Strict derivation of angular-averaged Ewald potential

In this work we strictly derive an angular-averaged Ewald potential suitable for numerical simulations of disordered Coulomb systems. The potential was first introduced by E. Yakub and C. Ronchi without strict mathematical justification. Two methods are used to find the coefficients of the series expansion of the potential: based on the Euler-Maclaurin and Poisson summation formulas. The expressions for each coefficient is represented as a finite series containing derivatives of Jacobi theta functions. We also demonstrate the formal equivalence of the Poisson and Euler-Maclaurin summation formulas in the three-dimensional case. The effectiveness of the angular-averaged Ewald potential is shown by the example of calculating the Madelung constant for a number of crystal lattices

Pressure of Coulomb systems with volume-dependent long-range potentials

In this work, we consider the pressure of Coulomb systems, in which particles interact via a volume-dependent potential (in particular, the Ewald potential). We confirm that the expression for virial pressure should be corrected in this case. We show that the corrected virial pressure coincides with the formula obtained by differentiation of free energy if the potential energy is a homogeneous function of particle coordinates and a cell length. As a consequence, we find out that the expression for pressure in the recent paper by J. Liang \textit{et al.} [\href{https://doi.org/10.1063/5.0107140}{J. Chem. Phys. \textbf{157}, 144102 (2022)}] is incorrect

Эпигенетические аспекты реабилитации онкогинекологических больных

The influence of epigenetic processes on the development of malignant diseases, including gynaecological cancers, is now beyond doubt. DNA methylation, histone modification and post-transcriptional regulation by microRNAs lead to changes in the activity of various genes, contributing to female genital cancers (cervix, endometrium, ovarian). It should be noted that disruptions in gene expression do not only occur in malignant cells, but also in the tumour microenvironment, resulting in disease progression and relapse. However, “epigenetic markers” of carcinogenesis can be useful in the treatment and rehabilitation of patients, making a personalized approach possible.На сегодняшний день влияние эпигенетических процессов на развитие злокачественных заболеваний, включая онкогинекологические, не вызывает сомнений. Метилирование ДНК, модификация гистонов и посттранскрипционная регуляция при помощи микроРНК приводят к изменению активности различных генов, способствуя возникновению рака женских половых органов (шейки матки, эндометрия, яичников). Следует отметить, что нарушения в экспрессии генов появляются не только в злокачественных клетках, но и в микроокружении опухоли, обусловливая прогрессирование и рецидив заболевания. Однако «эпигенетические метки» канцерогенеза могут быть полезными в лечении и реабилитации пациенток, делая возможным применение персонифицированного подхода

Spin physics with antiprotons

New possibilities arising from the availability at GSI of antiproton beams, possibly polarised, are discussed. The investigation of the nucleon structure can be boosted by accessing in Drell-Yan processes experimental asymmetries related to cross-sections in which the parton distribution functions (PDF) only appear, without any contribution from fragmentation functions; such processes are not affected by the chiral suppression of the transversity function $h_1(x)$. Spin asymmetries in hyperon production and Single Spin Asymmetries are discussed as well, together with further items like electric and magnetic nucleonic form factors and open charm production. Counting rates estimations are provided for each physical case. The sketch of a possible experimental apparatus is proposed.Comment: Presented for the proceedings of ASI "Spin and Symmetry", Prague, July 5-10, 2004, to be published in Czech. J. Phys. 55 (2005

