String diagram - Revision history

94.30.60.38: /* Other diagrammatic languages */

2014-11-10T13:18:51Z

Other diagrammatic languages

← Older revision		Revision as of 15:18, 10 November 2014
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	~~In [[neurobiology]], the~~ '''~~length constant''' ('''λ''') is a mathematical constant used~~ to ~~quantify the distance that~~ a [[membrane potential#Graded potentials\|graded]] [[electric potential]] will travel along a [[neurite]] via passive electrical conduction. The greater the value of the length constant, the further the potential will travel. A large length constant can contribute to [[spatial summation]]—the electrical addition of one potential with potentials from adjacent areas of the cell.		Jayson Berryhill is how I'm known as and my spouse doesn't like it at all. For a while I've been in Alaska but I will have to move in a year or two. Credit authorising is how she makes a living. Doing ballet is something she would by no means give up.<br><br>My homepage: [http://test.jeka-nn.ru/node/129 real psychic]

	~~The length constant can be defined as:~~

	~~:<math> \lambda \ = \ \sqrt{\frac {r_{m}} {(r_{i}+ r_{o})}} </math>~~

	~~where r<sub>m</sub>~~ is the membrane [[electrical resistance and conductance\|resistance]] (the force that impedes the flow of [[electric current]] from the outside of the membrane to the inside, and vice versa), r<sub>i</sub> is the axial resistance (the force that impedes current flow through the [[axoplasm]], parallel to the membrane), and r<sub>o</sub> is the extracellular resistance (the force that impedes current flow through the extracellular fluid, parallel to the membrane). ~~In calculation, the effects of r<sub>o</sub> are negligible, so the equation~~ is ~~typically expressed as:~~

	~~:<math> \lambda \ = \ \sqrt {\frac {r_{m}}{r_{i}}}</math>~~

	The membrane resistance is a function of the number of open [[ion channels]], and the axial resistance is generally a function of the [[diameter]] of the [[axon]]. The greater the diameter of the axon, the lower the r<sub>i</sub>.

	~~The length constant is used to describe the rise of [[potential difference]] across the membrane~~

	:<~~math~~> ~~V(x) \ = \ V_{max} (1 - e^{-x /\lambda})~~<~~/math~~>

	~~The fall of voltage can be expressed as:~~

	:~~<math> V(x) \ = \ V_{max} (e^{-x /\lambda})</math>~~

	~~Where~~ [~~[voltage]], V, is measured in millivolts, x is distance from the start of the potential (in millimeters), and λ is the length constant (in millimeters).~~

	~~V<sub>max</sub> is defined as the maximum voltage attained in the action potential, where:~~

	:~~<math>V_{max} \ = \ r_{m}I<~~/~~math>~~

	~~where r<sub>m<~~/~~sub> is the resistance across the membrane and I is the current flow.~~

	Setting for x= λ for the rise of voltage sets V(x) equal to .63 V<sub>max</sub>. This means that the length constant is the distance at which 63% of V<sub>max</sub> has been reached during the rise of voltage.

	~~Setting for x= λ for the fall of voltage sets V(x) equal to~~ .~~37 V<sub>max</sub>, meaning that the length constant is the distance at which 37% of V<sub>max</sub> has been reached during the fall of voltage.~~

	~~==By resistivity==~~
	Expressed with [[resistivity]] rather than resistance, the constant λ is (with negligible r<sub>o</sub>):<ref name=boron202>Page 202 in: {{cite book \|author=Walter F., PhD. Boron \|title=Medical Physiology: A Cellular And Molecular Approach \|publisher=Elsevier/Saunders \|location= \|year=2003 \|pages=1300 \|isbn=1-4160-2328-~~3 \|oclc= \|doi=}}</ref>~~

	~~:<math> \lambda = \sqrt{\frac {r \times \rho_{m}} {2 \times \rho_{i}}} </math>~~

	~~Where <math> r </math> is the radius of the neuron~~.

