Circuits that contain the Model Concept : Long-term Synaptic Plasticity

(The model is used to investigate the mechanisms and/or effects of long-term synaptic plasticity.)
Re-display model names without descriptions
    Models   Description
1. A 1000 cell network model for Lateral Amygdala (Kim et al. 2013)
1000 Cell Lateral Amygdala model for investigation of plasticity and memory storage during Pavlovian Conditioning.
2. A basal ganglia model of aberrant learning (Ursino et al. 2018)
A comprehensive, biologically inspired neurocomputational model of action selection in the Basal Ganglia allows simulation of dopamine induced aberrant learning in Parkinsonian subjects. In particular, the model simulates the Alternate Finger Tapping motor task as an indicator of bradykinesia.
3. Acetylcholine-modulated plasticity in reward-driven navigation (Zannone et al 2018)
"Neuromodulation plays a fundamental role in the acquisition of new behaviours. In previous experimental work, we showed that acetylcholine biases hippocampal synaptic plasticity towards depression, and the subsequent application of dopamine can retroactively convert depression into potentiation. We also demonstrated that incorporating this sequentially neuromodulated Spike- Timing-Dependent Plasticity (STDP) rule in a network model of navigation yields effective learning of changing reward locations. Here, we employ computational modelling to further characterize the effects of cholinergic depression on behaviour. We find that acetylcholine, by allowing learning from negative outcomes, enhances exploration over the action space. We show that this results in a variety of effects, depending on the structure of the model, the environment and the task. Interestingly, sequentially neuromodulated STDP also yields flexible learning, surpassing the performance of other reward-modulated plasticity rules."
4. Adaptive robotic control driven by a versatile spiking cerebellar network (Casellato et al. 2014)
" ... We have coupled a realistic cerebellar spiking neural network (SNN) with a real robot and challenged it in multiple diverse sensorimotor tasks. ..."
5. Biologically-plausible models for spatial navigation (Cannon et al 2003)
Hypotheses about how parahippocampal and hippocampal structures may be involved in spatial navigation tasks are implemented in a model of a virtual rat navigating through a virtual environment in search of a food reward. The model incorporates theta oscillations to separate encoding from retrieval and yields testable predictions about the phase relations of spiking activity to theta oscillations in different parts of the hippocampal formation at various stages of the behavioral task. See paper for more and details.
6. Cancelling redundant input in ELL pyramidal cells (Bol et al. 2011)
The paper investigates the property of the electrosensory lateral line lobe (ELL) of the brain of weakly electric fish to cancel predictable stimuli. Electroreceptors on the skin encode all signals in their firing activity, but superficial pyramidal (SP) cells in the ELL that receive this feedforward input do not respond to constant sinusoidal signals. This cancellation putatively occurs using a network of feedback delay lines and burst-induced synaptic plasticity between the delay lines and the SP cell that learns to cancel the redundant input. Biologically, the delay lines are parallel fibres from cerebellar-like granule cells in the eminentia granularis posterior. A model of this network (e.g. electroreceptors, SP cells, delay lines and burst-induced plasticity) was constructed to test whether the current knowledge of how the network operates is sufficient to cancel redundant stimuli.
7. Cerebellar memory consolidation model (Yamazaki et al. 2015)
"Long-term depression (LTD) at parallel fiber-Purkinje cell (PF-PC) synapses is thought to underlie memory formation in cerebellar motor learning. Recent experimental results, however, suggest that multiple plasticity mechanisms in the cerebellar cortex and cerebellar/vestibular nuclei participate in memory formation. To examine this possibility, we formulated a simple model of the cerebellum with a minimal number of components based on its known anatomy and physiology, implementing both LTD and long-term potentiation (LTP) at PF-PC synapses and mossy fiber-vestibular nuclear neuron (MF-VN) synapses. With this model, we conducted a simulation study of the gain adaptation of optokinetic response (OKR) eye movement. Our model reproduced several important aspects of previously reported experimental results in wild-type and cerebellum-related gene-manipulated mice. ..."
8. Computing with neural synchrony (Brette 2012)
"... In a heterogeneous neural population, it appears that synchrony patterns represent structure or sensory invariants in stimuli, which can then be detected by postsynaptic neurons. The required neural circuitry can spontaneously emerge with spike-timing-dependent plasticity. Using examples in different sensory modalities, I show that this allows simple neural circuits to extract relevant information from realistic sensory stimuli, for example to identify a fluctuating odor in the presence of distractors. ..."
