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Short-term plasticity (STP) ([[#Stevens95|Stevens 95]], [[#Markram96|Markram 96]], [[#Abbott97|Abbott 97]], [[#Zucker02|Zucker 02]], [[#Abbott04|Abbott 04]]), also called dynamical synapses, refers to a phenomenon in which synaptic efficacy changes over time in a way that reflects the history of presynaptic activity. Two types of STP, with opposite effects on synaptic efficacy, have been observed in experiments. They are known as Short-Term Depression (STD) and Short-Term Facilitation (STF). STD is caused by depletion of neurotransmitters consumed during the synaptic signaling process at the axon terminal of a pre-synaptic neuron, whereas STF is caused by influx of calcium into the axon terminal after spike generation, which increases the release probability of neurotransmitters. STP has been found in various cortical regions and exhibits great diversity in properties ([[#Markram98|Markram 98]], [[#Dittman00|Dittman 00]], [[#Wang06|Wang 06]]). Synapses in different cortical areas can have varied forms of plasticity, being either STD-dominated, STF-dominated, or showing a mixture of both forms.

Short-term plasticity (STP) ([[#Stevens95|Stevens 95]], [[#Markram96|Markram 96]], [[#Abbott97|Abbott 97]], [[#Zucker02|Zucker 02]], [[#Abbott04|Abbott 04]]), also called dynamical synapses, refers to a phenomenon in which synaptic efficacy changes over time in a way that reflects the history of presynaptic activity. Two types of STP, with opposite effects on synaptic efficacy, have been observed in experiments. They are known as Short-Term Depression (STD) and Short-Term Facilitation (STF). STD is caused by depletion of neurotransmitters consumed during the synaptic signaling process at the axon terminal of a pre-synaptic neuron, whereas STF is caused by influx of calcium into the axon terminal after spike generation, which increases the release probability of neurotransmitters. STP has been found in various cortical regions and exhibits great diversity in properties ([[#Markram98|Markram 98]], [[#Dittman00|Dittman 00]], [[#Wang06|Wang 06]]). Synapses in different cortical areas can have varied forms of plasticity, being either STD-dominated, STF-dominated, or showing a mixture of both forms.

Compared with long-term plasticity ([[#Bi01|Bi 01]]), which is hypothesized as the neural substrate for experience-dependent modification of neural circuit, STP has a shorter time scale, typically on the order of hundreds to thousands of milliseconds.  The modification it induces to synaptic efficacy is temporary.  Without continued presynaptic activity, the synaptic efficacy will quickly return to its baseline level.

Compared with long-term plasticity ([[#Bi01|Bi 01]]), which is hypothesized as the neural substrate for experience-dependent modification of neural circuit, STP has a shorter time scale, typically on the order of hundreds to thousands of milliseconds.  The modification it induces to synaptic efficacy is temporary.  Without continued presynaptic activity, the synaptic efficacy will quickly return to its baseline level.

与长期可塑性([[#Bi01|Bi 01]])相比，STP 具有更短的时间尺度，通常为数百到数千毫秒。 它对突触功效的改变是暂时的。 如果没有持续的突触前活动，突触功效将迅速恢复到其基线水平。

与长期可塑性（Bi 01）相比，STP 具有更短的时间尺度，通常为数百到数千毫秒。 它对突触功效的改变是暂时的。 如果没有持续的突触前活动，突触功效将迅速恢复到其基线水平。

Although STP appears to be an unavoidable consequence of synaptic physiology, theoretical studies suggest that its role in brain functions can be profound (see, e.g., publications in ([[#ResearchTopic|Research Topic]]) and the references therein). From a computational point of view, the time scale of STP lies between fast neural signaling (on the order of milliseconds) and experience-induced learning (on the order of minutes or more).  This is the time scale of many processes that occur in daily life, for example motor control, speech recognition and working memory. It is therefore plausible that STP might serve as a neural substrate for processing of temporal information on the relevant time scales. STP implies that the response of a post-synaptic neuron depends of the history of presynaptic activity, creating information that in principle can be extracted and used. In a large-size network, STP can greatly enrich the network's dynamical behaviors, endowing the neural system with information processing capacities that would be difficult to implement using static connections.  These possibilities have led to significant interest in the computational functions of STP within the field of Computational Neuroscience.

