Saturday, April 25, 2015

the optic nerve, which carries visual information from the retina to the brain, contains some 1.3 million (myelinated) fibers in young human adults

Structural evidence for the existence of a symmetrical high energy species in the degenerate vinylcyclopropane rearrangement

J. Am. Chem. Soc., 1969, 91 (15), pp 4310–4311
 
 

Relationship between nerves and axons

I just wanted to get a realistic viewpoint of our nervous system. I understand arteries and veins, but I wanted to know how similar our nervous system is to that?
I understand we have neurons (please correct me if I am wrong) all over the surface of body. Whenever we feel a touch a neuron fires a response, and that response travels through axons (myelin sheath).
My main question is what a nerve exactly is. Is it a long axon? How many axons (same thing as neuron body?) are in a nerve? I am sure it depends on different nerves.
share|improve this question
    
I vote to re-open - this question is not too broad. On the contrary, it is a set of highly specific questions, basically boiling down to terminology. I edited the question previously when the close-votes were already pouring in, and hence I vote now to re-open without editing any further. I think it is fine as is. Furthermore, there is background info, so there is no ground to 'leave-close' due to homework :-) –  AliceD Feb 17 at 12:36
    
Thanks for re-opening! –  AliceD Feb 18 at 11:07
    
I forgot to message you, but I edited your question to make it more compatible with Biology Stack Exchange. At Biology we like clear questions. Nice question +1 –  AliceD Feb 18 at 11:47
    
Chris, this was my first question on this website. I only knew of one rule and that was to be as specific as possible. I tried. I am not very familiar with the format of this website so I am not sure what "close-votes" or "re-open" you were talking about. I barely found out that my question was answered :) which I really appreciate. –  Jagmeet Singh Feb 20 at 5:48
    
@ChrisStronks I see a number 4 next to my question. What does that mean? Net positive votes I got? Also, can anyone edit my question? Or do you run this website? –  Jagmeet Singh Feb 20 at 5:49

1 Answer 1

I will go through your list of questions below:
  • I wanted to know how similar is our nervous system to [the circulatory system]?
    They are very different, but as in every comparison of very complex systems, there is some overlap. The circulatory system carries fluids, the nervous system electrical signals so they are functionally not alike. However, both systems run throughout the body and have a more or less central control unit (the brain and heart respectively). So there is a structural similarity. I reckon they are as much alike as a city's sewer system and electricity grid.
  • I understand we have neurons (please correct me if I am wrong) all over the surface of body.
    That is correct
  • Whenever we feel a touch (stimulus arises) a neuron fires a response, and that response travels through axons (myelin sheath).
    Tactile stimulation may result in firing of one or more neurons, dependent on the intensity of the stimulus. Larger stimuli will, obviously, recruit more fibers. Stronger stimuli will evoke stronger responses (increased firing). Axons indeed conduct the neuronal responses, like an electrical wire conducts electrical current. Longer axons are often myelinated (insulated). Not all neurons related to touch are myelinated, however.
  • So my main question is that what exactly is a nerve?
    A nerve is a bundle of axons that carry related functional information. Typically, nerves conduct information originating from locations closely located together in the body, and generally they convey this information to a localized spot in the body as well. For example, the optic nerve carries information from the photoreceptors (related information) from the retina (localized source) to the brainstem (localized target).
  • Is [a nerve] a long axon?
    A nerve contains many axons. 'Long' or 'short' is rather subjective.
  • How many axons (same thing as neuron body?) are in a nerve? I am sure it depends on different nerves.
    Neuronal cell bodies are typically located outside a nerve. Nerves contain varying numbers of fibers. For example, the auditory nerve harbors the axons of the spiral ganglion cells that transmit auditory information from the inner ear to the brain. It contains between 31k - 32k (myelinated) fibers in normal-hearing humans (Spoendlin & Schrott, 1989). In contrast, the optic nerve, which carries visual information from the retina to the brain, contains some 1.3 million (myelinated) fibers in young human adults (Jonas et al., 1992)

"生成方程 统计场论" 可积系统是指对应于一个自由度为N的动力学系统,存在有N个守恒量,这N个守恒量的对易关系给出N个微分方程,这样N个自由度都可以严格被限制在解上; 刘维尔可积系统都有拉克斯表示和零曲率表示(不唯一),反之未

系统可积
6米阳光

来自: 6米阳光(love the way you lie,,) 2012-09-30 15:38:39

利用闭路生成泛函的连续积分表示推导临界动力学的拉氏场论表述. 随机模型 研究非平衡态统计场论的有效方法 both systems run throughout the body and have a more or less central control unit (the brain and heart respectively).

