Signum Function Method for Generation of Correlated Dichotomic Chains

We analyze the signum-generation method for creating random dichotomic sequences with prescribed correlation properties. The method is based on a binary mapping of the convolution of continuous random numbers with some function originated from the Fourier transform of a binary correlator. The goal of our study is to reveal conditions under which one can construct binary sequences with a given pair correlator. Our results can be used in the construction of superlattices and waveguides with selective transport properties.Comment: 14 pages, 7 figure

The evaluation of approaches to the treatment of myasthenia gravis.

Myasthenia gravis is a relatively rare autoimmune disease with an undetermined aetiology which affects neuromuscular junctions. Currently, the following approaches to the treatment of myasthenia gravis are mainly distinguished: symptomatic treatment with anticholinesterase inhibitors (AChEIs), immunomodulatory therapy (“basic” therapy) with glucocorticoids, cytostatics, monoclonal antibodies; surgical treatment — thymectomy; short-term treatment with plasmapheresis and intravenous administration of immuno­globulin. The efficiency of treatment approaches to myasthenia gravis in Ukraine remains insufficiently studied. The purpose of this work is to analyse the therapeutic approaches in patients with myasthenia gravis depending on the clinical form and severity of the disease. Between 2014 and 2017, 182 patients with myasthenia gravis have been examined, out of which 147 (80.8%) were the patients with the generalized form of the disease and 35 (19.2%) — with its ocular form. The clinical neurological examination included the collection of complaints, an anamnesis of disease and life as well as a neurological examination. In all the patients, the level of antibodies to acetylcholine receptors (AchR) and to muscle-specific tyrosine kinase (MuSK) has been measured, in terms of quantity as well, using the enzyme-linked immunosorbent assay (ELISA), and the presence of antibodies to titin and SOX1 has also been detected by means of indirect immunofluorescence. Of the total sample, less than a third (28.0%) of the patients examined received basic therapy; among them, there were no patients with the ocular form and only 34.7% — with the generalized form (p<0.001). Basic therapy is found more often among the patients with class II myasthenia gravis (51.9%), with a statistically significant (p<0.001) higher share of the patients receiving such a therapy than in classes III and IV (26.6% and 22.6% respectively). The structure of therapy in patients with classes III and IV has not shown any statistically significant difference (p=0.658), with symptomatic treatment being the predominant type of therapy. Undergoing basic therapy reduces the chances of a severe clinical course of myasthenia gravis (the QMG score of 17 and higher) — OR=0.52 (95.0% CI 0.14-0.90), p=0.032; fatal cases of the disease — OR=0.36 (95.0% CI 0.02-0.70), p=0.049. When basic therapy is used, the survival rate of the patients (Figure 2) is 42.0 years on average (95% CI 42.0-42.7) which is considerably higher (p=0.021) compared to that of the patients receiving symptomatic treatment only — 33.0 years (95% CI 30.9-36.7). Immunomodulatory therapy was prescribed for only 28% of the patients in the total sample, for none of the patients with the ocular form of myasthenia gravis, and for 34.7% of the patients with the generalized myasthenia gravis. The prescription of immunomodulatory therapy reduces relative risks of a severe clinical course of myasthenia gravis — OR=0.52 (95.0% CI 0.14-0.90), p=0.032. The prescription of immunomo­dulatory therapy decreases the probability of a fatal outcome of the disease — OR=0.36 (95.0% CI 0.02-0.70), p=0.049). With the use of immunomodulatory therapy, the patient survival rate rises considerably reaching an average of 42.0 years (95% CI 42.0-42.7), which is much higher compared to that in the group of the patients receiving symptomatic treatment only — 33.0 years (95% CI 30.9-36.7), p=0.021

Critical curves in conformally invariant statistical systems

We consider critical curves -- conformally invariant curves that appear at critical points of two-dimensional statistical mechanical systems. We show how to describe these curves in terms of the Coulomb gas formalism of conformal field theory (CFT). We also provide links between this description and the stochastic (Schramm-) Loewner evolution (SLE). The connection appears in the long-time limit of stochastic evolution of various SLE observables related to CFT primary fields. We show how the multifractal spectrum of harmonic measure and other fractal characteristics of critical curves can be obtained.Comment: Published versio

Numerical simulation of mesomechanical behavior of porous brittle materials

The influence of the types of porous structure on the features of deformation, damage accumulation and fracture of mesovolumes of brittle materials is studied. At the mesoscale, the pores of different shape are taken into account explicitly. The digital models were made using random values of coordinates and radii of spherical voids or solid spheres. For numerical modeling of the mechanical behavior up to failure, the evolutionary approach is applied with considering the nonlinear constitutive equations to describe damage accumulation and its influence on the degradation of the strength properties of the frame of porous ceramics. The calculated averaged stress-strain diagrams were shown to be sensitive not only to the value of porosity but also to the shape of pores. The simulation results are validated with experimental data for zirconia and alumina ceramics. Good qualitative and quantitative agreement of modeling results with experimental data suggests that taking into account of two-scale porosity in the form of explicit consideration of large pores at the mesoscale and implicit integrated consideration of tiny pores and cracks from the microscale in the form of accumulated damage is quite sufficient in the framework of the hierarchical modeling

Search For Companions Of Nearby Isolated Galaxies

The radial velocities are measured for 45 galaxies located in the neighborhoods of 29 likely isolated galaxies in a new catalog. We find that about 85% of these galaxies actually are well isolated objects. 4% of nearby galaxies with V_LG<3500 km/s are this kind of cosmic "orphan".Comment: 7 pages, 2 figure

Off-Critical SLE(2) and SLE(4): a Field Theory Approach

Using their relationship with the free boson and the free symplectic fermion, we study the off-critical perturbation of SLE(4) and SLE(2) obtained by adding a mass term to the action. We compute the off-critical statistics of the source in the Loewner equation describing the two dimensional interfaces. In these two cases we show that ratios of massive by massless partition functions, expressible as ratios of regularised determinants of massive and massless Laplacians, are (local) martingales for the massless interfaces. The off-critical drifts in the stochastic source of the Loewner equation are proportional to the logarithmic derivative of these ratios. We also show that massive correlation functions are (local) martingales for the massive interfaces. In the case of massive SLE(4), we use this property to prove a factorisation of the free boson measure.Comment: 30 pages, 1 figures, Published versio

Temperature-dependent magnetospectroscopy of HgTe quantum wells

We report on magnetospectroscopy of HgTe quantum wells in magnetic fields up to 45 T in temperature range from 4.2 K up to 185 K. We observe intra- and inter-band transitions from zero-mode Landau levels, which split from the bottom conduction and upper valence subbands, and merge under the applied magnetic field. To describe experimental results, realistic temperature-dependent calculations of Landau levels have been performed. We show that although our samples are topological insulators at low temperatures only, the signature of such phase persists in optical transitions at high temperatures and high magnetic fields. Our results demonstrate that temperature-dependent magnetospectroscopy is a powerful tool to discriminate trivial and topological insulator phases in HgTe quantum wells