Dual Coding with STDP in a Spiking Recurrent Neural Network Model of the Hippocampus
Publication Date
July 01, 2010
Journal
PLOS Computational Biology
Authors
Daniel Bush, Andrew Philippides, Phil Husbands & Michael O'shea
Volume
6
Issue
7
Pages
e1000839
DOI
https://dx.plos.org/10.1371/journal.pcbi.1000839
Publisher URL
http://journals.plos.org/ploscompbiol/article?id=10.1371%2Fjournal.pcbi.1000839
PubMed
http://www.ncbi.nlm.nih.gov/pubmed/20617201
PubMed Central
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2895637
Europe PMC
http://europepmc.org/abstract/MED/20617201
Web of Science
000280528300008
Scopus
78049312831
Mendeley
http://www.mendeley.com/research/dual-coding-stdp-spiking-recurrent-neural-network-model-hippocampus
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CiteULike | Further Information

Mendeley | Further Information

{"title"=>"Dual coding with STDP in a spiking recurrent neural network model of the hippocampus", "type"=>"journal", "authors"=>[{"first_name"=>"Daniel", "last_name"=>"Bush", "scopus_author_id"=>"56273570100"}, {"first_name"=>"Andrew", "last_name"=>"Philippides", "scopus_author_id"=>"8398440500"}, {"first_name"=>"Phil", "last_name"=>"Husbands", "scopus_author_id"=>"56344953600"}, {"first_name"=>"Michael", "last_name"=>"O'Shea", "scopus_author_id"=>"7102635053"}], "year"=>2010, "source"=>"PLoS Computational Biology", "identifiers"=>{"issn"=>"1553734X", "scopus"=>"2-s2.0-78049312831", "sgr"=>"78049312831", "pui"=>"359856083", "isbn"=>"1553-7358 (Electronic)\\r1553-734X (Linking)", "pmid"=>"20617201", "doi"=>"10.1371/journal.pcbi.1000839"}, "id"=>"d73069ec-3697-3db8-b66f-3f86908bc60b", "abstract"=>"The firing rate of single neurons in the mammalian hippocampus has been demonstrated to encode for a range of spatial and non-spatial stimuli. It has also been demonstrated that phase of firing, with respect to the theta oscillation that dominates the hippocampal EEG during stereotype learning behaviour, correlates with an animal's spatial location. These findings have led to the hypothesis that the hippocampus operates using a dual (rate and temporal) coding system. To investigate the phenomenon of dual coding in the hippocampus, we examine a spiking recurrent network model with theta coded neural dynamics and an STDP rule that mediates rate-coded Hebbian learning when pre- and post-synaptic firing is stochastic. We demonstrate that this plasticity rule can generate both symmetric and asymmetric connections between neurons that fire at concurrent or successive theta phase, respectively, and subsequently produce both pattern completion and sequence prediction from partial cues. This unifies previously disparate auto- and hetero-associative network models of hippocampal function and provides them with a firmer basis in modern neurobiology. Furthermore, the encoding and reactivation of activity in mutually exciting Hebbian cell assemblies demonstrated here is believed to represent a fundamental mechanism of cognitive processing in the brain.", "link"=>"http://www.mendeley.com/research/dual-coding-stdp-spiking-recurrent-neural-network-model-hippocampus", "reader_count"=>89, "reader_count_by_academic_status"=>{"Unspecified"=>1, "Professor > Associate Professor"=>6, "Researcher"=>24, "Student > Doctoral Student"=>5, "Student > Ph. D. Student"=>28, "Student > Postgraduate"=>2, "Student > Master"=>8, "Other"=>4, "Student > Bachelor"=>4, "Lecturer > Senior Lecturer"=>1, "Professor"=>6}, "reader_count_by_user_role"=>{"Unspecified"=>1, "Professor > Associate Professor"=>6, "Researcher"=>24, "Student > Doctoral Student"=>5, "Student > Ph. D. Student"=>28, "Student > Postgraduate"=>2, "Student > Master"=>8, "Other"=>4, "Student > Bachelor"=>4, "Lecturer > Senior Lecturer"=>1, "Professor"=>6}, "reader_count_by_subject_area"=>{"Unspecified"=>4, "Engineering"=>8, "Environmental Science"=>1, "Mathematics"=>2, "Agricultural and Biological Sciences"=>27, "Medicine and Dentistry"=>4, "Neuroscience"=>14, "Physics and Astronomy"=>5, "Psychology"=>2, "Computer Science"=>21, "Linguistics"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>8}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>4}, "Neuroscience"=>{"Neuroscience"=>14}, "Physics and Astronomy"=>{"Physics and Astronomy"=>5}, "Psychology"=>{"Psychology"=>2}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>27}, "Computer Science"=>{"Computer Science"=>21}, "Linguistics"=>{"Linguistics"=>1}, "Mathematics"=>{"Mathematics"=>2}, "Unspecified"=>{"Unspecified"=>4}, "Environmental Science"=>{"Environmental Science"=>1}}, "reader_count_by_country"=>{"Republic of Singapore"=>1, "United States"=>5, "United Kingdom"=>5, "Belarus"=>1, "Greece"=>2, "Canada"=>2, "South Korea"=>1, "China"=>2, "Brazil"=>2, "Italy"=>1, "Chile"=>1, "France"=>1, "Germany"=>6}, "group_count"=>3}