[PDF]Page 1 Page 2 970 物理学报29 卷 _言砸一M9 一z厉9]). (1.7 ...
www.itp.ac.cn/~hao/CTPGF80Cb.pdf
轉為繁體網頁
由 Z GUANG-ZHAO 著作 - ‎2005 - ‎相關文章
这就是拉氏形式的经典统计场论生成泛函. Martin, ... 8 期周光召等: 非平衡统计场论与临界动力学(H) 971 ... 这就是没有随机力的广义朗之万方程(即TDGL 方程).
  • 量子場論- 維基百科,自由的百科全書 - Wikipedia

    zh.wikipedia.org/zh-hk/量子场论
    一致而且方便地處理多粒子系統的統計,是促使量子場論發展的第三個動機。 ... 量子場論中計算格林方程式之關聯函數時將遭遇到發散困難,這種困難很自然地出現在 ...
  • 非平衡统计场论与临界动力学(Ⅰ) 广义朗之万方程_CNKI学问

    xuewen.cnki.net/CJFD-WLXB198008000.html
    轉為繁體網頁
    文献[3—5】中指出,它足研究非平衡态统计场论的有效方法.文献[6】中用它 ... 本文中利用闭路生成泛函的连续积分表示推导临界动力学的拉氏场论表述. 在随机模型中 ...

  •  
    系统可积

    6米阳光

    来自: 6米阳光(love the way you lie,,) 2012-09-30 15:38:39



    Structural evidence for the existence of a symmetrical high energy species in the degenerate vinylcyclopropane rearrangement

    J. Am. Chem. Soc., 1969, 91 (15), pp 4310–4311
     
     

    Relationship between nerves and axons

    I just wanted to get a realistic viewpoint of our nervous system. I understand arteries and veins, but I wanted to know how similar our nervous system is to that?
    I understand we have neurons (please correct me if I am wrong) all over the surface of body. Whenever we feel a touch a neuron fires a response, and that response travels through axons (myelin sheath).
    My main question is what a nerve exactly is. Is it a long axon? How many axons (same thing as neuron body?) are in a nerve? I am sure it depends on different nerves.
    share|improve this question
        
    I vote to re-open - this question is not too broad. On the contrary, it is a set of highly specific questions, basically boiling down to terminology. I edited the question previously when the close-votes were already pouring in, and hence I vote now to re-open without editing any further. I think it is fine as is. Furthermore, there is background info, so there is no ground to 'leave-close' due to homework :-) –  AliceD Feb 17 at 12:36
        
    Thanks for re-opening! –  AliceD Feb 18 at 11:07
        
    I forgot to message you, but I edited your question to make it more compatible with Biology Stack Exchange. At Biology we like clear questions. Nice question +1 –  AliceD Feb 18 at 11:47
        
    Chris, this was my first question on this website. I only knew of one rule and that was to be as specific as possible. I tried. I am not very familiar with the format of this website so I am not sure what "close-votes" or "re-open" you were talking about. I barely found out that my question was answered :) which I really appreciate. –  Jagmeet Singh Feb 20 at 5:48
        
    @ChrisStronks I see a number 4 next to my question. What does that mean? Net positive votes I got? Also, can anyone edit my question? Or do you run this website? –  Jagmeet Singh Feb 20 at 5:49

