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第83行： − + − 上述分析仅描述了具有固定放电率的神经群体放电。 方程。 当突触前群体放电率随时间任意变化时，\ref{poisson} 可用于推导动态突触的过滤特性。 在附录 A 中，我们给出了抑郁支配突触的相应计算 ([math]\displaystyle{ u^+ \approx U }[/math])。 通过考虑小扰动 $R(t):=R_0 + R_1 \rho (t)$ 和 $R_1\ll R_0$ 在恒定速率 $R_0>0 $ 附近，突触电流 $I$ 的傅里叶变换近似为+ 第95行：
第95行： − + − <math>+ − \begin{eqnarray} − \widehat{\chi}(\omega) := 1- \frac{1/x_0 -1}{1/x_0 + j\omega \tau_{d}} = \frac{1+(\tau_{d}\omega)^2x_0+j\omega\tau_{d}(1-x_0)}{1/x_0+(\tau_{d}\omega)^2 x_0}\,, − \label{eq:chihat} − \end{eqnarray} − </math> − \begin{eqnarray} − \widehat{I}(\omega) \approx I_0 \delta(\omega) + \frac{I_0 R_1}{R_0} \widehat{\chi}(\omega) \widehat{\rho}(\omega) − \label{eq:Ihat_final} − \end{eqnarray} − </math>其中我们定义了过滤器<math> 第115行：
第105行： − $\widehat{\rho}$ is the Fourier transform of $\rho$, and $I_0$ and $x_0$ are the stationary values of $I$ and $x$, respectively [see Eq. \ref{stationary} with $u_0 = U$].+ − $\widehat{\rho}$ 是 $\rho$ 的傅里叶变换，$I_0$ 和 $x_0$ 分别是 $I$ 和 $x$ 的平稳值 [参见方程。 \ref{stationary} 与 $u_0 = U$]。 滤波器的幅度 [math]\displaystyle{ |\widehat{\chi}(w)| }[/math] 如图 2C 所示，说明了抑制突触的高通滤波器特性。 换句话说，突触前放电率的快速变化忠实地传递到突触后目标，而缓慢的变化则因抑郁而减弱。+ 第126行：
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第159行： − Consider a network that holds multiple attractor states competing with each other, STD destabilizing one of them can incur the network to switch to another attractor state ([[#Torres07|Torres 07]], [[#Katori11|Katori 11]], [[#Igarashi12|Igarashi 12]]). This property has been linked to spontaneous transition between up and down states of cortical neurons ([[#Holcman06|Holcman 06]]), to the binocular rivalry phenomenon ([[#Kilpatrick10|Kilpatrick 10]]), and to enhanced discrimination capacity for superimposed ambiguous inputs ([[#Fung13|Fung 13]]). STF can also induce state switching, but this is achieved in an indirect way through facilitating the excitatory synapses to interneurons, with the latter in turn suppressing excitatory neurons ([[#Melamed08|Melamed 08]]). + − The joint effect of STD and STF on the memory capacity of the classical Hopfield model has been investigated ([[#Mejías09|Mejías 09]]). It was found that STD degrades the memory capacity of the network, but induces a novel computationally desirable property, that is, the network can hop among memory states, which could be useful for memory searching. Interestingly, STF can compensate for the lost memory capacity caused by STD.+ − 诱导网络状态的不稳定性或移动性+ − 持续放电，指的是一组神经元在没有外部驱动的情况下继续放电的情况，被广泛认为是信息表示的神经基质（Fuster 71）。为了维持网络中的持续活动，需要神经元之间强烈的兴奋性反复相互作用来建立维持神经元反应的正反馈回路。在数学上，持续活动通常被建模为网络的活动静止状态（吸引子）。由于 STD 会根据神经元活动的水平削弱突触的功效，因此它可以抑制吸引子状态。但是，此属性可用于执行有价值的计算。+ − 考虑一个拥有多个相互竞争的吸引子状态的网络，STD 破坏其中一个可能会导致网络切换到另一个吸引子状态（Torres 07，Katori 11，Igarashi 12）。这种特性与皮层神经元上下状态之间的自发转换（Holcman 06）、双眼竞争现象（Kilpatrick 10）以及增强的叠加模糊输入的辨别能力（Fung 13）有关。 STF 也可以诱导状态转换，但这是通过促进中间神经元的兴奋性突触以间接方式实现的，后者反过来抑制兴奋性神经元 (Melamed 08)。+ − + + + + + + + 第190行：
第188行： − 吸引子动力学的丰富+ − − 连续吸引子神经网络 (CANN)，也称为神经场模型或环模型 (Amari 77)，已广泛用于描述神经系统中连续刺激的编码，例如头部方向、方向、运动方向和物体的空间位置。由于神经元之间的平移不变循环交互，CANN 拥有一系列连续的局部静止状态，称为颠簸。这些静止状态形成了一个子空间，网络在该子空间上是中性稳定的，使网络能够平滑地跟踪随时间变化的刺激。 − − 在包含 STP 的情况下，CANN 会显示出新的有趣的动态行为。其中之一是自发行波现象（York 09、Fung 12、Bressloff 12）（图 3C）。考虑一个最初处于局部碰撞状态的网络。由于 STD，凹凸区域的神经相互作用被削弱。由于来自相邻吸引子状态的竞争，一个小的位移会将凸起推开，并且由于 STD 效应，它将继续朝那个方向移动。如果网络由连续移动的输入驱动，则在适当的参数状态下，无论输入移动速度如何，颠簸运动甚至可以引导外部驱动一段恒定的时间，从而实现让人联想到头部预测响应的预期行为。啮齿动物中的方向神经元（图 3D；Fung 12）。 − − − −