Although STP appears to be an unavoidable consequence of synaptic physiology, theoretical studies suggest that its role in brain functions can be profound (see, e.g., publications in ([[#ResearchTopic|Research Topic]]) and the references therein). From a computational point of view, the time scale of STP lies between fast neural signaling (on the order of milliseconds) and experience-induced learning (on the order of minutes or more).  This is the time scale of many processes that occur in daily life, for example motor control, speech recognition and working memory. It is therefore plausible that STP might serve as a neural substrate for processing of temporal information on the relevant time scales. STP implies that the response of a post-synaptic neuron depends of the history of presynaptic activity, creating information that in principle can be extracted and used. In a large-size network, STP can greatly enrich the network's dynamical behaviors, endowing the neural system with information processing capacities that would be difficult to implement using static connections.  These possibilities have led to significant interest in the computational functions of STP within the field of Computational Neuroscience.

尽管 STP 似乎是突触生理学的一个不可避免的结果，但理论研究表明它在大脑功能中的作用可能是深远的（例如，参见（[[#ResearchTopic|Research Topic]]）中的出版物和其中的参考文献）。从计算的角度来看，STP 的时间尺度介于快速神经信号（毫秒级）和经验诱导学习（分钟级或更长时间）之间。这是日常生活中许多过程的时间尺度，例如运动控制、语音识别和工作记忆。因此，STP 可能作为处理相关时间尺度上的时间信息的神经基质是合理的。 STP 意味着突触后神经元的反应取决于突触前活动的历史，从而产生原则上可以提取和使用的信息。在大型网络中，STP 可以极大地丰富网络的动态行为，赋予神经系统以静态连接难以实现的信息处理能力。这些可能性引起了计算神经科学领域对 STP 计算功能的极大兴趣。

尽管 STP 似乎是突触生理学的一个不可避免的结果，但理论研究表明它在大脑功能中的作用可能是深远的（例如，参见（研究主题）中的出版物和其中的参考文献）。从计算的角度来看，STP 的时间尺度介于快速神经信号（毫秒级）和经验诱导学习（分钟级或更长时间）之间。这是日常生活中许多过程的时间尺度，例如运动控制、语音识别和工作记忆。因此，STP 可能作为处理相关时间尺度上的时间信息的神经基质是合理的。 STP 意味着突触后神经元的反应取决于突触前活动的历史，从而产生原则上可以提取和使用的信息。在大型网络中，STP 可以极大地丰富网络的动态行为，赋予神经系统以静态连接难以实现的信息处理能力。这些可能性引起了计算神经科学领域对 STP 计算功能的极大兴趣。

==现象学模型Phenomenological model==

==现象学模型Phenomenological model==

The biophysical processes underlying STP are complex. Studies of the computational roles of STP have relied on the creation of simplified phenomenological models ([[#Abbott97|Abbott 97]],[[#Markram98|Markram 98]],[[#Tsodyks98|Tsodyks 98]]).

The biophysical processes underlying STP are complex. Studies of the computational roles of STP have relied on the creation of simplified phenomenological models ([[#Abbott97|Abbott 97]],[[#Markram98|Markram 98]],[[#Tsodyks98|Tsodyks 98]]).

STP 背后的生物物理过程很复杂。 对 STP 计算作用的研究依赖于创建简化的现象学模型([[#Abbott97|Abbott 97]],[[#Markram98|Markram 98]],[[#Tsodyks98|Tsodyks 98]])。

STP 背后的生物物理过程很复杂。 对 STP 计算作用的研究依赖于创建简化的现象学模型（Abbott 97，Markram 98，Tsodyks 98）。

In the model proposed by Tsodyks and Markram ([[#Tsodyks98|Tsodyks 98]]), the STD effect is modeled by a normalized variable <math>x</math> (<math>0\leq x \leq1</math>), denoting the fraction of resources that remain available after neurotransmitter depletion. The STF effect is modeled by a utilization parameter <math>u</math>, representing the fraction of available resources ready for use (release probability). Following a spike, (i) <math>u</math> increases due to spike-induced calcium influx to the presynaptic terminal, after which (ii) a fraction <math>u</math> of available resources is consumed to produce the post-synaptic current. Between spikes, <math>u</math> decays back to zero with time constant <math>\tau_f</math> and <math>x</math> recovers to 1 with time constant <math>\tau_d </math>. In summary, the dynamics of STP is given by