Scopus | Further Information

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  • {"files"=>["https://ndownloader.figshare.com/files/842539"], "description"=>"<p>(<b>a, b</b>) Each theoretical place field and theta cycle (as defined by the value of <i>θ</i>) are divided into eight equally sized sub-sections. At each millisecond time step, the theoretical position within a place field dictates the theta phase window during which the corresponding place cell receives external excitatory input. Hence, when the theoretical animal enters a place field (segment 1), the corresponding place cell receives external stimulation late in the theta cycle (phase window 1); in the centre of the place field (segment 4), the corresponding place cell receives external, excitatory stimulation in the middle of the theta cycle (phase window 4); and as the place field is exited (segment 7), the corresponding place cell receives external, excitatory stimulation early in the theta cycle (phase window 7). The interplay of this external, excitatory stimulation with the constant, oscillatory inhibitory input to each place cell directs place cells to fire complex spike bursts when theoretical position is near the centre of the place field, and single spikes upon entry to or exit from the place field. Importantly, the random distribution of both inhibitory and excitatory inputs to each place cell produce stochastic firing activity within the corresponding phase window, such that place cells which encode for the same place field will fire with the same mean phase, but not necessarily in the same millisecond time step(s). (<b>c</b>) The phenomenological phase precession model creates a theta coding mechanism, whereby the sequence of place fields being traversed on a behavioural time scale is represented by a compressed sequence of activity in the corresponding place cells, repeated in every theta cycle.</p>", "links"=>[], "tags"=>["phenomenological", "precession", "theta", "coding"], "article_id"=>512994, "categories"=>["Neuroscience", "Medicine"], "users"=>["Daniel Bush", "Andrew Philippides", "Phil Husbands", "Michael O'Shea"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000839.g001", "stats"=>{"downloads"=>1, "page_views"=>41, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_Phenomenological_Phase_Precession_Model_and_Theta_Coding_Mechanism_/512994", "title"=>"The Phenomenological Phase Precession Model and Theta Coding Mechanism.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 00:45:56"}
  • {"files"=>["https://ndownloader.figshare.com/files/843342"], "description"=>"<p>(<b>a</b>) Statistics relating to dual coded recall following learning with the triplet-based BCM type STDP rule, when all background connections (i.e. between place cells and those encoding for all place fields that are not within three steps on the learned route) are set to <i>0</i> following learning. Data shown for <i>Φ</i> = <i>0.111</i> and averaged over <i>1000</i> randomly initialised recall epochs, illustrating the relative frequency of neurons that fired before (dark grey); at the same time as (medium grey); and after (light grey) the first action potential in any simulated neuron encoding for the next place field on the learned route. This can be directly compared with <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000839#pcbi-1000839-g006\" target=\"_blank\">Figure 6f</a>. (<b>b</b>) Histogram of temporal magnitude for every erroneous spike fired during <i>1000</i> randomly initialised dual coded recall epochs with <i>Φ</i> = <i>0.111</i> following learning with the triplet-based BCM type STDP rule and theta modulated plasticity (that being the lowest recall fidelity displayed in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000839#pcbi-1000839-g006\" target=\"_blank\">Figure 6f</a>). (<b>c</b>) The mean percentage of incorrectly timed recall spikes observed during sharp wave ripple recall activity, displayed in terms of the distance along the learned route, in place fields, from the externally stimulated place cells. Data is averaged over <i>1000</i> randomly initialised dual coded recall epochs for the BCM type STDP rules with <i>Φ</i> = <i>0.111</i>. (<b>d</b>) The effective speed of SWR activity – calculated using the time interval between the first spike caused by superthreshold external stimulation and the first subsequent spike in a place field encoding for the same place field following the propagation of activity along the entire length of the learned route – for different concentrations of ACh. Data is averaged over <i>1000</i> randomly initialised dual coded recall epochs, following learning with theta modulated plasticity.