometimes caused by an increase in positive charge outflow. The flow of ions that causes an EPSP is an excitatory postsynaptic current (EPSC). EPSPs, like IPSPs, are graded (i.e. they have an additive effect). When multiple EPSPs occur on a single patch of postsynaptic membrane, their combined effect is the sum of the individual EPSPs. Larger EPSPs result in greater membrane ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Van Der Pol Oscillator
In dynamical system, dynamics, the Van der Pol oscillator is a Conservative force, non-conservative oscillator with nonlinearity, non-linear Damping ratio, damping. It evolves in time according to the second-order differential equation: :-\mu(1-x^2)+x= 0, where ''x'' is the position coordinate system, coordinate—which is a function (mathematics), function of the time ''t'', and ''μ'' is a scalar (mathematics), scalar parameter indicating the nonlinearity and the strength of the damping. History The Van der Pol oscillator was originally proposed by the Dutch electrical engineering, electrical engineer and physicist Balthasar van der Pol while he was working at Philips. Van der Pol found stable oscillations, which he subsequently called relaxation oscillator, relaxation-oscillations and are now known as a type of limit cycle in electrical circuits employing vacuum tubes. When these circuits are driven near the limit cycle, they become entrainment (physics), entrained, i.e. the d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Balthasar Van Der Pol
Balthasar van der Pol (27 January 1889 – 6 October 1959) was a Dutch physicist. Life and work Van der Pol began his studies of physics in Utrecht in 1911. J. A. Fleming offered van der Pol the use of the Pender Electrical Laboratory at University College for a study of the heuristics of wireless reception on board ships. In England he also worked with J. J. Thomson. Upon his return to the Netherlands, Balthsar worked with Hendrik Lorentz at Teylers Stichting. For his thesis he wrote ''The effect of an ionised gas on electro-magnetic wave propagation and its application to radio, as demonstrated by glow-discharge measurement'' under the supervision of Willem Henri Julius. He was awarded his Ph.D. in 1920. He joined Philips Research Laboratories in 1921, where he worked until his retirement in 1949. As observed by Hendrik Casimir, "Radio might have remained a field of haphazard empiricism along with wild commercial ventures, but for the influence of men like Van der Pol wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tunnel Diode
A tunnel diode or Esaki diode is a type of semiconductor diode that has effectively "negative resistance" due to the quantum mechanical effect called tunneling. It was invented in August 1957 by Leo Esaki, Yuriko Kurose, and Takashi Suzuki when they were working at Tokyo Tsushin Kogyo, now known as Sony. In 1973, Esaki received the Nobel Prize in Physics, jointly with Brian Josephson, for discovering the electron tunneling effect used in these diodes. Robert Noyce independently devised the idea of a tunnel diode while working for William Shockley, but was discouraged from pursuing it. Tunnel diodes were first manufactured by Sony in 1957, followed by General Electric and other companies from about 1960, and are still made in low volume today. Tunnel diodes have a heavily doped positive-to-negative (P-N) junction that is about 10 nm (100 Å) wide. The heavy doping results in a broken band gap, where conduction band electron states on the N-side are more or le ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Negative Differential Resistance
In electronics, negative resistance (NR) is a property of some electrical circuits and devices in which an increase in voltage across the device's terminals results in a decrease in electric current through it. This is in contrast to an ordinary resistor in which an increase of applied voltage causes a proportional increase in current due to Ohm's law, resulting in a positive resistance. While a positive resistance consumes power from current passing through it, a negative resistance produces power. Under certain conditions it can increase the power of an electrical signal, amplifying it. Negative resistance is an uncommon property which occurs in a few nonlinear electronic components. In a nonlinear device, two types of resistance can be defined: 'static' or 'absolute resistance', the ratio of voltage to current v / i, and ''differential resistance'', the ratio of a change in voltage to the resulting change in current \Delta v/\Delta i. The term negative resistance means ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bursting
Bursting, or burst firing, is an extremely diverse general phenomenon of the activation patterns of neurons in the central nervous system and spinal cord where periods of rapid action potential spiking are followed by quiescent periods much longer than typical inter-spike intervals. Bursting is thought to be important in the operation of robust central pattern generators, the transmission of neural codes, and some neuropathologies such as epilepsy. The study of bursting both directly and in how it takes part in other neural phenomena has been very popular since the beginnings of cellular neuroscience and is closely tied to the fields of neural synchronization, neural coding, plasticity, and attention. Observed bursts are named by the number of discrete action potentials they are composed of: a ''doublet'' is a two-spike burst, a ''triplet'' three and a ''quadruplet'' four. Neurons that are intrinsically prone to bursting behavior are referred to as ''bursters'' and this tendency t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philip Holmes
