Review

markov chain model (Geotech Inc)

About

News

Press Release

Team

Advisors

Partners

Contact

Bioz Stars

Bioz vStars

Buy from Supplier

Structured Review

Geotech Inc markov chain model
Markov Chain Model, supplied by Geotech Inc, used in various techniques. Bioz Stars score: 86/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
https://www.bioz.com/result/markov chain model/product/Geotech Inc
Average 86 stars, based on 1 article reviews

markov chain model - by Bioz Stars, 2026-05

86/100 stars

Images

Image Search Results

In this video, we show how a finer-grained reconstruction, with an increasing number of Markov elements, more accurately represents the dynamics in spontaneous neural activity in mesoscale cortical calcium imaging.

Journal: Cell Reports Methods

Article Title: Neural barcoding representing cortical spatiotemporal dynamics based on continuous-time Markov chains

doi: 10.1016/j.crmeth.2025.101294

Figure Lengend Snippet: In this video, we show how a finer-grained reconstruction, with an increasing number of Markov elements, more accurately represents the dynamics in spontaneous neural activity in mesoscale cortical calcium imaging.

Article Snippet: • We develop a compact, low-dimensional representation of cortical dynamics • We utilize a continuous-time Markov chain modeling framework • We demonstrate model sensitivity to individual animal signatures • We also demonstrate model robustness to experimental manipulations

Techniques:

In this video, Markov element reconstructions are given (top) for 4 repeated homecage protocol recordings from the same animal. The TPMs are generated in time (bottom) for each of these reconstructions. Here, the TPMs are sorted into common modules by the Louvain community sort algorithm. Note the similarity across TPMs and the relatively quick convergence of the TPMs after approximately 120 s of recording data.

Journal: Cell Reports Methods

Article Title: Neural barcoding representing cortical spatiotemporal dynamics based on continuous-time Markov chains

doi: 10.1016/j.crmeth.2025.101294

Figure Lengend Snippet: In this video, Markov element reconstructions are given (top) for 4 repeated homecage protocol recordings from the same animal. The TPMs are generated in time (bottom) for each of these reconstructions. Here, the TPMs are sorted into common modules by the Louvain community sort algorithm. Note the similarity across TPMs and the relatively quick convergence of the TPMs after approximately 120 s of recording data.

Techniques:

A Markovian neural barcode is sensitive to individual animal-specific dynamical signature (A) A schematic representation of a repeated imaging protocol. (B) The Louvain sorted TPMs for two mice imaged across the 4 time points (baseline, +1 h, +2 h, and +24 h). Note the consistent features within TPMs for the two animals. (C) The Louvain sorted occupancy distribution histogram for 4 recordings from 2 mice presented in (B). The green lines denote the separation between Louvain modules. (D) The estimated Markovian neural barcode is presented for the full dataset comprising 160 recordings from n = 40 mice. The probability of a particular transition/Markov element occupancy is indicated by its darkness. Note banding within each grouping of 4 recordings per animal. (E) The estimated Markovian neural barcode is presented for 24 recordings from n = 6 mice as per the schematic in (A). The probability of a particular transition/Markov element occupancy is indicated by its darkness. Note banding within each grouping of 4 recordings per animal. (F) Zoom perspectives of a selection of segments (approximately 100 transitions each) of the Markovian neural barcode. Note the commonality and intra-animal banding among transitions, indicating shared and intra-animal-specific variation encoded in Markov element transitions. (G) PC projections for PC 1 vs. PC 2 (left), PC 1 vs. PC 3 (middle), and PC 2 vs. PC 3 (right) for the four separate recordings for 6 mice selected mice from (E). Note the four recordings from each animal cluster in PC space. (H) The matrix of PC distances for the 6 mice shown in (E) and (G), (6 mice at 4 time points). Note there is a clear block structure with dark 4 × 4 blocks along the main diagonal. These blocks are due to the clustering of repeated recordings for individual mice. (I) A schematic for measuring the differences/similarities between the neural barcodes of two separate mice in which individual specific dynamics captured by the Markovian neural barcode are either absent (top) or present (bottom). (J) Statistical quantification of the intra- and inter-mouse PC distances, where individual data points measured distances between recordings. The distributions are significantly different (Wilcoxon rank-sum test; intra: 0.0506, inter: 0.1308, p = 2.94 e -75), whereby inter-mouse PC distances are significantly larger than intra-mouse PC distances, indicating the presence of individual-specific dynamics within the Markovian neural barcode. See also .

