Phakic intraocular lens: Difference between revisions

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[[Image:Entropy-mutual-information-relative-entropy-relation-diagram.svg|thumb|256px|right|Individual (H(X),H(Y)), joint (H(X,Y)), and conditional entropies for a pair of correlated subsystems X,Y with mutual information I(X; Y).]]
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'''Joint [[entropy (information theory)|entropy]]''' is a measure of the uncertainty associated with a set of [[random variables|variables]].
 
==Definition==
The joint Shannon entropy of two variables <math>X</math> and <math>Y</math> is defined as
 
:<math>H(X,Y) = -\sum_{x} \sum_{y} P(x,y) \log_2[P(x,y)] \!</math>
 
where <math>x</math> and <math>y</math> are particular values of <math>X</math> and <math>Y</math>, respectively, <math>P(x,y)</math> is the probability of these values occurring together, and <math>P(x,y) \log_2[P(x,y)]</math> is defined to be 0 if <math>P(x,y)=0</math>.
 
For more than two variables <math>X_1, ..., X_n</math> this expands to
 
:<math>H(X_1, ..., X_n) = -\sum_{x_1} ... \sum_{x_n} P(x_1, ..., x_n) \log_2[P(x_1, ..., x_n)] \!</math>
 
where <math>x_1,...,x_n</math> are particular values of <math>X_1,...,X_n</math>, respectively, <math>P(x_1, ..., x_n)</math> is the probability of these values occurring together, and <math>P(x_1, ..., x_n) \log_2[P(x_1, ..., x_n)]</math> is defined to be 0 if <math>P(x_1, ..., x_n)=0</math>.
 
==Properties==
 
===Greater than individual entropies===
 
The joint entropy of a set of variables is greater than or equal to all of the individual entropies of the variables in the set.
 
:<math>H(X,Y) \geq \max[H(X),H(Y)]</math>
 
:<math>H(X_1, ..., X_n) \geq \max[H(X_1), ..., H(X_n)]</math>
.
 
===Less than or equal to the sum of individual entropies===
 
The joint entropy of a set of variables is less than or equal to the sum of the individual entropies of the variables in the set. This is an example of [[subadditivity]].  This inequality is an equality if and only if <math>X</math> and <math>Y</math> are [[statistically independent]].
 
:<math>H(X,Y) \leq H(X) + H(Y)</math>
 
:<math>H(X_1, ..., X_n) \leq H(X_1) + ... + H(X_n)</math>
 
==Relations to other entropy measures==
 
Joint entropy is used in the definition of [[conditional entropy]]
 
:<math>H(X|Y) = H(Y,X) - H(Y)\,</math>
 
and [[mutual information]]
 
:<math>I(X;Y) = H(X) + H(Y) - H(X,Y)\,</math>
 
In [[quantum information theory]], the joint entropy is generalized into the [[joint quantum entropy]].
 
[[Category:Entropy and information]]
 
[[de:Bedingte Entropie#Blockentropie]]

Revision as of 22:51, 20 February 2014

Have we been thinking "how do I speed up my computer" lately? Well odds are if you are reading this article; then you are experiencing one of several computer issues which thousands of people discover that they face on a regular basis.

You have to recognize certain easy and cheap methods which will resolve the problem of the computer and speed it up. The earlier we fix it, the less damage your computer gets. I might tell about several beneficial techniques which can assist we to accelerate you computer.

If you compare registry products we need a fast acting registry cleaning. It's no superior spending hours plus the PC waiting for your registry cleaning to complete its task. You need a cleaner to complete its task inside minutes.

The way to fix this problem is to initially reinstall the program(s) causing the mistakes. There are a lot of different programs that use this file, but 1 will have placed their own faulty adaptation of the file onto the program. By reinstalling any programs that are causing the error, you'll not merely enable your PC to run the program properly, nevertheless a new file will be placed onto the system - leaving a computer running as smoothly as possible again. If you try this, plus find it does not work, then you need to look to update a program & any software we have on a PC. This will probably update the Msvcr71.dll file, permitting a computer to read it properly again.

The tuneup utilities could come as standard with a back up and restore facility. This should be an effortless to apply process.That signifies that when you encounter a issue with your PC following utilizing a registry cleaning you are able to merely restore a settings.

Files with the DOC extension are furthermore susceptible to viruses, however, this is solved by advantageous antivirus programs. Another issue is the fact that .doc files can be corrupted, unreadable or damaged due to spyware, adware, and malware. These instances will avoid users from properly opening DOC files. This is when powerful registry cleaners become practical.

Reboot PC - Simply reboot the PC to see if the error is gone. Often, rebooting the PC readjusts the internal settings and software and hence fixes the problem. If it doesn't then move on to follow the instructions below.

There are many businesses that provide the service of troubleshooting a PC every time we call them, all you must do is sign up with them plus for a small fee, you have a machine usually working perfectly and serve you greater.

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