</p>", "links"=>[], "tags"=>["details", "putative", "ripple"], "article_id"=>513798, "categories"=>["Neuroscience", "Medicine"], "users"=>["Daniel Bush", "Andrew Philippides", "Phil Husbands", "Michael O'Shea"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000839.g007", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Further_Details_of_Putative_Sharp_Wave_Ripple_Recall_Activity_/513798", "title"=>"Further Details of Putative Sharp Wave Ripple Recall Activity.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 00:50:17"}
  • {"files"=>["https://ndownloader.figshare.com/files/843406"], "description"=>"<p>Computational details of the STDP rules.</p>", "links"=>[], "tags"=>["details", "stdp"], "article_id"=>513865, "categories"=>["Neuroscience", "Medicine"], "users"=>["Daniel Bush", "Andrew Philippides", "Phil Husbands", "Michael O'Shea"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000839.t001", "stats"=>{"downloads"=>0, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Computational_details_of_the_STDP_rules_/513865", "title"=>"Computational details of the STDP rules.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-21 00:50:42"}
  • {"files"=>["https://ndownloader.figshare.com/files/843178"], "description"=>"<p>(<b>a</b>) Typical spike raster observed in the network during recall simulations following hetero-associative learning (as described in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000839#pcbi-1000839-g002\" target=\"_blank\">Figure 2</a>). Externally stimulated firing of a single neuron produces sequential recall activity in all neurons that constitute the originally learned pattern; (<b>b</b>) Statistics relating to hetero-associative recall for each STDP rule and plasticity modulation scheme examined. Figures shown represent data averaged over <i>1000</i> randomly initialised recall epochs with <i>Φ</i> = <i>0.05</i> following hetero-associative learning simulations with the (A) pair-based BCM type; (B) triplet-based BCM type; (C) pair-based non-BCM type STDP rules. Data illustrated for the relative frequency of neurons that fired before (dark grey); at the same time as (medium grey); and after (light grey) the simulated neuron encoding for the next place field on the learned route. (<b>c</b>) Typical spike raster observed in the network during recall simulations following auto-associative learning (as described in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000839#pcbi-1000839-g003\" target=\"_blank\">Figure 3</a>). External stimulation of a random subset of (cued) neurons from each learned pattern (five out of ten, in this case) generates selective firing in (uncued) neurons that encode for the same place field/pattern after <i>5–10</i>ms (depending on the plasticity rule employed during learning, and the concentration of ACh employed during recall). (<b>d</b>) Statistics relating to auto-associative recall for each STDP rule and plasticity modulation scheme examined. Figures shown represent data averaged over <i>1000</i> randomly initialised recall epochs following learning with the (A) pair-based BCM type STDP rule, and <i>Φ</i> = <i>0.05</i>; (B) triplet-based BCM type STDP rule, and <i>Φ</i> = <i>0.083</i>; (C) pair-based non-BCM type STDP rule, and <i>Φ</i> = <i>0.05</i>. Data illustrated for the relative frequency of uncued neurons that fire within <i>20</i>ms of externally cued activity in other neurons within the same pattern (dark grey) and the relative frequency of neurons in different, uncued patterns that fire within the same temporal window (light grey). (<b>e</b>) Typical spike raster observed in the network during recall simulations following dual coded learning (as described in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000839#pcbi-1000839-g005\" target=\"_blank\">Figure 