Shared2018-11-23-102108.sagewsOpen in CoCalc
Authors: Joel Dahne, Raazesh Sainudiin, Julian Salas
Views : 27
Description: randomWalkersSimulations

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

δ=i=1nxi \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
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