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sdo analysis toolkit  (MathWorks Inc)


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    MathWorks Inc sdo analysis toolkit
    <t>SDOs</t> alter background state transition matrices to compose spike-triggered transition matrices. In this example, pre-spike and post-spike distributions of signal state were generated from the spikes of a single motor unit in the vastus externus against the analog EMG signal recorded in the biceps femoris, using a time interval of 10 ms for both the pre-spike and post-spike distributions. A , The spike-triggered average joint distribution of the pre-spike and post-spike state distributions behaves as the description of state transitions around spike. B , A spike-triggered <t>SDO</t> captures the change of state probability across the 10 ms pre-spike and post-spike distribution of states, given an occurrence of spike. This SDO shows strong directional effects, evidenced by the asymmetrical banding relative to the diagonal. C , Normalization of each column of the joint distribution to 1 creates a left transition matrix, representing the expected probability of post-spike state distribution given a pre-spike state distribution. D , Normalizing the columns of the SDO by the same factor used in the joint distribution ( C ) creates the normalized SDO. This form is used to predict the conditional change of state distributions.
    Sdo Analysis Toolkit, supplied by MathWorks Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
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    1) Product Images from "A Stochastic Dynamic Operator Framework That Improves the Precision of Analysis and Prediction Relative to the Classical Spike-Triggered Average Method, Extending the Toolkit"

    Article Title: A Stochastic Dynamic Operator Framework That Improves the Precision of Analysis and Prediction Relative to the Classical Spike-Triggered Average Method, Extending the Toolkit

    Journal: eNeuro

    doi: 10.1523/ENEURO.0512-23.2024

    SDOs alter background state transition matrices to compose spike-triggered transition matrices. In this example, pre-spike and post-spike distributions of signal state were generated from the spikes of a single motor unit in the vastus externus against the analog EMG signal recorded in the biceps femoris, using a time interval of 10 ms for both the pre-spike and post-spike distributions. A , The spike-triggered average joint distribution of the pre-spike and post-spike state distributions behaves as the description of state transitions around spike. B , A spike-triggered SDO captures the change of state probability across the 10 ms pre-spike and post-spike distribution of states, given an occurrence of spike. This SDO shows strong directional effects, evidenced by the asymmetrical banding relative to the diagonal. C , Normalization of each column of the joint distribution to 1 creates a left transition matrix, representing the expected probability of post-spike state distribution given a pre-spike state distribution. D , Normalizing the columns of the SDO by the same factor used in the joint distribution ( C ) creates the normalized SDO. This form is used to predict the conditional change of state distributions.
    Figure Legend Snippet: SDOs alter background state transition matrices to compose spike-triggered transition matrices. In this example, pre-spike and post-spike distributions of signal state were generated from the spikes of a single motor unit in the vastus externus against the analog EMG signal recorded in the biceps femoris, using a time interval of 10 ms for both the pre-spike and post-spike distributions. A , The spike-triggered average joint distribution of the pre-spike and post-spike state distributions behaves as the description of state transitions around spike. B , A spike-triggered SDO captures the change of state probability across the 10 ms pre-spike and post-spike distribution of states, given an occurrence of spike. This SDO shows strong directional effects, evidenced by the asymmetrical banding relative to the diagonal. C , Normalization of each column of the joint distribution to 1 creates a left transition matrix, representing the expected probability of post-spike state distribution given a pre-spike state distribution. D , Normalizing the columns of the SDO by the same factor used in the joint distribution ( C ) creates the normalized SDO. This form is used to predict the conditional change of state distributions.

