Biomod/2011/Caltech/DeoxyriboNucleicAwesome/Simulation

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(Updating documentation to current revision of simulation.)
(Updating code to current revision)
Line 35: Line 35:
==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 cargo-bearing (one-cargo one-goal) and a purely random-walk mode. The former has cargo positions corresponding to our particular origami pre-programmed 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 of all walkers positions over time, 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 cargo-bearing and random-walk data collection programs that call the function many times over a range of parameters.
+
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 cargo-bearing (one-cargo one-goal) and a purely random-walk mode. The former has cargo positions corresponding to our particular origami pre-programmed 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 of all walkers positions over time, a log reporting when cargos were picked up and dropped off, a count of the number of steps the simulation took, and if desired, a move of the random walk. This function is utilized by separate cargo-bearing and random-walk data collection programs that call the function many times over a range of parameters.
The function code (saved as randomWalkFunction.m):
The function code (saved as randomWalkFunction.m):
Line 46: Line 46:
       padding-left: 10px;
       padding-left: 10px;
       background-color: #FEF7EA;"><code><syntaxhighlight lang="matlab">
       background-color: #FEF7EA;"><code><syntaxhighlight lang="matlab">
-
function [log, cargoLog, steps] = randomWalkFunction(x, y, length, ...
+
function [log, cargoLog, steps, M] = randomWalkFunctionGeneric(...
-
     numWalkers, startPos, endPos, cargoBearing, restricted, error)
+
     length, layoutMode, startPos, numWalkers, cargoBearing, error,...
 +
    record, spaceWalkOnly, departThreshold, arriveThreshold)
-
%x: Width        y: Height
+
%Random walking / cargo sorting  simulation for more general form
-
%length: max # of steps to run simulation
+
%track layouts. More flexible in terms of layout but ultimately
-
%numWalkers = number of walkers to simulate in cargoBearing state
+
%probably a touch slower.
-
%startPos = starting position for walker in randomwalk state
+
%Gregory Izatt & Caltech BIOMOD 2011
-
%endPos = irreversible track location in randomwalk state
+
%20110713: Init revision
-
%cargoBearing = running cargoBearing (1) vs randomWalking (0)
+
%20110714: Continuing init revision.
-
%restricted = whether we're paying attention to borders
+
%20110715: Continuing debugging of init revision.
-
%error = the chance of the failure of any single track
+
%20110718: Debugging issue where walkers n>=2 have occasional
 +
%          unexplained jaints to 0,0 in the log
 +
%20110719: Adding full movie capture capability, mostly working on
 +
%           rendering origami during movie production
 +
%20110816: Adding support for spacewalking and random
 +
%           walker appearance / departure
 +
%20110817: Adding support for ability to do /just/ a spacewalk
 +
%           for diagnostic / control purposes
 +
%Defines layouts:
-
%Random walking cargo pickup/dropoff simulation
+
%Layouts:
-
%for origami tile, x (horizontal) by y (vertical) dim.
+
%1 = Standard
-
%Locations index by 1. x+ = right, y+ = up
+
%2 = Mini-playground
-
% Gregory Izatt & Caltech BIOMOD 2011
+
%3 = 1D random walk / cargo sort
-
% 20110615: Initial revision
+
%4 = Wide & long random walk
-
% 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
+
-
% 20110628-30: Modified to take into account omitted positions
+
-
%          , new probe layout, and automatic halting when
+
-
%          starting on impossible positions.
+
-
% 20110706: Fixed walker collision. It detects collisions properly
+
-
%          now.
+
-
% 20110707: Adding support for errors -- cycles through and
+
-
%          omits each track position at an input error rate
+
-
%Initialize some things:
+
%In layout specification:
-
%Cargo positions:
+
%0 = nothing
-
cargoPos = [[3, 5]; [9, 5]; [15, 5]; [7, 7]; [11, 7]];
+
%1 = track 1
-
filledGoals = [];
+
%10 = walker on track 1
-
omitPos = [[3, 6]; [7, 8]; [8, 5]; [11, 8]; [15, 6]];
+
%2 = track 2
 +
%20 = walker on track 2
 +
%3 = cargo
 +
%4 = cargo goal
 +
%40 = filled cargo goal
 +
%5 = walker goal
 +
%50 = filled walker goal
 +
%Specification arrays are in origami coodinates as
 +
%defined on the BIOMOD wiki's simulation page.
 +
%Walking will assume that system, so make sure
 +
%they're right!
 +
%Also, make sure you start with an odd row (a high one)
 +
% or the movement will be messed up.
-
steps = 0;  
+
if layoutMode == 1
-
hasCargo = zeros(numWalkers);
+
    layout = ...
-
sorted = 0;
+
    [[1, 1, 2, 2, 1, 1, 0, 2, 1, 1, 0, 2, 1, 1, 2, 2]
-
trackAPoss = [0, 1; 0, -1; 1, 0; -1, -1];  %Movement rules, even column
+
    [2, 2, 1, 1, 2, 2, 3, 1, 2, 2, 3, 1, 2, 2, 1, 1]
-
trackBPoss = [0, 1; 0, -1; -1, 0; 1, 1]; %'', odd column
+
    [1, 1, 0, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 0, 2]
 +
    [2, 2, 3, 1, 2, 2, 1, 0, 3, 2, 1, 1, 2, 2, 3, 1]
 +
    [1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2]
 +
