Developers Club geek daily blog

New in Wolfram Language | the Analytical solution of partial equations

1 year, 10 months ago

Transfer of a post of Devendra Kapadia "New in the Wolfram Language: Symbolic PDEs".
The code given in article can be downloaded here.
I express huge gratitude to Kirill Guzenko of KirillGuzenko for the help in transfer and preparation of the publication
.
Partial equations (UrChP) play very important role in mathematics and its applications. They can be used for modeling of the real phenomena, such as fluctuations of the tense string, distribution of a heat flow in a rod, in financial areas. The purpose of this article — to slightly open a veil to the world of UrChP (who else is not familiar to those with it) and to acquaint the reader with how it is possible to solve effectively UrChP in Wolfram Language, using new functionality for a solution of boundary value problems in DSolve, and also new DEigensystem function which appeared in version 10.3.

History UrChP goes back to works of the famous mathematicians of the eighteenth century — Euler,Dalambera,Laplace, however development of this area in the last three centuries did not stop. And therefore I will provide both classical, and modern examples of UrChP in article that will allow to consider this knowledge domain under different corners.

Let's begin with consideration of fluctuations of the tense string with a length π, fixed on both ends. Fluctuations of a string can be simulated by means of the one-dimensional wave equation given below. Here u (x, t) — vertical shift of a point of a string with coordinate x in t timepoint:


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Happy birthday, Donald Cnut

1 year, 10 months ago
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Birthday, on January 10, 78 years


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The overview of an example of application of training with a reinforcement with use of TensorFlow

1 year, 10 months ago
КПДВ. В Karpathy game играет нейронная сеть

Hi everyone!
I think that many heard about Google DeepMind. About that as they train programs to play the games Atari better than the person. Today I want to provide you article about how to make something similar. This article is an overview of idea and a code of an example of application Q-learning which is a special case of training with a reinforcement. The example is based on article of employees of Google DeepMind.

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"Other" logic and reversible calculations

1 year, 10 months ago
камень-ножницы-бумага (на ауребеш) At the end of last year the Google Translate Aurebesh added support of "Galactic language" to an output of a new episode of "Star wars". The truth it turned out that at the choice of this language just there is transfer into English. If to use Chrome or Firefox, then there is a font in which instead of Latin characters aurebesh are substituted, and in IE without special cunnings the English text is output.

Began to remember other examples of creation of "languages of strangers". For example, language Klingonov from "Star Trek" is based on Latin too, but at the same time is worked rather out, has the syntax and the dictionary. Languages of the people of Sredizemya from "Lord of the Rings" – in general separate history.

And still there are such languages as the Linkos which is specially developed by Hans Freudental for interplanetary communication and based on the assumption that the mathematics is a universal language of communication for any reasonable beings.

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Yandex. Meteum – new development or a marketing mix?

1 year, 10 months ago
At the end of November Yandex Company announced the updated weather service under the name "Yandex. Meteum". Allegedly new program software development to the algorithms is capable to calculate the forecast to within the house. I as the amateur meteorologist could not but be interested in a new product. I was always respectful to Yandex, even despite unsuccessful restart of Kinopoisk, but having studied the announcement published on the website "Habrakhabr" in detail I found in it a number of not joining and logical errors. Then I decided to conduct the research of accuracy of new service, concerning other weather resources, namely my website "Weather 45" (A weather forecast for Kurgan) and Foreca (from which basic resource Yandex takes data).

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Further I will rely on the expanded announcement published on Habrakhabr. Let's investigate this not joining and logical inaccuracies which were found by me in this announcement.

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Universal Memcomputing Machines as alternative to the Turing machine

1 year, 10 months ago
This article can be considered as loose translation (though rather an attempt to understand) this article. And yes, it is written rather for mathematicians, than for wide audience.

Small spoiler: at the beginning it seemed to me some magic, but then I understood a dirty trick …

Today the Turing machine (further MT) — universal determination of concept of algorithm, so and universal determination of "problem solver". There is a set of other models of algorithm — a lambda calculation, Markov's algorithms, etc., but all of them are mathematically equivalent to MT so though they also are interesting, but in the theoretical world anything is changed significantly.