Journal: Cell Reports Methods

Article Title: Neural barcoding representing cortical spatiotemporal dynamics based on continuous-time Markov chains

doi: 10.1016/j.crmeth.2025.101294

Figure Lengend Snippet: A Markovian neural barcode is sensitive to individual animal-specific dynamical signature (A) A schematic representation of a repeated imaging protocol. (B) The Louvain sorted TPMs for two mice imaged across the 4 time points (baseline, +1 h, +2 h, and +24 h). Note the consistent features within TPMs for the two animals. (C) The Louvain sorted occupancy distribution histogram for 4 recordings from 2 mice presented in (B). The green lines denote the separation between Louvain modules. (D) The estimated Markovian neural barcode is presented for the full dataset comprising 160 recordings from n = 40 mice. The probability of a particular transition/Markov element occupancy is indicated by its darkness. Note banding within each grouping of 4 recordings per animal. (E) The estimated Markovian neural barcode is presented for 24 recordings from n = 6 mice as per the schematic in (A). The probability of a particular transition/Markov element occupancy is indicated by its darkness. Note banding within each grouping of 4 recordings per animal. (F) Zoom perspectives of a selection of segments (approximately 100 transitions each) of the Markovian neural barcode. Note the commonality and intra-animal banding among transitions, indicating shared and intra-animal-specific variation encoded in Markov element transitions. (G) PC projections for PC 1 vs. PC 2 (left), PC 1 vs. PC 3 (middle), and PC 2 vs. PC 3 (right) for the four separate recordings for 6 mice selected mice from (E). Note the four recordings from each animal cluster in PC space. (H) The matrix of PC distances for the 6 mice shown in (E) and (G), (6 mice at 4 time points). Note there is a clear block structure with dark 4 × 4 blocks along the main diagonal. These blocks are due to the clustering of repeated recordings for individual mice. (I) A schematic for measuring the differences/similarities between the neural barcodes of two separate mice in which individual specific dynamics captured by the Markovian neural barcode are either absent (top) or present (bottom). (J) Statistical quantification of the intra- and inter-mouse PC distances, where individual data points measured distances between recordings. The distributions are significantly different (Wilcoxon rank-sum test; intra: 0.0506, inter: 0.1308, p = 2.94 e -75), whereby inter-mouse PC distances are significantly larger than intra-mouse PC distances, indicating the presence of individual-specific dynamics within the Markovian neural barcode. See also .

Techniques: Imaging, Selection, Blocking Assay

Markovian dynamics in mesoscale cortical calcium activity (A) A schematic representation of mesoscale cortical imaging and pre-processing of the recordings. The raw fluorescence stack is first aligned to the Allen Institute Mouse Brain Atlas, followed by spatial filtering to identify epochs of movement with sensitivity comparable to behavioral cameras. Following temporal filtering, the final signal Δ F / F is computed. (B) An annotated mesoscale fluorescence image is shown after alignment to the Allen Institute Mouse Brain Atlas. (C) In the upper montage, mesoscale cortical imaging spatiotemporal dynamics are illustrated with frames every 200 ms, and in the lower montage are frames selected every 1 s. (D) (Left) The cumulative variance explained by PCs in a low-dimensional representation of the ( n = 80) randomly selected spontaneous activity recordings as given in the discovery set ( and ). Approximately 87% of the cumulative variance can be explained with the first three PCs and approximately 92% of the explained variance with the first 5 principal components. Error bars denote ± 1 standard deviation. (Right) The individual variance explained by PCs similarly shows that the first PCs explain the majority of the explained variance. Error bars denote ± 1 standard deviation. (E) A schematic representation of discretizing high-dimensional state space into a series of Voronoi cells in a Voronoi diagram, where each cell is described by the centroid or Markov element. The trajectory of frames from mesoscale cortical imaging can be approximated by the Markov element with the transitioning between centroids modeled as a CTMC. (F) Schematic representation of (left) the TPM estimated with the relative frequency of transitioning from one Voronoi cell to another. The entry P ( i , j ) in this matrix denotes the probability of moving from state i to state j , where the states correspond to the Voronoi cells in (D). (Right) The gray system is a schematic of a chaotic regime, whereas the pink system is a schematic of a more oscillatory dynamical regime with its associated sparser TPM. (G) The application of Markov element assignment with increasing number of Markov elements for a CTMC model. Note the relative paucity of transitions with fewer Markov elements, and as more Markov elements are used the CTMC approximation to the mesoscale imaging data also improves. See also and .