5</a>). External stimulation of a random subset of neurons from a single pattern (three out of five, in this case) produces sequential recall activity in simulated neurons that encode for each successive place field on the learned route. This neural activity pattern is reminiscent of sharp wave/ripple dynamics observed during putative recall activity in the hippocampus; (<b>f</b>) Statistics relating to dual coded recall for each STDP rule and plasticity modulation scheme examined. Figures shown represent data averaged over <i>1000</i> randomly initialised recall epochs with <i>Φ</i> = <i>0.111</i> following dual coded learning for the (A) pair-based BCM type; (B) triplet-based BCM type; and (C) pair-based non-BCM type STDP rules. Data illustrated for the relative frequency of neurons that fired before (dark grey); at the same time as (medium grey); and after (light grey) the first action potential in any simulated neuron encoding for the next place field on the learned route.</p>", "links"=>[], "tags"=>["ripple", "theta", "coded"], "article_id"=>513634, "categories"=>["Neuroscience", "Medicine"], "users"=>["Daniel Bush", "Andrew Philippides", "Phil Husbands", "Michael O'Shea"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000839.g006", "stats"=>{"downloads"=>1, "page_views"=>15, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Putative_Sharp_Wave_Ripple_Recall_Activity_Following_Theta_Coded_Learning_/513634", "title"=>"Putative Sharp Wave Ripple Recall Activity Following Theta Coded Learning.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 00:49:22"}
  • {"files"=>["https://ndownloader.figshare.com/files/842964"], "description"=>"<p>(<b>a</b>) Theoretical details of dual coding simulations. <i>20</i> equidistant and overlapping place fields of <i>80</i>cm diameter, offset by <i>10</i>cm, form a circular route that is traversed repeatedly at a constant speed of <i>10</i>cms<sup>−1</sup>. Each place field is encoded by five place cells. (<b>b</b>) Representative spike raster in thirty-five place cells encoding for seven separate but overlapping place fields. Place cells encoding for different place fields fire stochastically within different theta phase windows. (<b>c</b>) Typical synaptic weight matrix following ten traversals of the route for the BCM type STDP rules. Synaptic connections between place cells that encode for successive place fields on the theoretical route saturate at the upper weight bounds and synaptic connections between place cells that encode for the same place field are selectively and significantly potentiated. Data illustrated for triplet-based STDP with theta modulated plasticity. (<b>d</b>) Dynamic changes in the relative mean weight (<i>w</i>/<i>w<sub>max</sub></i>) of auto-associative (between place cells encoding for the same place field), hetero-associative (between place cells encoding for a place field and that either one or two steps further along the route), and background (between place cells and those encoding for place fields not within three steps further along the route) connections. Data illustrated is for the triplet-based BCM type STDP rule with theta modulated plasticity. (<b>e</b>) Typical synaptic weight matrix following ten traversals of the route when the non-BCM type STDP rule is employed with theta modulated plasticity. In contrast to (c), auto-associative connections between place cells that encode for the same place field are depressed, while hetero-associative connections between place cells that encode for successive place fields saturate at the upper weight bounds. (<b>f</b>) The relative mean weight of synapses connecting each place cell to those that encode for the same place field (dark grey), the next place field on the learned route (medium grey), and all place fields not within three steps ahead on the learned route (light grey) following ten traversals, averaged over <i>50</i> separate simulations, with the pair- and triplet- based BCM type STDP rules (A and B respectively) and the non-BCM type STDP rule (C).</p>", "links"=>[], "tags"=>["coded", "spiking", "recurrent", "neural"], "article_id"=>513422, "categories"=>["Neuroscience", "Medicine"], "users"=>["Daniel Bush", "Andrew Philippides", "Phil Husbands", "Michael O'Shea"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000839.g005", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Dual_Coded_Learning_in_a_Spiking_Recurrent_Neural_Network_/513422", "title"=>"Dual Coded Learning in a Spiking Recurrent Neural Network.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 00:48:13"}