Перспективы этиопатогенетического лечения болезни Гентингтона

Huntington’s disease is a serious inherited neurodegenerative disorder characterized by of motor, cognitive and psychiatric features. The disease is caused by an abnormally expanded CAG repeat expansion in the HTT gene and the production of mutant huntingtin protein.The disease usually manifests in adulthood, but the manifestation in childhood and youth is also described, which is noted in 5–10 % of cases. The disease predominantly affects the neostriatum, resulting in a characteristic clinical picture.The most promising approaches to etiotropic therapy of Huntington’s disease are a number of DNA- (CRISPR/Cas9 system) and RNA-directed methods (antisense oligonucleotides, RNA interference), methods that directly reduce the level of mutant gentingtin (chimera molecules), as well as approaches based on inactivating the DNA mismatch repair system using the FAN1 enzyme. Болезнь Гентингтона – тяжелое наследственное нейродегенеративное заболевание, характеризующееся развитием двигательных, когнитивных и психических нарушений. Заболевание обусловлено увеличением числа тринуклео‑ тидных CAG-повторов в гене HTT и продукцией мутантного белка гентингтина, обычно проявляется во взрослом возрасте, но в 5–10 % случаев описана также манифестация в детском и юношеском возрасте. Болезнь Гентингто‑ на преимущественно затрагивает неостриатум, что вызывает характерную клиническую картину. Наиболее перспективными подходами к этиотропной терапии болезни Гентингтона являются ряд ДНК- (CRISPR/Cas9-сис‑ тема) и РНК-направленных методов (антисмысловые олигонуклеотиды, РНК-интерференция), методы, непосредственно снижающие уровень мутантного гентингтина (молекулы-химеры), а также подходы, основанные на инактивации си‑ стемы восстановления несоответствия ДНК с использованием фермента FAN1.

Advances in low-memory subgradient optimization

One of the main goals in the development of non-smooth optimization is to cope with high dimensional problems by decomposition, duality or Lagrangian relaxation which greatly reduces the number of variables at the cost of worsening differentiability of objective or constraints. Small or medium dimensionality of resulting non-smooth problems allows to use bundle-type algorithms to achieve higher rates of convergence and obtain higher accuracy, which of course came at the cost of additional memory requirements, typically of the order of n2, where n is the number of variables of non-smooth problem. However with the rapid development of more and more sophisticated models in industry, economy, finance, et all such memory requirements are becoming too hard to satisfy. It raised the interest in subgradient-based low-memory algorithms and later developments in this area significantly improved over their early variants still preserving O(n) memory requirements. To review these developments this chapter is devoted to the black-box subgradient algorithms with the minimal requirements for the storage of auxiliary results, which are necessary to execute these algorithms. To provide historical perspective this survey starts with the original result of N.Z. Shor which opened this field with the application to the classical transportation problem. The theoretical complexity bounds for smooth and non-smooth convex and quasi-convex optimization problems are briefly exposed in what follows to introduce to the relevant fundamentals of non-smooth optimization. Special attention in this section is given to the adaptive step-size policy which aims to attain lowest complexity bounds. Unfortunately the non-differentiability of objective function in convex optimization essentially slows down the theoretical low bounds for the rate of convergence in subgradient optimization compared to the smooth case but there are different modern techniques that allow to solve non-smooth convex optimization problems faster then dictate lower complexity bounds. In this work the particular attention is given to Nesterov smoothing technique, Nesterov Universal approach, and Legendre (saddle point) representation approach. The new results on Universal Mirror Prox algorithms represent the original parts of the survey. To demonstrate application of non-smooth convex optimization algorithms for solution of huge-scale extremal problems we consider convex optimization problems with non-smooth functional constraints and propose two adaptive Mirror Descent methods. The first method is of primal-dual variety and proved to be optimal in terms of lower oracle bounds for the class of Lipschitz-continuous convex objective and constraints. The advantages of application of this method to sparse Truss Topology Design problem are discussed in certain details. The second method can be applied for solution of convex and quasi-convex optimization problems and is optimal in a sense of complexity bounds. The conclusion part of the survey contains the important references that characterize recent developments of non-smooth convex optimization

ОСОБЕННОСТИ ФОРМИРОВАНИЯ МЕДНОГО ОСАДКА В ПОРАХ ДИОКСИДА КРЕМНИЯ

Using the SiO2 porous templates on silicon substrate, Si/SiO2(Cu) nanostructures have been synthesized by electrochemical method. A comprehensive study by means of scanning electron, transmission electron, atomic force microscopy and diffraction analysis techniques have been conducted. The morphological features and the lateral dimensions of metal nanostructures, deposited in the pores, have been defined. A tendency to form copper agglomerates with dendritic shape have been shown. This structures are promising for using as catalyst or substrates for SERS.С использованием SiO2-пористых шаблонов на кремниевой подложке электрохимическим методом синтезированы наноструктуры Si/SiO2(Cu). Проведено их всестороннее изучение посредством электронной сканирующей, электронной просвечивающей, атомно-силовой микроскопии и дифракционных методов анализа. Определены морфологические особенности и латеральные размеры металлического осадка в порах. Показана тенденция к образованию агломератов меди дендритной формы, что указывает на перспективность использования таких структур при катализе и в спектроскопии гигантского комбинационного рассеяния света