Journal: Cell Reports Methods

Article Title: Neural barcoding representing cortical spatiotemporal dynamics based on continuous-time Markov chains

doi: 10.1016/j.crmeth.2025.101294

Figure Lengend Snippet: Markovian dynamics in mesoscale cortical calcium activity (A) A schematic representation of mesoscale cortical imaging and pre-processing of the recordings. The raw fluorescence stack is first aligned to the Allen Institute Mouse Brain Atlas, followed by spatial filtering to identify epochs of movement with sensitivity comparable to behavioral cameras. Following temporal filtering, the final signal Δ F / F is computed. (B) An annotated mesoscale fluorescence image is shown after alignment to the Allen Institute Mouse Brain Atlas. (C) In the upper montage, mesoscale cortical imaging spatiotemporal dynamics are illustrated with frames every 200 ms, and in the lower montage are frames selected every 1 s. (D) (Left) The cumulative variance explained by PCs in a low-dimensional representation of the ( n = 80) randomly selected spontaneous activity recordings as given in the discovery set ( and ). Approximately 87% of the cumulative variance can be explained with the first three PCs and approximately 92% of the explained variance with the first 5 principal components. Error bars denote ± 1 standard deviation. (Right) The individual variance explained by PCs similarly shows that the first PCs explain the majority of the explained variance. Error bars denote ± 1 standard deviation. (E) A schematic representation of discretizing high-dimensional state space into a series of Voronoi cells in a Voronoi diagram, where each cell is described by the centroid or Markov element. The trajectory of frames from mesoscale cortical imaging can be approximated by the Markov element with the transitioning between centroids modeled as a CTMC. (F) Schematic representation of (left) the TPM estimated with the relative frequency of transitioning from one Voronoi cell to another. The entry P ( i , j ) in this matrix denotes the probability of moving from state i to state j , where the states correspond to the Voronoi cells in (D). (Right) The gray system is a schematic of a chaotic regime, whereas the pink system is a schematic of a more oscillatory dynamical regime with its associated sparser TPM. (G) The application of Markov element assignment with increasing number of Markov elements for a CTMC model. Note the relative paucity of transitions with fewer Markov elements, and as more Markov elements are used the CTMC approximation to the mesoscale imaging data also improves. See also and .

Techniques: Activity Assay, Imaging, Fluorescence, Standard Deviation

Louvain community sorted modules in the Markovian neural barcode (A) (Left) A Louvain sorted TPM for a single recording with boundaries between the modules denoted by a green border. (Right) A schematic of the TPM is shown color coded for transitions and the Markov element occupancy distribution. (B) A t-distributed stochastic neighbor embedding (t-SNE) dimensionality reduction was performed on a repeated protocol acquisition dataset recording where each dataframe in the corresponding visualization was colorized by its associated Markov element’s module assignment. Note the module clustering in this low-dimensional embedding implying the high intra-module spatial similarity. (C) A Markov element reconstruction raster of the repeated protocol acquisition recording used in (B) as sorted by module. Note the temporal streaking of within-module elements. (D) A module TPM was computed from the Markov element reconstruction of the repeated protocol acquisition recording used in (B) and (C). Note the high intra-module transition probabilities (mean ± SD, 0.8706 ± 0.0519) compared to inter-module transition probabilities (mean ± SD, 0.0431 ± 0.0281). (E) The Pearson correlation matrix computed for the 100 Markov elements and subsequently sorted by module assignment. Note the higher within-module correlation along the main diagonal indicating a higher spatial correlation among within-intra-module elements. (F) Representative color-coded Markov elements depicted after Louvain community detection applied to TPMs. (G) For each module, the mean pixel value (left, within each module) was computed across elements within each module. The standard deviation across pixel values (right, within each module) was also computed. (H) A schematic color-coded legend to facilitate visualization and interpretation of the barcode and individual rows for n = 80 recordings. All entries in the neural barcode are probabilities, with darker colors denoting higher probabilities. (I) A schematic color-coded legend of the occupancy distribution. Here, darker colors denote greater proportions.

