fit 2d gaussian function to data  (MathWorks Inc)

Journal: Nmr in Biomedicine

Article Title: Cluster Analysis of VERDICT MRI for Cancer Tissue Characterization in Neuroendocrine Tumors

doi: 10.1002/nbm.70050

Figure Lengend Snippet: Scatterplot of R against f IC for all tumor voxels ( n = 11,519) and subjects (A; left side). The black contours show the 2D Gaussian mixture model (GMM) fit with each voxel data point color‐coded based on the probability of belonging to each component (blue, green, and red). Contours of the three individual GMM components are shown as smaller plots (right side). R and f IC maps of tumor ROIs were used to generate color‐coded posterior probability maps of each GMM component (B; Subject 6 shown as example).

Article Snippet: A 2D Gaussian mixture model (GMM) was then fitted to the f IC and R values of all tumor voxels using an algorithm based on the MATLAB function fitgmdist with 20 random initializations to avoid local optima and a regularization value of 3.5 × 10 −3 to avoid overfitting ( mathworks.com/matlabcentral/fileexchange/71496‐identification‐of‐subregions‐in‐parameter‐maps‐by‐gmm ) [ ].

Techniques:

Journal: Nmr in Biomedicine

Article Title: Cluster Analysis of VERDICT MRI for Cancer Tissue Characterization in Neuroendocrine Tumors

doi: 10.1002/nbm.70050

Figure Lengend Snippet: Model fit output of the Gaussian mixture model (GMM) of three clusters fitted to R and f IC for all tumor voxels. The table shows cluster ID as defined by histological analysis (Figures 4 and 6 ), mean values of R and f IC ( μ ) for each cluster, and the cluster fraction indicating the percentage of tumor voxel data that is associated with each Gaussian component.

Article Snippet: A 2D Gaussian mixture model (GMM) was then fitted to the f IC and R values of all tumor voxels using an algorithm based on the MATLAB function fitgmdist with 20 random initializations to avoid local optima and a regularization value of 3.5 × 10 −3 to avoid overfitting ( mathworks.com/matlabcentral/fileexchange/71496‐identification‐of‐subregions‐in‐parameter‐maps‐by‐gmm ) [ ].

Techniques:

Journal: Nmr in Biomedicine

Article Title: Cluster Analysis of VERDICT MRI for Cancer Tissue Characterization in Neuroendocrine Tumors

doi: 10.1002/nbm.70050

Figure Lengend Snippet: Gaussian mixture model (GMM) probability maps from the VERDICT cluster analysis of R and f IC (left columns) and classification maps from the histology analysis (right columns). The colors in the histology classification maps represent different tissue types: necrotic (red), fibrotic (blue), and viable cancer cells (green). Black pixels indicate areas where no stain was present. The colors in the VERDICT cluster maps represent the probability of each voxel belonging to the GMM clusters, with colors chosen for each cluster to best match with the histology maps.

Article Snippet: A 2D Gaussian mixture model (GMM) was then fitted to the f IC and R values of all tumor voxels using an algorithm based on the MATLAB function fitgmdist with 20 random initializations to avoid local optima and a regularization value of 3.5 × 10 −3 to avoid overfitting ( mathworks.com/matlabcentral/fileexchange/71496‐identification‐of‐subregions‐in‐parameter‐maps‐by‐gmm ) [ ].

Techniques: Staining

Journal: Nature Communications

Article Title: Hand position fields of neurons in the premotor cortex of macaques during natural reaching

doi: 10.1038/s41467-025-58786-3

Figure Lengend Snippet: A Recording sites mainly covered the hand area of the dorsal premotor cortex in each monkey. Black squares denote the position of inserted Utah arrays (96 electrodes for Monkey X, 48 electrodes for Monkey A, B, and Z). Black lines denote brain sulci used to locate the implantation site. PS, principal sulcus; AS, accurate sulcus. B Diagram of the naturalistic reach-and-grasp task. C Upper row: trajectories (black lines) of monkeys’ hand from four example sessions (one for each monkey). Spikes from four exemplary cells in each corresponding session are plotted as circular markers. The color and size of the circles are set according to the spike counts. The brown triangle indicates the position of the monkey’s nose (facing right). Peak firing rate for each cell is labeled on the top of panels. The vertical scale bars represent 5 cm along the x axis and the horizontal scale bars represent 5 cm along the y axis in each panel. Bottom row: corresponding 2D spatial firing rate maps, denoted with SI. Dark blue indicates the minimal firing rate within the map, and dark red indicates the maximal firing rate within the map. D The distribution of SI of hand position-tuned cells ( n = 132). E Fitting the hand position firing fields using a 2D Gaussian function. Left, color-coded firing activity of the first cell in ( C ), shown as a function of hand position. The area outside the field is masked with gray. Right, fitted Gaussian function of the field, coefficient of determination, r 2 = 0.83, one-sided F-test, F-statistic = 170.75, P = 0.0000. F Comparison between the r 2 of Gaussian fitting and that of linear fitting, P = 2.46 × 10 −26 , n = 132 cells, one-sided paired t-test. *** P < 0.001. Source data is provided as a Source Data file.

Article Snippet: Each map was then smoothed by a 2D Gaussian filter (standard deviation: 1.5 bin, Matlab function imgaussfilt ).

Techniques: Labeling, Activity Assay, Comparison