	~~The radius and number 2 come from that:~~

	*<math> \rho_{m} = r_{m} \times 2\pi r </~~math>~~
	*<math> \rho_{i} = r_{i} \times \pi r^2 </~~math>~~

	~~Expressed in this way, it can be seen that the length constant increases with increasing radius of the neuron.~~

	~~==References==~~

	~~{{reflist}}~~

	~~==See also==~~
	*[[Isopotential muscle]]
	*[[Time constant]]

	~~[[Category:Electrophysiology]~~]

en>Spectral sequence: disambiguate: Adjoint functors

2013-06-07T19:22:31Z

disambiguate: Adjoint functors

← Older revision		Revision as of 21:22, 7 June 2013
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	~~The author~~'~~s title~~ is ~~Christy~~. ~~I am currently a~~ travel ~~agent~~. ~~Mississippi~~ is ~~where his house~~ is. The ~~favorite hobby for him~~ and ~~his children~~ is to ~~play lacross~~ and ~~he would never give it up~~.<br><br>~~my blog email psychic readings~~ ([~~http~~://~~Conniecolin~~.~~com~~/xe/~~community/24580 great post to read~~])		In [[neurobiology]], the '''length constant''' ('''λ''') is a mathematical constant used to quantify the distance that a [[membrane potential#Graded potentials\|graded]] [[electric potential]] will travel along a [[neurite]] via passive electrical conduction. The greater the value of the length constant, the further the potential will travel. A large length constant can contribute to [[spatial summation]]—the electrical addition of one potential with potentials from adjacent areas of the cell.

			The length constant can be defined as:

			:<math> \lambda \ = \ \sqrt{\frac {r_{m}} {(r_{i}+ r_{o})}} </math>

			where r<sub>m</sub> is the membrane [[electrical resistance and conductance\|resistance]] (the force that impedes the flow of [[electric current]] from the outside of the membrane to the inside, and vice versa), r<sub>i</sub> is the axial resistance (the force that impedes current flow through the [[axoplasm]], parallel to the membrane), and r<sub>o</sub> is the extracellular resistance (the force that impedes current flow through the extracellular fluid, parallel to the membrane). In calculation, the effects of r<sub>o</sub> are negligible, so the equation is typically expressed as:

			:<math> \lambda \ = \ \sqrt {\frac {r_{m}}{r_{i}}}</math>

			The membrane resistance is a function of the number of open [[ion channels]], and the axial resistance is generally a function of the [[diameter]] of the [[axon]]. The greater the diameter of the axon, the lower the r<sub>i</sub>.

			The length constant is used to describe the rise of [[potential difference]] across the membrane

			:<math> V(x) \ = \ V_{max} (1 - e^{-x /\lambda})</math>

			The fall of voltage can be expressed as:

			:<math> V(x) \ = \ V_{max} (e^{-x /\lambda})</math>

			Where [[voltage]], V, is measured in millivolts, x is distance from the start of the potential (in millimeters), and λ is the length constant (in millimeters).

			V<sub>max</sub> is defined as the maximum voltage attained in the action potential, where:

			:<math>V_{max} \ = \ r_{m}I</math>

			where r<sub>m</sub> is the resistance across the membrane and I is the current flow.

			Setting for x= λ for the rise of voltage sets V(x) equal to .63 V<sub>max</sub>. This means that the length constant is the distance at which 63% of V<sub>max</sub> has been reached during the rise of voltage.

			Setting for x= λ for the fall of voltage sets V(x) equal to .37 V<sub>max</sub>, meaning that the length constant is the distance at which 37% of V<sub>max</sub> has been reached during the fall of voltage.

			==By resistivity==
			Expressed with [[resistivity]] rather than resistance, the constant λ is (with negligible r<sub>o</sub>):<ref name=boron202>Page 202 in: {{cite book \|author=Walter F., PhD. Boron \|title=Medical Physiology: A Cellular And Molecular Approach \|publisher=Elsevier/Saunders \|location= \|year=2003 \|pages=1300 \|isbn=1-4160-2328-3 \|oclc= \|doi=}}</ref>

			:<math> \lambda = \sqrt{\frac {r \times \rho_{m}} {2 \times \rho_{i}}} </math>

			Where <math> r </math> is the radius of the neuron.

			The radius and number 2 come from that:

			*<math> \rho_{m} = r_{m} \times 2\pi r </math>
			*<math> \rho_{i} = r_{i} \times \pi r^2 </math>

			Expressed in this way, it can be seen that the length constant increases with increasing radius of the neuron.

			==References==

			{{reflist}}

			==See also==
			*[[Isopotential muscle]]
			*[[Time constant]]

			[[Category:Electrophysiology]]

en>Cai: add more references and brief description of connection to other graphical languages.

2012-03-13T14:05:39Z

add more references and brief description of connection to other graphical languages.

New page

The author's title is Christy. I am currently a travel agent. Mississippi is where his house is. The favorite hobby for him and his children is to play lacross and he would never give it up.<br><br>my blog email psychic readings ([http://Conniecolin.com/xe/community/24580 great post to read])