Biomod/2011/Caltech/DeoxyriboNucleicAwesome/Simulation
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==MATLAB Code==  ==MATLAB Code==  
  At the core of the simulation is a function which runs runs one random walk on an origami of specified size. It can run in both a cargobearing (onecargo onegoal) and a purely randomwalk mode. The former has cargo positions corresponding to our particular origami preprogrammed and starting with multiple (specified by user) walkers at random locations on the origami, and terminates when all of the cargos have been "sorted" to the goal location (the x axis). The latter runs one walker starting at a specified location, and terminates when that walker reaches the specified irreversible track location. The function returns a log reporting when cargos were picked up and dropped off, and a count of the number of steps the simulation took.  +  At the core of the simulation is a function which runs runs one random walk on an origami of specified size. It can run in both a cargobearing (onecargo onegoal) and a purely randomwalk mode. The former has cargo positions corresponding to our particular origami preprogrammed and starting with multiple (specified by user) walkers at random locations on the origami, and terminates when all of the cargos have been "sorted" to the goal location (the x axis). The latter runs one walker starting at a specified location, and terminates when that walker reaches the specified irreversible track location. The function returns a log reporting when cargos were picked up and dropped off, and a count of the number of steps the simulation took. This function is utilized by separate cargobearing and randomwalk data collection programs that call the function many times over a range of parameters. 
  +  The function code (saved as randomWalkFunction.m):  
  <  +  <code><pre> 
  </code>  +  function [cargoLog, steps] = randomWalkFunction(x, y, length, numWalkers, ... 
+  startPos, endPos, cargoBearing, restricted)  
+  %x: Width y: Height  
+  %length: max # of steps to run simulation  
+  %numWalkers = number of walkers to simulate in cargoBearing state  
+  %startPos = starting position for walker in randomwalk state  
+  %endPos = irreversible track location in randomwalk state  
+  %cargoBearing = running cargoBearing (1) vs randomWalking (0)  
+  %restricted = whether we're paying attention to borders  
+  
+  %Random walking cargo pickup/dropoff simulation  
+  %for origami tile, x (horizontal) by y (vertical) dim.  
+  %Locations index by 1. x+ = right, y+ = up  
+  % Gregory Izatt & Caltech BIOMOD 2011  
+  % 20110615: Initial revision  
+  % 20110615: Continuing development  
+  % Added simulation for cargo pickup/dropoff  
+  % Adding support for multiple walkers  
+  % 20110616: Debugging motion rules, making display better  
+  % 20110616: Modified to be a random walk function, to be  
+  % called in a data accumulator program  
+  
+  %Walkers:  
+  % Set position randomly if we're doing cargo bearing simulation,  
+  % or set to supplied startPos if not.  
+  if cargoBearing  
+  currentPos = zeros(numWalkers, 2);  
+  for i=1:numWalkers  
+  currentPos(i, :) = [randi(x, 1), randi(y, 1)];  
+  end  
+  % If doing a cargobearing walk, set these to cargo positions too:  
+  cargoPos = [[3, 5]; [9, 5]; [15, 5]; [7, 2]; [11, 2]];  
+  else  
+  currentPos = startPos;  
+  numWalkers = 1; %Want to make sure this is one for this case  
+  end  
+  
+  
+  
+  %Initialize some things:  
+  steps = 0;  
+  hasCargo = zeros(numWalkers);  
+  sorted = 0;  
+  cargoAPoss = [0, 1; 0, 1; 1, 0; 1, 1]; %Movement rules  
+  cargoBPoss = [0, 1; 0, 1; 1, 0; 1, 1]; %''  
+  log = zeros(length, 2*numWalkers + 1);  
+  cargoLog = [];  
+  collisionLog = [];  
+  
+  for i=1:length,  
+  for walker=1:numWalkers  
+  %Add current pos to log  
+  log(steps + 1, 2*walker1:2*walker) = currentPos(walker, :);  
+  
+  %Update pos to randomly  
+  %chosen neighbor  remember,  
+  %these are the only valid neighbors:  
+  % (0, +1), (0, 1)  
+  % IF (x/2)%1 = 0:  
+  % (+1, 0), (1, 1)  
+  % ELSE:  
+  % (1, 0), (+1, +1)  
+  
+  temp = randi(4, 1);  
+  if (mod(currentPos(walker, 1),2) == 0)  
+  newPos = currentPos(walker, :) + cargoAPoss(temp, :);  
+  else  
+  newPos = currentPos(walker, :) + cargoBPoss(temp, :);  
+  end  
+  
+  %If we just went out of bounds in the y direction (toward  
+  % a goal) and had cargos, we drop off  
+  if cargoBearing && (hasCargo(walker) == 1 && (newPos(2) < 1))  
+  %Drop cargo, increment cargodroppedcount  
+  hasCargo(walker) = 0;  
+  sorted = sorted + 1;  
+  %Don't move  
+  newPos = currentPos(walker, :);  
+  cargoLog = [cargoLog; steps, walker];  
+  end  
+  
+  %General outofbounds case without cargo drop:  
+  if restricted && ((newPos(1) > x  newPos(1) < 1  ...  