Journal: Cell Reports Methods

Article Title: Neural barcoding representing cortical spatiotemporal dynamics based on continuous-time Markov chains

doi: 10.1016/j.crmeth.2025.101294

Figure Lengend Snippet: Louvain community sorted modules in the Markovian neural barcode (A) (Left) A Louvain sorted TPM for a single recording with boundaries between the modules denoted by a green border. (Right) A schematic of the TPM is shown color coded for transitions and the Markov element occupancy distribution. (B) A t-distributed stochastic neighbor embedding (t-SNE) dimensionality reduction was performed on a repeated protocol acquisition dataset recording where each dataframe in the corresponding visualization was colorized by its associated Markov element’s module assignment. Note the module clustering in this low-dimensional embedding implying the high intra-module spatial similarity. (C) A Markov element reconstruction raster of the repeated protocol acquisition recording used in (B) as sorted by module. Note the temporal streaking of within-module elements. (D) A module TPM was computed from the Markov element reconstruction of the repeated protocol acquisition recording used in (B) and (C). Note the high intra-module transition probabilities (mean ± SD, 0.8706 ± 0.0519) compared to inter-module transition probabilities (mean ± SD, 0.0431 ± 0.0281). (E) The Pearson correlation matrix computed for the 100 Markov elements and subsequently sorted by module assignment. Note the higher within-module correlation along the main diagonal indicating a higher spatial correlation among within-intra-module elements. (F) Representative color-coded Markov elements depicted after Louvain community detection applied to TPMs. (G) For each module, the mean pixel value (left, within each module) was computed across elements within each module. The standard deviation across pixel values (right, within each module) was also computed. (H) A schematic color-coded legend to facilitate visualization and interpretation of the barcode and individual rows for n = 80 recordings. All entries in the neural barcode are probabilities, with darker colors denoting higher probabilities. (I) A schematic color-coded legend of the occupancy distribution. Here, darker colors denote greater proportions.

Techniques: Standard Deviation

The Markovian neural barcode reveals dynamical differences and novel activity motifs after extreme excitation (A) A schematic representation of the integration of the MES model of seizure and mesoscale cortical imaging in the awake mouse. (B) A voltage trace representing neural activity preceding the induction of a seizure with MES (baseline), during the seizure (MES), and following termination of the seizure (Post). (C) The Markovian neural barcode with color legend. The darker colors denote higher probabilities/proportions. (D) Zoom perspectives of a selection of segments (approximately 100 transitions each) of the Markovian neural barcode. Note the commonality and banding among intra-baseline transitions, vs. specific variation encoded in the post-MES transitions. (E) A PC projection of Markovian neural barcode. The PC 1 vs. PC 2 (left), PC 1 vs. PC 3 (middle), and PC 2 vs. PC 3 (right) projections for the neural barcode in (C). The controls are plotted as green (baseline) and black (post) dots, while the MESs are plotted as red (baseline) and black (post) dots. Note the clustering of the post-MES epochs in all three projections. (F) Statistical quantification of the PC distance of the four conditions depicted in (C) and (D), as well as an additional n = 4 animals who received MES in a hold-out sample. The two post-MES samples separate from the control conditions when tested against MES-baseline (Wilcoxon rank-sum test; MES baseline: 0.1667; MES post: 0.3682, p = 5.4227 e -07; MES-hold out post: 0.4959, p = 1.175581 e -07). Please see figure for interquartile range. (G) The continuous Markov chain reconstruction of the post-MES epochs revealed a greater number of high-reconstruction error frames than would be expected in control conditions. Repeating the SBNMF procedure on these frames identifies 119 novel MES elements. The number of high-reconstruction error frames explained with each additional novel Markov element is illustrated, and the point of inflection in reconstruction improvement highlighted with a green dot and on the x axis. (H) Markov element exemplars generated from the SBNMF of high-reconstruction errors, revealing novel MES Markov elements that are not present in normative mesoscale cortical dynamics. These novel elements ( n = 8) explain an order-of-magnitude increase in variance explained in post-MES epochs (mean: 0.0290) compared to MES baseline epochs (mean: 0.0023) ( p = 1.556 e -04). (I) A PC projection of Markovian neural barcode results in the clustering of the post-MES epochs in all three projections. By analyzing the loadings and scores of the PC projections, we can identify which transitions of the Markovian neural barcode are associated with the visually identified clustering. The most extreme valued transition projections along PC 2 (transitions 307 and 2,107) have been denoted. (J) Distributions of the condition-specific transition probabilities from the Markovian neural barcode along the most extreme valued transition projections from PC 2 as given in (I). Note the upregulation of transition 2,107 in the post-MES epoch as compared the baseline conditions, and likewise the downregulation of transition 307 in the post-MES epoch. (Means; [Transition 2,107] control baseline: 0.0167, control post: 0, MES baseline: 0, MES post: 0.3602; [Transition 307] control baseline: 0.6636, control post: 0.7220, MES baseline: 0.7969, MES post: 0.1995). (K) Visual representation of the most up and downregulated Markovian neural barcode transitions in the MES post epochs. See also .

