Dice Statistics - Revision history

Ist165721: Text replacement - "|left" to "|center"

2015-05-28T13:12:06Z

Text replacement - "|left" to "|center"

Ist165721: Text replacement - "#evp" to "#ev"

2015-05-24T19:52:23Z

Text replacement - "#evp" to "#ev"

Ist165721: Text replacement - "\]" to ""

2015-05-24T19:40:21Z

Text replacement - "\]" to "</math>"

Ist165721: Text replacement - "\[" to " $"$

2015-05-24T19:02:46Z

Text replacement - "\[" to "<math>"

Ist165721 at 10:45, 28 October 2013

2013-10-28T10:45:37Z

Ist165721: /* Advanced Protocol */

2013-10-18T17:17:48Z

Advanced Protocol

Ist165721: /* Advanced Protocol */

2013-10-18T16:06:49Z

Advanced Protocol

Ist165721 at 15:56, 18 October 2013

2013-10-18T15:56:50Z

Show changes

Ist165721 at 11:43, 18 October 2013

2013-10-18T11:43:42Z

Ist128595 at 22:59, 16 October 2013

2013-10-16T22:59:05Z

← Older revision		Revision as of 13:12, 28 May 2015
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−	{{#ev:youtube\|_qUFqXJQOpM\|Dice in slow motion taken from the experiment (12x slow).\|~~left~~}}	+	{{#ev:youtube\|_qUFqXJQOpM\|Dice in slow motion taken from the experiment (12x slow).\|center}}

	=Experimental Apparatus=		=Experimental Apparatus=

← Older revision		Revision as of 19:52, 24 May 2015
Line 22:		Line 22:


−	{{#~~evp~~:youtube\|_qUFqXJQOpM\|Dice in slow motion taken from the experiment (12x slow).\|left}}	+	{{#ev:youtube\|_qUFqXJQOpM\|Dice in slow motion taken from the experiment (12x slow).\|left}}

	=Experimental Apparatus=		=Experimental Apparatus=

@@ Line 99: / Line 99: @@
 <math>
 p(x) = y_0 + A e ^{- \frac{(x- \mu)^2}{\sigma ^2}}
-\]
+</math>
 [[File:EstatDados-grafico.png|thumb|Figure 5: Example distribution]]
@@ Line 111: / Line 111: @@
 <math>
 \bar{\mu} = \frac{6N+N}{2}
-\]
+</math>
@@ Line 136: / Line 136: @@
 <math>
 t = \sqrt{\frac{A- 2 A cos (2 \pi f t)}{g}}
-\]
+</math>
 So solve this equation, we have to use a computational method which, having been given an inicial value for t, will evaluate the root and then use the value it finds for t. This process is repeated until t is stationary. Obviouslly, we have to have the values for amplitude, frequency and acceleration. For the first we use 3mm, beteween 1 and 500Hz for the second and 9,81 \(ms^{-2}\) for the last.

@@ Line 97: / Line 97: @@
 After a  number of samples a graph can be constructed with the number of times each number is recorded in each bin and a Gaussian distribution can be fitted:
-\[
+<math>
 p(x) = y_0 + A e ^{- \frac{(x- \mu)^2}{\sigma ^2}}
 \]
@@ Line 109: / Line 109: @@
 The expected value for the average of N 6-sided dice is:
-\[
+<math>
 \bar{\mu} = \frac{6N+N}{2}
 \]
@@ Line 134: / Line 134: @@
 Equalizing and solving for t, we get:
-\[
+<math>
 t = \sqrt{\frac{A- 2 A cos (2 \pi f t)}{g}}
 \]

@@ Line 246: / Line 246: @@
 </div>
 </div>
 =Links=
 *[[Estatística de Dados | Portuguese version (versão em português)]]

@@ Line 119: / Line 119: @@
 <div class="mw-collapsible-content">
-Under construction
+We assume:
 </div>
 </div>

@@ Line 116: / Line 116: @@
 <div class="toccolours mw-collapsible mw-collapsed" style="width:600px">
-'''Estudo da frequância ideal para excitar os dados'''
+'''What is the best frequency to randomize the dice?'''
 <div class="mw-collapsible-content">
-Suposições:
+Under construction
 </div>
 </div>
 =Links=
 *[[Estatística de Dados | Portuguese version (versão em português)]]