→Temporal filtering
===Temporal filtering===
===Temporal filtering===
The above analysis only describes neural population firing with stationary firing rates. Eq. \ref{poisson} can be used to derive the filtering properties of dynamic synapses when the presynaptic population firing rate changes arbitrarily with time. In [[#Appendix A: Derivation of a temporal filter for short-term depression|Appendix A]] we present the corresponding calculation for depression-dominated synapses (<math>u^+ \approx U</math>). By considering small perturbations $R(t):=R_0 + R_1 \rho (t)$ with $R_1\ll R_0$ around the constant rate $R_0>0 $, the Fourier transform of the synaptic current $I$ is approximated by
The above analysis only describes neural population firing with stationary firing rates. Eq. （3）can be used to derive the filtering properties of dynamic synapses when the presynaptic population firing rate changes arbitrarily with time. In [[#Appendix A: Derivation of a temporal filter for short-term depression|Appendix A]] we present the corresponding calculation for depression-dominated synapses (<math>u^+ \approx U</math>). By considering small perturbations<math>R(t):=R_0 + R_1 \rho (t)</math>with <math>R_1\ll R_0</math>around the constant rate <math>R_0>0</math>, the Fourier transform of the synaptic current <math>I</math>is approximated by
'''时间过滤'''
'''时间过滤'''
上述分析仅描述了具有固定放电率的神经群体放电。当突触前群体放电率随时间任意变化时， 方程（3）可用于推导动态突触的过滤特性。 在附录 A 中，我们给出了抑郁支配突触的相应计算 (<math>u^+ \approx U</math>)。 通过考虑小扰动<math>R(t):=R_0 + R_1 \rho (t)</math>和<math>R_1\ll R_0</math>在恒定速率<math>R_0>0</math>附近，突触电流 <math>I</math>的傅里叶变换近似为
<math>
<math>
\end{eqnarray}
\end{eqnarray}
</math>
</math>
where we defined the filter
where we defined the filter其中我们定义了过滤器
<math>
<math>
\begin{eqnarray}
\begin{eqnarray}
\widehat{\chi}(\omega) := 1- \frac{1/x_0 -1}{1/x_0 + j\omega \tau_{d}} = \frac{1+(\tau_{d}\omega)^2x_0+j\omega\tau_{d}(1-x_0)}{1/x_0+(\tau_{d}\omega)^2 x_0}\,,
\widehat{\chi}(\omega) := 1- \frac{1/x_0 -1}{1/x_0 + j\omega \tau_{d}} = \frac{1+(\tau_{d}\omega)^2x_0+j\omega\tau_{d}(1-x_0)}{1/x_0+(\tau_{d}\omega)^2 x_0}\,,
</math>
</math>
<math>\widehat{\rho}</math>is the Fourier transform of <math>\rho</math>, and<math>I_0</math>and<math>x_0</math>are the stationary values of<math>I</math>and<math>x</math>, respectively [see Eq. （4） with <math>u_0 = U</math>].
The amplitude of the filter <math>|\widehat{\chi}(w)|</math> is shown in Fig. 2C, illustrating the high-pass filter properties of depressing synapses. In other words, fast changes in presynaptic firing rates are faithfully transmitted to the postsynaptic targets, while slow changes are attenuated by depression.
The amplitude of the filter <math>|\widehat{\chi}(w)|</math> is shown in Fig. 2C, illustrating the high-pass filter properties of depressing synapses. In other words, fast changes in presynaptic firing rates are faithfully transmitted to the postsynaptic targets, while slow changes are attenuated by depression.
