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I'm doing a project on single precision floating numbers. I was wondering in what fields or areas are these concepts used? Thanks in advance.
For anything requiring larger range than available with integers, and where limited accuracy of number representation isn't important enough to use longer floats. In terms of accuracy, nothing beats integer or fixed point, at the price of their limited range. Say if i wanted cosmological distances in a unit which can be used for both nearer and far objects at the same time, i could think of using those - after all, i'd be mostly interested in the most significant parts of the distance, not in the submillimeter portion.
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I need to do a job where I need to place a particular object(Hanger) in a standard distance.
The rules are:
We should try to place each object in a given standard distance from each other.
There is a max distance from one object to adjacent object which in no way should be violated.
From the start and end also similar standard and maximum distance rule applies.
And there are some portions given where the objects placement needs to be avoided.
I'm not even able to start... which algorithm to use.
If anyone has any suggestion how I can achieve this or some related source please let me know.
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I'm researching on compression algorithms (huffman coding and LZ77) and was wondering how I would evaluate their efficiency depending on the input image. I know how they work but I can't find information on their evaluation (mathematically). Thanks!
General-purpose (universal) compressors like LZ77 are usually compared by testing them against a standard set of sources and comparing the results, see: http://www.maximumcompression.com/, http://www.maximumcompression.com/data/summary_mf.php, for example.
Compressors for specific purposes are tested against source sets that are chosen to be as representative as possible.
For some applications it is also useful to place mathematical bounds on compression efficiency in terms of the source entropy.
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I'm reading about AI and in the notes it is mentioned
A lookup table in chess would have roughly 35^100 entries.
But what does this mean? Is there any way we could find out how long it would take the computer to search through and find it's entry? Would we assume thereis some order or that there is no order?
The number of atoms in the known universe is estimated to be around 10^80 which is much less than 35^100. With current technology, at least a few thousand atoms are required to store a single bit. I assume that each entry of your table would have multiple bits. You would need some really advanced technology to implement the memory of your computer.
So the answer is: With current technology it is not a matter of time, it is simply impossible.
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I'm working on a pseudorandom number generator for an assignment and I'm having a hard time wrapping my head around how state is used in it. What does it mean to advance to the next one? I'm not looking for tips on implementation, just an explanation of the concept. Thanks!
A PRNG generates a sequence of numbers.
To calculate the next number, you have some internal state (variables set to specific values, if you will). That's the state referred to in the context of PRNG. This state can often be represented by just a single number.
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Are there any algorithms for finding the maximum value of a continuous function, which is proofed to be bounded upside?
For example, a function similar to sin.
I think Newton's method and Mid-point method are for finding a fixed value, any other methods for finding maximum value?
For general functions that are "Lipschitz-continuous" (meaning that the output changes by at most a constant factor times the change in input) see e.g. http://link.springer.com/article/10.1007%2FBF00938542#page-1 and http://link.springer.com/article/10.1007%2Fs10898-012-9937-9#page-1 . If your function is arbitrary continuous and not Lipschitz-continuous, then in theory the function could change to an arbitrarily high or low value over an arbitrarily small region, so provable global optimization is very hard.