Journal: Cell Reports Methods

Article Title: Neural barcoding representing cortical spatiotemporal dynamics based on continuous-time Markov chains

doi: 10.1016/j.crmeth.2025.101294

Figure Lengend Snippet: The Markovian neural barcode reveals dynamical differences and novel activity motifs after extreme excitation (A) A schematic representation of the integration of the MES model of seizure and mesoscale cortical imaging in the awake mouse. (B) A voltage trace representing neural activity preceding the induction of a seizure with MES (baseline), during the seizure (MES), and following termination of the seizure (Post). (C) The Markovian neural barcode with color legend. The darker colors denote higher probabilities/proportions. (D) Zoom perspectives of a selection of segments (approximately 100 transitions each) of the Markovian neural barcode. Note the commonality and banding among intra-baseline transitions, vs. specific variation encoded in the post-MES transitions. (E) A PC projection of Markovian neural barcode. The PC 1 vs. PC 2 (left), PC 1 vs. PC 3 (middle), and PC 2 vs. PC 3 (right) projections for the neural barcode in (C). The controls are plotted as green (baseline) and black (post) dots, while the MESs are plotted as red (baseline) and black (post) dots. Note the clustering of the post-MES epochs in all three projections. (F) Statistical quantification of the PC distance of the four conditions depicted in (C) and (D), as well as an additional n = 4 animals who received MES in a hold-out sample. The two post-MES samples separate from the control conditions when tested against MES-baseline (Wilcoxon rank-sum test; MES baseline: 0.1667; MES post: 0.3682, p = 5.4227 e -07; MES-hold out post: 0.4959, p = 1.175581 e -07). Please see figure for interquartile range. (G) The continuous Markov chain reconstruction of the post-MES epochs revealed a greater number of high-reconstruction error frames than would be expected in control conditions. Repeating the SBNMF procedure on these frames identifies 119 novel MES elements. The number of high-reconstruction error frames explained with each additional novel Markov element is illustrated, and the point of inflection in reconstruction improvement highlighted with a green dot and on the x axis. (H) Markov element exemplars generated from the SBNMF of high-reconstruction errors, revealing novel MES Markov elements that are not present in normative mesoscale cortical dynamics. These novel elements ( n = 8) explain an order-of-magnitude increase in variance explained in post-MES epochs (mean: 0.0290) compared to MES baseline epochs (mean: 0.0023) ( p = 1.556 e -04). (I) A PC projection of Markovian neural barcode results in the clustering of the post-MES epochs in all three projections. By analyzing the loadings and scores of the PC projections, we can identify which transitions of the Markovian neural barcode are associated with the visually identified clustering. The most extreme valued transition projections along PC 2 (transitions 307 and 2,107) have been denoted. (J) Distributions of the condition-specific transition probabilities from the Markovian neural barcode along the most extreme valued transition projections from PC 2 as given in (I). Note the upregulation of transition 2,107 in the post-MES epoch as compared the baseline conditions, and likewise the downregulation of transition 307 in the post-MES epoch. (Means; [Transition 2,107] control baseline: 0.0167, control post: 0, MES baseline: 0, MES post: 0.3602; [Transition 307] control baseline: 0.6636, control post: 0.7220, MES baseline: 0.7969, MES post: 0.1995). (K) Visual representation of the most up and downregulated Markovian neural barcode transitions in the MES post epochs. See also .