<math>\widehat{\rho}</math>是<math>\rho</math>的傅里叶变换，<math>I_0</math>和<math>x_0</math>分别是<math>I</math>和<math>x</math>的平稳值 [参见方程（4）与 <math>u_0 = U</math>]。 滤波器的幅度<math>|\widehat{\chi}(w)|</math>如图 2C 所示，说明了抑制突触的高通滤波器特性。 换句话说，突触前放电率的快速变化忠实地传递到突触后目标，而缓慢的变化则因抑郁而减弱。
STP can also regulate information transmission in other ways. For instance, STD may contribute to remove auto-correlation in temporal inputs, since temporally proximal spikes tend to magnify the depression effect and hence reduce the output correlation of the post-synaptic potential ([[#Goldman02|Goldman 02]]). On the other hand, STF, whose effect is enlarged by temporally proximal spikes, improves the sensitivity of a post-synaptic neuron to temporally correlated inputs ([[#Mejías08|Mejías 08]], [[#Bourjaily12|Bourjaily 12]]).
STP can also regulate information transmission in other ways. For instance, STD may contribute to remove auto-correlation in temporal inputs, since temporally proximal spikes tend to magnify the depression effect and hence reduce the output correlation of the post-synaptic potential ([[#Goldman02|Goldman 02]]). On the other hand, STF, whose effect is enlarged by temporally proximal spikes, improves the sensitivity of a post-synaptic neuron to temporally correlated inputs ([[#Mejías08|Mejías 08]], [[#Bourjaily12|Bourjaily 12]]).
By combining STD and STF, neural information transmission could be further improved. For example, by combining STF-dominated excitatory and STD-dominated inhibitory synapses, the detection of high-frequency epochs by a postsynaptic neuron can be enhanced ([[#Klyachko06|Klyachko 06]]). In a postsynaptic neuron receiving both STD-dominated and STF-dominated inputs, the neural response can show both low- and high-pass filtering properties ([[#Fortune01|Fortune 01]]).
By combining STD and STF, neural information transmission could be further improved. For example, by combining STF-dominated excitatory and STD-dominated inhibitory synapses, the detection of high-frequency epochs by a postsynaptic neuron can be enhanced ([[#Klyachko06|Klyachko 06]]). In a postsynaptic neuron receiving both STD-dominated and STF-dominated inputs, the neural response can show both low- and high-pass filtering properties ([[#Fortune01|Fortune 01]]).
通过结合STD和STF，可以进一步改善神经信息传输。 例如，通过结合 STF 主导的兴奋性突触和 STD 主导的抑制性突触，可以增强突触后神经元对高频时期的检测 (Klyachko 06)。 在同时接收 STD 主导和 STF 主导输入的突触后神经元中，神经反应可以显示低通和高通滤波特性（财富 01）。
通过结合STD和STF，可以进一步改善神经信息传输。 例如，通过结合 STF 主导的兴奋性突触和 STD 主导的抑制性突触，可以增强突触后神经元对高频时期的检测 (Klyachko 06)。 在同时接收 STD 主导和 STF 主导输入的突触后神经元中，神经反应可以显示低通和高通滤波特性（[[#Fortune01|Fortune 01]]）。
===Gain control===
===Gain control===
Since STD suppresses synaptic efficacy in a frequency-dependent manner, it has been suggested that STD provides an automatic mechanism to achieve gain control, namely, by assigning high gain to slowly firing afferents and low gain to rapidly firing afferents ([[#Abbott97|Abbott 97]], [[#Abbott04|Abbott 04]], [[#Cook03|Cook 03]]). If a steady presynaptic firing rate <math>R</math> changes abruptly by an amount <math>\Delta R</math>, the first spike at the new rate will be transmitted with the efficacy <math>E</math> before the synapse is further depressed. Thus, the transient increase in synaptic input will be proportional to <math>\Delta R E(R)</math>, which is approximately proportional to <math>\Delta R/R</math> for large rates (see above). This is reminiscent of Weber’s law, which states that a transient synaptic response is roughly proportional to the percentage change of the input firing rate. Fig. 2D shows that for a fixed-size rate change <math>\Delta R</math>, the response decreases as a function of the steady input value; whereas without STD, the response would be constant for a fixed-size rate change.
Since STD suppresses synaptic efficacy in a frequency-dependent manner, it has been suggested that STD provides an automatic mechanism to achieve gain control, namely, by assigning high gain to slowly firing afferents and low gain to rapidly firing afferents ([[#Abbott97|Abbott 97]], [[#Abbott04|Abbott 04]], [[#Cook03|Cook 03]]). If a steady presynaptic firing rate <math>R</math> changes abruptly by an amount <math>\Delta R</math>, the first spike at the new rate will be transmitted with the efficacy <math>E</math> before the synapse is further depressed. Thus, the transient increase in synaptic input will be proportional to <math>\Delta R E(R)</math>, which is approximately proportional to <math>\Delta R/R</math> for large rates (see above). This is reminiscent of Weber’s law, which states that a transient synaptic response is roughly proportional to the percentage change of the input firing rate. Fig. 2D shows that for a fixed-size rate change <math>\Delta R</math>, the response decreases as a function of the steady input value; whereas without STD, the response would be constant for a fixed-size rate change.