    [2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1]
 +
    [1, 4, 2, 4, 1, 4, 2, 2, 1, 4, 2, 4, 1, 4, 2, 4]
 +
    [2, 4, 1, 4, 2, 4, 1, 1, 2, 4, 1, 4, 2, 4, 1, 4]];
 +
elseif layoutMode == 2
 +
    layout = ...
 +
    [[0, 1, 0, 2, 1, 1, 0, 2]
 +
    [0, 2, 3, 1, 2, 2, 3, 1]
 +
    [0, 1, 2, 2, 1, 1, 2, 2]
 +
    [0, 2, 1, 0, 3, 2, 1, 1]
 +
    [0, 1, 2, 2, 1, 1, 2, 2]
 +
    [0, 2, 1, 1, 2, 2, 1, 1]
 +
    [0, 4, 2, 2, 1, 4, 2, 4]
 +
    [0, 4, 1, 1, 2, 4, 1, 4]];
 +
elseif layoutMode == 3
 +
    layout = ...
 +
    [[0, 2, 0]
 +
    [0, 1, 0]
 +
    [3, 2, 0]
 +
    [0, 1, 3]
 +
    [0, 2, 0]
 +
    [0, 1, 0]
 +
    [3, 2, 0]
 +
    [0, 1, 0]
 +
    [0, 2, 0]
 +
    [1, 4, 0]
 +
    [2, 4, 0]];
 +
elseif layoutMode == 4
 +
    layout = ...
 +
    [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1]
 +
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 5]
 +
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 2, 2, 1]
 +
    [0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 2, 2, 1, 0, 0]
 +
    [0, 0, 0, 0, 0, 2, 1, 1, 2, 2, 1, 0, 0, 0, 0]
 +
    [0, 0, 0, 2, 1, 1, 2, 2, 1, 0, 0, 0, 0, 0, 0]
 +
    [0, 2, 1, 1, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0]
 +
    [1, 1, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
 +
    [2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]];
 +
elseif layoutMode == 410
 +
    layout = ...
 +
    [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1]
 +
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 5]
 +
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 2, 2, 1]
 +
    [0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 2, 2, 1, 0, 0]
 +
    [0, 0, 0, 0, 0, 2, 1, 1, 2, 2, 1, 0, 0, 0, 0]
 +
    [0, 0, 0, 2, 1, 1, 2, 2, 1, 0, 0, 0, 0, 0, 0]
 +
    [0, 0, 1, 1, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0]
 +
    [0, 0, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
 +
    [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]];
 +
  elseif layoutMode == 416
 +
    layout = ...
 +
    [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1]
 +
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 5]
 +
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 2, 2, 1]
 +
    [0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 2, 2, 1, 0, 0]
 +
    [0, 0, 0, 0, 0, 2, 1, 1, 2, 2, 1, 0, 0, 0, 0]
 +
    [0, 0, 0, 0, 1, 1, 2, 2, 1, 0, 0, 0, 0, 0, 0]
 +
    [0, 0, 0, 0, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0]
 +
    [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
 +
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]];
 +
elseif layoutMode == 422
 +
    layout = ...
 +
    [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1]
 +
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 5]
 +
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 2, 2, 1]
 +
    [0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 2, 2, 1, 0, 0]
 +
    [0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1, 0, 0, 0, 0]
 +
    [0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 0, 0, 0, 0]
 +
    [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
 +
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
 +
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]];
 +
elseif layoutMode == 457
 +
    layout = ...
 +
    [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1]
 +
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 5]
 +
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 2, 2, 1]
 +
    [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1, 0, 0]
 +
    [0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 0, 0]
 +
    [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]
 +
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
 +
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
 +
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]];
 +
elseif layoutMode == 434
 +
    layout = ...
 +
    [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1]
 +
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 5]
 +
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1]
 +
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0]
 +
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]
 +
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
 +
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
 +
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
 +
    [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]];
 +
elseif layoutMode == 5
 +
    layout = ...
 +
    [[1, 1, 2, 2, 1, 1, 0, 2, 1, 1, 0, 2, 1, 1, 5, 2]
 +
    [2, 2, 1, 1, 2, 2, 0, 1, 2, 2, 0, 1, 2, 2, 1, 1]
 +
    [1, 1, 0, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 0, 2]
 +
    [2, 2, 0, 1, 2, 2, 1, 0, 0, 2, 1, 1, 2, 2, 0, 1]
 +
    [1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2]
 +
    [2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1]
 +
    [1, 0, 2, 0, 1, 0, 2, 2, 1, 0, 2, 0, 1, 0, 2, 0]
 +
    [2, 0, 1, 0, 2, 0, 1, 1, 2, 0, 1, 0, 2, 0, 1, 0]];
 +
end
 +
%Get the orientation right:
 +
layoutSize = size(layout);
 +
layout = flipud(layout);
 +
startPos(1) = layoutSize(1) - startPos(1) + 1;
 +
layout = transpose(layout);
 +
startPos = [startPos(2), startPos(1)];
 +
layoutSize = [layoutSize(2), layoutSize(1)];
 +
 