@@ Line 17: / Line 17: @@
 </div>
 <swf height="320" width="320">http://www.elab.tecnico.ulisboa.pt/anexos/descricoes-flash/EstatisticaDados.swf</swf>
@@ Line 23: / Line 22: @@
+{{#evp:youtube|_qUFqXJQOpM|Dice in slow motion taken from the experiment (12x slow).|left}}
 =Experimental Apparatus=
@@ Line 34: / Line 33: @@
 This platform has a wall that prevents the dice from leaving the platform (and the web-cam field of view). The wall is quite high to block the entry of light from the outside of the lighting system.
-With this apparatus, pictures are obtained as we can see in picture 2.
+With this apparatus, pictures are obtained as we can see in figure 2.
 The image processing is made according to the flowchart below and the result of this process leads to an image like the one in picture 3.
@@ Line 69: / Line 68: @@
 Since the video feed has a high demand on the internet connection, the user is advised to use it only once, as its purpose is merely to satisfy curiosity.
 =Advanced Protocol=

@@ Line 1: / Line 1: @@
 =Description=
-This experiment consists on an apparatus that automatically shuffles a set of six-sided dice. To count the spots, it acquires and processes an image recognition pattern from the top side of each dice.
+This experiment consists of an apparatus that automatically shuffles a set of six-sided dice. To count the spots, it acquires and processes an image recognition pattern from the top side of each dice.
 By recording the number of times each side appears, you can study the law of probability and develop a statistical study of random phenomena. Using the images produced by this experiment, you can also develop your own algorithms using them in the study of computer recognition software.
@@ Line 32: / Line 32: @@
 The release (i.e. shuffling) of  the dice is achieved through the speaker's stimulus with a sound wave, which makes the platform vibrate with the same frequency of the wave.
-This platform has a wall that prevents the dice from leaving the platform (and the web-cam field of view). The wall is quite high to prevent the entry of light from the outside of the lighting system.
+This platform has a wall that prevents the dice from leaving the platform (and the web-cam field of view). The wall is quite high to block the entry of light from the outside of the lighting system.
 With this apparatus, pictures are obtained as we can see in picture 2.
@@ Line 47: / Line 47: @@
 =Protocol=
-The experience execution protocol is simple because it consists in stimulating the platform conveniently,  so that it can scramble the dice. And then, we describe the main features of the configurator control room for a better understanding.
+The experience execution protocol is simple because it consists in stimulating the platform conveniently,  so that it can scramble the dice. The main features of the configurator control room are described below for a better understanding.
 <!-- [[File:EstatDados-interface.gif|thumb|Picture 4: The experiment "Control room" configuration ]] -->
@@ Line 71: / Line 71: @@
 =Advanced Protocol=
-After enough samples a graph can be constructed with the number of times each number is recorded in each bin and a Gaussian distribution can be fitted:
+After a  number of samples a graph can be constructed with the number of times each number is recorded in each bin and a Gaussian distribution can be fitted:
 \[
@@ Line 81: / Line 81: @@
 Since there are 14 dice, the expected mean value is 49 (why?), which is confirmed by the build-up of values fitting.
-The best way to conduct this study is to merge the results of several users and see if the fit is improved with increasing number of samples.
+The best way to conduct this study is to merge the results of several users and see if the fit is improved by an increasing number of samples.
 The expected value for the average of N 6-sided dice is:
@@ Line 103: / Line 103: @@
 ** ''Threshold1'': value above which a pixel from the Hough Transform image is taken to post processing.
 ** ''Threshold2'': averages the pixels near the one that passed the previous test and, if that value is above Threshold2, this pixel is taken to post processing.
-** ''Threshold3'': in theory, any pixel in a white zone is ignored but, if the average (calculated for the previous test) is above Threshold3, the pixel is NOT ignored. This is used because some of the dice have white spots inside the black marks.
+** ''Threshold3'': in theory, any pixel in a white zone is ignored but, if the average (calculated in the previous test) is above Threshold3, the pixel is NOT ignored. This is used because some of the dice have white spots inside the black marks.
 * ''Convolution Threshold'': the value above which a pixel from the convolution image is taken to post processing.

Dice Statistics - Revision history

Ist165721: Text replacement - "|left" to "|center"

Ist165721: Text replacement - "#evp" to "#ev"

Ist165721: Text replacement - "\]" to ""

Ist165721: Text replacement - "\[" to ""

Ist165721 at 10:45, 28 October 2013

Ist165721: /* Advanced Protocol */

Ist165721: /* Advanced Protocol */

Ist165721 at 15:56, 18 October 2013

Ist165721 at 11:43, 18 October 2013

Ist128595 at 22:59, 16 October 2013

Ist165721: Text replacement - "\[" to " $"$