由于 STD 以频率依赖性方式抑制突触功效，因此有人提出 STD 提供了一种自动机制来实现增益控制，即通过将高增益分配给缓慢放电的传入神经并将低增益分配给快速放电的传入神经（Abbott 97, Abbott 04 , 库克 03)。如果一个稳定的突触前放电率 [math]\displaystyle{ R }[/math] 突然改变了 [math]\displaystyle{ \Delta R }[/math] 的量，那么新的突触前放电率将与在突触被进一步抑制之前的功效 [math]\displaystyle{ E }[/math]。因此，突触输入的瞬时增加将与 [math]\displaystyle{ \Delta R E(R) }[/math] 成正比，这与 [math]\displaystyle{ \Delta R/R }[/math] 大致成正比] 对于大利率（见上文）。这让人想起韦伯定律，该定律指出瞬态突触反应大致与输入放电率的百分比变化成正比。图 2D 显示对于固定大小的速率变化 [math]\displaystyle{ \Delta R }[/math]，响应随着稳定输入值的变化而减小；而在没有 STD 的情况下，对于固定大小的速率变化，响应将是恒定的。
增益控制
由于 STD 以频率依赖性方式抑制突触功效，因此有人提出 STD 提供了一种自动机制来实现增益控制，即<math>\Delta R</math>通过将高增益分配给缓慢放电的传入神经并将低增益分配给快速放电的传入神经（[[#Abbott97|Abbott 97]], [[#Abbott04|Abbott 04]], [[#Cook03|Cook 03]])。如果一个稳定的突触前放电率 <math>R</math>突然改变了<math>\Delta R</math>的量，那么新的突触前放电率将与在突触被进一步抑制之前的功效 <math>E</math>。因此，突触输入的瞬时增加将与 <math>\Delta R E(R)</math>成正比，这与<math>\Delta R/R</math>大致成正比] 对于大利率（见上文）。这让人想起韦伯定律，该定律指出瞬态突触反应大致与输入放电率的百分比变化成正比。图 2D 显示对于固定大小的速率变化<math>\Delta R</math>，响应随着稳定输入值的变化而减小；而在没有 STD 的情况下，对于固定大小的速率变化，响应将是恒定的。
[[Image:Fig2A_short_term_plasticity.png|300px|链接=Special:FilePath/Fig2A_short_term_plasticity.png]]
[[Image:Fig2A_short_term_plasticity.png|300px|链接=Special:FilePath/Fig2A_short_term_plasticity.png]]
[[Image:Fig2B_short_term_plasticity.png|300px|链接=Special:FilePath/Fig2B_short_term_plasticity.png]]
[[Image:Fig2B_short_term_plasticity.png|300px|链接=Special:FilePath/Fig2B_short_term_plasticity.png]]
[[Image:Fig2C_short_term_plasticity.png|300px|链接=Special:FilePath/Fig2C_short_term_plasticity.png]]
[[Image:Fig2C_short_term_plasticity.png|300px|链接=Special:FilePath/Fig2C_short_term_plasticity.png]]
[[Image:Fig2D_short_term_plasticity.png|300px|链接=Special:FilePath/Fig2D_short_term_plasticity.png]] <br />Figure 2. (A) The steady values of the efficacy of an STD-dominated synapse and the postsynaptic currents it generates, measured by <math>ux</math> and <math>uxR</math>, respectively. The parameters are the same as in Fig.1B. (B) Same as (A) for an STF-dominated synapse. The parameters are the same as in Fig. 1C. (C) The filtering properties of an STD-dominated synapse, measured by <math>|\widehat{\chi}(w)|</math> [Eq. \ref{eq:chihat}]. (D) The neural response to an abrupt input change <math>\Delta R</math> vs. the steady rate value for a STD-dominating synapse. <math>\Delta R=5</math>Hz. The parameters are the same as in Fig.1B.
