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In [[information theory]], '''dual total correlation''' (Han 1978) or excess entropy (Olbrich 2008) is one of the two known non-negative generalizations of [[mutual information]]. While [[total correlation]] is bounded by the sum entropies of the ''n'' elements, the dual total correlation is bounded by the joint-entropy of the ''n'' elements. Although well behaved, dual total correlation has received much less attention than the total correlation.  A measure known as "TSE-complexity" defines a continuum between the total correlation and dual total correlation (Ay 2001).
 
==Definition==
For a set of ''n'' [[random variable]]s <math>\{X_1,\ldots,X_n\}</math>, the dual total correlation <math>D(X_1,\ldots,X_n)</math> is given by
 
:<math> D(X_1,\ldots,X_n) = H\left( X_1, \ldots, X_n \right) - \sum_{i=1}^n H\left( X_i | X_1, \ldots, X_{i-1}, X_{i+1}, \ldots, X_n \right) ,</math>
 
where <math>H(X_{1},\ldots,X_{n})</math> is the [[joint entropy]] of the variable set <math>\{X_{1},\ldots,X_{n}\}</math> and <math>H(X_{i}| ... )</math> is the [[conditional entropy]] of variable <math>X_{i}</math>, given the rest.
 
==Normalized==
The dual total correlation normalized between [0,1] is simply the dual total correlation divided by its maximum value <math>H(X_{1}, \ldots, X_{n})</math>,
 
:<math>ND(X_1,\ldots,X_n) = \frac{D(X_1,\ldots,X_n)}{H(X_1,\ldots,X_n)} .</math>
 
==Bounds==
Dual total correlation is non-negative and bounded above by the joint entropy <math>H(X_1, \ldots, X_n)</math>.
 
:<math> 0 \leq D(X_1, \ldots, X_n) \leq H(X_1, \ldots, X_n) .</math>
 
Secondly, Dual total correlation has a close relationship with total correlation, <math>C(X_1, \ldots, X_n)</math>. In particular,
 
:<math> \frac{C(X_1, \ldots, X_n)}{n-1} \leq D(X_1, \ldots, X_n) \leq (n-1) \; C(X_1, \ldots, X_n) .</math>
 
==History==
Han (1978) originally defined the dual total correlation as,
: <math>
\begin{align}
& {} \qquad  D(X_1,\ldots,X_n) \\[10pt]
& \equiv \left[ \sum_{i=1}^n H(X_1, \ldots, X_{i-1}, X_{i+1}, \ldots, X_n ) \right] - (n-1) \; H(X_1, \ldots, X_n) \; .
\end{align}
</math>
However Abdallah and Plumbley (2010) showed its equivalence to the easier-to-understand form of the joint entropy minus the sum of conditional entropies via the following:
 
: <math>
\begin{align}
& {} \qquad  D(X_1,\ldots,X_n) \\[10pt]
& \equiv \left[ \sum_{i=1}^n H(X_1, \ldots, X_{i-1}, X_{i+1}, \ldots, X_n ) \right] - (n-1) \; H(X_1, \ldots, X_n) \\
& = \left[ \sum_{i=1}^n H(X_1, \ldots, X_{i-1}, X_{i+1}, \ldots, X_n ) \right] + (1-n) \; H(X_1, \ldots, X_n) \\
& = H(X_1, \ldots, X_n) + \left[ \sum_{i=1}^n H(X_1, \ldots, X_{i-1}, X_{i+1}, \ldots, X_n ) - H(X_1, \ldots, X_n) \right] \\
& = H\left( X_1, \ldots, X_n \right) - \sum_{i=1}^n H\left( X_i | X_1, \ldots, X_{i-1}, X_{i+1}, \ldots, X_n \right)\; .
\end{align}
</math>
 
==See also==
*[[Mutual information]]
*[[Total correlation]]
 
{{no footnotes|date=June 2011}}
 
==References==
* Han T. S. (1978). Nonnegative entropy measures of multivariate symmetric correlations, ''Information and Control'' '''36''', 133&ndash;156.
* Fujishige Satoru (1978). Polymatroidal Dependence Structure of a Set of Random Variables, ''Information and Control'' '''39''', 55&ndash;72. {{doi|10.1016/S0019-9958(78)91063-X}}.
* Olbrich, E. and Bertschinger, N. and Ay, N. and Jost, J. (2008). How should complexity scale with system size?, ''The European Physical Journal B - Condensed Matter and Complex Systems''. {{doi|10.1140/epjb/e2008-00134-9}}.
* Abdallah S. A. and Plumbley, M. D. (2010).  A measure of statistical complexity based on predictive information, ''ArXiv e-prints''. {{arxiv|1012.1890v1}}.
 
