Wolfram Data Repository

Immediate Computable Access to Curated Contributed Data

Sample Data: Beta Cells

Source Notebook

Locations of retinal ganglia cells annotated with on/off and area (in square microns) marks

Details

Locations of retinal ganglia cells in the observation region Rectangle[{28.08, 16.2}, {778.08, 1007.02}] microns, annotated with on/off and area (in square microns) marks.

Examples

Basic Examples (1) 

In[1]:=
ResourceData[\!\(\* TagBox["\"\<Sample Data: Beta Cells\>\"", #& , BoxID -> "ResourceTag-Sample Data: Beta Cells-Input", AutoDelete->True]\), "Data"]
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Summary of the spatial point data:

In[2]:=
ResourceData[\!\(\* TagBox["\"\<Sample Data: Beta Cells\>\"", #& , BoxID -> "ResourceTag-Sample Data: Beta Cells-Input", AutoDelete->True]\), "Data"]["Summary"]
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Visualizations (4) 

Plot the spatial point data:

In[3]:=
ListPlot[ResourceData[\!\(\* TagBox["\"\<Sample Data: Beta Cells\>\"", #& , BoxID -> "ResourceTag-Sample Data: Beta Cells-Input", AutoDelete->True]\), "Data"]]
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Visualize data with categorical annotations:

In[4]:=
PointValuePlot[ResourceData[\!\(\* TagBox["\"\<Sample Data: Beta Cells\>\"", #& , BoxID -> "ResourceTag-Sample Data: Beta Cells-Input", AutoDelete->True]\), "Data"], PlotLegends -> Automatic]
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Visualize data with both annotations:

In[5]:=
PointValuePlot[ResourceData[\!\(\* TagBox["\"\<Sample Data: Beta Cells\>\"", #& , BoxID -> "ResourceTag-Sample Data: Beta Cells-Input", AutoDelete->True]\), "Data"], {1 -> "Shape", 2 -> "Size"}, PlotLegends -> Automatic]
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Visualize smooth point density:

In[6]:=
density = SmoothPointDensity[ResourceData[\!\(\* TagBox["\"\<Sample Data: Beta Cells\>\"", #& , BoxID -> "ResourceTag-Sample Data: Beta Cells-Input", AutoDelete->True]\), "Data"]]
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In[7]:=
Show[ContourPlot[density[{x, y}], {x, y} \[Element] ResourceData[\!\(\* TagBox["\"\<Sample Data: Beta Cells\>\"", #& , BoxID -> "ResourceTag-Sample Data: Beta Cells-Input", AutoDelete->True]\), "ObservationRegion"], ColorFunction -> "Rainbow"], ListPlot[ResourceData[\!\(\* TagBox["\"\<Sample Data: Beta Cells\>\"", #& , BoxID -> "ResourceTag-Sample Data: Beta Cells-Input", AutoDelete->True]\), "Locations"], PlotStyle -> Black]]
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Analysis (6) 

Compute probability of finding a point within given radius of an existing point - NearestNeighborG is the CDF of the nearest neighbor distribution:

In[8]:=
nnG = NearestNeighborG[ResourceData[\!\(\* TagBox["\"\<Sample Data: Beta Cells\>\"", #& , BoxID -> "ResourceTag-Sample Data: Beta Cells-Input", AutoDelete->True]\), "Data"]]
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In[9]:=
maxR = nnG["MaxRadius"]
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In[10]:=
DiscretePlot[nnG[r], {r, maxR/100, maxR, maxR/100}, AxesLabel -> {"radius", "probability"}]
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NearestNeighborG as the CDF of nearest neighbor distribution can be used to compute the mean distance between a typical point and its nearest neighbor - the mean of a positive support distribution can be approximated via a Riemann sum of 1- CDF. To use Riemann approximation create the partition of the support interval from 0 to maxR into 100 parts and compute the value of the NearestNeighborG at the middle of each subinterval:

In[11]:=
step = maxR/100; middles = Subdivide[step/2, maxR - step/2, 99]; values = nnG[middles];

Now compute the Riemann sum to find the mean distance between a typical point and its nearest neighbor:

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Total[(1 - values)*step]
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Account for scale and units:

In[13]:=
%*ResourceData[\!\(\* TagBox["\"\<Sample Data: Beta Cells\>\"", #& , BoxID -> "ResourceTag-Sample Data: Beta Cells-Input", AutoDelete->True]\), "RegionScale"]
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Test for complete spatial randomness:

In[14]:=
SpatialRandomnessTest[ResourceData[\!\(\* TagBox["\"\<Sample Data: Beta Cells\>\"", #& , BoxID -> "ResourceTag-Sample Data: Beta Cells-Input", AutoDelete->True]\), "Data"], {"PValue", "TestConclusion"}] // Column
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Fit a Poisson point process to data:

In[15]:=
Clear[\[Mu]]; EstimatedPointProcess[ResourceData[\!\(\* TagBox["\"\<Sample Data: Beta Cells\>\"", #& , BoxID -> "ResourceTag-Sample Data: Beta Cells-Input", AutoDelete->True]\), "Data"], PoissonPointProcess[\[Mu], 2]]
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Gosia Konwerska, "Sample Data: Beta Cells" from the Wolfram Data Repository (2022)  

Data Resource History

  • Date Created:

Source Metadata

  • Citation:
    • Wässle H., Boycott B., Illing RB., (1981). Morphology and Mosaic of On- and Off-Beta Cells in the Cat Retina and some Functional Considerations. Proceedings of the Royal Society London Ser. B, 212, 177-195.

Publisher Information

  • Prepared for the Wolfram Data Repository By: Gosia Konwerska
    (Wolfram Research, Inc.)
  • Publisher of Record: Gosia Konwerska