[[Image:Fig2D_short_term_plasticity.png|300px|链接=Special:FilePath/Fig2D_short_term_plasticity.png]] <br />Figure 2. (A) The steady values of the efficacy of an STD-dominated synapse and the postsynaptic currents it generates, measured by <math>ux</math> and <math>uxR</math>, respectively. The parameters are the same as in Fig.1B. (B) Same as (A) for an STF-dominated synapse. The parameters are the same as in Fig. 1C. (C) The filtering properties of an STD-dominated synapse, measured by <math>|\widehat{\chi}(w)|</math> [Eq.（6）]. (D) The neural response to an abrupt input change <math>\Delta R</math> vs. the steady rate value for a STD-dominating synapse. <math>\Delta R=5</math>Hz. The parameters are the same as in Fig.1B.
图 2. (A) 由 [math]\displaystyle{ ux }[/math] 和 [math]\displaystyle{ uxR }[/ 数学]，分别。 参数与图 1B 相同。 (B) 对于 STF 主导的突触，与 (A) 相同。 参数与图 1C 中的相同。 (C) 以 [math]\displaystyle{ |\widehat{\chi}(w)| 衡量的 STD 主导突触的过滤特性 }[/数学] [等式。 \ref{eq:chihat}]。 (D) 对突然输入变化的神经反应 [math]\displaystyle{ \Delta R}[/math] 与 STD 主导突触的稳定速率值。 [数学]\displaystyle{ \Delta R=5 }[/math]Hz. 参数与图 1B 相同。
图 2. (A) 由 <math>ux</math>和 <math>uxR</math>，分别。 参数与图 1B 相同。 (B) 对于 STF 主导的突触，与 (A) 相同。 参数与图 1C 中的相同。 (C) 以 <math>|\widehat{\chi}(w)|</math>衡量的 STD 主导突触的过滤特性[等式（6）]。 (D) 对突然输入变化的神经反应<math>\Delta R=5</math>与 STD 主导突触的稳定速率值。 <math>\Delta R=5</math>Hz. 参数与图 1B 相同。
==对网络动态的影响Effects on network dynamics==
==对网络动态的影响Effects on network dynamics==
===Prolongation of neural responses to transient inputs===
===Prolongation of neural responses to transient inputs===
Since STP has a much longer time scale than that of single neuron dynamics (the latter is typically in the time order of <math>10-20</math> milliseconds), a new feature STP can bring to the network dynamics is prolongation of neural responses to a transient input. This stimulus-induced residual activity therefore holds a memory trace of the input, lasting up to several hundred milliseconds in a large-size network, and can serve as a buffer for information processing. For example, it has been shown that STD-mediated residual activity can cause a neural system to discriminate between rhythmic inputs of different periods ([[#Karmorkar07|Karmorkar 07]]). STP also plays an important role in a general computation framework called a reservoir network. In this framework, STP, together with other dynamical elements of a large-size network, effectively map the input features from a low-dimensional space to the high-dimensional state space of the network that includes both active (neural) and hidden (synaptic) components, so that the input information can be more easily read out ([[#Buonomano09|Buonomano 09]]). In a recent development it was proposed that STF-enhanced synapses themselves can hold the memory trace of an input without recruiting persistent firing of neurons, potentially providing the most economical and robust way to implement working memory ([[#Mongillo08|Mongillo 08]]).
Since STP has a much longer time scale than that of single neuron dynamics (the latter is typically in the time order of <math>10-20</math> milliseconds), a new feature STP can bring to the network dynamics is prolongation of neural responses to a transient input. This stimulus-induced residual activity therefore holds a memory trace of the input, lasting up to several hundred milliseconds in a large-size network, and can serve as a buffer for information processing. For example, it has been<math>10-20</math> shown that STD-mediated residual activity can cause a neural system to discriminate between rhythmic inputs of different periods ([[#Karmorkar07|Karmorkar 07]]). STP also plays an important role in a general computation framework called a reservoir network. In this framework, STP, together with other dynamical elements of a large-size network, effectively map the input features from a low-dimensional space to the high-dimensional state space of the network that includes both active (neural) and hidden (synaptic) components, so that the input information can be more easily read out ([[#Buonomano09|Buonomano 09]]). In a recent development it was proposed that STF-enhanced synapses themselves can hold the memory trace of an input without recruiting persistent firing of neurons, potentially providing the most economical and robust way to implement working memory ([[#Mongillo08|Mongillo 08]]).
