New alphabet-dependent morphological transition in a random RNA alignment

We study the fraction $f$ of nucleotides involved in the formation of a cactus--like secondary structure of random heteropolymer RNA--like molecules. In the low--temperature limit we study this fraction as a function of the number $c$ of different nucleotide species. We show, that with changing $c$, the secondary structures of random RNAs undergo a morphological transition: $f(c)\to 1$ for $c \le c_{\rm cr}$ as the chain length $n$ goes to infinity, signaling the formation of a virtually "perfect" gapless secondary structure; while $f(c)c_{\rm cr}$, what means that a non-perfect structure with gaps is formed. The strict upper and lower bounds $2 \le c_{\rm cr} \le 4$ are proven, and the numerical evidence for $c_{\rm cr}$ is presented. The relevance of the transition from the evolutional point of view is discussed.Comment: 4 pages, 3 figures (title is changed, text is essentially reworked), accepted in PR

Necklace-Cloverleaf Transition in Associating RNA-like Diblock Copolymers

We consider a ${\rm A}_m{\rm B}_n$ diblock copolymer, whose links are capable of forming local reversible bonds with each other. We assume that the resulting structure of the bonds is RNA--like, i.e. topologically isomorphic to a tree. We show that, depending on the relative strengths of A--A, A--B and B--B contacts, such a polymer can be in one of two different states. Namely, if a self--association is preferable (i.e., A--A and B--B bonds are comparatively stronger than A--B contacts) then the polymer forms a typical randomly branched cloverleaf structure. On the contrary, if alternating association is preferable (i.e. A--B bonds are stronger than A--A and B--B contacts) then the polymer tends to form a generally linear necklace structure (with, probably, some rear side branches and loops, which do not influence the overall characteristics of the chain). The transition between cloverleaf and necklace states is studied in details and it is shown that it is a 2nd order phase transition.Comment: 17 pages, 9 figure

Thermodynamics and Topology of Disordered Systems: Statistics of the Random Knot Diagrams on Finite Lattice

The statistical properties of random lattice knots, the topology of which is determined by the algebraic topological Jones-Kauffman invariants was studied by analytical and numerical methods. The Kauffman polynomial invariant of a random knot diagram was represented by a partition function of the Potts model with a random configuration of ferro- and antiferromagnetic bonds, which allowed the probability distribution of the random dense knots on a flat square lattice over topological classes to be studied. A topological class is characterized by the highest power of the Kauffman polynomial invariant and interpreted as the free energy of a q-component Potts spin system for q->infinity. It is shown that the highest power of the Kauffman invariant is correlated with the minimum energy of the corresponding Potts spin system. The probability of the lattice knot distribution over topological classes was studied by the method of transfer matrices, depending on the type of local junctions and the size of the flat knot diagram. The obtained results are compared to the probability distribution of the minimum energy of a Potts system with random ferro- and antiferromagnetic bonds.Comment: 37 pages, latex-revtex (new version: misprints removed, references added

Radiation-induced hydrogen transfer in metals

The paper presents processes of hydrogen (deuterium) diffusion and release from hydrogen-saturated condensed matters in atomic, molecular and ionized states under the influence of the electron beam and X-ray radiation in the pre-threshold region. The dependence is described between the hydrogen isotope release intensity and the current density and the electron beam energy affecting sample, hydrogen concentration in the material volume and time of radiation exposure to the sample. The energy distribution of the emitted positive ions of hydrogen isotopes is investigated herein. Mechanisms of radiation-induced hydrogen transfer in condensed matters are suggested

Nucleon-nucleon interaction in the JJ-matrix inverse scattering approach and few-nucleon systems

The nucleon-nucleon interaction is constructed by means of the $J$-matrix version of inverse scattering theory. Ambiguities of the interaction are eliminated by postulating tridiagonal and quasi-tridiagonal forms of the potential matrix in the oscillator basis in uncoupled and coupled waves, respectively. The obtained interaction is very accurate in reproducing the $NN$ scattering data and deuteron properties. The interaction is used in the no-core shell model calculations of $^3$H and $^4$He nuclei. The resulting binding energies of $^3$H and $^4$He are very close to experimental values.Comment: Text is revised, new figures and references adde

NN potentials from inverse scattering in the J-matrix approach

An approximate inverse scattering method [7,8] has been used to construct separable potentials with the Laguerre form factors. As an application, we invert the phase shifts of proton-proton in the $^1S_0$ and $^3P_2-^3F_2$ channels and neutron-proton in the $^3S_1-^3D_1$ channel elastic scattering. In the latter case the deuteron wave function of a realistic $np$ potential was used as input.Comment: LaTex2e, 17 pages, 3 Postscript figures; corrected typo

Reassessment of disease severity routine laboratory tests in the COVID-19 infection

Introduction. Publications demonstrate some limitations of National Early Warning Score 2 (NEWS-2) accuracy in assessment on coronavirus infection severity.The purpose of this study was to determine the value of the patient’s age and routine laboratory parameters in the assessment of patient’s general condition in coronavirus pneumonia and their relation to NEWS-2 scale parameters.Materials and methods. 50 case reports of patients with COVID-19 infection observed in the Sechenov University in January–March 2021 were analyzed. 34 % of patients were males aged 31 to 89 years (average age 55 years) and 66 % — females aged 40 to 91 (mean age 63). The diagnosis of pneumonia was confirmed by computed tomography. NEWS-2 scale total score was assessed.Results. According to the physician’s subjective assessment the condition was significantly more often assessed as moderate and severe. There was only a weak correlation between the blood oxygen saturation and the total NEWS-2 score (r = 0.165, α = 0.1). We found a mild correlation (r = 0.341, α = 0.1) between the patient’s age and NEWS2 score. Among the most significantly interrelated parameters were age, neutrophil count, serum creatinine, CRP, fibrinogen level. Seven interrelated parameters (age, body temperature, blood oxygen saturation, the neutrophils count, creatinine, CRP, fibrinogen), for which a reliable relation with other tests has been shown, were assigned with its special index according to their contribution to the assessment of the overall condition severity. An aggregated score (criterion X) was proposed for assessment of disease severity according to equation. The proportions of mild, moderate, and severe cases according to criterion X were 12 %, 64 % and 24 %.Conclusion. The preliminary results obtained in the study emphasize the importance of routine laboratory tests in assessment of coronavirus infection severity. An evident discrepancy between NEWS-2 score and X criterion may be very important for practice

Critical exponents for random knots

The size of a zero thickness (no excluded volume) polymer ring is shown to scale with chain length $N$ in the same way as the size of the excluded volume (self-avoiding) linear polymer, as $N^{\nu}$, where $\nu \approx 0.588$. The consequences of that fact are examined, including sizes of trivial and non-trivial knots.Comment: 4 pages, 0 figure