9. Cortical model with reinforcement learning drives realistic virtual arm (Dura-Bernal et al 2015)
We developed a 3-layer sensorimotor cortical network of consisting of 704 spiking model-neurons, including excitatory, fast-spiking and low-threshold spiking interneurons. Neurons were interconnected with AMPA/NMDA, and GABAA synapses. We trained our model using spike-timing-dependent reinforcement learning to control a virtual musculoskeletal human arm, with realistic anatomical and biomechanical properties, to reach a target. Virtual arm position was used to simultaneously control a robot arm via a network interface.
10. Diffusive homeostasis in a spiking network model (Sweeney et al. 2015)
In this paper we propose a new mechanism, diffusive homeostasis, in which neural excitability is modulated by nitric oxide, a gas which can flow freely across cell membranes. Our model simulates the activity-dependent synthesis and diffusion of nitric oxide in a recurrent network model of integrate-and-fire neurons. The concentration of nitric oxide is then used as homeostatic readout which modulates the firing threshold of each neuron.
11. Distributed cerebellar plasticity implements adaptable gain control (Garrido et al., 2013)
We tested the role of plasticity distributed over multiple synaptic sites (Hansel et al., 2001; Gao et al., 2012) by generating an analog cerebellar model embedded into a control loop connected to a robotic simulator. The robot used a three-joint arm and performed repetitive fast manipulations with different masses along an 8-shape trajectory. In accordance with biological evidence, the cerebellum model was endowed with both LTD and LTP at the PF-PC, MF-DCN and PC-DCN synapses. This resulted in a network scheme whose effectiveness was extended considerably compared to one including just PF-PC synaptic plasticity. Indeed, the system including distributed plasticity reliably self-adapted to manipulate different masses and to learn the arm-object dynamics over a time course that included fast learning and consolidation, along the lines of what has been observed in behavioral tests. In particular, PF-PC plasticity operated as a time correlator between the actual input state and the system error, while MF-DCN and PC-DCN plasticity played a key role in generating the gain controller. This model suggests that distributed synaptic plasticity allows generation of the complex learning properties of the cerebellum.
12. Distributed synaptic plasticity and spike timing (Garrido et al. 2013)
Here we have used a computational model to simulate the impact of multiple distributed synaptic weights in the cerebellar granular layer network. In response to mossy fiber bursts, synaptic weights at multiple connections played a crucial role to regulate spike number and positioning in granule cells. Interestingly, different combinations of synaptic weights optimized either first-spike timing precision or spike number, efficiently controlling transmission and filtering properties. These results predict that distributed synaptic plasticity regulates the emission of quasi-digital spike patterns on the millisecond time scale and allows the cerebellar granular layer to flexibly control burst transmission along the mossy fiber pathway.
13. Effects of increasing CREB on storage and recall processes in a CA1 network (Bianchi et al. 2014)
Several recent results suggest that boosting the CREB pathway improves hippocampal-dependent memory in healthy rodents and restores this type of memory in an AD mouse model. However, not much is known about how CREB-dependent neuronal alterations in synaptic strength, excitability and LTP can boost memory formation in the complex architecture of a neuronal network. Using a model of a CA1 microcircuit, we investigate whether hippocampal CA1 pyramidal neuron properties altered by increasing CREB activity may contribute to improve memory storage and recall. With a set of patterns presented to a network, we find that the pattern recall quality under AD-like conditions is significantly better when boosting CREB function with respect to control. The results are robust and consistent upon increasing the synaptic damage expected by AD progression, supporting the idea that the use of CREB-based therapies could provide a new approach to treat AD.
14. Efficient simulation environment for modeling large-scale cortical processing (Richert et al. 2011)
"We have developed a spiking neural network simulator, which is both easy to use and computationally efficient, for the generation of large-scale computational neuroscience models. The simulator implements current or conductance based Izhikevich neuron networks, having spike-timing dependent plasticity and short-term plasticity. ..."