延长对瞬态输入的神经反应
延长对瞬态输入的神经反应
由于 STP 的时间尺度比单神经元动力学要长得多（后者的时间顺序通常为 [math]\displaystyle{ 10-20 }[/math] 毫秒），因此 STP 可以为网络带来一个新功能动力学是对瞬态输入的神经反应的延长。因此，这种刺激引起的残余活动保留了输入的记忆轨迹，在大型网络中持续长达数百毫秒，并且可以作为信息处理的缓冲区。例如，已经表明 STD 介导的残余活动可以导致神经系统区分不同时期的节律输入（Karmorkar 07）。 STP 在称为水库网络的通用计算框架中也起着重要作用。在这个框架中，STP 与大型网络的其他动态元素一起，有效地将输入特征从低维空间映射到网络的高维状态空间，包括活动（神经）和隐藏（突触） ) 组件，从而可以更轻松地读出输入信息（Buonomano 09）。在最近的一项发展中，有人提出 STF 增强的突触本身可以保持输入的记忆轨迹，而无需招募神经元的持续放电，这可能为实现工作记忆提供最经济和最稳健的方式 (Mongillo 08)。
由于 STP 的时间尺度比单神经元动力学要长得多（后者的时间顺序通常为 <math>10-20</math>毫秒），因此 STP 可以为网络带来一个新功能动力学是对瞬态输入的神经反应的延长。因此，这种刺激引起的残余活动保留了输入的记忆轨迹，在大型网络中持续长达数百毫秒，并且可以作为信息处理的缓冲区。例如，<math>10-20</math>已经表明 STD 介导的残余活动可以导致神经系统区分不同时期的节律输入（[[#Karmorkar07|Karmorkar 07]]）。STP 在称为水库网络的通用计算框架中也起着重要作用。在这个框架中，STP 与大型网络的其他动态元素一起，有效地将输入特征从低维空间映射到网络的高维状态空间，包括活动（神经）和隐藏（突触） ) 组件，从而可以更轻松地读出输入信息（[[#Buonomano09|Buonomano 09]]）。在最近的一项发展中，有人提出 STF 增强的突触本身可以保持输入的记忆轨迹，而无需招募神经元的持续放电，这可能为实现工作记忆提供最经济和最稳健的方式 ([[#Mongillo08|Mongillo 08]])。
===Modulation of network responses to external input===
===Modulation of network responses to external input===
调制网络对外部输入的响应
调制网络对外部输入的响应
由于 STP 会立即修改突触功效，因此它可以调节网络对持续外部输入的响应。这方面的一个例子是 STD 主导网络中的突发同步触发，无论是自发地还是响应外部输入。由此产生的活动爆发称为人口高峰（Loebel 02）。要理解这种效应，请考虑一个神经元之间具有强循环交互的网络。当足够大的一组神经元一起发射时，例如由外部刺激触发，它们可以通过类似雪崩的过程招募其他神经元。然而，在大量同步突发活动之后，突触被 STD 削弱，快速减少循环电流，因此网络活动恢复到基线。在突触从抑郁症中充分恢复之前，网络不会再次被激活。因此，人口峰值的速率由 STD 的时间常数决定（图 3A，B）。 STF 还可以调制网络对外部输入的响应，但方式非常不同（Barak 07）。由 STP 介导的不同响应属性可以提供在网络中表示和传达刺激信息的不同方式。
由于 STP 会立即修改突触功效，因此它可以调节网络对持续外部输入的响应。这方面的一个例子是 STD 主导网络中的突发同步触发，无论是自发地还是响应外部输入。由此产生的活动爆发称为人口高峰（[[#Loebel02|Loebel 02]]）。要理解这种效应，请考虑一个神经元之间具有强循环交互的网络。当足够大的一组神经元一起发射时，例如由外部刺激触发，它们可以通过类似雪崩的过程招募其他神经元。然而，在大量同步突发活动之后，突触被 STD 削弱，快速减少循环电流，因此网络活动恢复到基线。在突触从抑郁症中充分恢复之前，网络不会再次被激活。因此，人口峰值的速率由 STD 的时间常数决定（图 3A，B）。STF 还可以调制网络对外部输入的响应，但方式非常不同（([[#Barak07|Barak 07]]）。由 STP 介导的不同响应属性可以提供在网络中表示和传达刺激信息的不同方式。
===Induction of instability or mobility of network state===
===Induction of instability or mobility of network state===
Persistent firing, referring to situations in which a group of neurons continue firing without external drive, is widely regarded as a neural substrate for information representation ([[#Fuster71|Fuster 71]]). To maintain persistent activity in a network, strong excitatory recurrent interactions between neurons are needed to establish a positive-feedback loop sustaining neuronal responses. Mathematically, persistent activity is often modeled as an active stationary state (attractor) of the network. Since STD weakens synaptic efficacy depending on the level of neuronal activity, it can suppress an attractor state. This property, however, can be used to carry out valuable computations.
Persistent firing, referring to situations in which a group of neurons continue firing without external drive, is widely regarded as a neural substrate for information representation ([[#Fuster71|Fuster 71]]). To maintain persistent activity in a network, strong excitatory recurrent interactions between neurons are needed to establish a positive-feedback loop sustaining neuronal responses. Mathematically, persistent activity is often modeled as an active stationary state (attractor) of the network. Since STD weakens synaptic efficacy depending on the level of neuronal activity, it can suppress an attractor state. This property, however, can be used to carry out valuable computations.