  • {"files"=>["https://ndownloader.figshare.com/files/842614"], "description"=>"<p>(<b>a</b>) Theoretical details of theta coded hetero-associative learning simulations. <i>100</i> equidistant and overlapping place fields of <i>80</i>cm diameter, offset by <i>10</i>cm, form a circular route that is traversed repeatedly at a constant speed of <i>10</i>cms<sup>−1</sup>. Each place field is encoded by the activity of a single place cell. (<b>b</b>) Typical spike raster in seven representative place cells with consecutive and overlapping place fields, showing theta coded neural dynamics generated by the phenomenological phase precession model. For illustrative purposes, this figure was generated with much smaller place fields (<i>10</i>cm diameter) such that active place cells fire in each theta phase window for one oscillatory cycle only. (<b>c</b>) Typical synaptic weight matrix following learning. Asymmetric connections between place cells which correspond to consecutive place fields on the learned route are selectively and significantly potentiated. Inset: synaptic weight histograms for foreground and background connections (i.e. between a neuron and those that encode for either the three successive place fields on the learned route, or all other neurons in the network respectively). Data illustrated for the triplet based BCM type STDP rule with no plasticity modulation. (<b>d</b>) Mean phase of firing in all place cells at place field entry and exit on successive traversals of the route, averaged over <i>50</i> separate simulations. This demonstrates the asymmetric expansion of place fields against the direction of motion during spatial learning. Data illustrated for the triplet based BCM type STDP rule with no plasticity modulation. (<b>e</b>) The relative mean weight of synaptic connections between place cells in typical simulations with every combination of STDP rule and plasticity modulation scheme examined. The value of the post-synaptic neuron index corresponds to the distance – in place fields – between the pre- and post- synaptic place cell. (<b>f</b>) The mean rate of synaptic weight change at synapses connecting each place cell to that immediately ahead of it on the theoretical route averaged over <i>50</i> separate simulations, which correlates with mean in-field firing rate for (A) the pair-based BCM type; (B) the triplet-based BCM type; and (C) the non-BCM type STDP rule. Data illustrated for simulations with theta modulated plasticity, and synaptic weight change averaged over all neurons until synaptic weights saturate at the upper bounds.</p>", "links"=>[], "tags"=>["coded", "hetero-associative", "spiking", "recurrent", "neural"], "article_id"=>513071, "categories"=>["Neuroscience", "Medicine"], "users"=>["Daniel Bush", "Andrew Philippides", "Phil Husbands", "Michael O'Shea"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000839.g002", "stats"=>{"downloads"=>4, "page_views"=>14, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Theta_Coded_Hetero_associative_Learning_in_a_Spiking_Recurrent_Neural_Network_/513071", "title"=>"Theta Coded Hetero-associative Learning in a Spiking Recurrent Neural Network.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 00:46:24"}
  • {"files"=>["https://ndownloader.figshare.com/files/842714"], "description"=>"<p>(<b>a</b>) Theoretical details of theta coded auto-associative learning simulations. <i>10</i> equidistant but non-overlapping place fields of <i>80</i>cm diameter, offset by <i>80</i>cm, form a circular route that is traversed repeatedly at a constant speed of <i>10</i>cms<sup>−1</sup>. Each place field is encoded for by ten place cells. This form of input effectively corresponds to repeated presentations of ten binary and orthogonal activity patterns. (<b>b</b>) Typical spike raster in place cells encoding for a single place field. For illustrative purposes, this figure was generated with much smaller place fields (<i>10</i>cm diameter) such that typical activity at each phase of theta can be seen more clearly. (<b>c</b>) Typical synaptic weight matrix following learning with the BCM type STDP rules, illustrating how connections between neurons that encode for the same place field are selectively