15. Electrostimulation to reduce synaptic scaling driven progression of Alzheimers (Rowan et al. 2014)
"... As cells die and synapses lose their drive, remaining cells suffer an initial decrease in activity. Neuronal homeostatic synaptic scaling then provides a feedback mechanism to restore activity. ... The scaling mechanism increases the firing rates of remaining cells in the network to compensate for decreases in network activity. However, this effect can itself become a pathology, ... Here, we present a mechanistic explanation of how directed brain stimulation might be expected to slow AD progression based on computational simulations in a 470-neuron biomimetic model of a neocortical column. ... "
16. Encoding and retrieval in a model of the hippocampal CA1 microcircuit (Cutsuridis et al. 2009)
This NEURON code implements a small network model (100 pyramidal cells and 4 types of inhibitory interneuron) of storage and recall of patterns in the CA1 region of the mammalian hippocampus. Patterns of PC activity are stored either by a predefined weight matrix generated by Hebbian learning, or by STDP at CA3 Schaffer collateral AMPA synapses.
17. Fast convergence of cerebellar learning (Luque et al. 2015)
The cerebellum is known to play a critical role in learning relevant patterns of activity for adaptive motor control, but the underlying network mechanisms are only partly understood. The classical long-term synaptic plasticity between parallel fibers (PFs) and Purkinje cells (PCs), which is driven by the inferior olive (IO), can only account for limited aspects of learning. Recently, the role of additional forms of plasticity in the granular layer, molecular layer and deep cerebellar nuclei (DCN) has been considered. In particular, learning at DCN synapses allows for generalization, but convergence to a stable state requires hundreds of repetitions. In this paper we have explored the putative role of the IO-DCN connection by endowing it with adaptable weights and exploring its implications in a closed-loop robotic manipulation task. Our results show that IO-DCN plasticity accelerates convergence of learning by up to two orders of magnitude without conflicting with the generalization properties conferred by DCN plasticity. Thus, this model suggests that multiple distributed learning mechanisms provide a key for explaining the complex properties of procedural learning and open up new experimental questions for synaptic plasticity in the cerebellar network.
18. First-Spike-Based Visual Categorization Using Reward-Modulated STDP (Mozafari et al. 2018)
"...Here, for the first time, we show that (Reinforcement Learning) RL can be used efficiently to train a spiking neural network (SNN) to perform object recognition in natural images without using an external classifier. We used a feedforward convolutional SNN and a temporal coding scheme where the most strongly activated neurons fire first, while less activated ones fire later, or not at all. In the highest layers, each neuron was assigned to an object category, and it was assumed that the stimulus category was the category of the first neuron to fire. ..."
19. Formation of synfire chains (Jun and Jin 2007)
"Temporally precise sequences of neuronal spikes that span hundreds of milliseconds are observed in many brain areas, including songbird premotor nucleus, cat visual cortex, and primary motor cortex. Synfire chains—networks in which groups of neurons are connected via excitatory synapses into a unidirectional chain—are thought to underlie the generation of such sequences. It is unknown, however, how synfire chains can form in local neural circuits, especially for long chains. Here, we show through computer simulation that long synfire chains can develop through spike-time dependent synaptic plasticity and axon remodeling—the pruning of prolific weak connections that follows the emergence of a finite number of strong connections. ..."
20. Functional balanced networks with synaptic plasticity (Sadeh et al, 2015)
The model investigates the impact of learning on functional sensory networks. It uses large-scale recurrent networks of excitatory and inhibitory spiking neurons equipped with synaptic plasticity. It explains enhancement of orientation selectivity and emergence of feature-specific connectivity in visual cortex of rodents during development, as reported in experiments.
21. Hebbian STDP for modelling the emergence of disparity selectivity (Chauhan et al 2018)
This code shows how Hebbian learning mediated by STDP mechanisms could explain the emergence of disparity selectivity in the early visual system. This upload is a snapshot of the code at the time of acceptance of the paper. For a link to a soon-to-come git repository, consult the author's website: www.tusharchauhan.com/research/ . The datasets used in the paper are not provided due to size, but download links and expected directory-structures are. The user can (and is strongly encouraged to) experiment with their own dataset. Let me know if you find something interesting! Finally, I am very keen on a redesign/restructure/adaptation of the code to more applied problems in AI and robotics (or any other field where a spiking non-linear approach makes sense). If you have a serious proposal, don't hesitate to contact me [research AT tusharchauhan DOT com ].
