Biomod/2011/Caltech/DeoxyriboNucleicAwesome/Simulation - Revision history

Gregory Izatt: /* Cargo Sorting Simulation */

2011-10-31T22:57:33Z

Cargo Sorting Simulation

←Older revision		Revision as of 22:57, 31 October 2011
Line 517:		Line 517:

	==Cargo Sorting Simulation==		==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: <span class="_toggler-codeC">Toggle Code</span>	+	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. [[Image:250iters0ErrorCargoSort.jpg \| thumb \| 300px \| right \| 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.]] 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: <span class="_toggler-codeC">Toggle Code</span>
	<div class="codeC" style="display:none;		<div class="codeC" style="display:none;
	border: 1px dashed rgb(0, 0, 0);		border: 1px dashed rgb(0, 0, 0);
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	(Note: this code is now obsolete (as it relies on an obsolete version of the randomWalkFunction script), and may be rewritten in the future. This should not, however, impact the validity of this code's results.		(Note: this code is now obsolete (as it relies on an obsolete version of the randomWalkFunction script), and may be rewritten in the future. This should not, however, impact the validity of this code's results.
	===Results===		===Results===
-	[[Image:250iters0ErrorCargoSort.jpg \| thumb \| 300px \| right \| 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.		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.

	{{Template:DeoxyriboNucleicAwesomeFooter}}		{{Template:DeoxyriboNucleicAwesomeFooter}}

Gregory Izatt: /* Random-Walk Simulation */

2011-10-31T22:56:00Z

Random-Walk Simulation

←Older revision		Revision as of 22:56, 31 October 2011
Line 460:		Line 460:

	==Random-Walk Simulation==		==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 <math>(fluorescence_{initial} - fluorescence_{current})</math> 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: <span class="_toggler-codeB">Toggle Code</span>	+	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. [[Image:Caltech5000iter0ErrorRRWideLinearTrack.jpg \| thumb \| 300 px \| right \| A plot of the number of steps (on an average over 5000 iterations) it takes a walker to random walk from any point on the origami to the irreversible track at one end. This test was done assuming a 0% error rate, on the 3-track-wide linear random walking playground that we are using to investigate random walking (in a pseudolinear environment).]]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 <math>(fluorescence_{initial} - fluorescence_{current})</math> 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: <span class="_toggler-codeB">Toggle Code</span>
	<div class="codeB" style="display:none;		<div class="codeB" style="display:none;
	border: 1px dashed rgb(0, 0, 0);		border: 1px dashed rgb(0, 0, 0);
Line 513:		Line 513:
	matlabpool close		matlabpool close
	</syntaxhighlight></code></div>		</syntaxhighlight></code></div>
-	[[Image:Caltech5000iter0ErrorRRWideLinearTrack.jpg \| thumb \| 300 px \| right \| A plot of the number of steps (on an average over 5000 iterations) it takes a walker to random walk from any point on the origami to the irreversible track at one end. This test was done assuming a 0% error rate, on the 3-track-wide linear random walking playground that we are using to investigate random walking (in a pseudolinear environment).]]
	===Results===		===Results===
	Results of the bulk data collection at right show that the average random-walk duration, and thus the time for <math>(fluorescence_{initial} - fluorescence_{current})</math> to reach some standard level, increases with distance, though it changes less significantly the farther out one gets. We can also use a similar simulation (run instead with tracks that don't continue past the start location of the walker, an arrangement which we have found to behave more like a linear track) data to generate approximate half-completion times, which we can compare with the SPEX results of the same random walk to both estimate the amount of time it takes the walker to perform a single branch migration on our origami, and to see if whatever our walker is doing on origami is looking like a random walk, as compared to a repeated jumping across or between origami platforms (whose half-completion times for this test would presumably not depend on the track length at all). That data is detailed on the SPEX results page.		Results of the bulk data collection at right show that the average random-walk duration, and thus the time for <math>(fluorescence_{initial} - fluorescence_{current})</math> to reach some standard level, increases with distance, though it changes less significantly the farther out one gets. We can also use a similar simulation (run instead with tracks that don't continue past the start location of the walker, an arrangement which we have found to behave more like a linear track) data to generate approximate half-completion times, which we can compare with the SPEX results of the same random walk to both estimate the amount of time it takes the walker to perform a single branch migration on our origami, and to see if whatever our walker is doing on origami is looking like a random walk, as compared to a repeated jumping across or between origami platforms (whose half-completion times for this test would presumably not depend on the track length at all). That data is detailed on the SPEX results page.