 +
 
 +
%Initialize some logging variables we'll need:
 +
steps = 0;
log = zeros(length, 2*numWalkers + 1);
log = zeros(length, 2*numWalkers + 1);
cargoLog = [];
cargoLog = [];
-
collisionLog = [];
 
-
%Walkers:
+
%Movement rules:
 +
evenPoss = [0, 1 ; 0, -1; 1, 0; -1, 0; 1, -1; -1, -1]; %For even columns
 +
oddPoss = [0, 1 ; 0, -1; 1, 0; -1, 0; 1, 1; -1, 1]; %For odd columns
 +
 
 +
%Walkers positioning:
% Set position randomly if we're doing cargo bearing simulation,
% Set position randomly if we're doing cargo bearing simulation,
% or set to supplied startPos if not.
% or set to supplied startPos if not.
Line 100: Line 227:
       done = 0;
       done = 0;
       while done ~= 1
       while done ~= 1
-
             currentPos(i, :) = [randi(x, 1), randi(y, 1)];
+
             currentPos(i, :) = [randi(layoutSize(1), 1), ...
-
             done = checkPossible(numWalkers, currentPos, omitPos, ...
+
                                randi(layoutSize(2), 1)];
-
                                    cargoPos);
+
             done = (layout(currentPos(i, 1), currentPos(i, 2)) == 1 || ...
 +
                    layout(currentPos(i, 1), currentPos(i, 2)) == 2);
       end
       end
 +
      layout(currentPos(i, 1), currentPos(i, 2)) = ...
 +
              layout(currentPos(i, 1), currentPos(i, 2)) * 10;
     end
     end
else
else
     numWalkers = 1; %Want to make sure this is one for this case
     numWalkers = 1; %Want to make sure this is one for this case
     currentPos = startPos;
     currentPos = startPos;
-
     if checkPossible(numWalkers, currentPos, omitPos, ...
+
     if currentPos(1) < 1 || currentPos(1) > layoutSize(1) || ...
-
                                    cargoPos) ~= 1
+
      currentPos(2) < 1 || currentPos(2) > layoutSize(2) || ...
 +
        (layout(currentPos(1), currentPos(2)) ~= 1 && ...
 +
        layout(currentPos(1), currentPos(2)) ~= 2)
           'Invalid start position.';
           'Invalid start position.';
 +
          layout
 +
          currentPos
           cargoLog = [];
           cargoLog = [];
           steps = -1;
           steps = -1;
 +
          M = [];
           return
           return
     end
     end
 +
    layout(currentPos(1), currentPos(2)) = ...
 +
        layout(currentPos(1), currentPos(2)) * 10;
end
end
 +
 +
%Something to keep track of which walkers is carrying cargos:
 +
hasCargo = zeros(numWalkers);
%Error: If there's a valid error rate, go omit some positions:
%Error: If there's a valid error rate, go omit some positions:
if error > 0
if error > 0
-
     for xPos=1:x
+
     for y=1:layoutSize(2)
-
         for yPos=1:y
+
         for x=1:layoutSize(1)
             %Only omit if it's not already blocked by something
             %Only omit if it's not already blocked by something
-
             if checkPossible(0, [xPos, yPos], omitPos, cargoPos)
+
             if rand <= error
-
                if rand <= error
+
                layout(x, y) = 0;
-
                    omitPos = [omitPos; [xPos, yPos]];
+
-
                end
+
             end
             end
         end
         end
Line 132: Line 270:
%Convenience:
%Convenience:
-
numOmitPos = size(omitPos, 1);
+
if cargoBearing == 1
-
numCargoPos = size(cargoPos, 1);
+
    numCargoPos = 0;
 +
    for y=1:layoutSize(2)
 +
        for x=1:layoutSize(1)
 +
            if layout(x, y) == 3
 +
                numCargoPos = numCargoPos + 1;
 +
            end
 +
        end
 +
    end
 +
end
 +
 