22. Learning spatial transformations through STDP (Davison, Frégnac 2006)
A common problem in tasks involving the integration of spatial information from multiple senses, or in sensorimotor coordination, is that different modalities represent space in different frames of reference. Coordinate transformations between different reference frames are therefore required. One way to achieve this relies on the encoding of spatial information using population codes. The set of network responses to stimuli in different locations (tuning curves) constitute a basis set of functions which can be combined linearly through weighted synaptic connections in order to approximate non-linear transformations of the input variables. The question then arises how the appropriate synaptic connectivity is obtained. This model shows that a network of spiking neurons can learn the coordinate transformation from one frame of reference to another, with connectivity that develops continuously in an unsupervised manner, based only on the correlations available in the environment, and with a biologically-realistic plasticity mechanism (spike timing-dependent plasticity).
23. Linking STDP and Dopamine action to solve the distal reward problem (Izhikevich 2007)
"... How does the brain know what firing patterns of what neurons are responsible for the reward if 1) the patterns are no longer there when the reward arrives and 2) all neurons and synapses are active during the waiting period to the reward? Here, we show how the conundrum is resolved by a model network of cortical spiking neurons with spike-timing-dependent plasticity (STDP) modulated by dopamine (DA). Although STDP is triggered by nearly coincident firing patterns on a millisecond timescale, slow kinetics of subsequent synaptic plasticity is sensitive to changes in the extracellular DA concentration during the critical period of a few seconds. ... This study emphasizes the importance of precise firing patterns in brain dynamics and suggests how a global diffusive reinforcement signal in the form of extracellular DA can selectively influence the right synapses at the right time." See paper for more and details.
24. Microsaccades and synchrony coding in the retina (Masquelier et al. 2016)
We show that microsaccades (MS) enable efficient synchrony-based coding among the primate retinal ganglion cells (RGC). We find that each MS causes certain RGCs to fire synchronously, namely those whose receptive fields contain contrast edges after the MS. The emitted synchronous spike volley thus rapidly transmits the most salient edges of the stimulus. We demonstrate that the readout could be done rapidly by simple coincidence-detector neurons, and that the required connectivity could emerge spontaneously with spike timing-dependent plasticity.
25. Modeling dendritic spikes and plasticity (Bono and Clopath 2017)
Biophysical model and reduced neuron model with voltage-dependent plasticity.
26. Motor system model with reinforcement learning drives virtual arm (Dura-Bernal et al 2017)
"We implemented a model of the motor system with the following components: dorsal premotor cortex (PMd), primary motor cortex (M1), spinal cord and musculoskeletal arm (Figure 1). PMd modulated M1 to select the target to reach, M1 excited the descending spinal cord neurons that drove the arm muscles, and received arm proprioceptive feedback (information about the arm position) via the ascending spinal cord neurons. The large-scale model of M1 consisted of 6,208 spiking Izhikevich model neurons [37] of four types: regular-firing and bursting pyramidal neurons, and fast-spiking and low-threshold-spiking interneurons. These were distributed across cortical layers 2/3, 5A, 5B and 6, with cell properties, proportions, locations, connectivity, weights and delays drawn primarily from mammalian experimental data [38], [39], and described in detail in previous work [29]. The network included 486,491 connections, with synapses modeling properties of four different receptors ..."
27. Neural model of two-interval discrimination (Machens et al 2005)
Two-interval discrimination involves comparison of two stimuli that are presented at different times. It has three phases: loading, in which the first stimulus is perceived and stored in working memory; maintenance of working memory; decision making, in which the second stimulus is perceived and compared with the first. In behaving monkeys, each phase is associated with characteristic firing activity of neurons in the prefrontal cortex. This model implements both working memory and decision making with a mutual inhibition network that reproduces all three phases of two-interval discrimination. Machens, C.K., Romo, R., and Brody, C.D. Flexible control of mutual inhibition: a neural model of two-interval discrimination. Science 307:1121-1124, 2005.
28. Olfactory bulb mitral and granule cell column formation (Migliore et al. 2007)
In the olfactory bulb, the processing units for odor discrimination are believed to involve dendrodendritic synaptic interactions between mitral and granule cells. There is increasing anatomical evidence that these cells are organized in columns, and that the columns processing a given odor are arranged in widely distributed arrays. Experimental evidence is lacking on the underlying learning mechanisms for how these columns and arrays are formed. We have used a simplified realistic circuit model to test the hypothesis that distributed connectivity can self-organize through an activity-dependent dendrodendritic synaptic mechanism. The results point to action potentials propagating in the mitral cell lateral dendrites as playing a critical role in this mechanism, and suggest a novel and robust learning mechanism for the development of distributed processing units in a cortical structure.