    Techniques Used: Generated

    SDO analysis of a spinal interneuron and EMG amplitude: The spikes from a single spinal interneuron were compared against EMG signal amplitude from the vastus externus muscle (filtered zero-phase, acausally). A , The spike-triggered SDO matrix (here, Gaussian smoothed for visualization). Spike-triggered effects are primarily associated with higher states (15–19), with an increased probability of transition toward relatively greater states, as positive elements are above the diagonal. B , The extended STIRPD of the EMG signal shows a coarse relationship between spike time and signal state. After spike time, signal state appears to converge on state 18–19 with a probability ∼0.6. C , The shear SDO shows the positive elements of the matrix are primarily concentrated above the diagonal over states 15–19. This suggests the spike-triggered SDO is consistent with a transition toward higher post-spike states for input states in this region. The slight diagonal orientation of the domains (parallel to the sheared top of the matrix) suggests the post-spike signal state is “stepping-up” to a particular state, rather than broadly increasing state, as first suggested by the STIRPD. D , The SDO quiver plot shows the coarse directional effects of the SDO for each input state. Consistent with the shear SDO, the effect of this spike-triggered SDO is to support a transition toward higher states for input states 15–19, indicated by vectors above and below the abscissa pointing upward for these states. E–G , For a subset of 50 spiking events, the predicted post-spike state distributions were calculated for each spike using the STA or SDO. Each predicted post-spike state distribution was represented as a column vector, ordered according to state at spike, and horizontally concatenated into a matrix, displayed here as a grayscale image. The single observed post-spike state for each spike is overlaid as a red x in the respective column. E , The background SDO demonstrates state-dependent predictions independent of spike-triggered effects. Here the background SDO is well-suited to predict post-spike distributions when in a “lower” initial state but makes overly broad predictions at higher states. F , Here, the STA can predict the post-spike state only over a limited range of experimental data (ordered spiking event 25+). The STA fails to accurately predict post-spike state distributions when predicting from a lower pre-spike state (indicated by the blue circle of observed post-spike states not covered by STA-predicted post-spike state distributions) but is accurate at higher states. G , In contrast, predictions of post-spike state by the SDO are valid over the entirety of the dataset. H , When predicting to single states, the SDO reduces both the frequency ( e 0), ( I ) magnitude ( e 1), and ( J ) sum-squared magnitude ( e 2) of prediction errors relative to the STA. This predictive accuracy is state dependent: The SDO and STA have equivalent performance at high input states, but the STA significantly underperforms the SDO's prediction error at lower states, consistent with D. K , When predicting post-spike distributions, the SDO outperforms the STA [as measured by the Kullback–Leibler divergence (KLD) between predicted and observed post-spike states]. The distribution of KLD, calculated for every observed spiking event, is given as a violin plot. Here, lower values indicate less divergence from the observed distribution and hence, a better fit. Here the bimodality of the STA violin plot demonstrates the insufficiency of the STA to predict the post-spike state distribution for spikes occurring at “lower” states. L , Significance of cumulative errors were tested using 1,000 bootstraps of e 1 errors for all seven matrix hypotheses. Here, the distributions of SDO-predicted and STA-predicted errors do not overlap; p values are arbitrarily small.