and significantly potentiated. Data shown for triplet-based STDP with theta modulated plasticity. (<b>d</b>) Synaptic weight matrix following learning with the non-BCM type STDP rule and theta modulated plasticity. Under these conditions, synapses between place cells that encode for the same place field are depressed below the mean weight of other connections in the network. (<b>e</b>) The mean weight of synapses connecting each place cell to those that encode for the same place field (dark grey) and different place fields (light grey) following ten traversals of the theoretical route, averaged over <i>50</i> separate simulations, for the pair- and triplet- based BCM type STDP rules (A and B respectively) and the non-BCM type STDP rule (C). (<b>f</b>) The relative mean asymptotic weight of auto-associative connections averaged over <i>50</i> separate simulations, illustrating that the relative strength of auto-associative connections is positively correlated with mean in-field firing rate for (A) the pair based BCM type STDP rule (with theta modulated plasticity); and (B) the triplet based BCM type STDP rule (with theta modulated plasticity); but negatively correlated with mean in-field firing rate for (C) the pair based non-BCM type STDP rule (with inversely modulated plasticity).</p>", "links"=>[], "tags"=>["coded", "auto-associative", "spiking", "recurrent", "neural"], "article_id"=>513169, "categories"=>["Neuroscience", "Medicine"], "users"=>["Daniel Bush", "Andrew Philippides", "Phil Husbands", "Michael O'Shea"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000839.g003", "stats"=>{"downloads"=>0, "page_views"=>14, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Theta_Coded_Auto_associative_Learning_in_a_Spiking_Recurrent_Neural_Network_/513169", "title"=>"Theta Coded Auto-associative Learning in a Spiking Recurrent Neural Network.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 00:46:55"}
  • {"files"=>["https://ndownloader.figshare.com/files/842812"], "description"=>"<p>(<b>a</b>) Action potentials in bi-directionally connected neurons are more likely to reach the pre-synaptic terminal before the end of synchronous (but stochastic) complex bursts, and therefore induce the potentiation of inter-connecting synapses, if axonal delays are shorter. (<b>b</b>) Conversely, action potentials in each simulated neuron are more likely to arrive at the pre-synaptic terminal after the end of synchronous (but stochastic) complex bursts, and therefore induce depression of the inter-connecting synapses, if axonal delays are longer. (<b>c</b>) Relative mean synaptic weight (<i>w</i>/<i>w<sub>max</sub></i>) of auto-associative and background connections (i.e. between neurons that are in the same or different patterns respectively) produced by the BCM type STDP rules following ten traversals of the theoretical route described in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000839#pcbi-1000839-g003\" target=\"_blank\">Figure 3a</a> with a varying scale of axonal delays (<i>D</i>). Data is averaged over <i>50</i> separate simulations. (<b>d</b>) Relative mean synaptic weight (<i>w</i>/<i>w<sub>max</sub></i>) of auto-associative and background connections produced by the pair- and triplet- based BCM type STDP rules following ten traversals of the theoretical route described in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000839#pcbi-1000839-g003\" target=\"_blank\">Figure 3a</a> with varying values of A<sub>+</sub> and therefore different positions of the theoretical modification threshold (<i>θ<sub>m</sub></i>). Data is averaged over <i>50</i> separate simulations.</p>", "links"=>[], "tags"=>["axonal", "asymmetric", "auto-associative"], "article_id"=>513276, "categories"=>["Neuroscience", "Medicine"], "users"=>["Daniel Bush", "Andrew Philippides", "Phil Husbands", "Michael O'Shea"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000839.g004", "stats"=>{"downloads"=>1, "page_views"=>13, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Effects_of_Axonal_Delay_and_Profile_of_the_Asymmetric_Learning_Window_on_Auto_associative_Learning_/513276", "title"=>"Effects of Axonal Delay and Profile of the Asymmetric Learning Window on Auto-associative Learning.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 00:47:25"}

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Relative Metric

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