Formal concept analysis for evaluating intrinsic dimension of a natural language

Some results of a computational experiment for determining the intrinsic dimension of linguistic varieties for the Bengali and Russian languages are presented. At the same time, both sets of words and sets of bigrams in these languages were considered separately. The method used to solve this problem was based on formal concept analysis algorithms. It was found that the intrinsic dimensions of these languages are significantly less than the dimensions used in popular neural network models in natural language processing.Comment: Preprint, 10th International Conference on Pattern Recognition and Machine Intelligence (PReMI 2023

On the origin of the dressing phase in N=4 Super Yang-Mills

We derive the phase factor proposed by Beisert, Eden and Staudacher for the S-matrix of planar N=4 Super Yang-Mills, from the all-loop Bethe ansatz equations without the dressing factor. We identify a configuration of the Bethe roots, from which the closed integral formula of the phase factor is reproduced in the thermodynamic limit. This suggests that our configuration describes the ``physical vacuum'' in the sense that the dressing phase is nothing but the effective phase for the scattering of fundamental excitations above this vacuum, providing an interesting clue to the physical origin of the dressing phase.Comment: 8 pages, no figures; (v2) comments and references added; (v3) changes in presentation and titl

Molecular Interactions behind the Self-Assembly and Microstructure of Mixed Sterol Organogels

In this work, we have employed docking and atomistic molecular dynamics (MD) simulations supported by complementary experiments using atomic force microscopy, rheology and spectroscopy to investigate the self-assembled structure of β-sitosterol and γ-oryzanol molecules into cylindrical tubules in a non-aqueous solvent. Docking models of several phytosterols, including sitosterol, with oryzanol and other sterol-esters demonstrate that for systems to form tubules, the phytosterol sterane group must be stacked in a wedge shape with the esters sterane group, and a hydrogen bond must form between the hydroxyl group of the phytosterol and the carbonyl group of the ester. Molecular dynamics of the self-assembled structure were initiated with the molecules in a roughly cylindrical configuration, as suggested from previous experimental studies, and the configurations were found to be stable during 50 ns simulations. We performed MD simulations of two tubules in proximity to better understand the aggregation of these fibrils and how the fibrils interact in order to stick together. We found that an interfibril network of non-covalent bonds, in particular van der Waals and π-π contacts, which is formed between the ferulic acid groups of oryzanol through the hydroxyl, methoxy and aromatic groups, is responsible for the surface-to-surface interactions between fibrils; an observation supported by molecular spectroscopy. We believe these interactions are of primary importance in creating a strong organogel network

Changes in the electrical and viscoelastic parameters of erythrocytes in patients with manifestations of metabolic syndrome, COVID-19 convalescents, when exposed to citicoline in an in vitro experiment

Aim. To study changes in the electrical and viscoelastic parameters of erythrocytes using the method of dielectrophoresis in patients with manifestations of the metabolic syndrome who underwent COVID-19, when exposed to the drug citicoline in an in vitro experiment to reduce the severity of microcirculatory disorders. Materials and methods. 31 men were examined with manifestations of metabolic syndrome (50.6±9.9 years), COVID-19 convalescences, within 8 to 12 months after the disease, the diagnosis was confirmed by PCR, ELISA. The electrical and viscoelastic parameters of erythrocytes were studied by dielectrophoresis twice: the initial levels of indicators were determined and after 30 minutes of exposure with after 30 minutes of exposure to a solution of the drug Ronocyte (oral solution with the active substance citicoline sodium – 104.50 mg., which is equivalent to 100.00 mg citicoline at a concentration of 0.01 µl per 0.3 µl of red blood cell suspension in 0.3M sucrose solution (pH 7.36). Results. Exposure of erythrocyte suspension of patients with Ronocyte solution led to change in the levels of electrical, viscoelastic parameters: an increase in the average cell diameter (p=0.0003), the proportion of discocytes (p=0.0004), the amplitude of cell deformation at high frequencies of the electric field (p=0.000002), cell capacity (p=0.000007), the velocity of erythrocytes to the electrodes (p=0.003), dipole moment (p=0.002), polarizability at 106 and 0.5×106 Hz (p=0.000019 and p=0.0015, respectively), relative polarizability (p0.05) and, conversely, to reduce summarized rigidity (p=0.000003), viscosity (p=0.000002), electrical conductivity (p0.000001), aggregation indices (p=0.00003), destruction at frequencies of 106 Hz (p=0.003), 0.5x106 Hz (p=0.00002), 0.1×106 Hz (p0.00001), polarizability at low frequencies of the electric field (p=0.02). Under the influence of the drug, the equilibrium frequency of erythrocytes shifted to the low-frequency range compared to the initial values (p0.0000001). The revealed changes indicate an increase in the surface charge of erythrocytes, their ability to deform, and cell resistance under the action of citicoline. Conclusion. For the first time, the effect of the drug with the active substance citicoline, improving the rheological properties of erythrocytes, was discovered. Preparations with the active substance - citicoline should be considered promising for conducting a full-fledged clinical study to study the reduction of circulatory disorders at the microcirculatory level in patients with manifestations of metabolic syndrome who have undergone COVID-19 coronavirus infection