In the model proposed by Tsodyks and Markram ([[#Tsodyks98|Tsodyks 98]]), the STD effect is modeled by a normalized variable <math>x</math> (<math>0\leq x \leq1</math>), denoting the fraction of resources that remain available after neurotransmitter depletion. The STF effect is modeled by a utilization parameter <math>u</math>, representing the fraction of available resources ready for use (release probability). Following a spike, (i) <math>u</math> increases due to spike-induced calcium influx to the presynaptic terminal, after which (ii) a fraction <math>u</math> of available resources is consumed to produce the post-synaptic current. Between spikes, <math>u</math> decays back to zero with time constant <math>\tau_f</math> and <math>x</math> recovers to 1 with time constant <math>\tau_d </math>. In summary, the dynamics of STP is given by

在 Tsodyks 和 Markram ([[#Tsodyks98|Tsodyks 98]]) 提出的模型中，STD 效应由归一化变量 <math>x</math> (<math>0\leq x \leq1</math>），表示在神经递质耗尽后仍然可用的资源比例。 STF 效应由利用率参数 建模，表示可供使用的可用资源的比例（释放概率）。 在一个尖峰之后，(i)由于尖峰诱导的钙流入突触前末端而增加，之后 (ii) 一小部分<math>u</math> 的可用资源被消耗以产生突触后电流。 在尖峰之间，<math>u</math>衰减回零，时间常数为 <math>\tau_f</math>和 <math>x</math>恢复到 1 具有时间常数 <math>\tau_d </math>。 总之，STP 的动态由下式给出

在 Tsodyks 和 Markram (Tsodyks 98) 提出的模型中，STD 效应由归一化变量 <math>x</math> (<math>0\leq x \leq1</math>），表示在神经递质耗尽后仍然可用的资源比例。 STF 效应由利用率参数 建模，表示可供使用的可用资源的比例（释放概率）。 在一个尖峰之后，(i)由于尖峰诱导的钙流入突触前末端而增加，之后 (ii) 一小部分<math>u</math> 的可用资源被消耗以产生突触后电流。 在尖峰之间，<math>u</math>衰减回零，时间常数为 <math>\tau_f</math>和 <math>x</math>恢复到 1 具有时间常数 <math>\tau_d </math>。 总之，STP 的动态由下式给出

:<math>\begin{aligned}

:<math>\begin{aligned}

图 1. (A) 由 Eqs.\ref{model} 和 \ref{current} 给出的 STP 现象学模型。 (B) 由 STD 主导的突触产生的突触后电流。 神经元放电率 [math]\displaystyle{ R=15 }[/math]Hz。 参数 [math]\displaystyle{ A=1 }[/math], [math]\displaystyle{ U=0.45 }[/math], [math]\displaystyle{ \tau_s=20 }[/math]ms, [ math]\displaystyle{ \tau_d=750 }[/math]ms 和 [math]\displaystyle{ \tau_f=50 }[/math]ms。 (C) STF 主导突触的动力学。 参数 [math]\displaystyle{ U=0.15 }[/math]、[math]\displaystyle{ \tau_f=750 }[/math]ms 和 [math]\displaystyle{ \tau_d=50 }[/math] 小姐。

图 1. (A) 由 Eqs.\ref{model} 和 \ref{current} 给出的 STP 现象学模型。 (B) 由 STD 主导的突触产生的突触后电流。 神经元放电率 [math]\displaystyle{ R=15 }[/math]Hz。 参数 [math]\displaystyle{ A=1 }[/math], [math]\displaystyle{ U=0.45 }[/math], [math]\displaystyle{ \tau_s=20 }[/math]ms, [ math]\displaystyle{ \tau_d=750 }[/math]ms 和 [math]\displaystyle{ \tau_f=50 }[/math]ms。 (C) STF 主导突触的动力学。 参数 [math]\displaystyle{ U=0.15 }[/math]、[math]\displaystyle{ \tau_f=750 }[/math]ms 和 [math]\displaystyle{ \tau_d=50 }[/math] 小姐。