Techniques: Activity Assay, Imaging, Selection, Control, Generated

The Markovian neural barcode and sensory evoked processing (A) A schematic representation of mesoscale cortical imaging during full-field visual flash experiments. Awake head-fixed animals were imaged as a 450-nm LED placed adjacent to the right eye delivered full-field visual flashes. (B) Visual evoked responses from a full-field flash produce a characteristic response in V1 as shown in the montage depicting an average of 100 trials (top) and a single trial (bottom). The montage represents the visual evoked response pre-stimulation (−100 ms), the stimulation denoted by a schematic LED and blue line, and post-stimulation (+100, +300, and +500 ms). Note the considerable variability in the late component (+300 ms) of the visual evoked response as exemplified by the difference seen between the average and the single trial. (C) The heterogeneity in visual evoked response amplitudes is shown on a per trial basis (gray lines) representing the Δ F / F signal within a 10 × 10 pixel region of interest in V1. The average visual evoked response trace is shown in red, revealing the primary and secondary visual evoked responses (the secondary response is highlighted by the blue arrow). (D) A “raster plot” of the Markov state occupancy ( y axis) vs. time ( x axis), with the states color coded according to the Louvain sorted activity modules. The blue vertical lines denote full-field LED flashes. (E) The histogram of the Markov state occupancy across time, organized by modules and separated by green boundaries, for the second preceding and following a full-field LED flash. Brighter colors denote higher occupancy in time. (F) A sample set of 4 Markov elements from different modules that were upregulated by the stimulus flash immediately after the full-field visual flash as compared to pre-stimulus. (G) The Louvain sorted TPMs derived from transitions occurring prior to the full-field visual flash (left) and after the flash onset (right). Note the upregulation of inter-module transition probabilities. Brighter colors denote higher probabilities of transitions. (H) The Markovian neural barcode for the same animals imaged under a control quiet wakefulness condition and with field visual flashes occurring every 3 s with 1-s jitter (as described in A). The red vertical lines denote the boundary between modules as well as the occupancy distribution in the Markovian neural barcode. Darker colors denote higher probabilities/proportions in the neural barcode. (I) The first two PC projections of the neural barcode for the full barcode (left), the TPMs only (middle), and the occupancy distribution only (right) for the control (white circles) and visual stimulation protocol recordings (blue circles). Note the condition clustering and separation. (J) Statistical quantification of the PC distance distributions displayed as violin plots for the controls (white circles) vs. the visual stimulation (blue circles). Recordings in which animals receive a full-field visual flash differ from control recordings for the full neural barcode ([left] Wilcoxon rank-sum test; control: 0.2517, visual: 0.5045, p = 3.1908 e -3), the TPMs only ([middle] Wilcoxon rank-sum test; control: 0.2507, visual: 0.5041, p = 3.2795 e -03), and the occupancy distribution only ([right] Wilcoxon rank-sum test; control: 0.3670, visual: 0.5829, p = 4.9088 e -3). Please see figure for interquartile range. (K) Visual flash trials are dichotomized according to a median split of the secondary response amplitude from n = 8 mice. The projections of the Markovian neural barcode along the first two PCs plotted for (left) the full barcode, (middle) transitions only, and (right) occupancy only in the second preceding the flash. Clustering is evident along the PC projection for the occupancy distribution. (L) Quantification of the PC projections from the first three components reveals that only the Markov element occupancy distribution distinguishes visual evoked response trials with high and low Δ F / F secondary responses (Wilcoxon rank-sum test; [Full] low: 0.3870, high: 0.3004, p = 6.9315 e -01; [TPM] low: 0.3822, high: 0.3024, p = 7.3749 e -01; [OCC] low: 0.3766, high: 0.5639, p = 6.5393 e -05). Please see figure for interquartile range. (OCC, occupancy distribution). (M) The Markov element occupancy bar code is presented for n = 8 animals for trials that elicited high and low Δ F / F secondary responses. This reveals a marked upregulation of Module 2 Markov elements in trials that elicited Δ F / F amplitude secondary responses and an upregulation of Module 1 Markov elements in trials that elicited Δ F / F amplitude secondary responses.

Journal: Cell Reports Methods

Article Title: Neural barcoding representing cortical spatiotemporal dynamics based on continuous-time Markov chains