    Figure Legend Snippet: SDO analysis of a spinal interneuron and EMG amplitude: The spikes from a single spinal interneuron were compared against EMG signal amplitude from the vastus externus muscle (filtered zero-phase, acausally). A , The spike-triggered SDO matrix (here, Gaussian smoothed for visualization). Spike-triggered effects are primarily associated with higher states (15–19), with an increased probability of transition toward relatively greater states, as positive elements are above the diagonal. B , The extended STIRPD of the EMG signal shows a coarse relationship between spike time and signal state. After spike time, signal state appears to converge on state 18–19 with a probability ∼0.6. C , The shear SDO shows the positive elements of the matrix are primarily concentrated above the diagonal over states 15–19. This suggests the spike-triggered SDO is consistent with a transition toward higher post-spike states for input states in this region. The slight diagonal orientation of the domains (parallel to the sheared top of the matrix) suggests the post-spike signal state is “stepping-up” to a particular state, rather than broadly increasing state, as first suggested by the STIRPD. D , The SDO quiver plot shows the coarse directional effects of the SDO for each input state. Consistent with the shear SDO, the effect of this spike-triggered SDO is to support a transition toward higher states for input states 15–19, indicated by vectors above and below the abscissa pointing upward for these states. E–G , For a subset of 50 spiking events, the predicted post-spike state distributions were calculated for each spike using the STA or SDO. Each predicted post-spike state distribution was represented as a column vector, ordered according to state at spike, and horizontally concatenated into a matrix, displayed here as a grayscale image. The single observed post-spike state for each spike is overlaid as a red x in the respective column. E , The background SDO demonstrates state-dependent predictions independent of spike-triggered effects. Here the background SDO is well-suited to predict post-spike distributions when in a “lower” initial state but makes overly broad predictions at higher states. F , Here, the STA can predict the post-spike state only over a limited range of experimental data (ordered spiking event 25+). The STA fails to accurately predict post-spike state distributions when predicting from a lower pre-spike state (indicated by the blue circle of observed post-spike states not covered by STA-predicted post-spike state distributions) but is accurate at higher states. G , In contrast, predictions of post-spike state by the SDO are valid over the entirety of the dataset. H , When predicting to single states, the SDO reduces both the frequency ( e 0), ( I ) magnitude ( e 1), and ( J ) sum-squared magnitude ( e 2) of prediction errors relative to the STA. This predictive accuracy is state dependent: The SDO and STA have equivalent performance at high input states, but the STA significantly underperforms the SDO's prediction error at lower states, consistent with D. K , When predicting post-spike distributions, the SDO outperforms the STA [as measured by the Kullback–Leibler divergence (KLD) between predicted and observed post-spike states]. The distribution of KLD, calculated for every observed spiking event, is given as a violin plot. Here, lower values indicate less divergence from the observed distribution and hence, a better fit. Here the bimodality of the STA violin plot demonstrates the insufficiency of the STA to predict the post-spike state distribution for spikes occurring at “lower” states. L , Significance of cumulative errors were tested using 1,000 bootstraps of e 1 errors for all seven matrix hypotheses. Here, the distributions of SDO-predicted and STA-predicted errors do not overlap; p values are arbitrarily small.