Generally speaking, there are other models — the Nondeterministic Turing machine, Quantum computers of Turing. However they (so far) are only abstract modeliya, not implemented in practice.

Half a year ago in Science Advances there was interesting article with model of calculations which significantly differs from MT and which is quite possible for implementing in practice (actually article and was how they counted a problem of SSP on real iron).

And yes. The most interesting in this model the fact that, on assurance of authors, in it it is possible to solve (some) problems from the class NP of complete tasks for a polynom of time and memory.

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Theory of information visualization. Part 2 (final)

1 year, 10 months ago


In the first part of the story we got acquainted with the information theory on a specific example and today we will continue our research. This tool allows to describe strong ideas which have a set of scopes of application: from data compression to quantum physics and machine learning.

Let's remind that costs for the message L long make. We can transform expression and receive message length cost. As a result, we spend p(x) for the code word x length.

It is the best length of the message.

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About complexity of cultivation of an Oriental cherry: as I participated in Ludum Dare 34

1 year, 10 months ago
Hi, habr!

In this post it will be a question of my participation in the tender Ludum Dare 34 which was about three weeks ago.

As a result the puzzle under the name Growing Sakura which gameplay it is possible to see on a gif image turned out (be not frightened, it weighs only 300 KB):


Briefly about rules of the game: initially we have a hexagonal field and several root buds (or one, as on a gif image above). From it it is possible to start up 3 branches (by two methods — clicking left or the right mouse button). On a branch the left click of a mouse can be made of each bud a Y-branching, and right — it is simple to continue a branch further (I-branching). If the branch cannot grow in any direction (the corresponding cage is occupied or in the necessary direction there is no cage) — that the branch does not grow. According to the last condition it is necessary to select correctly poryadkok "deployment" of branches. As a result the tree (or several trees) it that between two adjacent branches there are no acute angles will turn out. The game purpose — to cover all cages of a game field.

Without looking under kat try to think seconds 10 and to estimate how difficult can be this game.

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We draw elliptic curves by means of SQL

1 year, 10 months ago
The benefit of approach on the basis of elliptic curves in comparison with a problem of the factorization of number used in RSA, or the problem of integer logarithming applied in Diffie-Hellman's algorithm and in DSS is that in this case equivalent protection at smaller key length is provided.

Generally the equation of an elliptic curve E in the field of real numbers of R has an appearance:

— y^2+a1*x*y+a3*y = x^3+a2*x^2+a4*x+a6

or in case of a final ring of deductions of Z|n:

— y^2+a1*x*y+a3*y = x^3+a2*x^2+a4*x+a6 mod N

Let's set for ourselves the task of visualization of an elliptic curve.

Elliptic curve E in the field of real numbers of R


If the elliptic curve E is considered in the field of real numbers of R, then creation of the diagram can be described, using only knowledge of algebra and geometry of the senior classes of school

arguments of N a1 a2 a3 a4 a6 xmin xmax
  1. We select the range [xmin — xmax] of argument x
  2. We note on the selected range of argument x necessary number of x1 values..., xN
  3. Each of x1 values..., x^3+a2*x^2+a4*x+a6 is substituted xN in y^2+a1*x*y+a3*y equation = and we receive the normal square equation of argument of y
  4. We find roots of the square equation of argument of y
  5. If the square equation of argument of y has solutions, then we add two points on the diagram
  6. We connect lines all "upper" points on the diagram and all "lower" points on the diagram

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Multiplication tables … kind of

1 year, 10 months ago
Preface
This post — short retelling of this video in English.
If there is no time to read — a living example here. In the field of factor it is possible to substitute any non-negative values. My darlings — 51, 99, 106, 134, 150.


The mathematics never ceases to surprise with the beauty. This post how to turn such simple operation as multiplication into something surprising. Now answer a question — that the general between it pictures?


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