* Nihat Ay, E. Olbrich, N. Bertschinger (2001).  A unifying framework for complexity measures of finite systems. European Conference on Complex Systems. [http://www.cabdyn.ox.ac.uk/complexity_PDFs/ECCS06/Conference_Proceedings/PDF/p202.pdf pdf].
 
[[Category:Information theory]]
[[Category:Probability theory]]
[[Category:Statistical dependence]]

Latest revision as of 18:57, 1 April 2014

Your back bears the brunt of significantly of your day to day activity. Therefore, it is essential to treat it proper. In order to have a wonderful evening for your back is by going to a nearby massage parlor. If a professional massage is out of attain of your wallet, continue reading to learn suggestions that a pal or loved a single can use to give you a massage.

The use of massage oil really does help usher in the added feeling and sensation. This aids lessen tension and anxiety in the muscles. Technique is one particular issue, and obtaining the right massage oil truly does do the further trick. Massaging the oil into the skin as you deep tissue massage is just superb.

When you are providing your massage, try to have music playing in the space. This music must be really soothing and calm, without having a lot of words. Music therapy can support soothe the muscle tissues so that you can maximize the general expertise and help your general technique throughout the massage that you give.

You must attempt different strategies when giving a massage. Use your hands and fingers to rub, apply pressure or even give gentle taps. Use the tip of your fingers if you require precision, for instance to relax a tense muscle. You could also attempt covering as a lot surface as attainable by making use of the palm of your hands to apply stress.

Maintain the area at a great temperature throughout the complete massage. This lovely more information URL has a pile of original cautions for the reason for it. If you are giving a massage in the course of the winter, attempt to have the heat on so that items are not uncomfortable. On the other hand, if it is quite hot outside, maintain the air conditioning on at a reasonable level.

Begin your massage at the top of the back. This is critical as there are a lot of muscles and knots tied up in this location. This technique will assist you to soothe the person you are massaging and serves as a great bridge to the other areas of the physique.

An straightforward way to give a relaxing massage is by using a technique called "raking". In it, you just run your fingertips (spread hands) down the person"s back, gently moving back and forth. Genuinely, you are performing a raking motion up and down. For added impact, attempt alternating your hands - 1 rakes up even though the other rakes down.

The raking method is a well-liked way to give a back massage. To get one more interpretation, consider checking out: in english. Spread your fingers out wide and use your fingertips to carry out a raking motion down the back, from shoulders to hips. You can improve the pressure to the recipient"s liking. This is a easy way to loosen up your considerable other and devote some good quality time with each other.

A popular back massage you can attempt out on an individual is named a "Raking Massage". With this technique, you spread your fingers apart and use your ideas to give the massage. Commence in the shoulder region and function your way down the back using a raking motion. Visit this URL Dooce | The Next Web - Technology News, Business and Culture to check up how to engage in it. Then, you move your fingers down the spine without having actually touching it. Move a single hand down as the other hand moves up.

If you have not too long ago contracted the flu, a massage might help alleviate the pain and stiffness generally related with the flu. For the very best relief, gently rub warmed lotion more than your complete physique using a circular motion. This will not only alleviate aches, but it will also support re-hydrate your skin.

Use candles to set the mood. Candles provide subtle lighting, although simultaneously generating a relaxing atmosphere. Scented candles are also a wonderful concept. Spot them evenly all through the room, at varying elevations. It is also critical to be secure when utilizing candles. Keep them away from hanging fabric such as curtains.

Surprisingly sufficient, a massage exists that should be carried out by absolutely everyone following a meal is eaten. It demands you to location the palms onto the abdomen and start moving each in circular motions. This helps each circulation and digestion.

Aromatherapy massage makes use of scented therapeutic massage oils along with gentle kneading motions. These scented oils add yet another dimension to the normal massage by incorporating the sense of smell into the massage therapy. Aromatherapy frequently makes use of lavender, eucalyptus and chamomile. This kind of massage is ideal for men and women suffering for stress connected discomfort.

Performing ankle rotations is an outstanding way to loosen the joints and relax your feet. You"ll want to place 1 hand below your heel and the other hand is utilized to grab the ball of the foot. Then, turn your ankle 4 occasions in a single path, and then four instances in the other direction.

You never need to have to fork out the best-dollar costs to enjoy a massage of the highest top quality. You may not be able to profit from the industry, but you will be capable to teach your close friends a valuable trade. If you have hands, and a sore back, that"s genuinely all you require for a massage..

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