I have two 32bit vectors one derived from other by mathematical/logical transform.
Is there a Perl/C library which can look up what kind of transform(Or list of all possible transforms that library is capable of inferring) has been applied ?
Case1. 968eac37 -> 968eac37
Case2. 12345678 -> 23456781
Case3. 614e1973 -> 30f7150d
Output
1. No transform
2. Bit wise shift left 4 or trivial addition
3. Trivial subtraction or something else or unknown
No, this would involve actually applying all the transforms to check the results. Any transform that involved encryption would be by definition not determinable.
Take the case of "trivial subtraction". How would you distinguish that from "trivial addition/multiplication modulo 32 bits"?
Your underlying question is really "how do I undo encryption", which for any sufficiently strong encryption is impossible. For "weak" encryptions there can be multiple answers, so there is no such library.
Related
I'm working on a simple search engine where I use the TF-IDF formula to score how important a search word is. I see people using different bases for the formula, but I see no explanation for when to use which. Does it matter at all, and do you have any recommendations?
My current implementation uses the regular log() function of the math.h library
TF-IDF literature usually uses base 2, although a common implementation sklearn uses natural logarithms for example. Just take in count that the lower the base, the bigger the score, which can affect truncation of search resultset by score.
Note that from a mathematical point of view, the base can always be changed later. It's easy to convert from one base to another, because the following equality holds:
log_a(x)/log_a(y) = log_b(x)/log_b(y)
You can always convert from one base to another. It's actually very easy. Just use this formula:
log_b(x) = log_a(x)/log_a(b)
Often bases like 2 and 10 are preferred among engineers. 2 is good for halftimes, and 10 is our number system. Math people prefer the natural logarithm, because it makes calculus a lot easier. The derivative of the function b^x where b is a constant is k*b^x. Bur if b is equal to e (the natural logarithm) then k is 1.
So let's say that you want to send in the 2-logarithm of 5.63 using log(). Just use log(5.63)/log(2).
If you have the need for it, just use this function for arbitrary base:
double logb(double x, double b) {
return log(x)/log(b);
}
Good morning, I'm trying to perform a 2D FFT as 2 1-Dimensional FFT.
The problem setup is the following:
There's a matrix of complex numbers generated by an inverse FFT on an array of real numbers, lets call it arr[-nx..+nx][-nz..+nz].
Now, since the original array was made up of real numbers, I exploit the symmetry and reduce my array to be arr[0..nx][-nz..+nz].
My problem starts here, with arr[0..nx][-nz..nz] provided.
Now I should come back in the domain of real numbers.
The question is what kind of transformation I should use in the 2 directions?
In x I use the fftw_plan_r2r_1d( .., .., .., FFTW_HC2R, ..), called Half complex to Real transformation because in that direction I've exploited the symmetry, and that's ok I think.
But in z direction I can't figure out if I should use the same transformation or, the Complex to complex (C2C) transformation?
What is the correct once and why?
In case of needing here, at page 11, the HC2R transformation is briefly described
Thank you
"To easily retrieve a result comparable to that of fftw_plan_dft_r2c_2d(), you can chain a call to fftw_plan_dft_r2c_1d() and a call to the complex-to-complex dft fftw_plan_many_dft(). The arguments howmany and istride can easily be tuned to match the pattern of the output of fftw_plan_dft_r2c_1d(). Contrary to fftw_plan_dft_r2c_1d(), the r2r_1d(...FFTW_HR2C...) separates the real and complex component of each frequency. A second FFTW_HR2C can be applied and would be comparable to fftw_plan_dft_r2c_2d() but not exactly similar.
As quoted on the page 11 of the documentation that you judiciously linked,
'Half of these column transforms, however, are of imaginary parts, and should therefore be multiplied by I and combined with the r2hc transforms of the real columns to produce the 2d DFT amplitudes; ... Thus, ... we recommend using the ordinary r2c/c2r interface.'