29. Oscillations, phase-of-firing coding and STDP: an efficient learning scheme (Masquelier et al. 2009)
The model demonstrates how a common oscillatory drive for a group of neurons formats and reliabilizes their spike times - through an activation-to-phase conversion - so that repeating activation patterns can be easily detected and learned by a downstream neuron equipped with STDP, and then recognized in just one oscillation cycle.
30. Parallel odor processing by mitral and middle tufted cells in the OB (Cavarretta et al 2016, 2018)
"[...] experimental findings suggest that MC and mTC may encode parallel and complementary odor representations. We have analyzed the functional roles of these pathways by using a morphologically and physiologically realistic three-dimensional model to explore the MC and mTC microcircuits in the glomerular layer and deeper plexiform layers. [...]"
31. Polychronization: Computation With Spikes (Izhikevich 2005)
"We present a minimal spiking network that can polychronize, that is, exhibit reproducible time-locked but not synchronous firing patterns with millisecond precision, as in synfire braids. The network consists of cortical spiking neurons with axonal conduction delays and spiketiming- dependent plasticity (STDP); a ready-to-use MATLAB code is included. It exhibits sleeplike oscillations, gamma (40 Hz) rhythms, conversion of firing rates to spike timings, and other interesting regimes. ... To our surprise, the number of coexisting polychronous groups far exceeds the number of neurons in the network, resulting in an unprecedented memory capacity of the system. ..."
32. Reinforcement learning of targeted movement (Chadderdon et al. 2012)
"Sensorimotor control has traditionally been considered from a control theory perspective, without relation to neurobiology. In contrast, here we utilized a spiking-neuron model of motor cortex and trained it to perform a simple movement task, which consisted of rotating a single-joint “forearm” to a target. Learning was based on a reinforcement mechanism analogous to that of the dopamine system. This provided a global reward or punishment signal in response to decreasing or increasing distance from hand to target, respectively. Output was partially driven by Poisson motor babbling, creating stochastic movements that could then be shaped by learning. The virtual forearm consisted of a single segment rotated around an elbow joint, controlled by flexor and extensor muscles. ..."
33. Relative spike time coding and STDP-based orientation selectivity in V1 (Masquelier 2012)
Phenomenological spiking model of the cat early visual system. We show how natural vision can drive spike time correlations on sufficiently fast time scales to lead to the acquisition of orientation-selective V1 neurons through STDP. This is possible without reference times such as stimulus onsets, or saccade landing times. But even when such reference times are available, we demonstrate that the relative spike times encode the images more robustly than the absolute ones.
34. Reward modulated STDP (Legenstein et al. 2008)
"... This article provides tools for an analytic treatment of reward-modulated STDP, which allows us to predict under which conditions reward-modulated STDP will achieve a desired learning effect. These analytical results imply that neurons can learn through reward-modulated STDP to classify not only spatial but also temporal firing patterns of presynaptic neurons. They also can learn to respond to specific presynaptic firing patterns with particular spike patterns. Finally, the resulting learning theory predicts that even difficult credit-assignment problems, where it is very hard to tell which synaptic weights should be modified in order to increase the global reward for the system, can be solved in a self-organizing manner through reward-modulated STDP. This yields an explanation for a fundamental experimental result on biofeedback in monkeys by Fetz and Baker. In this experiment monkeys were rewarded for increasing the firing rate of a particular neuron in the cortex and were able to solve this extremely difficult credit assignment problem. ... In addition our model demonstrates that reward-modulated STDP can be applied to all synapses in a large recurrent neural network without endangering the stability of the network dynamics."