doi: 10.1016/j.crmeth.2025.101294

Figure Lengend Snippet: The Markovian neural barcode and sensory evoked processing (A) A schematic representation of mesoscale cortical imaging during full-field visual flash experiments. Awake head-fixed animals were imaged as a 450-nm LED placed adjacent to the right eye delivered full-field visual flashes. (B) Visual evoked responses from a full-field flash produce a characteristic response in V1 as shown in the montage depicting an average of 100 trials (top) and a single trial (bottom). The montage represents the visual evoked response pre-stimulation (−100 ms), the stimulation denoted by a schematic LED and blue line, and post-stimulation (+100, +300, and +500 ms). Note the considerable variability in the late component (+300 ms) of the visual evoked response as exemplified by the difference seen between the average and the single trial. (C) The heterogeneity in visual evoked response amplitudes is shown on a per trial basis (gray lines) representing the Δ F / F signal within a 10 × 10 pixel region of interest in V1. The average visual evoked response trace is shown in red, revealing the primary and secondary visual evoked responses (the secondary response is highlighted by the blue arrow). (D) A “raster plot” of the Markov state occupancy ( y axis) vs. time ( x axis), with the states color coded according to the Louvain sorted activity modules. The blue vertical lines denote full-field LED flashes. (E) The histogram of the Markov state occupancy across time, organized by modules and separated by green boundaries, for the second preceding and following a full-field LED flash. Brighter colors denote higher occupancy in time. (F) A sample set of 4 Markov elements from different modules that were upregulated by the stimulus flash immediately after the full-field visual flash as compared to pre-stimulus. (G) The Louvain sorted TPMs derived from transitions occurring prior to the full-field visual flash (left) and after the flash onset (right). Note the upregulation of inter-module transition probabilities. Brighter colors denote higher probabilities of transitions. (H) The Markovian neural barcode for the same animals imaged under a control quiet wakefulness condition and with field visual flashes occurring every 3 s with 1-s jitter (as described in A). The red vertical lines denote the boundary between modules as well as the occupancy distribution in the Markovian neural barcode. Darker colors denote higher probabilities/proportions in the neural barcode. (I) The first two PC projections of the neural barcode for the full barcode (left), the TPMs only (middle), and the occupancy distribution only (right) for the control (white circles) and visual stimulation protocol recordings (blue circles). Note the condition clustering and separation. (J) Statistical quantification of the PC distance distributions displayed as violin plots for the controls (white circles) vs. the visual stimulation (blue circles). Recordings in which animals receive a full-field visual flash differ from control recordings for the full neural barcode ([left] Wilcoxon rank-sum test; control: 0.2517, visual: 0.5045, p = 3.1908 e -3), the TPMs only ([middle] Wilcoxon rank-sum test; control: 0.2507, visual: 0.5041, p = 3.2795 e -03), and the occupancy distribution only ([right] Wilcoxon rank-sum test; control: 0.3670, visual: 0.5829, p = 4.9088 e -3). Please see figure for interquartile range. (K) Visual flash trials are dichotomized according to a median split of the secondary response amplitude from n = 8 mice. The projections of the Markovian neural barcode along the first two PCs plotted for (left) the full barcode, (middle) transitions only, and (right) occupancy only in the second preceding the flash. Clustering is evident along the PC projection for the occupancy distribution. (L) Quantification of the PC projections from the first three components reveals that only the Markov element occupancy distribution distinguishes visual evoked response trials with high and low Δ F / F secondary responses (Wilcoxon rank-sum test; [Full] low: 0.3870, high: 0.3004, p = 6.9315 e -01; [TPM] low: 0.3822, high: 0.3024, p = 7.3749 e -01; [OCC] low: 0.3766, high: 0.5639, p = 6.5393 e -05). Please see figure for interquartile range. (OCC, occupancy distribution). (M) The Markov element occupancy bar code is presented for n = 8 animals for trials that elicited high and low Δ F / F secondary responses. This reveals a marked upregulation of Module 2 Markov elements in trials that elicited Δ F / F amplitude secondary responses and an upregulation of Module 1 Markov elements in trials that elicited Δ F / F amplitude secondary responses.

Techniques: Imaging, Activity Assay, Derivative Assay, Control

Quantification of the Markovian neural barcode (A) Using BIC and the ( n = 160) repeated acquisition ( x 4) protocol recordings described in , a zeroth- and first-order Markov model were compared to a second-order Markov model. Given the first-order Markov model estimates (median BIC = −16,055.5567) and zeroth-order Markov model estimates (median BIC = 554.4835), using the selection criterian for Markov chain order, a first-order model is chosen. See figure for interquartile range. (B) Using BIC and the ( n = 88) repeated acquisition protocol ( x 8) recordings, a zeroth- and first-order Markov model were compared to a second-order Markov model. Given the first-order Markov model estimates (median BIC = −15,999.0733) and zeroth-order Markov model estimates (median BIC = 9.2736), using the selection criterian for Markov chain order, a first-order model is chosen. See figure for interquartile range. (C) Using AIC and the ( n = 160) repeated acquisition ( x 4) protocol recordings described in , a zeroth- and first-order Markov model were compared to a second-order Markov model. Given the first-order Markov model estimates (median AIC = 13,947.7911) and zeroth-order Markov model estimates (median AIC = 44,659.5781), using the selection criterian for Markov chain order, a first-order model is chosen. See figure for interquartile range. (D) Using AIC and the ( n = 88) repeated acquisition protocol ( x 8) recordings, a zeroth- and first-order Markov model were compared to a second-order Markov model. Given the first-order Markov model estimates (median AIC = 13,246.6989) and zeroth-order Markov model estimates (median AIC = 41,921.8211), using the selection criterian for Markov chain order, a first-order model is chosen. See figure for interquartile range. (E) The relative error across sequential TPMs as more frames are used to estimate the temporal dynamics. The relative error is estimated as the matrix 2-norm between TPM computed from Markov logs of increasing temporal size with the full TPM model computed from 15,000 frames. Simulations were computed from the repeated acquisition protocol, ( n = 160). Error bars denote ± 1 standard deviation. (F) The distribution of correlation between the TPMs within recordings from the discovery set ( n = 80) across different simulation conditions. The median Pearson correlation between TPMs in the discovery set was r = 0.7018, the median Pearson correlation between TPMs generated from permutations of the original Markov logs was lower at r = 0.1917, and the median Pearson correlation between TPMs generated from row permutations of the original TPMs was r = −0.0017. The median Pearson correlation between occupancy distributions was also computed at r = 0.5684 across all conditions. See figure for interquartile range. (G) To explore the commonality of motifs within and between animals, we computed the Pearson correlation between occupancy distributions within and between animals from the repeated acquisition protocol, ( n = 160). The median Pearson correlation within animals was r = 0.8553 and median Pearson correlation between animals was r = 0.5623. These distributions were statistically significant (Wilcoxon rank-sum test; within: 0.8553, between: 0.5623, p = 1.28 e -27). See figure for interquartile range.