    1 Answer 1

    I will go through your list of questions below:
    • I wanted to know how similar is our nervous system to [the circulatory system]?
      They are very different, but as in every comparison of very complex systems, there is some overlap. The circulatory system carries fluids, the nervous system electrical signals so they are functionally not alike. However, both systems run throughout the body and have a more or less central control unit (the brain and heart respectively). So there is a structural similarity. I reckon they are as much alike as a city's sewer system and electricity grid.
    • I understand we have neurons (please correct me if I am wrong) all over the surface of body.
      That is correct
    • Whenever we feel a touch (stimulus arises) a neuron fires a response, and that response travels through axons (myelin sheath).
      Tactile stimulation may result in firing of one or more neurons, dependent on the intensity of the stimulus. Larger stimuli will, obviously, recruit more fibers. Stronger stimuli will evoke stronger responses (increased firing). Axons indeed conduct the neuronal responses, like an electrical wire conducts electrical current. Longer axons are often myelinated (insulated). Not all neurons related to touch are myelinated, however.
    • So my main question is that what exactly is a nerve?
      A nerve is a bundle of axons that carry related functional information. Typically, nerves conduct information originating from locations closely located together in the body, and generally they convey this information to a localized spot in the body as well. For example, the optic nerve carries information from the photoreceptors (related information) from the retina (localized source) to the brainstem (localized target).
    • Is [a nerve] a long axon?
      A nerve contains many axons. 'Long' or 'short' is rather subjective.
    • How many axons (same thing as neuron body?) are in a nerve? I am sure it depends on different nerves.
      Neuronal cell bodies are typically located outside a nerve. Nerves contain varying numbers of fibers. For example, the auditory nerve harbors the axons of the spiral ganglion cells that transmit auditory information from the inner ear to the brain. It contains between 31k - 32k (myelinated) fibers in normal-hearing humans (Spoendlin & Schrott, 1989). In contrast, the optic nerve, which carries visual information from the retina to the brain, contains some 1.3 million (myelinated) fibers in young human adults (Jonas et al., 1992)

    生成方程组 自定义函数 在 3x3 的正方格点上, 每个格点都对应一个变量 格点不要太大, 老板说 20~30个变量就好了. 太大了最优化算法不收敛.最小化一个 hamiltonian

    如何生成方程组 - 豆瓣

    www.douban.com/group/topic/50480424/ 轉為繁體網頁
    2014年3月22日 - 每个格点都和它周围的四个格点有关系. 用了周期性边界条件, 最左边/上面的会和最右边/下面的连上. 然后我希望对每个格点i, 生成一个方程. 例如

    生成方程组
    cmp

    来自: cmp(const void*, const void*) 2014-03-22 11:24:32

    • Everett

      Everett (╮(╯▽╰)╭ ~(= ̄ U  ̄=)~) 2014-03-22 13:40:51

      线性方程的话直接构造矩阵求解就可以了。矩阵的构造方法是 SparseArray
    • cmp

      cmp (const void*, const void*) 2014-03-22 14:03:37

      线性方程的话直接构造矩阵求解就可以了。矩阵的构造方法是 SparseArray 线性方程的话直接构造矩阵求解就可以了。矩阵的构造方法是 SparseArray Everett
      嗯不是线性的… 是 J sum{ -cos θ_i sin θ_j - Δ sin θ_i cos θ_j} - h sin θ_i == 0 这样的。

      我想了想用了 Table + 用于处理下标的自定义的函数,貌似可行。然后用 NSolve 一下。

      还剩几个问题。像这样一大群待求变量,用 Mathematica 怎么处理比较好呢?用下标,List 还是什么?

      另外,像这种自定义函数,如何封装比较好? Module 么?
    • Everett

      Everett (╮(╯▽╰)╭ ~(= ̄ U  ̄=)~) 2014-03-22 14:37:23

      变量本身是下标的函数,比如θ[i]
    • Everett

      Everett (╮(╯▽╰)╭ ~(= ̄ U  ̄=)~) 2014-03-22 14:38:29

      嗯不是线性的… 是 J sum{ -cos θ_i sin θ_j - Δ sin θ_i cos θ_j} - h sin θ_i == 0 这样 嗯不是线性的… 是 J sum{ -cos θ_i sin θ_j - Δ sin θ_i cos θ_j} - h sin θ_i == 0 这样的。 我想了想用了 Table + 用于处理下标的自定义的函数,貌似可行。然后用 NSolve 一下。 还剩几个问题。像这样一大群待求变量,用 Mathematica 怎么处理比较好呢?用下标,List 还是什么? 另外,像这种自定义函数,如何封装比较好? Module 么? ... cmp
      未必需要定义处理下标的函数,一般是用模式匹配 {i_,j_}/;Mod[j-i,L]==1
    • cmp

      cmp (const void*, const void*) 2014-03-28 12:53:50

      未必需要定义处理下标的函数,一般是用模式匹配 {i_,j_}/;Mod[j-i,L]==1 未必需要定义处理下标的函数,一般是用模式匹配 {i_,j_}/;Mod[j-i,L]==1 Everett
      我终于解决了这些问题!