ЗАВИСИМОСТЬ СИГНАЛА ГИГАНТСКОГО КОМБИНАЦИОННОГО РАССЕЯНИЯ СВЕТА ОТ ФОРМЫ СЕРЕБРЯНЫХ НАНОСТРУКТУР, ВЫРАЩЕННЫХ В ПОРАХ SiO2 /n-Si-ШАБЛОНА

Surface-enhanced Raman scattering is a powerful method used in chemoand biosensorics. The aim of this work was to determine the relationship between the signal of Surface-enhanced Raman scattering and the shape of silver nanostructures under the influence of laser radiation with different power.Plasmonic nanostructures were synthesized in silicon dioxide pores on monocrystalline silicon n-type substrate. The pores were formed using ion-track technology and selective chemical etching. Silver deposition was carried out by galvanic displacement method. Synthesis time was chosen as a parameter that allows controlling the shape of a silver deposit in the pores of silicon dioxide on the surface of single-crystal n-silicon during electrodeless deposition. Deposition time directly effects on the shape of metal nanostructures.Analysis of the dynamics of changing the morphology of the metal deposit showed that as the deposition time increases, the metal evolves from individual metallic crystallites within the pores at a short deposition time to dendritic-like nanostructures at a long time. The dependence of the intensity of Surface-enhanced Raman scattering spectra on the shape of the silver deposit is studied at the powers of a green laser (λ = 532 nm) from 2.5 μW to 150 μW on the model dye analyte Rodamin 6G. The optimum shape of the silver deposit and laser power is analyzed from this point of view design of active surfaces for Surface-enhanced Raman scattering with nondestructive control of small concentrations of substances.The silver nanostructures obtained in porous template SiO2 on n-type silicon substrate could be used as plasmon-active surfaces for nondestructive investigations of substances with low concentrations at low laser powers. Гигантское комбинационное рассеяние, усиленное поверхностью, является мощным методом, применяемым в хемо- и биосенсорике. Целью данной работы являлось определение взаимосвязи сигнала гигантского комбинационного рассеяния света с формой серебряных наноструктур при воздействии лазерного излучения с различной мощностью.Плазмонные наноструктуры синтезировались в порах диоксида кремния на подложке монокристаллического кремния n-типа, в котором поры формировались с использованием ионно-трековой технологии и селективного химического травления. Синтез серебра проводился методом безэлектродного осаждения. В качестве параметра, позволяющего управлять формой серебряного осадка в порах диоксида кремния на поверхности монокристаллического n-кремния при безэлектродном осаждении, выбрано время синтеза, которое непосредственно влияет на степень разрастания металлических наноструктур. Анализ динамики изменения морфологии металлического осадка показал, что при увеличении времени осаждения металл эволюционирует от отдельных металлических кристаллитов внутри пор при малых временах осаждения до дендритоподобных наноструктур при больших временах. Изучена зависимость интенсивности спектров гигантского комбинационного рассеяния света от формы серебряного осадка при мощностях зеленого лазера (λ = 532 нм) от 2,5 до 150 мкВт на модельном аналите Родамин 6Ж. Проведен анализ оптимальной формы серебряного осадка и мощности лазера с точки зрения последующего конструирования активных поверхностей для гигантского комбинационного рассеяния света при неразрушающем контроле малых концентраций веществ.Полученные серебряные наноструктуры в порах шаблона SiO2 на кремниевой подложке n-типа могут использоваться в качестве плазмонно-активных поверхностей при неразрушающем исследовании низких концентраций веществ на малых мощностях лазера.