诱导网络状态的不稳定性或移动性
持续放电，指的是一组神经元在没有外部驱动的情况下继续放电的情况，被广泛认为是信息表示的神经基质（[[#Fuster71|Fuster 71]]）。为了维持网络中的持续活动，需要神经元之间强烈的兴奋性反复相互作用来建立维持神经元反应的正反馈回路。在数学上，持续活动通常被建模为网络的活动静止状态（吸引子）。由于 STD 会根据神经元活动的水平削弱突触的功效，因此它可以抑制吸引子状态。但是，此属性可用于执行有价值的计算。
Consider a network that holds multiple attractor states competing with each other, STD destabilizing one of them can incur the network to switch to another attractor state ([[#Torres07|Torres 07]], [[#Katori11|Katori 11]], [[#Igarashi12|Igarashi 12]]). This property has been linked to spontaneous transition between up and down states of cortical neurons ([[#Holcman06|Holcman 06]]), to the binocular rivalry phenomenon ([[#Kilpatrick10|Kilpatrick 10]]), and to enhanced discrimination capacity for superimposed ambiguous inputs ([[#Fung13|Fung 13]]). STF can also induce state switching, but this is achieved in an indirect way through facilitating the excitatory synapses to interneurons, with the latter in turn suppressing excitatory neurons ([[#Melamed08|Melamed 08]]).
考虑一个拥有多个相互竞争的吸引子状态的网络，STD 破坏其中一个可能会导致网络切换到另一个吸引子状态 ([[#Torres07|Torres 07]], [[#Katori11|Katori 11]], [[#Igarashi12|Igarashi 12]])。这种特性与皮层神经元上下状态之间的自发转换 ([[#Holcman06|Holcman 06]])、双眼竞争现象 ([[#Kilpatrick10|Kilpatrick 10]])以及增强的叠加模糊输入的辨别能力([[#Fung13|Fung 13]])有关。 STF 也可以诱导状态转换，但这是通过促进中间神经元的兴奋性突触以间接方式实现的，后者反过来抑制兴奋性神经元 ([[#Melamed08|Melamed 08]])。
The joint effect of STD and STF on the memory capacity of the classical Hopfield model has been investigated ([[#Mejías09|Mejías 09]]). It was found that STD degrades the memory capacity of the network, but induces a novel computationally desirable property, that is, the network can hop among memory states, which could be useful for memory searching. Interestingly, STF can compensate for the lost memory capacity caused by STD.
已经研究了 STD 和 STF 对经典 Hopfield 模型的记忆容量的联合影响 (Mejías 09)。研究发现，STD 会降低网络的记忆容量，但会产生一种新的计算上理想的特性，即网络可以在记忆状态之间跳跃，这可能对记忆搜索很有用。有趣的是，STF 可以弥补 STD 造成的内存容量损失。
已经研究了 STD 和 STF 对经典 Hopfield 模型的记忆容量的联合影响([[#Mejías09|Mejías 09]])。研究发现，STD 会降低网络的记忆容量，但会产生一种新的计算上理想的特性，即网络可以在记忆状态之间跳跃，这可能对记忆搜索很有用。有趣的是，STF 可以弥补 STD 造成的内存容量损失。
===Enrichment of attractor dynamics===
===Enrichment of attractor dynamics===
Continuous Attractor Neural Networks (CANNs), also called neural field models or ring models ([[#Amari77|Amari 77]]), have been widely used to describe the encoding of continuous stimuli in the neural system, such as for head-direction, orientation, movement direction, and spatial location of objects. A CANN, due to its translation-invariant recurrent interactions between neurons, holds a continuous family of localized stationary states, called bumps. These stationary states form a subspace on which the network is neutrally stable, enabling the network to track time-varying stimuli smoothly.
Continuous Attractor Neural Networks (CANNs), also called neural field models or ring models ([[#Amari77|Amari 77]]), have been widely used to describe the encoding of continuous stimuli in the neural system, such as for head-direction, orientation, movement direction, and spatial location of objects. A CANN, due to its translation-invariant recurrent interactions between neurons, holds a continuous family of localized stationary states, called bumps. These stationary states form a subspace on which the network is neutrally stable, enabling the network to track time-varying stimuli smoothly.
