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"]
Out[1]=

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"]
Out[2]=

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"]]
Out[3]=

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]
Out[4]=

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]
Out[5]=

Visualize smooth point density:

In[6]:=
density = SmoothPointDensity[ResourceData[\!\(\*
TagBox["\"\<Sample Data: Beta Cells\>\"",
#& ,
BoxID -> "ResourceTag-Sample Data: Beta Cells-Input",
AutoDelete->True]\), "Data"]]
Out[6]=
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]]
Out[7]=

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"]]
Out[8]=
In[9]:=
maxR = nnG["MaxRadius"]
Out[9]=
In[10]:=
DiscretePlot[nnG[r], {r, maxR/100, maxR, maxR/100}, AxesLabel -> {"radius", "probability"}]
Out[10]=

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:

In[12]:=
Total[(1 - values)*step]
Out[12]=

Account for scale and units:

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

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
Out[14]=

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]]
Out[16]=

Gosia Konwerska, "Sample Data: Beta Cells" from the Wolfram Data Repository (2022)  

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