In situ Raman studies of single-walled carbon nanotubes grown by local catalyst heating

Using in situ Raman spectroscopy we investigate single wall carbon nanotube growth on Mo electrodes,using a highly localized resistive heating technique. Small diameter semiconducting single wall nanotubesgrow very rapidly when the catalyst support is heated to a temperature of 800 C. The G/D ratioshows an interesting time-dependent behaviour. It first decreases, indicating the presence of amorphouscarbon and then significantly increases again after ca. 5 min growth while retaining the position andshape expected for predominantly semiconducting carbon nanotubes

Finite-gap equations for strings on AdS_3 x S^3 x T^4 with mixed 3-form flux

We study superstrings on AdS_3 x S^3 x T^4 supported by a combination of Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz three form fluxes, and construct a set of finite-gap equations that describe the classical string spectrum. Using the recently proposed all-loop S-matrix we write down the all-loop Bethe ansatz equations for the massive sector. In the thermodynamic limit the Bethe ansatz reproduces the finite-gap equations. As part of this derivation we propose expressions for the leading order dressing phases. These phases differ from the well-known Arutyunov-Frolov-Staudacher phase that appears in the pure Ramond-Ramond case. We also consider the one-loop quantization of the algebraic curve and determine the one-loop corrections to the dressing phases. Finally we consider some classical string solutions including finite size giant magnons and circular strings.Comment: 44 pages, 3 figures. v2: references and a discussion about perturbative results adde

The Bethe ansatz approach for factorizable centrally extended S-matrices

We consider the Bethe ansatz solution of integrable models interacting through factorized $S$-matrices based on the central extention of the $\bf{su}(2|2)$ symmetry. The respective $\bf{su}(2|2)$ $R$-matrix is explicitly related to that of the covering Hubbard model through a spectral parameter dependent transformation. This mapping allows us to diagonalize inhomogeneous transfer matrices whose statistical weights are given in terms of $\bf{su}(2|2)$ $S$-matrices by the algebraic Bethe ansatz. As a consequence of that we derive the quantization condition on the circle for the asymptotic momenta of particles scattering by the $\bf{su}(2|2) \otimes \bf{su}(2|2)$ $S$-matrix. The result for the quantization rule may be of relevance in the study of the energy spectrum of the $AdS_5 \times S^{5}$ string sigma model in the thermodynamic limit. \Comment: 22 pages, published versio

Review of AdS/CFT Integrability, Chapter III.2: Exact world-sheet S-matrix

We review the derivation of the S-matrix for planar N=4 supersymmetric Yang-Mills theory and type IIB superstring theory on an AdS5xS5 background. After deriving the S-matrix for the su(2) and su(3) sectors at the one-loop level based on coordinate Bethe ansatz, we show how su(2|2) symmetry leads to the exact asymptotic S-matrix up to an overall scalar function. We then briefly review the spectrum of bound states by relating these states to simple poles of the S-matrix. Finally, we review the derivation of the asymptotic Bethe equations, which can be used to determine the asymptotic multiparticle spectrum.Comment: 20 pages, see also overview article arXiv:1012.3982, v2: references to other chapters updated, v3: references added and minor change