Journal: Cell Reports Methods

Article Title: Neural barcoding representing cortical spatiotemporal dynamics based on continuous-time Markov chains

doi: 10.1016/j.crmeth.2025.101294

Figure Lengend Snippet: Quantification of the Markovian neural barcode (A) Using BIC and the ( n = 160) repeated acquisition ( x 4) protocol recordings described in , a zeroth- and first-order Markov model were compared to a second-order Markov model. Given the first-order Markov model estimates (median BIC = −16,055.5567) and zeroth-order Markov model estimates (median BIC = 554.4835), using the selection criterian for Markov chain order, a first-order model is chosen. See figure for interquartile range. (B) Using BIC and the ( n = 88) repeated acquisition protocol ( x 8) recordings, a zeroth- and first-order Markov model were compared to a second-order Markov model. Given the first-order Markov model estimates (median BIC = −15,999.0733) and zeroth-order Markov model estimates (median BIC = 9.2736), using the selection criterian for Markov chain order, a first-order model is chosen. See figure for interquartile range. (C) Using AIC and the ( n = 160) repeated acquisition ( x 4) protocol recordings described in , a zeroth- and first-order Markov model were compared to a second-order Markov model. Given the first-order Markov model estimates (median AIC = 13,947.7911) and zeroth-order Markov model estimates (median AIC = 44,659.5781), using the selection criterian for Markov chain order, a first-order model is chosen. See figure for interquartile range. (D) Using AIC and the ( n = 88) repeated acquisition protocol ( x 8) recordings, a zeroth- and first-order Markov model were compared to a second-order Markov model. Given the first-order Markov model estimates (median AIC = 13,246.6989) and zeroth-order Markov model estimates (median AIC = 41,921.8211), using the selection criterian for Markov chain order, a first-order model is chosen. See figure for interquartile range. (E) The relative error across sequential TPMs as more frames are used to estimate the temporal dynamics. The relative error is estimated as the matrix 2-norm between TPM computed from Markov logs of increasing temporal size with the full TPM model computed from 15,000 frames. Simulations were computed from the repeated acquisition protocol, ( n = 160). Error bars denote ± 1 standard deviation. (F) The distribution of correlation between the TPMs within recordings from the discovery set ( n = 80) across different simulation conditions. The median Pearson correlation between TPMs in the discovery set was r = 0.7018, the median Pearson correlation between TPMs generated from permutations of the original Markov logs was lower at r = 0.1917, and the median Pearson correlation between TPMs generated from row permutations of the original TPMs was r = −0.0017. The median Pearson correlation between occupancy distributions was also computed at r = 0.5684 across all conditions. See figure for interquartile range. (G) To explore the commonality of motifs within and between animals, we computed the Pearson correlation between occupancy distributions within and between animals from the repeated acquisition protocol, ( n = 160). The median Pearson correlation within animals was r = 0.8553 and median Pearson correlation between animals was r = 0.5623. These distributions were statistically significant (Wilcoxon rank-sum test; within: 0.8553, between: 0.5623, p = 1.28 e -27). See figure for interquartile range.

Techniques: Selection, Standard Deviation, Generated

Review

Structured Review

Images

Similar Products

Image Search Results