    Techniques Used: Shear, Plasmid Preparation

    SDO analysis of a single motor unit and synergist muscle EMG: The spike train of a single motor unit (SMU) in the vastus externus muscle was compared against EMG signal amplitude of the biceps femoris (as in ). A , The SDO matrix. Effects are localized in two regions, about State 8–10 and 12–14. B , The extended STIRPD of the EMG shows this SMU is tuned to two different states of EMG signal amplitude, as indicated by the bimodal behavior of p (state|spike). In the top “arc”, at state 14, the post-spike state distribution appears mostly symmetrical to the pre-spike state. However, in the lower arc (state at spike = 10), the post-spike states are increased relative to spike. C , The shear SDO shows the positive elements of the matrix are primarily concentrated above the diagonal over states 8–12, corresponding to the lower “arc”, but minimal effects outside this region. D , Similarly, the quiver SDO demonstrates coarse directional bias toward higher post-spike states for input states 8–12, corresponding to the “lower arc” on the STIRPD, but minimal effects for input states 13–16, consistent with minimal change to the “upper arc” of the STIRPD. E–G , For a subset of 50 spiking events, the predicted post-spike state distribution was calculated for each spike using the STA or SDO. Each predicted post-spike state distribution was represented as a column vector, ordered according to state at spike, and horizontally concatenated into a matrix, displayed as a grayscale image. The single observed post-spike state for each spike is overlaid as a red x in the respective column. E , Predictions from the background SDO are state dependent although inadequately capture spike effects. F , The bimodal post-spike distribution predicted from the STA suboptimally predicts the observed post-spike state, while ( G ) the SDO-predicted distribution of post-spike state more tightly fits the observed post-spike state, across all signal states. Thus, the SDO provides a more reliable method of predicting signal behavior. H–J , When predicting single post-spike states, the rate of error accumulation for different hypotheses depends on state. Post-spike signal state was predicted for every spiking event, for all hypotheses, and the error between each event-wise prediction was accumulated for all spikes. Spiking events were sorted by state at time of spike to uncover state-dependent error rates. Here the rate of accumulation for the ( H ) frequency (e0), ( I ) magnitude (e1), and ( J ) sum-squared magnitude (e2) of error are comparable for states 7–10 for the STA and SDO as indicated by the parallel traces of the cumulative error over this region), but the STA performs poorly at lower and higher states, whereas the SDO maintains prediction accuracy over all states. K , The similarity between each predicted and observed post-spike distribution was assessed as the Kullback–Leibler divergence (KLD). The distribution of the KLD over all spiking events is displayed as a violin plot. Predicted distributions using the SDO resulted in a better fit than the STA. L , Significance of cumulative errors were tested using 1,000 bootstraps of e 1 errors (for all 7 matrix hypotheses, below). As suggested by E and F , the STA results in a better prediction than the background SDO but worse than the spike-triggered SDO. Here, the distributions of SDO-predicted and STA-predicted errors do not overlap; p values are arbitrarily small.
    Figure Legend Snippet: SDO analysis of a single motor unit and synergist muscle EMG: The spike train of a single motor unit (SMU) in the vastus externus muscle was compared against EMG signal amplitude of the biceps femoris (as in ). A , The SDO matrix. Effects are localized in two regions, about State 8–10 and 12–14. B , The extended STIRPD of the EMG shows this SMU is tuned to two different states of EMG signal amplitude, as indicated by the bimodal behavior of p (state|spike). In the top “arc”, at state 14, the post-spike state distribution appears mostly symmetrical to the pre-spike state. However, in the lower arc (state at spike = 10), the post-spike states are increased relative to spike. C , The shear SDO shows the positive elements of the matrix are primarily concentrated above the diagonal over states 8–12, corresponding to the lower “arc”, but minimal effects outside this region. D , Similarly, the quiver SDO demonstrates coarse directional bias toward higher post-spike states for input states 8–12, corresponding to the “lower arc” on the STIRPD, but minimal effects for input states 13–16, consistent with minimal change to the “upper arc” of the STIRPD. E–G , For a subset of 50 spiking events, the predicted post-spike state distribution was calculated for each spike using the STA or SDO. Each predicted post-spike state distribution was represented as a column vector, ordered according to state at spike, and horizontally concatenated into a matrix, displayed as a grayscale image. The single observed post-spike state for each spike is overlaid as a red x in the respective column. E , Predictions from the background SDO are state dependent although inadequately capture spike effects. F , The bimodal post-spike distribution predicted from the STA suboptimally predicts the observed post-spike state, while ( G ) the SDO-predicted distribution of post-spike state more tightly fits the observed post-spike state, across all signal states. Thus, the SDO provides a more reliable method of predicting signal behavior. H–J , When predicting single post-spike states, the rate of error accumulation for different hypotheses depends on state. Post-spike signal state was predicted for every spiking event, for all hypotheses, and the error between each event-wise prediction was accumulated for all spikes. Spiking events were sorted by state at time of spike to uncover state-dependent error rates. Here the rate of accumulation for the ( H ) frequency (e0), ( I ) magnitude (e1), and ( J ) sum-squared magnitude (e2) of error are comparable for states 7–10 for the STA and SDO as indicated by the parallel traces of the cumulative error over this region), but the STA performs poorly at lower and higher states, whereas the SDO maintains prediction accuracy over all states. K , The similarity between each predicted and observed post-spike distribution was assessed as the Kullback–Leibler divergence (KLD). The distribution of the KLD over all spiking events is displayed as a violin plot. Predicted distributions using the SDO resulted in a better fit than the STA. L , Significance of cumulative errors were tested using 1,000 bootstraps of e 1 errors (for all 7 matrix hypotheses, below). As suggested by E and F , the STA results in a better prediction than the background SDO but worse than the spike-triggered SDO. Here, the distributions of SDO-predicted and STA-predicted errors do not overlap; p values are arbitrarily small.