 +
if record == 0
 +
    M = [];
 +
else
 +
    aviobj = avifile('RR2.avi');
 +
end
 +
 
 +
%Indicator for premature completion
 +
done = 0;
%Main loop:
%Main loop:
-
for i=1:length,
+
for i=1:length
     for walker=1:numWalkers
     for walker=1:numWalkers
-
       
+
         %Add current pos to log:
-
         %Add current pos to log
+
         log(steps + 1, 2*walker-1:2*walker) = currentPos(walker, :);
         log(steps + 1, 2*walker-1:2*walker) = currentPos(walker, :);
          
          
-
         %Update pos to randomly
+
         %Update pos to randomly chosen neighbor, based on motion rules
-
        %chosen neighbor -- remember,
+
         temp = randi(6, 1);
-
        %these are the only valid neighbors:
+
         if ~spaceWalkOnly
-
        %  (0, +1), (0, -1)
+
            if (mod(currentPos(walker, 1), 2) == 0)
-
        % IF x%2 = 0:
+
                newPos = currentPos(walker, :) + evenPoss(temp, :);
-
        %  (+1, 0), (-1, -1)
+
             else
-
        % ELSE:
+
                newPos = currentPos(walker, :) + oddPoss(temp, :);  
-
        %  (-1, 0), (+1, +1)
+
            end
-
 
+
-
         temp = randi(4, 1);
+
-
         if (mod(currentPos(walker, 1),2) == 0)
+
-
             newPos = currentPos(walker, :) + trackAPoss(temp, :);  
+
         else
         else
-
             newPos = currentPos(walker, :) + trackBPoss(temp, :);  
+
             newPos = currentPos(walker, :);
         end
         end
 +
       
 +
        %If this is out of defined boundaries, don't do anything:
 +
        if ~(newPos(1) > layoutSize(1) || newPos(1) < 1 || ...
 +
            newPos(2) > layoutSize(2) || newPos(2) < 1)       
 +
            %Now react based on what kind of spot the new position is:
 +
            oldPosIdent = layout(currentPos(walker, 1), ...
 +
                                currentPos(walker, 2)) / 10;
 +
            newPosIdent = layout(newPos(1), newPos(2));
-
        %If we tried to move onto the bottom two spots (in terms of y)
+
            %Can't move from one track to the same kind of track:
-
        %on an even column (i.e. a goal), we drop off cargo if we had it
+
            if newPosIdent == oldPosIdent
-
        %and there wasn't one there already.
+
                %'Cant step to same kind of track'
-
        %% Specific: 8th column has no goals! It has track instead.
+
            %Hitting cargos: pick up cargo if possible.
-
        if newPos(2) <= 2 && mod(newPos(1),2) == 0 && newPos(1) ~= 8
+
            elseif newPosIdent == 3 && cargoBearing
-
            if cargoBearing && hasCargo(walker) == 1
+
                if hasCargo(walker) == 0
-
                %Drop cargo, increment cargo-dropped-count, but
+
                    hasCargo(walker) = 1;
-
                %only if there isn't already a cargo here
+
                    layout(newPos(1), newPos(2)) = 0;
-
                temp = size(filledGoals);
+
                     cargoLog = [cargoLog; walker, newPos, steps];
-
                match = 0;
+
-
                for k=1:temp(1)
+
-
                    if filledGoals(k, :) == newPos
+
-
                        match = 1;
+
-
                        break
+
-
                     end
+
                 end
                 end
-
                 if match ~= 1
+
                 %'Hit cargo planter'
 +
            %Hitting goals: drop a cargo if possible.
 +
            elseif newPosIdent == 4 && cargoBearing
 +
                if hasCargo(walker) == 1
                     hasCargo(walker) = 0;
                     hasCargo(walker) = 0;
-
                     cargoLog = [cargoLog; steps, walker];
+
                    layout(newPos(1), newPos(2)) = 40;
-
                     sorted = sorted + 1;
+
                     cargoLog = [cargoLog; walker, newPos, steps];
-
                    filledGoals = [filledGoals; newPos];
+
                     done = done + 1/numCargoPos;
                 end
                 end
 +
                %'Hit goal'
 +
            %Hitting walker goal: go there and trigger completion.
 +
            elseif newPosIdent == 5 
 +
                %'Hit walker goal'
 +
                currentPos(walker, :) = newPos;
 +
                layout(newPos(1), newPos(2)) = 50;
 +
                done = 1;
 +
            %Valid move, and we haven't been shot down yet?
 +
            % Then actually move, and update layout to reflect that.
 +
            elseif newPosIdent == 1 || newPosIdent == 2
 +
                %'Moving'
 +
                layout(currentPos(walker, 1), currentPos(walker, 2)) =  ...
 +
                layout(currentPos(walker, 1), currentPos(walker, 2)) / 10;
 +
                currentPos(walker, :) = newPos;
 +
                layout(currentPos(walker, 1), currentPos(walker, 2)) =  ...
 +
                layout(currentPos(walker, 1), currentPos(walker, 2)) * 10;
 +
            end 
 +
      end 
 +
    end
 +
   