==对信息传输的影响Effects on information transmission==

==对信息传输的影响Effects on information transmission ==

Because STP modifies synaptic efficacy based on the history of presynaptic activity, it can alter neural information transmission ([[#Abbott97|Abbott 97]], [[#Tsodyks97|Tsodyks 97]], [[#Fuhrmann02|Fuhrmann 02]], [[#Rotman11|Rotman 11]], [[#Rosenbaum12|Rosenbaum 12]]). In general, an STD-dominated synapse favors information transfer for low firing rates, since high-frequency spikes rapidly deactivate the synapse. An STF-dominated synapse, however, tends to optimize information transfer for high-frequency bursts, which increase the synaptic strength.  

Because STP modifies synaptic efficacy based on the history of presynaptic activity, it can alter neural information transmission ([[#Abbott97|Abbott 97]], [[#Tsodyks97|Tsodyks 97]], [[#Fuhrmann02|Fuhrmann 02]], [[#Rotman11|Rotman 11]], [[#Rosenbaum12|Rosenbaum 12]]). In general, an STD-dominated synapse favors information transfer for low firing rates, since high-frequency spikes rapidly deactivate the synapse. An STF-dominated synapse, however, tends to optimize information transfer for high-frequency bursts, which increase the synaptic strength.  

因为 STP 根据突触前活动的历史来修改突触功效，所以它可以改变神经信息传递 ([[#Abbott97|Abbott 97]], [[#Tsodyks97|Tsodyks 97]], [[#Fuhrmann02|Fuhrmann 02]], [[#Rotman11|Rotman 11]], [[#Rosenbaum12|Rosenbaum 12]])。 一般来说，以 STD 为主的突触有利于低发射率的信息传递，因为高频尖峰会迅速使突触失活。 然而，以 STF 为主的突触倾向于优化高频突发的信息传递，从而增加突触强度。  

因为 STP 根据突触前活动的历史来修改突触功效，所以它可以改变神经信息传递（Abbott 97、Tsodyks 97、Fuhrmann 02、Rotman 11、Rosenbaum 12）。 一般来说，以 STD 为主的突触有利于低发射率的信息传递，因为高频尖峰会迅速使突触失活。 然而，以 STF 为主的突触倾向于优化高频突发的信息传递，从而增加突触强度。  

Firing-rate-dependent transmission via dynamic synapses can be analyzed by examining the transmission of uncorrelated Poisson spike trains from a large neuronal population with global firing rate <math>R(t)</math>. The time evolution for the postsynaptic current <math>I(t)</math> can be obtained by averaging Eq. \ref{model} over different realization of Poisson processes corresponding to different spike trains ([[#Tsodyks98|Tsodyks 98]]):

Firing-rate-dependent transmission via dynamic synapses can be analyzed by examining the transmission of uncorrelated Poisson spike trains from a large neuronal population with global firing rate <math>R(t)</math>. The time evolution for the postsynaptic current <math>I(t)</math> can be obtained by averaging Eq. \ref{model} over different realization of Poisson processes corresponding to different spike trains ([[#Tsodyks98|Tsodyks 98]]):

可以通过检查来自具有全局放电率<math>R(t)</math>的大型神经元群体的不相关 Poisson 尖峰序列的传输来分析通过动态突触的放电率依赖性传输。 突触后电流<math>I(t)</math>的时间演化可以通过对等式求平均来获得。 \ref{model} 对应于不同尖峰序列的泊松过程的不同实现([[#Tsodyks98|Tsodyks 98]])：

可以通过检查来自具有全局放电率 [math]\displaystyle{ R(t) }[/math] 的大型神经元群体的不相关 Poisson 尖峰序列的传输来分析通过动态突触的放电率依赖性传输。 突触后电流 [math]\displaystyle{ I(t) }[/math] 的时间演化可以通过对等式求平均来获得。 \ref{model} 对应于不同尖峰序列的泊松过程的不同实现（Tsodyks 98）：

:<math>\begin{aligned}

:<math>\begin{aligned}

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]]).