    Techniques Used: Shear, Plasmid Preparation

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    <t>SDOs</t> alter background state transition matrices to compose spike-triggered transition matrices. In this example, pre-spike and post-spike distributions of signal state were generated from the spikes of a single motor unit in the vastus externus against the analog EMG signal recorded in the biceps femoris, using a time interval of 10 ms for both the pre-spike and post-spike distributions. A , The spike-triggered average joint distribution of the pre-spike and post-spike state distributions behaves as the description of state transitions around spike. B , A spike-triggered <t>SDO</t> captures the change of state probability across the 10 ms pre-spike and post-spike distribution of states, given an occurrence of spike. This SDO shows strong directional effects, evidenced by the asymmetrical banding relative to the diagonal. C , Normalization of each column of the joint distribution to 1 creates a left transition matrix, representing the expected probability of post-spike state distribution given a pre-spike state distribution. D , Normalizing the columns of the SDO by the same factor used in the joint distribution ( C ) creates the normalized SDO. This form is used to predict the conditional change of state distributions.
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    <t>SDOs</t> alter background state transition matrices to compose spike-triggered transition matrices. In this example, pre-spike and post-spike distributions of signal state were generated from the spikes of a single motor unit in the vastus externus against the analog EMG signal recorded in the biceps femoris, using a time interval of 10 ms for both the pre-spike and post-spike distributions. A , The spike-triggered average joint distribution of the pre-spike and post-spike state distributions behaves as the description of state transitions around spike. B , A spike-triggered <t>SDO</t> captures the change of state probability across the 10 ms pre-spike and post-spike distribution of states, given an occurrence of spike. This SDO shows strong directional effects, evidenced by the asymmetrical banding relative to the diagonal. C , Normalization of each column of the joint distribution to 1 creates a left transition matrix, representing the expected probability of post-spike state distribution given a pre-spike state distribution. D , Normalizing the columns of the SDO by the same factor used in the joint distribution ( C ) creates the normalized SDO. This form is used to predict the conditional change of state distributions.
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    SDOs alter background state transition matrices to compose spike-triggered transition matrices. In this example, pre-spike and post-spike distributions of signal state were generated from the spikes of a single motor unit in the vastus externus against the analog EMG signal recorded in the biceps femoris, using a time interval of 10 ms for both the pre-spike and post-spike distributions. A , The spike-triggered average joint distribution of the pre-spike and post-spike state distributions behaves as the description of state transitions around spike. B , A spike-triggered SDO captures the change of state probability across the 10 ms pre-spike and post-spike distribution of states, given an occurrence of spike. This SDO shows strong directional effects, evidenced by the asymmetrical banding relative to the diagonal. C , Normalization of each column of the joint distribution to 1 creates a left transition matrix, representing the expected probability of post-spike state distribution given a pre-spike state distribution. D , Normalizing the columns of the SDO by the same factor used in the joint distribution ( C ) creates the normalized SDO. This form is used to predict the conditional change of state distributions.

    Journal: eNeuro

    Article Title: A Stochastic Dynamic Operator Framework That Improves the Precision of Analysis and Prediction Relative to the Classical Spike-Triggered Average Method, Extending the Toolkit

    doi: 10.1523/ENEURO.0512-23.2024

    Figure Lengend Snippet: SDOs alter background state transition matrices to compose spike-triggered transition matrices. In this example, pre-spike and post-spike distributions of signal state were generated from the spikes of a single motor unit in the vastus externus against the analog EMG signal recorded in the biceps femoris, using a time interval of 10 ms for both the pre-spike and post-spike distributions. A , The spike-triggered average joint distribution of the pre-spike and post-spike state distributions behaves as the description of state transitions around spike. B , A spike-triggered SDO captures the change of state probability across the 10 ms pre-spike and post-spike distribution of states, given an occurrence of spike. This SDO shows strong directional effects, evidenced by the asymmetrical banding relative to the diagonal. C , Normalization of each column of the joint distribution to 1 creates a left transition matrix, representing the expected probability of post-spike state distribution given a pre-spike state distribution. D , Normalizing the columns of the SDO by the same factor used in the joint distribution ( C ) creates the normalized SDO. This form is used to predict the conditional change of state distributions.

    Article Snippet: To generate, visualize, and analyze SDOs, we developed the SDO Analysis Toolkit , written in the MATLAB programming language.