 +
    %Finish up bookkeeping log and step count for this step
 +
    log(steps + 1, 2*numWalkers + 1) = steps;
 +
    steps = steps + 1;
 +
   
 +
    if record
 +
        hold on;
 +
        xlim([0, layoutSize(1) + 1]);
 +
        ylim([0, layoutSize(2) + 1]);
 +
        %Plot walkers:
 +
        for walker=1:numWalkers
 +
            tempPos = currentPos(walker, :);
 +
            if mod(tempPos(1), 2) == 0
 +
                tempPos(2) = tempPos(2) - 0.5;
             end
             end
-
             %Don't move
+
             if hasCargo(walker)
-
            newPos = currentPos(walker, :);
+
                plot(tempPos(1), tempPos(2), ...
-
        end
+
                        'o', 'color', [0, 0.5, 0], 'MarkerSize', 15);
-
 
+
-
        %General out-of-bounds 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:
+
-
        for k=1:numCargoPos
+
-
            if cargoPos(k, :) == newPos
+
-
                %Remove the cargo from the list of cargos and "pick up"
+
-
                % if you don't already have a cargo
+
-
                if hasCargo(walker) == 0 && cargoBearing
+
-
                    cargoPos(k, :) = [-50, -50];
+
-
                    hasCargo(walker) = 1;
+
-
                    cargoLog = [cargoLog; steps, walker];
+
-
                end
+
-
                %Anyway, don't move there
+
-
                newPos = currentPos(walker, :);
+
             end
             end
-
        end
+
            plot(tempPos(1), tempPos(2), 'o', ...
-
 
+
                        'color', [0, 0, 0], 'MarkerSize', 25);
-
        % Already on irrev. cargo case:
+
-
        if (currentPos(walker, :) == endPos)
+
-
            return
+
         end
         end
          
          
-
         %Hitting other walkers case:
+
         %Plot origami:
-
         if numWalkers > 1
+
         for x=1:layoutSize(1)
-
             for k = 1:numWalkers
+
             for y=1:layoutSize(2)
-
                 if all(newPos == currentPos(k, :)) && k ~= walker
+
                %Plot with coloration specific to probe identity
-
                     newPos = currentPos(walker, :);
+
                 if layout(x, y) == 0  || ...
-
                     collisionLog = [collisionLog; newPos, walker, k];
+
                  layout(x, y) == 10 || ...
 +
                  layout(x, y) == 20
 +
                     color = [1 1 1];
 +
                elseif layout(x, y) == 1
 +
                    color = [1 0 0];
 +
                elseif layout(x, y) == 2
 +
                     color = [0 0 1];
 +
                elseif layout(x, y) == 3
 +
                    color = [0 .5 0];
 +
                elseif layout(x, y) == 4
 +
                    color = [0 1 1];
 +
                elseif layout(x, y) == 5
 +
                    color = [1 1 0];
 +
                elseif layout(x, y) == 40
 +
                    color = [0 .5 0];
 +
                elseif layout(x, y) == 50
 +
                    color = [.5 .5 .5];
                 end
                 end
 +
                tempY = y;
 +
                if mod(x, 2) == 0
 +
                    tempY = tempY - 0.5;
 +
                end
 +
                plot(x, tempY, 's', 'Color', color, 'MarkerSize', 10);
             end
             end
         end
         end
-
          
+
         M(i) = getframe;
-
        %Hitting the omitted positions case:
+
         aviobj = addframe(aviobj, M(i));
-
        %If we have any position matches with "omitted" list
+
         hold off;
-
        %, just don't go there.
+
         clf;
-
        match = 0;
+
-
        for k=1:numOmitPos
+
-
            if omitPos(k, :) == newPos
+
-
                match = 1;
+
-
            end
+
-
         end
+
-
        if match == 1
+
-
            newPos = currentPos(walker, :);
+
-
         end
+
-
          
+
-
        %Finally actually update the position
+
-
        currentPos(walker, :) = newPos;
+
-
       