Gregory Izatt: Adding note about how this code is actually obsolete

2011-10-31T22:54:31Z

Adding note about how this code is actually obsolete

←Older revision		Revision as of 22:54, 31 October 2011
Line 563:		Line 563:
	plot(averages)		plot(averages)
	</syntaxhighlight></code></div>		</syntaxhighlight></code></div>
		+	(Note: this code is now obsolete (as it relies on an obsolete version of the randomWalkFunction script), and may be rewritten in the future. This should not, however, impact the validity of this code's results.
	===Results===		===Results===
	[[Image:250iters0ErrorCargoSort.jpg \| thumb \| 300px \| right \| 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.]]		[[Image:250iters0ErrorCargoSort.jpg \| thumb \| 300px \| right \| 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.]]

Gregory Izatt: updating to current revision, switching to random walk data based on linear track

2011-10-31T22:51:53Z

updating to current revision, switching to random walk data based on linear track

←Older revision		Revision as of 22:51, 31 October 2011
Line 477:		Line 477:
	% 20110701: Updating to use new, updated randomWalkFunction		% 20110701: Updating to use new, updated randomWalkFunction
	% 20110707: Updated to use new error-allowing randomWalkFunction		% 20110707: Updated to use new error-allowing randomWalkFunction
		+	% 20110719: Updating to use new and hopefully much faster
		+	% randomWalkFunctionGeneric
		+	%% Dependency: makes calls to randomWalkFunctionGeneric.m
		+	%Layout modes:
		+	layoutMode = 4;
		+	if layoutMode == 4
		+	yMax = 15;
		+	xMax = 9;
		+	elseif layoutMode == 5
		+	yMax = 16;
		+	xMax = 8;
		+	else
		+	'Layout not yet implemented.'
		+	return
		+	end

