Malleability (cryptography): Difference between revisions

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Malleability does not imply encryption-breaking ability; make this clear to the reader.
Added a paragraph on the malleability property of CBC
 
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{{refimprove|date=May 2008}}
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[[Image:Logistic-curve.svg|thumb|320px|right|The [[logistic curve]]]]
[[Image:Error Function.svg|thumb|right|320px|Plot of the [[error function]]]]
 
A '''sigmoid function''' is a [[function (mathematics)|mathematical function]] having an "S" shape ('''sigmoid curve'''). Often, ''sigmoid function'' refers to the special case of the [[logistic function]] shown in the first figure and defined by the formula
:<math>S(t) = \frac{1}{1 + e^{-t}}.</math>
Another example is the [[Gompertz curve]]. It is used in modeling systems that saturate at large values of t.
Another example is the [[ogee curve]] as used in the [[spillway]] of some [[dam]]s.
A wide variety of sigmoid functions have been used as the [[activation function]] of [[artificial neuron]]s, including the logistic and [[hyperbolic tangent]] functions. Sigmoid curves are also common in statistics as [[cumulative distribution function]]s, such as the integrals of the [[logistic distribution]], the [[normal distribution]], and [[Student's t-distribution|Student's ''t'' probability density functions]].
 
==Definition==
A sigmoid function is a bounded differentiable real function that is defined for all real input values and has a positive derivative at each point.<ref>{{Cite book |last1=Han |first1=Jun |last2=Morag |first2=Claudio |title=From Natural to Artificial Neural Computation |chapter=The influence of the sigmoid function parameters on the speed of backpropagation learning |editor1-last=Mira |editor1-first=José |editor2-last=Sandoval |editor2-first=Francisco |pages=195–201 |year=1995 |url=http://dx.doi.org/10.1007/3-540-59497-3_175}}</ref>
 
==Properties==
In general, a sigmoid function is [[real number|real]]-valued and [[differentiable]], having either a [[non-negative]] or [[non-positive]] first [[derivative]]{{citation needed|date=November 2013}} which is bell shaped. There are also a pair of [[horizontal asymptotes]] as <math>t \rightarrow \pm \infty</math>.  The differential equation <math> \tfrac{d}{dt} S(t) = c_1 S(t) \left( c_2 - S(t) \right)</math>, with the inclusion of a [[boundary condition]] providing a third [[degree of freedom]], <math>c_3</math>, provides a class of functions of this type.
 
==Examples==
[[File:Gjl-t(x).svg|thumb|320px|right|Some sigmoid functions compared. In the drawing all functions are normalized in such a way that their slope at the origin is 1.]]
Many natural processes, including those of complex system [[learning curve]]s, exhibit a progression from small beginnings that accelerates and approaches a climax over time.   When a detailed description is lacking, a sigmoid function is often used<ref>{{cite journal
| last = Gibbs
| first = M.N.
|date=Nov 2000
| title = Variational Gaussian process classifiers
| journal = IEEE Transactions on Neural Networks
| volume = 11
| issue = 6
| pages = 1458–1464
| doi = 10.1109/72.883477
| accessdate = 21 Aug 2012
}}</ref>
.
 
Besides the [[logistic function]], sigmoid functions include the ordinary [[Inverse trigonometric function|arctangent]], the [[Hyperbolic function|hyperbolic tangent]], the [[Gudermannian function]], and the [[error function]], but also the [[generalised logistic function]] and [[algebraic function]]s like <math>f(x)=\tfrac{x}{\sqrt{1+x^2}}</math>.
 
The [[integral]] of any smooth, positive, "bump-shaped" function will be sigmoidal, thus the [[cumulative distribution function]]s for many common [[probability distribution]]s are sigmoidal. The most famous such example is the [[error function]], which is related to the [[Cumulative distribution function|Cumulative Distribution Function (CDF)]] of a [[normal distribution]].
 
==See also==
{{commons category|Sigmoid functions}}
* [[Cumulative distribution function]]
* [[Generalized logistic curve]]
* [[Logistic distribution]]
* [[Logistic regression]]
* [[Logit]]
* [[Hyperbolic function]]
* [[Weibull distribution]]
* [[Heaviside step function]]
* [[Gompertz function]]
 
== References ==
{{reflist}}
 
* {{ cite book | first1=Tom M. |last1= Mitchell | title=Machine Learning | publisher=WCB–McGraw–Hill |year=1997
|isbn=0-07-042807-7}}. In particular see "Chapter 4: Artificial Neural Networks" (in particular pp.&nbsp;96–97) where Mitchell uses the word "logistic function" and the "sigmoid function" synonymously – this function he also calls the "squashing function" – and the sigmoid (aka logistic) function is used to compress the outputs of the "neurons" in multi-layer neural nets.
* {{cite web|first1= Mark | last1= Humphrys | url =http://www.computing.dcu.ie/~humphrys/Notes/Neural/sigmoid.html
|title= Continuous output, the sigmoid function}} Properties of the sigmoid, including how it can shift along axes and how its domain may be transformed.
 
[[Category:Elementary special functions]]
[[Category:Neural networks]]
[[Category:Probability distributions]]

Latest revision as of 15:47, 15 March 2014

The skin may thicken all over or in certain places to have an "elephant" appearance -- grayish and flattened. 5 - Build-up the good bacteria in your digestive tract by eating natural yogurt every day. Simple apply it to your area and it will soothe the symptoms. Strong immunity systems easily fight off yeast infections. Yogurt is one home remedy that women use to end yeast infection, they use plain unsweetened yogurt since sugar feeds yeast and so sugar must be avoided.

If untreated it can lead to other infections deep inside the woman's female parts and also can be transmitted to their partner during sex. Treating yeast infection with hydrogen peroxide is one of the best methods you could ever use for treating yeast infections. * Probiotics are the primary option that women have when it comes to natural remedies, giving them the chance to get what they deserve out of their search for relief. Treating your symptoms and not addressing the root of the infection is what a lot of the over the counter yeast infection treatments will give you. Vaginal discharge that looks like cottage cheese.

You can also have your doctor or other healthcare provider order a test for you from a place like Genova Diagnostics who have excellent tests for food allergies, candida (yeast infection), etc. Amanda enjoys roller blading and spending time with her boyfriend visiting exciting places. The viruses frequently become latent and may not be expressed for years. Now for those of you who have done extensive research on hair loss. The side effects of taking prednisone may sound scary, but not all patients undergo all these symptoms.

In genitalia as well as the digestive system, you can find a white or else whitish mucous discharge. Because of this, it is difficult for post partum women who have undergone a cesarean operation to get back into shape. A person may get infected with thrush due to a weakened immune system or as the fungus is passed from the genital to the oral region. During the treatment patients are given up to three injections every 60 days for a maximum period of 2 years. Donning of open shoes will aid in keeping your feet well ventilated, lessening the possibilities of infection.

This will weaken the immune system and will result in Candida overgrowth. Garlic is another option you have at your disposal. However some people will suffer from chronic yeast infections and this can be difficult to get rid of. To use this herb, put 2 - 3 drops into warm water and swish it inside your mouth for about 30 seconds then spit it out. For instance, Monistat 1 products have the highest concentration of the active ingredient (1200 mg) vs.

If you beloved this short article and you would like to obtain additional data relating to medication for yeast infection kindly take a look at our own web page.

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