Institute for Information Transmission Problems

The Goeritz matrix is an alternative to the Kauffman bracket and, in addition, makes it possible to calculate the Jones polynomial faster with some minimal choice of a checkerboard surface of a link diagram. We introduce a modification of the Goeritz method that generalizes the Goeritz matrix for computing the HOMFLY–PT polynomials for any $$N$$ in the special case of bipartite links. Our method reduces to purely algebraic operations on matrices, and therefore, it can easily be implemented as a computer program. Bipartite links form a rather large family, including a special class of Montesinos links constructed from the so-called rational tangles. We demonstrate how to obtain a bipartite diagram of such links and calculate the corresponding HOMFLY–PT polynomials using our developed generalized Goeritz method.

This work deals with Reconfigurable Intelligent Surfaces or (also known as Intelligent Reflecting Surfaces) which provide an improvement of performance of wireless communications by utilizing software-controlled meta-surfaces for the reflected signals from the source to destination, especially when the direct path is weak and hence improving the antenna array. The performance evaluation is done by one of the techniques that utilizes the very high rates and/or large meta-surfaces to outperform the classic method of decode and forward, both in terms of the total transmit power and the energy efficiency. The channel measurements used by classifying them as a function of the frequency band, and usage of deployment scenarios such as indoor/outdoor, and system configuration. So, the 5G and beyond which is 6G use several antennas including the algorithms to make use of signal processing. This improves the antenna array technology. In the next steps, we work on machine learning-based performance prediction using a deep neural network (DNN) to evaluate the performance of the RIS-aided system in the low-frequency range. This would provide a greater influence of scatterers with a weaker signal attenuation allowing the neural network to pick up a larger number of features, e.g. accurately predicting the energy efficiency (EE), and outage probability (OP).

Матрица Гeрица является альтернативой скобке Кауффмана и, кроме того, позволяет быстрее вычислять многочлен Джонса при некотором минимальном выборе шахматной раскраски, построенной по зацеплению. Вводится модификация метода Гeрица, обобщающая матрицу Гeрица для вычисления полиномов ХОМФЛИ-ПТ при любых $N$ в частном случае бипартитных зацеплений. Метод сводится к чисто алгебраическим операциям над матрицами, поэтому его легко можно реализовать в виде компьютерной программы. Бипартитные зацепления образуют довольно большое семейство, включающее особый класс зацеплений Монтезиноса, построенных из так называемых рациональных тэнглов. Продемонстрировано, как получить бипартитную диаграмму таких зацеплений и вычислить соответствующие полиномы ХОМФЛИ-ПТ с помощью разработанного обобщенного метода Гeрица.

Abstract Biofilm formation in Escherichia coli arises from regulatory programs that can diverge even among genetically identical cultures. Exploiting spontaneous replicate-to-replicate variation in E. coli K-12 MG1655, we mapped expression modules whose behavior tracks biofilm abundance across four genetic backgrounds: wild type; strain with deleted gene for hexuronate regulator UxuR Δ uxuR ; an uxuR translation-disrupted retaining locus-derived sRNAs (Δ uxuR -tr), and strain with deleted gene for global carbon regulator cAMP-CRP (Δ crp ). In the wild type, regulator EcpR/MatA demonstrated the highest correlation with the biofilm intensity, and its role was, in particular, seemingly reinforced by stress/pH-homeostasis and c-di-GMP-linked factors. Δ uxuR exhibited the strongest stochasticity in biofilm formation, while in Δ uxuR -tr, replicate dispersion was mostly muted, indicating that uxuR -derived sRNAs buffer motility-adhesion switching. In Δ crp , pgaA was de-repressed due to the absence of CsrA, with expression being highly consistent with intensity of biofilm formation, alongside stress/ion-homeostasis genes. This is in line with the suggestion that CRP regulates biofilms and motility indirectly via regulation of more local transcription factors. Overall, replicate-resolved clustering converts apparent “noise” into structured regulatory patterns, which include genes whose role in biofilm formation was not yet evident, and helps identify switch nodes between planktonic and biofilm bacterial states.

We present a family of matrix models such that their partition functions are tau functions of the universal character (UC) hierarchy. We find new matrix models associated with the product of two spheres with embedded graphs via a gluing matrix. We also generalize these studies to the multi-matrix model case, which corresponds to the multi-component UC hierarchy.