+
     end
     end
      
      
-
     % Step forward, update log
+
     %If finished, done with everything
-
     steps = steps + 1;
+
     if done >= 1
-
    log(steps, 2*numWalkers + 1) = steps - 1;
+
        if record
 +
            aviobj = close(aviobj);
 +
        end
 +
        log((steps + 1):length, :) = [];
 +
        return
 +
    end 
      
      
-
     if (sorted == 5)
+
     %If we're thinking about astronaut / orphaned walkers, do it here:
-
         log(steps+1:end, :) = [];
+
    %(astronaut walking isn't yet considered for cargobearing walks,
-
         break
+
    %(but should be implemented in the future if it becomes an issue)
 +
    if rand() > departThreshold && cargoBearing == 0
 +
         numWalkers = numWalkers + 1;
 +
        log = [log(:, 1:end-1) zeros(length, 2) log(:, end)];
 +
        currentPos = [currentPos; [1, 1]];
 +
         landingDone = 0;
 +
        while landingDone ~= 1
 +
            currentPos(end, :) = [randi(layoutSize(1), 1), ...
 +
                                randi(layoutSize(2), 1)];
 +
            if layout(currentPos(end, 1), currentPos(end, 2)) == 4
 +
                done = 1;
 +
            end
 +
            landingDone = (layout(currentPos(end, 1), ...
 +
                                  currentPos(end, 2)) == 1 || ...
 +
                          layout(currentPos(end, 1), ...
 +
                                  currentPos(end, 2)) == 2);
 +
        end
 +
    end
 +
    if rand() > arriveThreshold && numWalkers > 0 && cargoBearing == 0
 +
        walkerToRemove = randi(numWalkers);
 +
        numWalkers = numWalkers - 1;
 +
        log(:, walkerToRemove*2-1:walkerToRemove*2) = [];
 +
        currentPos(walkerToRemove, :) = [];
     end
     end
      
      
end
end
-
 
+
if record
-
return
+
     aviobj = close(aviobj);
-
 
+
end
-
 
+
-
%%Checks if a position is a possible place for a walker to be:
+
-
function [possible] = checkPossible(numWalkers, currentPos, ...
+
-
                                    omitPos, cargoPos)
+
-
     % If we're starting on an omitted position, or a goal, a cargo,
+
-
    % or another walker, just give up immediately, and return a -1:
+
-
    numOmitPos = size(omitPos, 1);
+
-
    numCargoPos = size(cargoPos, 1);
+
-
    possible = 1;
+
-
    for walker = 1:numWalkers
+
-
        thisWalkerPos = currentPos(walker, :);
+
-
        % Only run this for this walker if it's placed somewhere
+
-
        % valid (i.e. not waiting to be placed, x,y = 0,0)
+
-
        if all(thisWalkerPos)
+
-
            %Omitted positions:
+
-
            for k=1:numOmitPos
+
-
                if omitPos(k, :) == thisWalkerPos
+
-
                    possible = 0;
+
-
                    return
+
-
                end
+
-
            end
+
-
            %Cargo positions:
+
-
            for k=1:numCargoPos
+
-
                if cargoPos(k, :) == thisWalkerPos
+
-
                    possible = 0;
+
-
                    return
+
-
                end
+
-
            end
+
-
            %Other walkers:
+
-
            for k=1:numWalkers
+
-
                if (all(currentPos(k, :) == thisWalkerPos)) && ...
+
-
                        (k ~= walker)
+
-
                    possible = 0;
+
-
                    return
+
-
                end
+
-
            end
+
-
            %Goal positions:
+
-
            if mod(thisWalkerPos(1), 2)==0 && thisWalkerPos(1) ~= 8 ...
+
-
                    && thisWalkerPos(2) <= 2
+
-
                possible = 0;
+
-
                return
+
-
            end
+
-
        end
+
-
    end
+
return
return
</syntaxhighlight></code></div>
</syntaxhighlight></code></div>
===Examining Errors in Origami===
===Examining Errors in Origami===
-
This code can be used to generate diagrams like those below, visualizing the mobility of the walker. One immediate question thus far unanswered is the vulnerability of this layout to errors in the laying of track. We investigate this by, when generating the track layout in the beginning of randomWalkFunction, introducing a small (specified by input) percent chance that any single track will be omitted. Error rates at around 10% are bearable; error rates greater than that, however, are catastrophic, causing walkers to become permanently trapped in small sections of the track field.
+
This code can be used to generate diagrams like those below, visualizing the mobility of the walker. One immediate question is the vulnerability of this layout to errors in the laying of track. We investigate this by, when generating the track layout in the beginning of randomWalkFunction, introducing a small (specified by input) percent chance that any single probe will be omitted. Error rates at around 10% are bearable; error rates greater than that, however, are catastrophic, causing walkers to become permanently trapped in small sections of the track field.
[[Image:FullGridErrors.png | center | 800 px | thumb | Node graphs showing walker mobility of origami. Each junction represents a track, and each edge represents a step a walker can take. The left diagram shows no error, whereas the other two show increasing error rates. We observe that 10% error rates decrease walker mobility, but tend not to trap the walker in any particular location; 20% error rates or greater, over several tests, tend to cause catastrophic loss of mobility, making the sorting task impossible.]]
[[Image:FullGridErrors.png | center | 800 px | thumb | Node graphs showing walker mobility of origami. Each junction represents a track, and each edge represents a step a walker can take. The left diagram shows no error, whereas the other two show increasing error rates. We observe that 10% error rates decrease walker mobility, but tend not to trap the walker in any particular location; 20% error rates or greater, over several tests, tend to cause catastrophic loss of mobility, making the sorting task impossible.]]