Since you have an array of complex numbers, you can either use c2r transforms or unfold real/imaginary parts and try to use HC2R transforms. The former option seems the most practical.Which one might solve your issue?"
-#Francis
I have a set of training data, each item in this set consists of 4 numerical values and 1 nominal-value which is the name of the method that these values have been calculated with. (There are 8 methods)
I'm training a Neural Network with these. To get rid of the nominal-value I simply assigned a value from 1 to 8 to each method and used one input to pass it to Neural Network and 4 other inputs for numerical-values. It is sort of working, but the result is not as amazing as I want.
So my question is could it be because of this simple assignment of numbers to nominal-values? or maybe it is because of mixing two different categories of inputs which are not really at the same level (numbers and method types)
As a general note, a better way for coding nominal values would be a binary vector. In your case, in addition to the 4 continuous-valued inputs, you'd have 8 binary input neurons, where only one is activated (1) and the other 7 are inactive.
The way you did it implies an artificial relationship between the computation methods, which is almost certainly an artifact. For example, 1 and 2 are numerically (and from your network's point of view!) nearer than 1 and 8. But are the methods nr. 1 and 2 really more similar, or related, than the methods 1 and 8?
Since you don't provide much detail, my answer can't be very specific.
Generally speaking neural networks tend to perform worse when coding nominal values as numeric values since the transformation will impose a (probably) false ordering on the variables. Mixing inputs with very varied levels also tend to worsen the performance.
However, given the little information provided here there is no way of telling if this is the reason that the networks performance is "not as amazing" as you want. It could just as well be the case that you don't have enough training data, or that your training data contains a lot of noise. Perhaps you need to pre-scale your data, perhaps there is an error in your network code, perhaps you have chosen ill-suited values of constants for your learning algorithm...
The reasons a neural network doesn't perform as expected are many and diverse (on of them beeing unreasonably high expectations). Without much more information there is no way of knowing what the problem is in your case.
Mapping categories to numerical values is not a good practice in statistics. Especially in the case of neural networks. Bear in mind that neural networks tend to map similar inputs to similar outputs. If you map category A to 1 and category B to 2 (both as inputs), the NN will try to output similar values for both categories, even if they have nothing to do with each other.
A sparser representation is preferred. If you have 4 categories, map them like this:
A -> 0001
B -> 0010
etc
Take a look at the "Subject: How should categories be encoded?" in this link:
ftp://ftp.sas.com/pub/neural/FAQ2.html#A_cat
The previous answers are right - do not map nominal values into arbitrary numeric ones. However, if the attribute has an ordinal nature ("Low", "Medium", High" for example), you can replace the nominal values by ascending numeric values. Note that this may not be the optimal solution - since there is no guarantee for example that "High"=3 by the nature of your data. Instead, use one-hot bit encoding as suggested.
The reason for this is that a neural network is very similar to regression in the sense that multiple numeric values go through some kind of an aggregating function - but this happens multiple times. Each input is also multiplied by a weight.
So when you enter a numeric value, it undergoes a series of mathematical manipulations that adjusts its weights in the network. So if you use numeric values for non-nomial data - nominal values that were mapped to closer numeric values will be treated about the same in the best case, in the worst case - it can harm your model.
I have a vector A, represented by an angle and a length. I want to add vector B, updating the original A. B comes from a lookup table, so it can be represented in which ever way makes the computation easier.
Specifically, A is defined thusly:
uint16_t A_angle; // 0-65535 = 0-2π
int16_t A_length;
Approximations are fine. Checking for overflow is not necessary. A fast sin/cos approximation is available.
The fastest way I can think is to have B represented as a component vector, convert A to component, add A and B, convert the result back to angle/length and replace A. (This requires the addition of a fast asin/acos)
I am not especially good at math and wonder if I am missing a more sensible approach?
I am primarily looking for a general approach, but specific answers/comments about useful micro-optimizations in C is also interesting.