吸引子动力学的丰富
连续吸引子神经网络 (CANN)，也称为神经场模型或环模型 ([[#Amari77|Amari 77]])，已广泛用于描述神经系统中连续刺激的编码，例如头部方向、方向、运动方向和物体的空间位置。由于神经元之间的平移不变循环交互，CANN 拥有一系列连续的局部静止状态，称为颠簸。这些静止状态形成了一个子空间，网络在该子空间上是中性稳定的，使网络能够平滑地跟踪随时间变化的刺激。
With STP included, a CANN displays new interesting dynamical behaviors. One of them is a spontaneous traveling wave phenomenon ([[#York09|York 09]], [[#Fung12a|Fung 12]], [[#Bressloff12|Bressloff 12]]) (Fig.3C). Consider a network that is initially in a localized bump state. Because of STD, the neural interactions in the bump region are weakened. As a result of competition from neighboring attractor states, a small displacement will push the bump away, and it will continue to move in that direction due to the STD effect. If the network is driven by a continuously moving input, in a proper parameter regime the bump movement can even lead the external drive by a constant time irrespective to the input moving speed, achieving an anticipative behavior that is reminiscent to the predictive responses of head-direction neurons in rodents (Fig.3D; [[#Fung12b|Fung 12]]).
With STP included, a CANN displays new interesting dynamical behaviors. One of them is a spontaneous traveling wave phenomenon ([[#York09|York 09]], [[#Fung12a|Fung 12]], [[#Bressloff12|Bressloff 12]]) (Fig.3C). Consider a network that is initially in a localized bump state. Because of STD, the neural interactions in the bump region are weakened. As a result of competition from neighboring attractor states, a small displacement will push the bump away, and it will continue to move in that direction due to the STD effect. If the network is driven by a continuously moving input, in a proper parameter regime the bump movement can even lead the external drive by a constant time irrespective to the input moving speed, achieving an anticipative behavior that is reminiscent to the predictive responses of head-direction neurons in rodents (Fig.3D; [[#Fung12b|Fung 12]]).
在包含 STP 的情况下，CANN 会显示出新的有趣的动态行为。其中之一是自发行波现象 ([[#York09|York 09]], [[#Fung12a|Fung 12]], [[#Bressloff12|Bressloff 12]])（图 3C）。考虑一个最初处于局部碰撞状态的网络。由于 STD，凹凸区域的神经相互作用被削弱。由于来自相邻吸引子状态的竞争，一个小的位移会将凸起推开，并且由于 STD 效应，它将继续朝那个方向移动。如果网络由连续移动的输入驱动，则在适当的参数状态下，无论输入移动速度如何，颠簸运动甚至可以引导外部驱动一段恒定的时间，从而实现让人联想到头部预测响应的预期行为。啮齿动物中的方向神经元(Fig.3D; [[#Fung12b|Fung 12]])。
[[Image:Fig3AB_short_term_plasticity.png|700px|链接=Special:FilePath/Fig3AB_short_term_plasticity.png]]
[[Image:Fig3AB_short_term_plasticity.png|700px|链接=Special:FilePath/Fig3AB_short_term_plasticity.png]]
Figure 3. (A,B) Population spikes generated by a STD-dominating network in response to external excitatory pulses. When the presentation rate of the pulses is low (A), the network responds to each one of them. For higher presentation rate (B), the network only responds to a fraction of the inputs. Adapted from ([[#Loebel02|Loebel 02]]). (C) The traveling wave generated by STD in a CANN. (D) The anticipative tracking behavior of a CANN with STD.
Figure 3. (A,B) Population spikes generated by a STD-dominating network in response to external excitatory pulses. When the presentation rate of the pulses is low (A), the network responds to each one of them. For higher presentation rate (B), the network only responds to a fraction of the inputs. Adapted from ([[#Loebel02|Loebel 02]]). (C) The traveling wave generated by STD in a CANN. (D) The anticipative tracking behavior of a CANN with STD.
图 3. (A,B) 以 STD 为主的网络响应外部兴奋性脉冲而产生的人口峰值。当脉冲的呈现率低 (A) 时，网络对它们中的每一个做出响应。对于更高的呈现率 (B)，网络仅响应一小部分输入。改编自([[#Loebel02|Loebel 02]])。 (C) STD 在 CANN 中产生的行波。 (D) 具有 STD 的 CANN 的预期跟踪行为。
图 3. (A,B) 以 STD 为主的网络响应外部兴奋性脉冲而产生的人口峰值。当脉冲的呈现率低 (A) 时，网络对它们中的每一个做出响应。对于更高的呈现率 (B)，网络仅响应一小部分输入。改编自 (Loebel 02)。 (C) STD 在 CANN 中产生的行波。 (D) 具有 STD 的 CANN 的预期跟踪行为。
==Appendix A: Derivation of a temporal filter for short-term depression==
==Appendix A: Derivation of a temporal filter for short-term depression==