35. Sensorimotor cortex reinforcement learning of 2-joint virtual arm reaching (Neymotin et al. 2013)
"... We developed a model of sensory and motor neocortex consisting of 704 spiking model-neurons. Sensory and motor populations included excitatory cells and two types of interneurons. Neurons were interconnected with AMPA/NMDA, and GABAA synapses. We trained our model using spike-timing-dependent reinforcement learning to control a 2-joint virtual arm to reach to a fixed target. ... "
36. Simulated cortical color opponent receptive fields self-organize via STDP (Eguchi et al., 2014)
"... In this work, we address the problem of understanding the cortical processing of color information with a possible mechanism of the development of the patchy distribution of color selectivity via computational modeling. ... Our model of the early visual system consists of multiple topographically-arranged layers of excitatory and inhibitory neurons, with sparse intra-layer connectivity and feed-forward connectivity between layers. Layers are arranged based on anatomy of early visual pathways, and include a retina, lateral geniculate nucleus, and layered neocortex. ... After training with natural images, the neurons display heightened sensitivity to specific colors. ..."
37. Spike burst-pause dynamics of Purkinje cells regulate sensorimotor adaptation (Luque et al 2019)
"Cerebellar Purkinje cells mediate accurate eye movement coordination. However, it remains unclear how oculomotor adaptation depends on the interplay between the characteristic Purkinje cell response patterns, namely tonic, bursting, and spike pauses. Here, a spiking cerebellar model assesses the role of Purkinje cell firing patterns in vestibular ocular reflex (VOR) adaptation. The model captures the cerebellar microcircuit properties and it incorporates spike-based synaptic plasticity at multiple cerebellar sites. ..."
38. Spikes,synchrony,and attentive learning by laminar thalamocort. circuits (Grossberg & Versace 2007)
"... The model hereby clarifies, for the first time, how the following levels of brain organization coexist to realize cognitive processing properties that regulate fast learning and stable memory of brain representations: single cell properties, such as spiking dynamics, spike-timing-dependent plasticity (STDP), and acetylcholine modulation; detailed laminar thalamic and cortical circuit designs and their interactions; aggregate cell recordings, such as current-source densities and local field potentials; and single cell and large-scale inter-areal oscillations in the gamma and beta frequency domains. ..."
39. Spiking GridPlaceMap model (Pilly & Grossberg, PLoS One, 2013)
Development of spiking grid cells and place cells in the entorhinal-hippocampal system to represent positions in large spaces
40. Stability of complex spike timing-dependent plasticity in cerebellar learning (Roberts 2007)
"Dynamics of spike-timing dependent synaptic plasticity are analyzed for excitatory and inhibitory synapses onto cerebellar Purkinje cells. The purpose of this study is to place theoretical constraints on candidate synaptic learning rules that determine the changes in synaptic efficacy due to pairing complex spikes with presynaptic spikes in parallel fibers and inhibitory interneurons. ..."
41. STDP allows fast rate-modulated coding with Poisson-like spike trains (Gilson et al. 2011)
The model demonstrates that a neuron equipped with STDP robustly detects repeating rate patterns among its afferents, from which the spikes are generated on the fly using inhomogenous Poisson sampling, provided those rates have narrow temporal peaks (10-20ms) - a condition met by many experimental Post-Stimulus Time Histograms (PSTH).
42. STDP promotes synchrony of inhibitory networks in the presence of heterogeneity (Talathi et al 2008)
"Recently Haas et al. (J Neurophysiol 96: 3305–3313, 2006), observed a novel form of spike timing dependent plasticity (iSTDP) in GABAergic synaptic couplings in layer II of the entorhinal cortex. Depending on the relative timings of the presynaptic input at time tpre and the postsynaptic excitation at time tpost, the synapse is strengthened (delta_t = t(post) - t(pre) > 0) or weakened (delta_t < 0). The temporal dynamic range of the observed STDP rule was found to lie in the higher gamma frequency band (> or = 40 Hz), a frequency range important for several vital neuronal tasks. In this paper we study the function of this novel form of iSTDP in the synchronization of the inhibitory neuronal network. In particular we consider a network of two unidirectionally coupled interneurons (UCI) and two mutually coupled interneurons (MCI), in the presence of heterogeneity in the intrinsic firing rates of each coupled neuron. ..."
43. Synaptic scaling balances learning in a spiking model of neocortex (Rowan & Neymotin 2013)
Learning in the brain requires complementary mechanisms: potentiation and activity-dependent homeostatic scaling. We introduce synaptic scaling to a biologically-realistic spiking model of neocortex which can learn changes in oscillatory rhythms using STDP, and show that scaling is necessary to balance both positive and negative changes in input from potentiation and atrophy. We discuss some of the issues that arise when considering synaptic scaling in such a model, and show that scaling regulates activity whilst allowing learning to remain unaltered.

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