      我最早想要的是最小化一个 hamiltonian. 后来发现还是用 NMinimize 比较好, 用 NSolve 经常跑不出来.

      然后格点不要太大, 老板说 20~30个变量就好了. 太大了最优化算法不收敛.


    生成函數與差分方程

    episte.math.ntu.edu.tw/articles/mm/mm_02_4_10/
    方程(1)之解是一用n 表達an 的一般形式。我們先討論應用生成函數 (generating function) 的方法求滿足邊界條件(2)之方程(1)的解。 我們先提出生成函數的定

    Ito stochastic differential equation dx = f (xt , t)dt + g(xt , t)dWt , Wt is a Wiener process (i.e. Gaussian white noise), and xt is the value of x at time t .

    [PDF]Path Integral Methods for Stochastic Differential Equations
    www.mathematical-neuroscience.com/content/.../s13408-015-0018-5.pd...


    [PDF]Page 1 Page 2 970 物理学报29 卷 _言砸一M9 一z厉9]). (1.7 ...
    www.itp.ac.cn/~hao/CTPGF80Cb.pdf 轉為繁體網頁
    由 Z GUANG-ZHAO 著作 - ‎2005 - ‎相關文章
    这就是拉氏形式的经典统计场论生成泛函. Martin, ... 8 期周光召等: 非平衡统计场论与临界动力学(H) 971 ... 这就是没有随机力的广义朗之万方程(即TDGL 方程).
  • 量子場論- 維基百科,自由的百科全書 - Wikipedia

    zh.wikipedia.org/zh-hk/量子场论
    一致而且方便地處理多粒子系統的統計,是促使量子場論發展的第三個動機。 ... 量子場論中計算格林方程式之關聯函數時將遭遇到發散困難,這種困難很自然地出現在 ...
  • 非平衡统计场论与临界动力学(Ⅰ) 广义朗之万方程_CNKI学问

    xuewen.cnki.net/CJFD-WLXB198008000.html 轉為繁體網頁
    文献[3—5】中指出,它足研究非平衡态统计场论的有效方法.文献[6】中用它 ... 本文中利用闭路生成泛函的连续积分表示推导临界动力学的拉氏场论表述. 在随机模型中 ...
  • by CC Chow - ‎2015
    Feb 12, 2015 - closed form and must be tackled approximately using methods that include ... Although Wiener introduced path integrals to study stochastic ... agrams as a tool for carrying out perturbative expansions and introduces the “loop.

    3 Application to SDE
    Building on the previous section, here we derive a generating functional for SDEs.
    Consider a Langevin equation,
    dx
    dt
    = f (x, t)+g(x, t)η(t), (3)
    on the domain t ∈ [0,T ] with initial condition x(t0) = y. The stochastic forcing term
    η(t) obeys η(t) = 0 and η(t)η(t

    ) = δ(t −t

    ). Equation (3) is to be interpreted as
    the Ito stochastic differential equation
    dx = f (xt , t)dt + g(xt , t)dWt , (4)
    where Wt is a Wiener process (i.e. Gaussian white noise), and xt is the value of x
    at time t . We show how to generalize to other stochastic processes later. Functions
    f and g are assumed to obey all the properties required for an Ito SDE to be well
    posed [31]. In particular, the stochastic increment dWt does not depend on f (xt , t)
    or g(xt , t) (i.e. xt is adapted to the filtration generated by the noise). The choice
    between Ito and Stratonovich conventions amounts to a choice of the measure for
    the path integrals, which will be manifested in a condition on the linear response or
    “propagator” that we introduce below.