    Techniques: Generated

    SDO analysis of a spinal interneuron and EMG amplitude: The spikes from a single spinal interneuron were compared against EMG signal amplitude from the vastus externus muscle (filtered zero-phase, acausally). A , The spike-triggered SDO matrix (here, Gaussian smoothed for visualization). Spike-triggered effects are primarily associated with higher states (15–19), with an increased probability of transition toward relatively greater states, as positive elements are above the diagonal. B , The extended STIRPD of the EMG signal shows a coarse relationship between spike time and signal state. After spike time, signal state appears to converge on state 18–19 with a probability ∼0.6. C , The shear SDO shows the positive elements of the matrix are primarily concentrated above the diagonal over states 15–19. This suggests the spike-triggered SDO is consistent with a transition toward higher post-spike states for input states in this region. The slight diagonal orientation of the domains (parallel to the sheared top of the matrix) suggests the post-spike signal state is “stepping-up” to a particular state, rather than broadly increasing state, as first suggested by the STIRPD. D , The SDO quiver plot shows the coarse directional effects of the SDO for each input state. Consistent with the shear SDO, the effect of this spike-triggered SDO is to support a transition toward higher states for input states 15–19, indicated by vectors above and below the abscissa pointing upward for these states. E–G , For a subset of 50 spiking events, the predicted post-spike state distributions were calculated for each spike using the STA or SDO. Each predicted post-spike state distribution was represented as a column vector, ordered according to state at spike, and horizontally concatenated into a matrix, displayed here as a grayscale image. The single observed post-spike state for each spike is overlaid as a red x in the respective column. E , The background SDO demonstrates state-dependent predictions independent of spike-triggered effects. Here the background SDO is well-suited to predict post-spike distributions when in a “lower” initial state but makes overly broad predictions at higher states. F , Here, the STA can predict the post-spike state only over a limited range of experimental data (ordered spiking event 25+). The STA fails to accurately predict post-spike state distributions when predicting from a lower pre-spike state (indicated by the blue circle of observed post-spike states not covered by STA-predicted post-spike state distributions) but is accurate at higher states. G , In contrast, predictions of post-spike state by the SDO are valid over the entirety of the dataset. H , When predicting to single states, the SDO reduces both the frequency ( e 0), ( I ) magnitude ( e 1), and ( J ) sum-squared magnitude ( e 2) of prediction errors relative to the STA. This predictive accuracy is state dependent: The SDO and STA have equivalent performance at high input states, but the STA significantly underperforms the SDO's prediction error at lower states, consistent with D. K , When predicting post-spike distributions, the SDO outperforms the STA [as measured by the Kullback–Leibler divergence (KLD) between predicted and observed post-spike states]. The distribution of KLD, calculated for every observed spiking event, is given as a violin plot. Here, lower values indicate less divergence from the observed distribution and hence, a better fit. Here the bimodality of the STA violin plot demonstrates the insufficiency of the STA to predict the post-spike state distribution for spikes occurring at “lower” states. L , Significance of cumulative errors were tested using 1,000 bootstraps of e 1 errors for all seven matrix hypotheses. Here, the distributions of SDO-predicted and STA-predicted errors do not overlap; p values are arbitrarily small.

    Journal: eNeuro

    Article Title: A Stochastic Dynamic Operator Framework That Improves the Precision of Analysis and Prediction Relative to the Classical Spike-Triggered Average Method, Extending the Toolkit