STP 还可以通过其他方式规范信息传输。 例如，STD 可能有助于消除时间输入中的自相关，因为时间近端尖峰倾向于放大抑郁效应，从而降低突触后电位的输出相关性 ([[#Goldman02|Goldman 02]]) 。 另一方面，STF 的效果因时间近端尖峰而扩大，提高了突触后神经元对时间相关输入的敏感性 ([[#Mejías08|Mejías 08]], [[#Bourjaily12|Bourjaily 12]])。

STP 还可以通过其他方式规范信息传输。 例如，STD 可能有助于消除时间输入中的自相关，因为时间近端尖峰倾向于放大抑郁效应，从而降低突触后电位的输出相关性 (Goldman 02)。 另一方面，STF 的效果因时间近端尖峰而扩大，提高了突触后神经元对时间相关输入的敏感性 (Mejías 08, 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 ([[#Klyachko06|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]]）。

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===

除了前馈和反馈传输之外，神经回路还会在神经元之间产生循环交互。由于 STP 包含在循环交互中，网络动力学表现出许多新的有趣行为，这些行为不会出现在纯静态突触中。因此，这些新的动态特性可以实现 STP 介导的网络计算。

除了前馈和反馈传输之外，神经回路还会在神经元之间产生循环交互。由于 STP 包含在循环交互中，网络动力学表现出许多新的有趣行为，这些行为不会出现在纯静态突触中。因此，这些新的动态特性可以实现 STP 介导的网络计算。

=== Prolongation of neural responses to transient inputs===

===延长对瞬态输入的神经反应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<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]]).

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]]).

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]])。

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===

===调制网络对外部输入的响应Modulation of network responses to external input===

Since STP modifies synaptic efficacy instantly, it can modulate the network response to sustained external inputs. An example of this is bursty synchronous firing in an STD-dominated network, either spontaneously or in response to external inputs.  The resulting bursts of activity are called population spikes ([[#Loebel02|Loebel 02]]). To understand this effect, consider a network with strong recurrent interactions between neurons. When a sufficiently large group of neurons fire together, e.g. triggered by external stimulus, they can recruit other neurons via an avalanche-like process. However, after a large synchronous burst of activity, the synapses are weakened by STD, reducing the recurrent currents rapidly, and consequently the network activity returns to baseline. The network will not be activated again until the synapses are sufficiently recovered from depression. Therefore, the rate of population spikes is determined by the time constant of STD (Fig.3A,B). STF can also modulate the network response to external inputs, but in a very different manner ([[#Barak07|Barak 07]]). The varied response properties mediated by STP may provide different ways of representing and conveying the stimulus information in a network.

Since STP modifies synaptic efficacy instantly, it can modulate the network response to sustained external inputs. An example of this is bursty synchronous firing in an STD-dominated network, either spontaneously or in response to external inputs.  The resulting bursts of activity are called population spikes ([[#Loebel02|Loebel 02]]). To understand this effect, consider a network with strong recurrent interactions between neurons. When a sufficiently large group of neurons fire together, e.g. triggered by external stimulus, they can recruit other neurons via an avalanche-like process. However, after a large synchronous burst of activity, the synapses are weakened by STD, reducing the recurrent currents rapidly, and consequently the network activity returns to baseline. The network will not be activated again until the synapses are sufficiently recovered from depression. Therefore, the rate of population spikes is determined by the time constant of STD (Fig.3A,B). STF can also modulate the network response to external inputs, but in a very different manner ([[#Barak07|Barak 07]]). The varied response properties mediated by STP may provide different ways of representing and conveying the stimulus information in a network.

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。

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===

===诱导网络状态的不稳定性或移动性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.

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。

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。

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。

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===

===吸引子动力学的丰富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.

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。

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。

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([[#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。

== Appendix A: Derivation of a temporal filter for short-term depression==

==附录A:短期抑郁的临时过滤器的推导Appendix A: Derivation of a temporal filter for short-term depression==

We consider the rate-based dynamics in Eq. （3）for depression-dominated synapses (<math>u^+ \approx U</math>) and for synaptic responses that are much faster than the depression dynamics (<math>\tau_s \ll \tau_d</math>):

We consider the rate-based dynamics in Eq. （3）for depression-dominated synapses (<math>u^+ \approx U</math>) and for synaptic responses that are much faster than the depression dynamics (<math>\tau_s \ll \tau_d</math>):