    生成方程组

    cmp

    来自: cmp(const void*, const void*) 2014-03-22 11:24:32

    • Everett

      Everett (╮(╯▽╰)╭ ~(= ̄ U  ̄=)~) 2014-03-22 13:40:51

      线性方程的话直接构造矩阵求解就可以了。矩阵的构造方法是 SparseArray
    • cmp

      cmp (const void*, const void*) 2014-03-22 14:03:37

      线性方程的话直接构造矩阵求解就可以了。矩阵的构造方法是 SparseArray 线性方程的话直接构造矩阵求解就可以了。矩阵的构造方法是 SparseArray Everett
      嗯不是线性的… 是 J sum{ -cos θ_i sin θ_j - Δ sin θ_i cos θ_j} - h sin θ_i == 0 这样的。

      我想了想用了 Table + 用于处理下标的自定义的函数,貌似可行。然后用 NSolve 一下。

      还剩几个问题。像这样一大群待求变量,用 Mathematica 怎么处理比较好呢?用下标,List 还是什么?

      另外,像这种自定义函数,如何封装比较好? Module 么?
    • Everett

      Everett (╮(╯▽╰)╭ ~(= ̄ U  ̄=)~) 2014-03-22 14:37:23

      变量本身是下标的函数,比如θ[i]
    • Everett

      Everett (╮(╯▽╰)╭ ~(= ̄ U  ̄=)~) 2014-03-22 14:38:29

      嗯不是线性的… 是 J sum{ -cos θ_i sin θ_j - Δ sin θ_i cos θ_j} - h sin θ_i == 0 这样 嗯不是线性的… 是 J sum{ -cos θ_i sin θ_j - Δ sin θ_i cos θ_j} - h sin θ_i == 0 这样的。 我想了想用了 Table + 用于处理下标的自定义的函数,貌似可行。然后用 NSolve 一下。 还剩几个问题。像这样一大群待求变量,用 Mathematica 怎么处理比较好呢?用下标,List 还是什么? 另外,像这种自定义函数,如何封装比较好? Module 么? ... cmp
      未必需要定义处理下标的函数,一般是用模式匹配 {i_,j_}/;Mod[j-i,L]==1
    • cmp

      cmp (const void*, const void*) 2014-03-28 12:53:50

      未必需要定义处理下标的函数,一般是用模式匹配 {i_,j_}/;Mod[j-i,L]==1 未必需要定义处理下标的函数,一般是用模式匹配 {i_,j_}/;Mod[j-i,L]==1 Everett
      我终于解决了这些问题!

      我最早想要的是最小化一个 hamiltonian. 后来发现还是用 NMinimize 比较好, 用 NSolve 经常跑不出来.

      然后格点不要太大, 老板说 20~30个变量就好了. 太大了最优化算法不收敛.

    mathematical-neuroscience.com The generating functional be an infinite dimensional generalization for the familiar generating function for a single random variable.

    single random variable.

    [PDF]Path Integral Methods for Stochastic Differential Equations
    www.mathematical-neuroscience.com/content/.../s13408-015-0018-5.pd...
    by CC Chow - ‎2015
    Feb 12, 2015 - closed form and must be tackled approximately using methods that include ... Although Wiener introduced path integrals to study stochastic ... agrams as a tool for carrying out perturbative expansions and introduces the “loop.

    2 Moment Generating Functionals
    The strategy of path integral methods is to derive a generating function or functional
    for the moments and response functions for SDEs. The generating functional will
    be an infinite dimensional generalization for the familiar generating function for a
    single random variable. In this section we review moment generating functions and
    show how they can be generalized to functional distributions.
    Consider a probability density function (PDF) P(x) for a single real variable x.
    The moments of the PDF are given by
    xn = xnP(x)dx
    and can be obtained directly by taking derivatives of the generating function
    Z(J ) = eJx = eJxP(x)dx,
    where J is a complex parameter, with
    xn = 1
    Z(0)
    dn
    dJn
    Z(J )

    J=0
    .
    Note that in explicitly including Z(0) we are allowing for the possibility that P(x)
    is not normalized. This freedom will be convenient especially when we apply perturbation
    theory. The generating function is



    The analogy between stochastic systems and quantum theory, where path integrals
    are commonly used, is seen by transforming the time coordinates in the path integrals
    via t →

    −1t . When the field ϕ is a function of a single variable t , then this would
    be analogous to single particle quantum mechanics where the quantum amplitude can
    be expressed in terms of a path integral over a configuration variable φ(t). When the
    field is a function of two or more variables ϕ(
    r, t), then this is analogous to quantum
    field theory, where the