    doi: 10.1523/ENEURO.0512-23.2024

    Figure Lengend Snippet: SDO analysis of a spinal interneuron and EMG amplitude: The spikes from a single spinal interneuron were compared against EMG signal amplitude from the vastus externus muscle (filtered zero-phase, acausally). A , The spike-triggered SDO matrix (here, Gaussian smoothed for visualization). Spike-triggered effects are primarily associated with higher states (15–19), with an increased probability of transition toward relatively greater states, as positive elements are above the diagonal. B , The extended STIRPD of the EMG signal shows a coarse relationship between spike time and signal state. After spike time, signal state appears to converge on state 18–19 with a probability ∼0.6. C , The shear SDO shows the positive elements of the matrix are primarily concentrated above the diagonal over states 15–19. This suggests the spike-triggered SDO is consistent with a transition toward higher post-spike states for input states in this region. The slight diagonal orientation of the domains (parallel to the sheared top of the matrix) suggests the post-spike signal state is “stepping-up” to a particular state, rather than broadly increasing state, as first suggested by the STIRPD. D , The SDO quiver plot shows the coarse directional effects of the SDO for each input state. Consistent with the shear SDO, the effect of this spike-triggered SDO is to support a transition toward higher states for input states 15–19, indicated by vectors above and below the abscissa pointing upward for these states. E–G , For a subset of 50 spiking events, the predicted post-spike state distributions were calculated for each spike using the STA or SDO. Each predicted post-spike state distribution was represented as a column vector, ordered according to state at spike, and horizontally concatenated into a matrix, displayed here as a grayscale image. The single observed post-spike state for each spike is overlaid as a red x in the respective column. E , The background SDO demonstrates state-dependent predictions independent of spike-triggered effects. Here the background SDO is well-suited to predict post-spike distributions when in a “lower” initial state but makes overly broad predictions at higher states. F , Here, the STA can predict the post-spike state only over a limited range of experimental data (ordered spiking event 25+). The STA fails to accurately predict post-spike state distributions when predicting from a lower pre-spike state (indicated by the blue circle of observed post-spike states not covered by STA-predicted post-spike state distributions) but is accurate at higher states. G , In contrast, predictions of post-spike state by the SDO are valid over the entirety of the dataset. H , When predicting to single states, the SDO reduces both the frequency ( e 0), ( I ) magnitude ( e 1), and ( J ) sum-squared magnitude ( e 2) of prediction errors relative to the STA. This predictive accuracy is state dependent: The SDO and STA have equivalent performance at high input states, but the STA significantly underperforms the SDO's prediction error at lower states, consistent with D. K , When predicting post-spike distributions, the SDO outperforms the STA [as measured by the Kullback–Leibler divergence (KLD) between predicted and observed post-spike states]. The distribution of KLD, calculated for every observed spiking event, is given as a violin plot. Here, lower values indicate less divergence from the observed distribution and hence, a better fit. Here the bimodality of the STA violin plot demonstrates the insufficiency of the STA to predict the post-spike state distribution for spikes occurring at “lower” states. L , Significance of cumulative errors were tested using 1,000 bootstraps of e 1 errors for all seven matrix hypotheses. Here, the distributions of SDO-predicted and STA-predicted errors do not overlap; p values are arbitrarily small.

    Article Snippet: To generate, visualize, and analyze SDOs, we developed the SDO Analysis Toolkit , written in the MATLAB programming language.

    Techniques: Shear, Plasmid Preparation

    SDO analysis of a single motor unit and synergist muscle EMG: The spike train of a single motor unit (SMU) in the vastus externus muscle was compared against EMG signal amplitude of the biceps femoris (as in ). A , The SDO matrix. Effects are localized in two regions, about State 8–10 and 12–14. B , The extended STIRPD of the EMG shows this SMU is tuned to two different states of EMG signal amplitude, as indicated by the bimodal behavior of p (state|spike). In the top “arc”, at state 14, the post-spike state distribution appears mostly symmetrical to the pre-spike state. However, in the lower arc (state at spike = 10), the post-spike states are increased relative to spike. C , The shear SDO shows the positive elements of the matrix are primarily concentrated above the diagonal over states 8–12, corresponding to the lower “arc”, but minimal effects outside this region. D , Similarly, the quiver SDO demonstrates coarse directional bias toward higher post-spike states for input states 8–12, corresponding to the “lower arc” on the STIRPD, but minimal effects for input states 13–16, consistent with minimal change to the “upper arc” of the STIRPD. E–G , For a subset of 50 spiking events, the predicted post-spike state distribution was calculated for each spike using the STA or SDO. Each predicted post-spike state distribution was represented as a column vector, ordered according to state at spike, and horizontally concatenated into a matrix, displayed as a grayscale image. The single observed post-spike state for each spike is overlaid as a red x in the respective column. E , Predictions from the background SDO are state dependent although inadequately capture spike effects. F , The bimodal post-spike distribution predicted from the STA suboptimally predicts the observed post-spike state, while ( G ) the SDO-predicted distribution of post-spike state more tightly fits the observed post-spike state, across all signal states. Thus, the SDO provides a more reliable method of predicting signal behavior. H–J , When predicting single post-spike states, the rate of error accumulation for different hypotheses depends on state. Post-spike signal state was predicted for every spiking event, for all hypotheses, and the error between each event-wise prediction was accumulated for all spikes. Spiking events were sorted by state at time of spike to uncover state-dependent error rates. Here the rate of accumulation for the ( H ) frequency (e0), ( I ) magnitude (e1), and ( J ) sum-squared magnitude (e2) of error are comparable for states 7–10 for the STA and SDO as indicated by the parallel traces of the cumulative error over this region), but the STA performs poorly at lower and higher states, whereas the SDO maintains prediction accuracy over all states. K , The similarity between each predicted and observed post-spike distribution was assessed as the Kullback–Leibler divergence (KLD). The distribution of the KLD over all spiking events is displayed as a violin plot. Predicted distributions using the SDO resulted in a better fit than the STA. L , Significance of cumulative errors were tested using 1,000 bootstraps of e 1 errors (for all 7 matrix hypotheses, below). As suggested by E and F , the STA results in a better prediction than the background SDO but worse than the spike-triggered SDO. Here, the distributions of SDO-predicted and STA-predicted errors do not overlap; p values are arbitrarily small.