Revision as of 18:31, 31 October 2011

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Sunday, July 13, 2014

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Contents

Overview

Our proposed sorting mechanism depends very heavily on a particular random-walking 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 SPEX experiments, a one-dimensional track is easy to construct, and will behave like a standard 1D random walk, showing an average translation on the order of n^{\frac{1}{2}} 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 one-dimensional 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 one-cargo, one-goal scenario, to give us some rudimentary numbers on how long sorting should take, with one vs multiple walkers.

Basic parameters and assumptions:

  • The unit of time is the step, which is the time it takes a walker to attempt to interact with one of the surrounding six locations.
  • Every probe on the origami are given coordinates like a grid (which shifts the even columns up by 0.5). The bottom-left is <1, 1>, the top-left <1, n>, and the bottom-right <m, 1>, <m, n> being the number of probes on the origami (which can be anything).
    • These layouts are inputted as a matrix in MATLAB, with the top-left being <1,1> and bottom-right being <m, n>; different objects on origami to be mounted on each probe are coded by number:
      • 0 = nothing
      • 1 = track 1
      • 10 = walker on track 1
      • 2 = track 2
      • 20 = walker on track 2
      • 3 = cargo
      • 4 = cargo goal
      • 40 = filled cargo goal
      • 5 = walker goal
      • 50 = filled walker goal
    • To turn a hexagonal grid into the square one that the grid layout implies, even columns are shifted up by 0.5 in this representation. This leads to the restriction that the first column must be a "high" column, as described in the code's documentation (see below).
  • Movement rules are based on column:
    • In even columns, a walker can move in directions <0, 1>, <0, -1>, <1, 0>, <-1, -1>, <-1, 1>, <1, 0>.
    • In odd columns, a walker can move in directions <0, 1>, <0, -1>, <-1, 0>, <1, 1>, <1, -1>, <-1, 0>.
  • Every time step, each walker being simulated takes a step in a random direction, and attempts to interact with whatever it hits:
    • If it tries to step off of the origami or onto something that isn't a track, it doesn't move.
    • If it tries to step to a track of the same type or an occupied track of either type, it does nothing.
    • If it tries to step to a track of the opposite type that's not occupied, it moves there.
    • If it tries to step onto a cargo, it'll pick it up but not move.
    • If it's carrying a cargo and tries to step onto a goal of the same type as the cargo, it'll drop the cargo but not move.
An illustration of the grid and motion rules (for walking; directions of motion that won't result in a step aren't shown) used in the simulation. The bottom-left is the origin (<1,1> because MATLAB indexes by 1). The 2D platform, including track A (red), track B (blue), the marker (tan), cargo (gold), and goal (green), is shown on the left. The grid on the right -- the grid corresponding to our numbering system and representing viable track for a random walk -- is created by shifting even columns up by 0.5. This arrangement (which is, in essence, a visualization tool) reveals through the vertical symmetry of the arrangement that movement rules are going to vary by column only. The valid moves in even and odd columns shown on the left are mapped onto the grid on the right to derive the moveset listed above.
An illustration of the grid and motion rules (for walking; directions of motion that won't result in a step aren't shown) used in the simulation. The bottom-left is the origin (<1,1> because MATLAB indexes by 1). The 2D platform, including track A (red), track B (blue), the marker (tan), cargo (gold), and goal (green), is shown on the left. The grid on the right -- the grid corresponding to our numbering system and representing viable track for a random walk -- is created by shifting even columns up by 0.5. This arrangement (which is, in essence, a visualization tool) reveals through the vertical symmetry of the arrangement that movement rules are going to vary by column only. The valid moves in even and odd columns shown on the left are mapped onto the grid on the right to derive the moveset listed above.

