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(1 + 1/n)ⁿ
- We use e in the natural exponential function (eˣ = e power x). In the eˣ function, the slope of the tangent line to any point on the graph is equal to its y-coordinate at that point. (1 + 1/n)ⁿ is the sequence that we use to estimate the value of e. The sequence gets closer to e the larger n is.
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Which sequence is used to estimate the value of E?
Why do sequence hits get Better E-values if a database is large?
Why does a sequence hit get a better E-value?
How do you calculate E -value?
Should the default e -value be increased if searching for short sequence matches?
What does an E -value of 1 mean?
How is the BLAST E-value calculated? The E-value is calculated based on the alignment score (S), the search space size (m × n), and the parameters derived from the scoring system and the database composition, such as the Karlin-Altschul parameters (K and λ). The formula for E-value is: E-value = K × m × n × e-λS. Where:
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We use e in the natural exponential function (eˣ = e power x). In the eˣ function, the slope of the tangent line to any point on the graph is equal to its y-coordinate at that point. (1 + 1/n)ⁿ is the sequence that we use to estimate the value of e. The sequence gets closer to e the larger n is.
- What Is Euler’s Number (e) and Where Did It Come from?
- Euler’s Number E and Compound Interest
- Calculating The Value of Euler’s Number E as A Limit
- Calculating The Value of Euler’s Number E Using An Infinite Series
- Continued Fractions and E
- Other Ways to Calculate E
Euler’s number has a value of 2.718… , however just like Pi, it is an irrational number, meaning that it cannot be written as a fraction and that it has a decimal expansion which will continue forever without repetition. Euler’s number e has become famous for two main reasons: firstly, it is used in lots of important real-life situations, and secon...
Euler’s Number was first discovered by Jacob Bernoulli in the 17thCentury when he studied the problem of Compound Interest. Imagine you have £1 and that you get interest twice a year at a rate of 50%. At the end of the year you would end up with £1 £= £2.25 Now imagine you have £1 and you get interest 12 times per year, or every month at a rate of ...
(Keep putting in bigger and bigger values of , until you get really close to the true value of .) Unfortunately, Jacob Bernoulli didn’t have a computer at his disposal and was only able to say that the value was between 2 and 3. Some years later Leonhard Euler, one of the greatest mathematicians in history managed to calculate the value of , correc...
(In case you are wondering, 5!means and is the factorial function) The more terms you calculate, the closer you will get to the true value of . You will only arrive at the exact value of if you carry on adding up the sequence forever. Nobody knows exactly how Euler calculated to 18 decimal places, however the best guess is that he used the sequence...
Euler was also able to represent in the form of a “continued fraction”. There are lots of different ways to represent eas an infinite continued fraction. Here is one of them: Calculating the value of Euler’s Number e as a continued fraction:
The three main ways of calculating have been listed above. There are however many other lesser known representations of such as: If you visit the Wolfram Mathworld page on e, you can browse through a huge collection of different ways of calculating, some of which are very complicated indeed. This same page also lists a collection of mnemonics to he...
The E-value (expectation value) is a corrected bit-score adjusted to the sequence database size. The E-value therefore depends on the size of the used sequence database. Since large databases increase the chance of false positive hits, the E-value corrects for the higher chance.
The E- value is the most widely used measure for estimating the quality of sequence alignment—that is, the extent of sequence similarity. The typical threshold for the E -value when judging homology, particularly using BLAST, is E ≤1e−5 (=1×10 −5), and the lower the value, the better it is.
There are several ways to calculate the value of e. Let's look at the historical development. Using a Binomial Expansion. If n is very large (approaches infinity) the value of `(1+1/n)^n`approaches e. This is not an efficient way to find `e`. Even if we go out to n = 100,000, our value is only correct to the 4th decimal place. `e~~[(1+1/n)^n ...
The E-value (expectation value) is a corrected bit-score adjusted to the sequence database size. The E-value therefore depends on the size of the used sequence database . Since large databases increase the chance of false positive hits, the E-value corrects for the higher chance.
