Sufficiently Sanitized Mobility Statistics

Raazesh Sainudiin and Joel Dahne

directed by Marina Toger and Julián Salas Piñón

This is mainly Raaz's simulations to limit the scope of needed mathematical statistics.

Working collaboratively in the cloud.

def makeRandomWalkTraj(ID=int(0), txy0 = [float(0.0),float(0.0),float(0.0)], steps = int(10),\
                       xy_move = float(1.0),t_rate = float(1.0)):
    itxy=[ID, txy0[0], txy0[1], txy0[2]]
    traj=[itxy]
    for i in range(steps):
        t = itxy[1] + (float(-1.0)/t_rate)*log(float(1.0) - random())
        x = itxy[2]+xy_move*random()*float(2.0)+float(-1.0)
        y = itxy[3]+xy_move*random()*float(2.0)+float(-1.0)
        itxy=[itxy[0], t , x, y]
        traj.append(itxy)
    return traj

ss=float(10.0) # spatial scale
t = makeRandomWalkTraj(23,\
                       [random()*float(2.0)+float(-1.0),random()*float(2.0*ss)+float(-1.0*ss),random()*float(2.0*ss)+float(-1.0*ss)],\
                       int(10),float(1.0),float(1.0))
t

[[23, -0.4659012343959228, -9.575607826557713, 0.17340282805104756], [23, 0.6126479891938093, -9.184760613690155, 0.4885329796159714], [23, 2.6957539280514533, -8.606602981320204, 0.9510692130506782], [23, 6.06959585684219, -8.681472704747904, 1.630766154509188], [23, 7.138921335368573, -7.7102766034082055, 2.4780067265426338], [23, 8.104735646981913, -8.464004907096287, 2.2487166415590747], [23, 8.899272762724815, -8.555205138914507, 1.5181199596044745], [23, 9.322957064997755, -9.38790099954956, 2.1838151104613814], [23, 10.251556511608827, -9.92669144859741, 2.933561360873518], [23, 12.35940116756471, -9.682509445817248, 3.46564251242195], [23, 12.885294796735993, -8.77343276984541, 3.8228980704770095]]

import numpy as np

def makeTraj3DImage(tr,rgb):
    a = np.array(tr)
    p=points(a[:,1:4],size=5,rgbcolor=rgb,opacity=.5)
    p+=line(a[:,1:4],size=5,rgbcolor=rgb,opacity=.5)
    return p

numOfIndividuals=50
numSteps=100
ss=float(1.0) # spatial scale
Ts=[]
for i in range(0,numOfIndividuals):
    t = makeRandomWalkTraj(i,\
                       [random()*float(2.0)+float(-1.0),random()*float(2.0*ss)+float(-1.0*ss),random()*float(2.0*ss)+float(-1.0*ss)],\
                       int(numSteps),float(1.0),float(1.0))
    Ts.append(t)

rgbRandomColorMap = [(random(),random(),random()) for i in range(numOfIndividuals)]
p=makeTraj3DImage(Ts[0], rgbRandomColorMap[0])
for i in range(1,numOfIndividuals):
    p+=makeTraj3DImage(Ts[i], rgbRandomColorMap[i])
p.show()

3D rendering not yet implemented

We can take a slice of time at the beginning from the above co-trajectories

\delta = \sum_{i=1}^n x_i

help(point3d)

%md
## Joel's Python code

Joel, you could put your python code ina  big block here so we can all play with it more easily.

Joel's Python code

Joel, you could put your python code ina big block here so we can all play with it more easily.

# Joel's Python code could go in this cell

5 + 5

10