    Journal: eNeuro

    Article Title: A Stochastic Dynamic Operator Framework That Improves the Precision of Analysis and Prediction Relative to the Classical Spike-Triggered Average Method, Extending the Toolkit

    doi: 10.1523/ENEURO.0512-23.2024

    Figure Lengend Snippet: SDO analysis of a single motor unit and synergist muscle EMG: The spike train of a single motor unit (SMU) in the vastus externus muscle was compared against EMG signal amplitude of the biceps femoris (as in ). A , The SDO matrix. Effects are localized in two regions, about State 8–10 and 12–14. B , The extended STIRPD of the EMG shows this SMU is tuned to two different states of EMG signal amplitude, as indicated by the bimodal behavior of p (state|spike). In the top “arc”, at state 14, the post-spike state distribution appears mostly symmetrical to the pre-spike state. However, in the lower arc (state at spike = 10), the post-spike states are increased relative to spike. C , The shear SDO shows the positive elements of the matrix are primarily concentrated above the diagonal over states 8–12, corresponding to the lower “arc”, but minimal effects outside this region. D , Similarly, the quiver SDO demonstrates coarse directional bias toward higher post-spike states for input states 8–12, corresponding to the “lower arc” on the STIRPD, but minimal effects for input states 13–16, consistent with minimal change to the “upper arc” of the STIRPD. E–G , For a subset of 50 spiking events, the predicted post-spike state distribution was calculated for each spike using the STA or SDO. Each predicted post-spike state distribution was represented as a column vector, ordered according to state at spike, and horizontally concatenated into a matrix, displayed as a grayscale image. The single observed post-spike state for each spike is overlaid as a red x in the respective column. E , Predictions from the background SDO are state dependent although inadequately capture spike effects. F , The bimodal post-spike distribution predicted from the STA suboptimally predicts the observed post-spike state, while ( G ) the SDO-predicted distribution of post-spike state more tightly fits the observed post-spike state, across all signal states. Thus, the SDO provides a more reliable method of predicting signal behavior. H–J , When predicting single post-spike states, the rate of error accumulation for different hypotheses depends on state. Post-spike signal state was predicted for every spiking event, for all hypotheses, and the error between each event-wise prediction was accumulated for all spikes. Spiking events were sorted by state at time of spike to uncover state-dependent error rates. Here the rate of accumulation for the ( H ) frequency (e0), ( I ) magnitude (e1), and ( J ) sum-squared magnitude (e2) of error are comparable for states 7–10 for the STA and SDO as indicated by the parallel traces of the cumulative error over this region), but the STA performs poorly at lower and higher states, whereas the SDO maintains prediction accuracy over all states. K , The similarity between each predicted and observed post-spike distribution was assessed as the Kullback–Leibler divergence (KLD). The distribution of the KLD over all spiking events is displayed as a violin plot. Predicted distributions using the SDO resulted in a better fit than the STA. L , Significance of cumulative errors were tested using 1,000 bootstraps of e 1 errors (for all 7 matrix hypotheses, below). As suggested by E and F , the STA results in a better prediction than the background SDO but worse than the spike-triggered SDO. Here, the distributions of SDO-predicted and STA-predicted errors do not overlap; p values are arbitrarily small.

    Article Snippet: To generate, visualize, and analyze SDOs, we developed the SDO Analysis Toolkit , written in the MATLAB programming language.

    Techniques: Shear, Plasmid Preparation