
In this article, we would like to compare the core mathematical bases of the two most popular theories and associative theory.
Mother of all sciences
In this article, we would like to compare the core mathematical bases of the two most popular theories and associative theory.
• The method of phase-magnitude interpolation (PMI)
• Accurate measure of frequency, magnitude and phase of signal harmonics
• Detection of resonances
The Fast Fourier Transform (FFT) algorithm is an important tool for analyzing and processing signals of various nature.
It allows to reconstruct magnitude and phase spectrum of a signal into the frequency domain by magnitude sample into the time domain, while the method is computationally optimized with modest memory consumption.
Although there is not losing of any information about the signal during the conversion process (calculations are reversible up to rounding), the algorithm has some peculiarities, which hinder high-precision analysis and fine processing of results further.
The article presents an effective way to overcome such "inconvenient" features of the algorithm.
I am not an economist, but in light of current events with cryptocurrencies and the economy in general, I would like to share my thoughts on some kind of ideal economy, around which everything is happening now.
It seems that the problem of calculating the absolute value of a number is completely trivial. If the number is negative, change the sign. Otherwise, just leave it as it is. In Java, it may look something like this:
public static double abs(double value) {
if (value < 0) {
return -value;
}
return value;
}
It seems to be too easy even for a junior interview question. Are there any pitfalls here?
Four months of awesome work together with a few new contributors finally result in a new major release, which I'm happy to announce about.
Now we get completely new matrices, improved parser, a lot of new functions, almost rewritten interactive package (for working in Jupyter) and many more.
This article about a big update in a FOSS symbolic algebra library for .NET, I hope it may be interesting for someone!
On implementing streaming algorithms, counting of events often occurs, where an event means something like a packet arrival or a connection establishment. Since the number of events is large, the available memory can become a bottleneck: an ordinary -bit counter allows to take into account no more than
events.
One way to handle a larger range of values using the same amount of memory would be approximate counting. This article provides an overview of the well-known Morris algorithm and some generalizations of it.
Another way to reduce the number of bits required for counting mass events is to use decay. We discuss such an approach here [3], and we are going to publish another blog post on this particular topic shortly.
In the beginning of this article, we analyse one straightforward probabilistic calculation algorithm and highlight its shortcomings (Section 2). Then (Section 3), we describe the algorithm proposed by Robert Morris in 1978 and indicate its most essential properties and advantages. For most non-trivial formulas and statements, the text contains our proofs, the demanding reader can find them in the inserts. In the following three sections, we outline valuable extensions of the classic algorithm: you can learn what Morris's counters and exponential decay have in common, how to improve the accuracy by sacrificing the maximum value, and how to handle weighted events efficiently.
Here I am going to cover my own approach to compilation of mathematical functions into Linq.Expression. What we are going to have implemented at the end:
1. Arithmetical operations, trigonometry, and other numerical functions
2. Boolean algebra (logic), less/greater and other operators
3. Arbitrary types as the function's input, output, and those intermediate
Hope it's going to be interesting!
After 210 days, 600 commits, tens of debugging nights, and thousands of messages in the project chat, I finally released AngouriMath 1.2.
This is an open-source symbolic algebra library for C# and F#, maybe it is interesting for someone?
There’s a lot of talk about machine learning nowadays. A big topic – but, for a lot of people, covered by this terrible layer of mystery. Like black magic – the chosen ones’ art, above the mere mortal for sure. One keeps hearing the words “numpy”, “pandas”, “scikit-learn” - and looking each up produces an equivalent of a three-tome work in documentation.
I’d like to shatter some of this mystery today. Let’s do some machine learning, find some patterns in our data – perhaps even make some predictions. With good old Python only – no 2-gigabyte library, and no arcane knowledge needed beforehand.
Interested? Come join us.
Entity
class from a symbolic algebra library:This is a fourth article in the series of works (see also first one, second one, and third one) describing Machine Learning system based on Lattice Theory named 'VKF-system'. The program uses Markov chain algorithms to generate causes of the target property through computing random subset of similarities between some subsets of training objects. This article describes bitset representations of objects to compute these similarities as bit-wise multiplications of corresponding encodings. Objects with discrete attributes require some technique from Formal Concept Analysis. The case of objects with continuous attributes asks for logistic regression, entropy-based separation of their ranges into subintervals, and a presentation corresponding to the convex envelope for subintervals those similarity is computed.
This is a third article in the series of works (see also first one and second one) describing Machine Learning system based on Lattice Theory named 'VKF-system'. It uses structural (lattice theoretic) approach to representing training objects and their fragments considered to be causes of the target property. The system computes these fragments as similarities between some subsets of training objects. There exists the algebraic theory for such representations, called Formal Concept Analysis (FCA). However the system uses randomized algorithms to remove drawbacks of the unrestricted approach. The details follow…