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 cargo-bearing (one-cargo one-goal) and a purely random-walk mode. The former has cargo positions corresponding to our particular origami pre-programmed 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 of all walkers positions over time, a log reporting when cargos were picked up and dropped off, a count of the number of steps the simulation took, and if desired, a move of the random walk. This function is utilized by separate cargo-bearing and random-walk data collection programs that call the function many times over a range of parameters.

The function code (saved as randomWalkFunction.m): Toggle Code

Examining Errors in Origami

This code can be used to generate diagrams like those below, visualizing the mobility of the walker. One immediate question is the vulnerability of this layout to errors in the laying of track. We investigate this by, when generating the track layout in the beginning of randomWalkFunction, introducing a small (specified by input) percent chance that any single probe will be omitted. Error rates at around 10% are bearable; error rates greater than that, however, are catastrophic, causing walkers to become permanently trapped in small sections of the track field.

Node graphs showing walker mobility of origami. Each junction represents a track, and each edge represents a step a walker can take. The left diagram shows no error, whereas the other two show increasing error rates. We observe that 10% error rates decrease walker mobility, but tend not to trap the walker in any particular location; 20% error rates or greater, over several tests, tend to cause catastrophic loss of mobility, making the sorting task impossible.
Node graphs showing walker mobility of origami. Each junction represents a track, and each edge represents a step a walker can take. The left diagram shows no error, whereas the other two show increasing error rates. We observe that 10% error rates decrease walker mobility, but tend not to trap the walker in any particular location; 20% error rates or greater, over several tests, tend to cause catastrophic loss of mobility, making the sorting task impossible.

Random-Walk Simulation

The data we need from this simulator is a rough projection of the fluorescence response from our test of 2D random walking, which should change based on the starting location of the walker. Because this fluorescence is changed by a fluorophore-quencher interaction upon a walker reaching its irreversible track, in the case where we plant all of the walkers on the same starting track, the time it takes (fluorescenceinitialfluorescencecurrent) in the sample to reach some standard value should be proportional to the average time it takes the walkers to reach the irreversible substrate. As this 'total steps elapsed' value is one of the outputs of our simulation function, we can generate a map of these average walk durations by running a large number of simulations at each point on the origami and averaging the results: Toggle Code

A plot of the number of steps (on an average over 2000 iterations) it takes a walker to random walk from any point on the origami to the irreversible track at <15, 7>. The holes are due to omitted, cargo, or goal strands blocking the walker's starting location.
A plot of the number of steps (on an average over 2000 iterations) it takes a walker to random walk from any point on the origami to the irreversible track at <15, 7>. The holes are due to omitted, cargo, or goal strands blocking the walker's starting location.

Results

Results of the bulk data collection at right show that the average random-walk duration, and thus the time for (fluorescenceinitialfluorescencecurrent) to reach some standard level, increases with distance, though it changes less significantly the farther out one gets. Also important to note is that the "effective distance" (in terms of steps) along the short axis of our platform is a significantly less than the same physical distance along the long axis. This difference is due to our arrangement of track A and B: as can be seen in the left half of the diagram at the end of the #Overview section, alternating tracks A and B create a straight vertical highway for the walker to follow. Horizontal movement, in contrast, cannot be accomplished by purely straight-line movement -- it requires a back-and-forth weave that makes motion in that direction slower. The disparity in "effective distances" between the vertical and horizontal dimensions is something, in particular, that we should test for; however, a simple series of tests running random walks at a variety of points across the surface, and the comparison of the resulting fluorescence data to the control provided by this simulation should be sufficient to prove that our walker can, indeed, perform a 2D random walk.

Cargo Sorting Simulation

This simulation investigates both the overall tractability of our sorting problem, and the degree to which it can be parallelized via the addition of multiple walkers onto a single origami. It runs by making repeated calls to randomWalkFunction in its cargo-bearing mode, testing the number of steps it takes to sort all five cargos to respective goals over a range of number of cooperating walkers: Toggle Code

Results

A plot of the number of steps (on an average over 250 iterations) it takes n walkers to sort all five cargos to respective goals on a perfectly formed 16x8 track, as detailed above. The jaggedness in the curve is a result of the large spread of results for any given test.
A plot of the number of steps (on an average over 250 iterations) it takes n walkers to sort all five cargos to respective goals on a perfectly formed 16x8 track, as detailed above. The jaggedness in the curve is a result of the large spread of results for any given test.

While a single walker takes over a thousand steps to complete the sorting challenge, the addition of even a single walker vastly decreases the completion time, and additional walkers decrease it further, until a critical point is reached where the walkers are more getting in the way than helping with the sorting process. This is visible in the positive slope visible in the diagram at right that starts at around the 20 walker point.


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