Philip John Holmes (born May 24, 1945) is the Eugene Higgins Professor of Mechanical and Aerospace Engineering at Princeton University. As a member of the Mechanical and Aerospace Engineering department, he formerly served as the interim chair until May 2007. Before moving to Princeton in 1994 he taught theoretical and applied mechanics at Cornell University from 1977 until 1994, when he was the Charles N. Mellowes Professor of Engineering and Professor of Mathematics. Holmes was educated in England at the University of Oxford, where he studied engineering from 1964 to 1967, and at the University of Southampton, where he obtained a Ph.D. in engineering in 1974. He has made solid contributions to the field of nonlinear dynamics and differential equations. His book on dynamical systems with John Guckenheimer is a landmark in the field. Holmes is a very creative researcher and scientist and an outstanding lecturer. The sheer breadth of his contributions to applied mathematics i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Guckenheimer
John Mark Guckenheimer (born 1945) joined the Department of Mathematics at Cornell University in 1985. He was previously at the University of California, Santa Cruz (1973-1985). He was a Guggenheim fellow in 1984, and was elected president of the Society for Industrial and Applied Mathematics (SIAM), serving from 1997 to 1998. Guckenheimer received his A.B. in 1966 from Harvard and his Ph.D. in 1970 from Berkeley, where his Ph.D. thesis advisor was Stephen Smale. His book ''Nonlinear Oscillations, Dynamical Systems and Bifurcation of Vector Fields'' (with Philip Holmes) is an extensively cited work on dynamical systems. Research Dr. John Guckenheimer's research has focused on three areas — neuroscience, algorithms for periodic orbits, and dynamics in systems with multiple time scales. Neuroscience Guckenheimer studies dynamical models of a small neural system, the stomatogastric ganglion of crustaceans — attempting to learn more about neuromodulation, the ways in which th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fixed Point (mathematics)
A fixed point (sometimes shortened to fixpoint, also known as an invariant point) is a value that does not change under a given transformation. Specifically, in mathematics, a fixed point of a function is an element that is mapped to itself by the function. In physics, the term fixed point can refer to a temperature that can be used as a reproducible reference point, usually defined by a phase change or triple point. Fixed point of a function Formally, is a fixed point of a function if belongs to both the domain and the codomain of , and . For example, if is defined on the real numbers by f(x) = x^2 - 3 x + 4, then 2 is a fixed point of , because . Not all functions have fixed points: for example, , has no fixed points, since is never equal to for any real number. In graphical terms, a fixed point means the point is on the line , or in other words the graph of has a point in common with that line. Fixed-point iteration In numerical analysis, ''fixed-point iter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independent Variable
Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables receive this name because, in an experiment, their values are studied under the supposition or demand that they depend, by some law or rule (e.g., by a mathematical function), on the values of other variables. Independent variables, in turn, are not seen as depending on any other variable in the scope of the experiment in question. In this sense, some common independent variables are time, space, density, mass, fluid flow rate, and previous values of some observed value of interest (e.g. human population size) to predict future values (the dependent variable). Of the two, it is always the dependent variable whose variation is being studied, by altering inputs, also known as regressors in a statistical context. In an experiment, any variable that can be attributed a value without attributing a value to any other variable is called an ind ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ordinary Differential Equation
In mathematics, an ordinary differential equation (ODE) is a differential equation whose unknown(s) consists of one (or more) function(s) of one variable and involves the derivatives of those functions. The term ''ordinary'' is used in contrast with the term partial differential equation which may be with respect to ''more than'' one independent variable. Differential equations A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form :a_0(x)y +a_1(x)y' + a_2(x)y'' +\cdots +a_n(x)y^+b(x)=0, where , ..., and are arbitrary differentiable functions that do not need to be linear, and are the successive derivatives of the unknown function of the variable . Among ordinary differential equations, linear differential equations play a prominent role for several reasons. Most elementary and special functions that are encountered in physics and applied mathematics are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
_8.5.7.1.c.svg "Click for more on -> Tunnel Diode")
