УЧНЕЦЕНТРИЧНА МАН-РОБОТА: ВІД ЦІКАВОЇ ТЕМИ ДО ВІДТВОРЮВАНИХ РЕЗУЛЬТАТІВ (НА ПРИКЛАДАХ КОМБІНАТОРИКИ Й ТЕОРІЇ ГРАФІВ)

The crystal and molecular structure of the cobalt(II) and nickel(II) derivatives of dithioacetylacetone (sacsacH) have been determined by X-ray diffraction methods. Both crystals, being isomorphous, are orthorhombic, with space group Cmca and Z= 4. For Co(sacsac)2: a= 15·64(2), b= 14·35(2), and c= 6·05(1)Å; for Ni(sacsac)2: a= 15·592(6), b= 14·348(8), and c= 5·950(3)Å. The cobalt(II) structure was solved by conventional Patterson and Fourier methods and was refined by a least-squares method to R 0·11 for 437 independent reflections derived by photographic methods. For the nickel structure, 585 independent reflections, collected by counter methods, were used and the structure refined, by least squares, to R 0·044. The crystals are molecular with discrete monomeric molecular units of composition M (sacsac)2. Each metal atom, located a site of symmetry 2/m, is precisely coplanar with the four sulphur atoms bonded to it and, with an S–M–S intraligand bond angle of ca. 97°, the metal environment is conveniently described as square planar. However, the molecule as a whole is not planar being folded so that the dihedral angle between the MS4 and the ligand planes is ca. 6°. The metal–sulphur bond distance is ca. 2·17 Å.

The incidence of psychiatric disorders, such as post-traumatic stress disorder (PTSD), anxiety, and depression, has been steadily increasing, while current treatment approaches remain limited in efficacy. As a result, there is an urgent need to explore more effective therapeutic interventions. In recent years, MDMA (3,4- methylenedioxymethamphetamine)-assisted therapy (MDMA-AT) has emerged as a promising and innovative approach, demonstrating favorable clinical potential in the treatment of these disorders. Although preliminary studies have confirmed its therapeutic efficacy, a comprehensive and systematic analysis of the research trends and current limitations of MDMA-AT remains lacking. This study employed a bibliometric approach to systematically retrieve and analyze research literature published between 1994 and 2023 on the application of MDMA in the treatment of PTSD, anxiety, and depression. Relevant data were obtained from three prominent databases: Web of Science Core Collection, PubMed, and Scopus. VOSviewer and Microsoft Excel were used to perform visual and quantitative analyses, focusing on publication trends, research hotspots, prolific authors, leading institutions, and international collaboration networks. The findings indicated a substantial increase in MDMA-related research over the past decade. The United States has led the field in publication output, with the Multidisciplinary Association for Psychedelic Studies (MAPS) identified as the most productive institution. Key figures, such as Rick Doblin, have demonstrated high influence and centrality within the global research network. The research focus has gradually shifted from investigations of the neurotoxic properties of MDMA to explorations of its therapeutic mechanisms, safety profiles, and clinical applications. This study provides a comprehensive synthesis of the past thirty years of research on MDMA-AT in the treatment of PTSD, anxiety, and depression, identifying major research trajectories and critical challenges in the field. While current findings highlight the therapeutic promise of MDMA and its translational potential, further research is needed to improve trial design, enhance sample diversity, and evaluate long-term effects in order to support the standardization and evidence-based integration of MDMA- assisted therapy into clinical practice.

Propagation of linear constraints has become a crucial sub-routine in modern Mixed-Integer Programming (MIP) solvers. In practice, iterative algorithms with tolerance-based stopping criteria are used to avoid problems with slow or infinite convergence. However, these heuristic stopping criteria can pose difficulties for fairly comparing the efficiency of different implementations of iterative propagation algorithms in a real-world setting. Most significantly, the presence of unbounded variable domains in the problem formulation makes it difficult to quantify the relative size of reductions performed on them. In this work, we develop a method to measure - independently of the algorithmic design - the progress that a given iterative propagation procedure has made at a given point in time during its execution. Our measure makes it possible to study and better compare the behavior of bounds propagation algorithms for linear constraints. We apply the new measure to answer two questions of practical relevance: (i) We investigate to what extent heuristic stopping criteria can lead to premature termination on real-world MIP instances. (ii) We compare a GPU-parallel propagation algorithm against a sequential state-of-the-art implementation and show that the parallel version is even more competitive in a real-world setting than originally reported.

Sets and sequences are the fundamental objects of study in discrete mathematics, and this chapter provides a review of naïve set theory. Formulas for counting sequences, subsets, and permutations are developed, followed by an algorithmic method for counting when no formula applies (or is obvious). The final section looks at infinite sequences, particularly complexity functions of algorithms.KeywordsProblem InstanceError BoundCharacteristic SequenceProduct RuleInfinite SequenceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Introduction: Data transmission reliability analysis when using noise-immune coding in channels with grouping of errors (in particular, in radio channels with interference and fading of the received signals) is complicated by the need to use discrete data transmission channel models which take into account the error grouping, differing from the traditional binomial model. The complexity of the analytical description of such models leads to the fact that the quality indicators of data transmission over channels with error grouping are usually analyzed by simulation methods, and the development of analytical models of data transmission discrete channels with grouping of errors is one of the modern direction in the noise-immune coding theory development. Purpose: Finding the additive boundary of a bit error probability for data transmission discrete channel with grouping of symbol errors, described by Elliot — Hilbert model. Results: For the case of data transmission using a group noise-immune code, analytical expressions are obtained for calculating the additive boundary of a bit error probability in a discrete data transmission channel with grouping of symbol errors. The obtained expressions take into account the features of data transmission over a channel with error grouping, in particular, the fact that the probabilities of various combinations of the same number of errors are not equal to each other. Examples are presented of calculating a bit error probability for the case of using noise-immune codes which correct errors. It is shown that for any code length, the use of the Elliot — Hilbert model allows you to substantially refine the results of calculating the probabilistic indicators of the reliability of data transmission in channels with error grouping, as compared to the original binomial model. The obtained results are compared to the results of the simulation. Practical relevance: The results can be used in the design and analysis of the characteristics of data transmission systems for various purposes, operating under conditions of error grouping. Using analytical expressions to calculate the probability indicators of the reliability of data transfer allows you to abandon complex simulation modeling of transmitting data in channels with error grouping at the stage of choosing a noise-immune code and its parameters.