If you need to do a lot of additive operations, it would probably be worth considering storing everything in Cartesian coordinates, rather than polar.
Polar is well-suited to rotation operations (and scaling, I guess), but sticking with Cartesian (where a rotation is four multiplies, see below) is probably going to be cheaper than using cos/sin/acos/asin every time you want to do a vector addition. Although, of course, it depends on the distribution of operations in your case.
FYI, a rotation in Cartesian coordinates is as follows (see http://en.wikipedia.org/wiki/Rotation_matrix):
x' = x.cos(a) - y.sin(a)
y' = x.sin(a) + y.cos(a)
If a is known ahead of time, then cos(a) and sin(a) can be precomputed.
I want to pack a giant DNA sequence with an iOS app (about 3,000,000,000 base pairs). Each base pair can have a value A, C, T or G. Storing each base pair in one bytes would give a file of 3 GB, which is way too much. :)
Now I though of storing each base pair in two bits (four base pairs per octet), which gives a file of 750 MB. 750 MB is still way too much, even when compressed.
Are there any better file formats for efficiently storing giant base pairs on disk? In memory is not a problem as I read in chunks.
I think you'll have to use two bits per base pair, plus implement compression as described in this paper.
"DNA sequences... are not random; they contain
repeating sections, palindromes, and other features that
could be represented by fewer bits than is required to spell
out the complete sequence in binary...
With the proposed algorithm, sequence will be compressed by 75%
irrespective of the number of repeated or non-repeated
patterns within the sequence."
DNA Compression Using Hash Based Data Structure, International Journal of Information Technology and Knowledge Management
July-December 2010, Volume 2, No. 2, pp. 383-386.
Edit: There is a program called GenCompress which claims to compress DNA sequences efficiently:
http://www1.spms.ntu.edu.sg/~chenxin/GenCompress/
Edit: See also this question on BioStar.
If you don't mind having a complex solution, take a look at this paper or this paper or even this one which is more detailed.
But I think you need to specify better what you're dealing with. Some specifics applications can lead do diferent storage. For example, the last paper I cited deals with lossy compression of DNA...
Base pairs always pair up, so you should only have to store one side of the strand. Now, I doubt that this works if there are certain mutations in the DNA (like a di-Thiamine bond) that cause the opposite strand to not be the exact opposite of the stored strand. Beyond that, I don't think you have many options other than to compress it somehow. But, then again, I'm not a bioinformatics guy, so there might be some pretty sophisticated ways to store a bunch of DNA in a small space. Another idea if it's an iOS app is just putting a reader on the device and reading the sequence from a web service.
Use a diff from a reference genome. From the size (3Gbp) that you post, it looks like you want to include a full human sequences. Since sequences don't differ too much from person to person, you should be able to compress massively by storing only a diff.
Could help a lot. Unless your goal is to store the reference sequence itself. Then you're stuck.
consider this, how many different combinations can you get? out of 4 (i think its about 16 )
actg = 1
atcg = 2
atgc = 3 and so on, so that
you can create an array like [1,2,3] then you can go one step further,
check if 1 is follow by 2, convert 12 to a, 13 = b and so on...
if I understand DNA a bit it means that you cannot get a certain value
as a must be match with c, and t with g or something like that which reduces your options,
so basically you can look for a sequence and give it a something you can also convert back...
You want to look into a 3d space-filling curve. A 3d sfc reduces the 3d complexity to a 1d complexity. It's a little bit like n octree or a r-tree. If you can store your full dna in a sfc you can look for similar tiles in the tree although a sfc is most likely to use with lossy compression. Maybe you can use a block-sorting algorithm like the bwt if you know the size of the tiles and then try an entropy compression like a huffman compression or a golomb code?
You can use the tools like MFCompress, Deliminate,Comrad.These tools provides entropy less than 2.That is for storing each symbol it will take less than 2 bits