Searching for Nearest Strings with Neural-Like String Embedding

We analyze an approach to a similarity preserving coding of symbol sequences based on neural distributed representations and show that it can be viewed as a metric embedding process.

Search for Wieferich Primes through the use of Periodic Binary Strings

The result of the distributed computing projectWieferich@Home is presented: the binary periodic numbers of bit pseudo-length j ≤ 3500 obtained by replication of a bit string of bit pseudo-length k ≤ 24 and increased by one are Wieferich primes only for the cases of 1092 or 3510.

Symplectic Representation of a Braid Group on 3-Sheeted Covers of the Riemann Sphere

We define Picard cycles on each smooth three-sheeted Galois cover C of the Riemann sphere. The moduli space of all these algebraic curves is a nice Shimura surface, namely a symmetric quotient of the projective plane uniformized by the complex two-dimensional unit ball. We show that all Picard cycles on C form a simple orbit of the Picard modular group of Eisenstein numbers. The proof uses a special surface classification in connection with the uniformization of a classical Picard-Fuchs system. It yields an explicit symplectic representation of the braid groups (coloured or not) of four strings.

Matrix Power S-box Analysis

* Work supported by the Lithuanian State Science and Studies Foundation.

String Measure Applied to String Self-Organizing Maps and Networks of Evolutionary Processors

* Supported by projects CCG08-UAM TIC-4425-2009 and TEC2007-68065-C03-02

Математика и музика (от Питагор до Бах и до наши дни)

Georgi Dimkov - Looking at the performance of a violonist we perceive that the four strings of the instrument produces tones different pitches. It is clear that the artist presses the strings on special places and that changes the pitch. These places are determined practically by the musicians. Is it possible to determine these places theoretically, from some abstract point of view? After the legend the first successive investigations in this field were done by Pythagoras. The development of the ideas for improvement and enlargement of the results of Pythagoras is the mane topic of the present paper.