-	~~%% Dependency: makes calls to randomWalkFunction.m~~	+	iterations = 500; %Test each case of random walk this # times
-		+
-	iterations = ~~2500~~; %Test each case of random walk this # times	+
-	~~xMax = 16; %Scale of platform for test~~	+
-	~~yMax = 8;~~	+
-	~~stopPos = [15, 7]; %Stop position~~	+
	averages = zeros(xMax, yMax); %Init'ing this		averages = zeros(xMax, yMax); %Init'ing this
	trash = []; %Trash storing variable		trash = []; %Trash storing variable
		+
	%Cycle over whole area, starting the walker at each position		%Cycle over whole area, starting the walker at each position
	%and seeing how long it takes it to get to the stop position		%and seeing how long it takes it to get to the stop position
-	matlabpool(4)	+	matlabpool(3)
	for x=1:xMax		for x=1:xMax
	for y=1:yMax		for y=1:yMax
	temp = zeros(iterations, 1);		temp = zeros(iterations, 1);
	parfor i=1:iterations		parfor i=1:iterations
-	[trash, trash2, temp(i)] = ~~randomWalkFunction~~(~~xMax, yMax,~~ ...	+	[trash, trash2, temp(i), trash3]=randomWalkFunctionGeneric(...
-	10000, 1, [x, y], ~~stopPos~~, 0, 1, 0.0);	+	10000, layoutMode, [x, y], 1, 0, 0.1, 0, 0, 1, 1);
	end		end
	stdDev(x, y) = std(temp);		stdDev(x, y) = std(temp);
Line 502:		Line 513:
	matlabpool close		matlabpool close
	</syntaxhighlight></code></div>		</syntaxhighlight></code></div>
-	[[Image:~~2000iter0ErrorTest~~.jpg \| thumb \| 300 px \| right \| 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~~.]]	+	[[Image:Caltech5000iter0ErrorRRWideLinearTrack.jpg \| thumb \| 300 px \| right \| A plot of the number of steps (on an average over 5000 iterations) it takes a walker to random walk from any point on the origami to the irreversible track at one end. This test was done assuming a 0% error rate, on the 3-track-wide linear random walking playground that we are using to investigate random walking (in a pseudolinear environment).]]
	===Results===		===Results===
-	Results of the bulk data collection at right show that the average random-walk duration, and thus the time for <math>(fluorescence_{initial} - fluorescence_{current})</math> 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~~.	+	Results of the bulk data collection at right show that the average random-walk duration, and thus the time for <math>(fluorescence_{initial} - fluorescence_{current})</math> to reach some standard level, increases with distance, though it changes less significantly the farther out one gets. We can also use a similar simulation (run instead with tracks that don't continue past the start location of the walker, an arrangement which we have found to behave more like a linear track) data to generate approximate half-completion times, which we can compare with the SPEX results of the same random walk to both estimate the amount of time it takes the walker to perform a single branch migration on our origami, and to see if whatever our walker is doing on origami is looking like a random walk, as compared to a repeated jumping across or between origami platforms (whose half-completion times for this test would presumably not depend on the track length at all). That data is detailed on the SPEX results page.

	==Cargo Sorting Simulation==		==Cargo Sorting Simulation==

Gregory Izatt: /* MATLAB Code */

2011-10-31T22:33:50Z

MATLAB Code

←Older revision		Revision as of 22:33, 31 October 2011
Line 37:		Line 37:
	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.		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 randomWalkFunctionGeneric.m):
	<span class="_toggler-codeA">Toggle Code</span>		<span class="_toggler-codeA">Toggle Code</span>
	<div class="codeA" style="display:none;		<div class="codeA" style="display:none;

Gregory Izatt: Updating code to current revision

2011-10-31T22:31:34Z

Updating code to current revision

Show changes

Gregory Izatt: Updating documentation to current revision of simulation.

2011-10-31T22:28:34Z

Updating documentation to current revision of simulation.

←Older revision		Revision as of 22:28, 31 October 2011
Line 8:		Line 8:

	Basic parameters and assumptions:		Basic parameters and assumptions:
-	*The unit of time is the '''step''', which is the time it takes a walker to ~~take a step given four good opposite track locations (good locations to step~~ to~~) around it~~.	+	*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.
-	*~~The walkable track~~ 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, 8>, and the bottom-right <16, 1>.	+	*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:		*Movement rules are based on column:
-	** In even columns, a walker can move in directions <0, 1>, <0, -1>, <1, 0>, <-1, -1>.	+	** 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>.	+	** 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.

-	[[Image:MotionRulesDerivation.png\|thumb\|center\|800px\|An illustration of the grid and motion rules 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.]]	+	[[Image:MotionRulesDerivation.png\|thumb\|center\|800px\|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==		==MATLAB Code==

Zibo Chen: /* Overview */

2011-10-02T12:35:35Z

Overview

←Older revision		Revision as of 12:35, 2 October 2011
Line 3:		Line 3:
	__TOC__		__TOC__
	==Overview==		==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 [[Biomod/2011/Caltech/DeoxyriboNucleicAwesome/SPEX ~~Experiment~~\|SPEX ~~experiment~~]], a one-dimensional track is easy to construct, and will behave like a [http://en.wikipedia.org/wiki/Random_walk#One-dimensional_random_walk standard 1D random walk], showing an average translation on the order of <math>n^{\frac{1}{2}}</math> 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 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 [[Biomod/2011/Caltech/DeoxyriboNucleicAwesome/SPEX Experiments\|SPEX experiments]], a one-dimensional track is easy to construct, and will behave like a [http://en.wikipedia.org/wiki/Random_walk#One-dimensional_random_walk standard 1D random walk], showing an average translation on the order of <math>n^{\frac{1}{2}}</math> 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.		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.