+  newPos(2) > y  newPos(2) < 1))  
+  %Don't go anywhere  
+  newPos = currentPos(walker, :);  
+  end  
+  
+  %Hitting cargos case:  
+  if cargoBearing  
+  m = (find(cargoPos(:, 1) == newPos(1)));  
+  for n=m  
+  if cargoPos(m, 2) == newPos(2)  
+  %Remove the cargo from the list of cargos and "pick up" if  
+  %you don't already have a cargo  
+  if hasCargo(walker) == 0  
+  cargoPos(m, :) = [50, 50];  
+  hasCargo(walker) = 1;  
+  cargoLog = [cargoLog; steps, walker];  
+  %Anyway, don't move there  
+  newPos = currentPos(walker, :);  
+  end  
+  end  
+  end  
+  end  
+  
+  % Already on irrev. cargo case:  
+  if (currentPos(walker, :) == endPos)  
+  return  
+  end  
+  
+  %Hitting other walkers case:  
+  if numWalkers > 1  
+  m = (find(currentPos(:, 1) == newPos(1)));  
+  for n=m  
+  if (currentPos(n, 2) == newPos(2))  
+  %Derp, don't go there  
+  newPos = currentPos(walker, :);  
+  collisionLog = [collisionLog; newPos, walker];  
+  end  
+  end  
+  end  
+  
+  %Finally actually update the position  
+  currentPos(walker, :) = newPos;  
+  
+  end  
+  
+  % Step forward, update log  
+  steps = steps + 1;  
+  log(steps, 2*numWalkers + 1) = steps  1;  
+  
+  if (sorted == 5)  
+  log(steps+1:end, :) = [];  
+  break  
+  end  
+  
+  end  
+  
+  return  
+  </pre></code>  
==RandomWalk Simulation==  ==RandomWalk Simulation== 
Revision as of 21:04, 22 June 2011
Wednesday, April 16, 2014

Simulations
OverviewOur proposed sorting mechanism depends very heavily on a particular randomwalking mechanism that has not been demonstrated in literature before. The verification of this mechanism is thus a vital step in our research. Verification of the random walk in one dimension is fairly straightforward: as discussed in <LINK TO THE EXPERIMENTAL DESIGN SECTION>, a onedimensional track is easy to construct, and will behave like a standard 1D random walk, showing an average translation on the order of after n steps. Thus, we should expect the time it takes to get to some specific level of fluorescence to be proportional to the square of the number of steps we start the walker from the irreversible substrate. If we can, in an experiment, record the fluorescence over time when the walker is planted at different starting points and show that that fluorescence varies by this relationship, we'll have fairly certainly verified onedimensional random walking. Our particular case of 2D random walking, however, is not as easily understood, especially considering the mobility restrictions (ability to move to only 4 of 6 surrounding locations at any particular time) of our particular walker. As a control for the verification of 2D random walking, though, we still need to get an idea how long the random walk should take, and how that time will change as we start the walker at different points on the origami. We opt to do this by simulating the system with a set of movement rules derived from our design. We also use the same basic simulation (with a few alterations and extra features) to simulate our entire sorting system in a onecargo, onegoal scenario, to give us some rudimentary numbers on how long sorting should take, with one vs multiple walkers. Basic parameters and assumptions:
MATLAB CodeAt the core of the simulation is a function which runs runs one random walk on an origami of specified size. It can run in both a cargobearing (onecargo onegoal) and a purely randomwalk mode. The former has cargo positions corresponding to our particular origami preprogrammed and starting with multiple (specified by user) walkers at random locations on the origami, and terminates when all of the cargos have been "sorted" to the goal location (the x axis). The latter runs one walker starting at a specified location, and terminates when that walker reaches the specified irreversible track location. The function returns a log reporting when cargos were picked up and dropped off, and a count of the number of steps the simulation took. This function is utilized by separate cargobearing and randomwalk data collection programs that call the function many times over a range of parameters. The function code (saved as randomWalkFunction.m):
RandomWalk Simulation 