    3 Application to SDE
    Building on the previous section, here we derive a generating functional for SDEs.
    Consider a Langevin equation,
    dx
    dt
    = f (x, t)+g(x, t)η(t), (3)
    on the domain t ∈ [0,T ] with initial condition x(t0) = y. The stochastic forcing term
    η(t) obeys η(t) = 0 and η(t)η(t

    ) = δ(t −t

    ). Equation (3) is to be interpreted as
    the Ito stochastic differential equation
    dx = f (xt , t)dt + g(xt , t)dWt , (4)
    where Wt is a Wiener process (i.e. Gaussian white noise), and xt is the value of x
    at time t . We show how to generalize to other stochastic processes later. Functions
    f and g are assumed to obey all the properties required for an Ito SDE to be well
    posed [31]. In particular, the stochastic increment dWt does not depend on f (xt , t)
    or g(xt , t) (i.e. xt is adapted to the filtration generated by the noise). The choice
    between Ito and Stratonovich conventions amounts to a choice of the measure for
    the path integrals, which will be manifested in a condition on the linear response or
    “propagator” that we introduce below.


    生成方程组
    cmp

    来自: cmp(const void*, const void*) 2014-03-22 11:24:32

    • Everett

      Everett (╮(╯▽╰)╭ ~(= ̄ U  ̄=)~) 2014-03-22 13:40:51

      线性方程的话直接构造矩阵求解就可以了。矩阵的构造方法是 SparseArray
    • cmp

      cmp (const void*, const void*) 2014-03-22 14:03:37

      线性方程的话直接构造矩阵求解就可以了。矩阵的构造方法是 SparseArray 线性方程的话直接构造矩阵求解就可以了。矩阵的构造方法是 SparseArray Everett
      嗯不是线性的… 是 J sum{ -cos θ_i sin θ_j - Δ sin θ_i cos θ_j} - h sin θ_i == 0 这样的。

      我想了想用了 Table + 用于处理下标的自定义的函数,貌似可行。然后用 NSolve 一下。

      还剩几个问题。像这样一大群待求变量,用 Mathematica 怎么处理比较好呢?用下标,List 还是什么?

      另外,像这种自定义函数,如何封装比较好? Module 么?
    • Everett

      Everett (╮(╯▽╰)╭ ~(= ̄ U  ̄=)~) 2014-03-22 14:37:23

      变量本身是下标的函数,比如θ[i]
    • Everett

      Everett (╮(╯▽╰)╭ ~(= ̄ U  ̄=)~) 2014-03-22 14:38:29

      嗯不是线性的… 是 J sum{ -cos θ_i sin θ_j - Δ sin θ_i cos θ_j} - h sin θ_i == 0 这样 嗯不是线性的… 是 J sum{ -cos θ_i sin θ_j - Δ sin θ_i cos θ_j} - h sin θ_i == 0 这样的。 我想了想用了 Table + 用于处理下标的自定义的函数,貌似可行。然后用 NSolve 一下。 还剩几个问题。像这样一大群待求变量,用 Mathematica 怎么处理比较好呢?用下标,List 还是什么? 另外,像这种自定义函数,如何封装比较好? Module 么? ... cmp
      未必需要定义处理下标的函数,一般是用模式匹配 {i_,j_}/;Mod[j-i,L]==1
    • cmp

      cmp (const void*, const void*) 2014-03-28 12:53:50

      未必需要定义处理下标的函数,一般是用模式匹配 {i_,j_}/;Mod[j-i,L]==1 未必需要定义处理下标的函数,一般是用模式匹配 {i_,j_}/;Mod[j-i,L]==1 Everett
      我终于解决了这些问题!

      我最早想要的是最小化一个 hamiltonian. 后来发现还是用 NMinimize 比较好, 用 NSolve 经常跑不出来.

      然后格点不要太大, 老板说 20~30个变量就好了. 太大了最优化算法不收敛.

    Feynman diagrams perturbative expansions and introduces the “loopexpansion,” a tool for constructing semiclassical approximations

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    Example of taking a closed line integral of a conservative field. ... Closed curve line integrals of conservative ...
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