Zibo Chen: /* Overview */

2011-10-02T12:33:43Z

Overview

←Older revision		Revision as of 12:33, 2 October 2011
Line 3:		Line 3:
	__TOC__		__TOC__
	==Overview==		==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 ~~<LINK TO THE EXPERIMENTAL DESIGN SECTION>~~, a one-dimensional track is easy to construct, and will behave like a [http://en.wikipedia.org/wiki/Random_walk#One-dimensional_random_walk standard 1D random walk], showing an average translation on the order of <math>n^{\frac{1}{2}}</math> 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 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 [[Biomod/2011/Caltech/DeoxyriboNucleicAwesome/SPEX Experiment\|SPEX experiment]], a one-dimensional track is easy to construct, and will behave like a [http://en.wikipedia.org/wiki/Random_walk#One-dimensional_random_walk standard 1D random walk], showing an average translation on the order of <math>n^{\frac{1}{2}}</math> 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.		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.

Gregory Izatt: Adding cargo sort code

2011-07-11T22:12:40Z

Adding cargo sort code

←Older revision		Revision as of 22:12, 11 July 2011
Line 333:		Line 333:

	==Cargo Sorting Simulation==		==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.	+	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: <span class="_toggler-codeC">Toggle Code</span>
		+	<div class="codeC" style="display:none;
		+	border: 1px dashed rgb(0, 0, 0);
		+	padding-top: 10px;
		+	padding-right: 10px;
		+	padding-bottom: 10px;
		+	padding-left: 10px;
		+	background-color: #FEF7EA;"><code><syntaxhighlight lang="matlab">
		+	%%% Cargo pickup/dropoff bulk simulation that
		+	%% runs a battery of tests and plots the results
		+	%% to see how long cargo sorts take on average
		+	% Gregory Izatt & Caltech BIOMOD 2011
		+	% 20110616: Initial revision
		+	% 20110616: Fixing to fit cargoSort.m revision
		+	% 20110623: Fixing documentation
		+	% 20110701: Updating to work with new and improved randomWalkFunction
		+	% 20110707: Updated to include error rate addition in randomWalkFunction
		+	%% Dependency: Makes calls to randomWalkFunction.m
		+
		+	iterations = 50; %Test each #walker scenario this many times
		+	maxNumWalkers = 30; %Test scenarios with up to this many walkers
		+	averages = zeros(maxNumWalkers, 1);
		+	medians = zeros(maxNumWalkers, 1);
		+
		+	'Initialized...'
		+
		+	matlabpool(3) %Built-in parallel processing for speedup.
		+	%Change "4" to your # of cores.
		+
		+	for numWalkers=1:maxNumWalkers %Iterate over possible #'s of walkers
		+	tempStorage = zeros(iterations, 1);
		+	parfor i=1:iterations %Iterate a bunch of times
		+	[trash, trash2, temp] = randomWalkFunction(16, 8, 10000, ...
		+	numWalkers, [1, 1], [-100, -100], 1, 1, 0.0);
		+	tempStorage(i) = temp;
		+	end
		+	averages(numWalkers) = mean(tempStorage); %Store the average
		+	medians(numWalkers) = median(tempStorage);
		+	numWalkers, averages
		+	end
		+	matlabpool close
		+
		+	averages
		+	plot(averages)
		+	</syntaxhighlight></code></div>
	===Results===		===Results===
	[[Image:250iters0ErrorCargoSort.jpg \| thumb \| 300px \| right \| 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.]]		[[Image:250iters0ErrorCargoSort.jpg \| thumb \| 300px \| right \| 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.]]