Systematic Enumeration Research Articles

A Contribution to the Flora of Udaipur Forests in Champaran District, North Bihar

The paper relates to a floristic account of Udaipur forests in Champaran District, North Bihar. The vegetation can be broadly classified as follows: Deciduous forest, Evergreen forest, Vegetation in plantation and open areas and Aquatic vegetation. A floristic analysis is presented and a systematic enumeration appended. The occurrence of Arnebia hispidissima DC. in Udaipur fotests constitutes a new record for Bihar state.

Flora of Sidhi District, Madhya Pradesh-II

Flora of Sidhi district, Madhya Pradesh based on the collections made during the 5 exploration tours conducted between l962 and 1971 is presented. A short account of the vegetatiot and its floristic composition along with other essential features of topography, climate, geology and soil are given in this paper. Systematic enumeration of about 680 species belonging to 417 genera under 103 families with keys to the taxa, reference citation, description and critical notes will be published in part II, which is under preparation. 8 species have been recorded for the first time from Madhya Pradesh.

The development of rbl-stem learning materials to improve students’ combinatorial thinking skill in solving local (a,d)-edge Antimagic coloring problems for Line Motif Batik Design

Combinatorial thinking is a problem-solving approach that involves analyzing and synthesizing different elements or possibilities to create new combinations or arrangements. It is a critical skill in various fields, including mathematics, computer science, biology, and optimization problems. Combinatorial thinking allows individuals to explore and understand the relationships between elements and discover novel solutions through systematic enumeration and manipulation. To develop students' combinatorial thinking skills, we need to support the learning process with learning materials of specific model and approach. In this study, we will develop RBL learning materials with a STEM approach to improve students' combinatorial thinking skills. We will use R&D (research and development) model for doing study of this research, namely Thiagarajan 4-D model. The developed learning materials met the criteria of being valid, effective and practical. The validity scores obtained for each material were 3.53 for RTM, 3.69 for LKM and 3.66 for THB. The observation results of learning implementation were 3.61 with a percentage of 90%, and the student responses were 3.75 with a percentage of 93.75 positive, so they met the practical criteria. Based on the test results, the researchers found that 82.75% of the students were complete so that they met the effective criteria.

Exploring the combinatorial explosion of amine–acid reaction space via graph editing

Amines and carboxylic acids are abundant chemical feedstocks that are nearly exclusively united via the amide coupling reaction. The disproportionate use of the amide coupling leaves a large section of unexplored reaction space between amines and acids: two of the most common chemical building blocks. Herein we conduct a thorough exploration of amine–acid reaction space via systematic enumeration of reactions involving a simple amine–carboxylic acid pair. This approach to chemical space exploration investigates the coarse and fine modulation of physicochemical properties and molecular shapes. With the invention of reaction methods becoming increasingly automated and bringing conceptual reactions into reality, our map provides an entirely new axis of chemical space exploration for rational property design.

Spatial predictors of immunotherapy response in triple-negative breast cancer

Immune checkpoint blockade (ICB) benefits some patients with triple-negative breast cancer, but what distinguishes responders from non-responders is unclear1. Because ICB targets cell–cell interactions2, we investigated the impact of multicellular spatial organization on response, and explored how ICB remodels the tumour microenvironment. We show that cell phenotype, activation state and spatial location are intimately linked, influence ICB effect and differ in sensitive versus resistant tumours early on-treatment. We used imaging mass cytometry3 to profile the in situ expression of 43 proteins in tumours from patients in a randomized trial of neoadjuvant ICB, sampled at three timepoints (baseline, n = 243; early on-treatment, n = 207; post-treatment, n = 210). Multivariate modelling showed that the fractions of proliferating CD8+TCF1+T cells and MHCII+ cancer cells were dominant predictors of response, followed by cancer–immune interactions with B cells and granzyme B+ T cells. On-treatment, responsive tumours contained abundant granzyme B+ T cells, whereas resistant tumours were characterized by CD15+ cancer cells. Response was best predicted by combining tissue features before and on-treatment, pointing to a role for early biopsies in guiding adaptive therapy. Our findings show that multicellular spatial organization is a major determinant of ICB effect and suggest that its systematic enumeration in situ could help realize precision immuno-oncology.

Some green algae of Ajodhya hills and forest area of Baghmundi (Purulia district, West Bengal)

Fresh water resources are depleting at a fast rate throughout the world affecting diverse aquatic flora and fauna. Algal flora responds to the adverse changes in habitat which is reflected by their morphotaxonomical deformation and occurrences of pollution tolerant taxa in the changed habitat. Based on the findings of more than five decades, it has been established that such taxa are labeled as bioindicator because of their pollution tolerance. Taking into account, these attributes; a systematic enumeration of phytoplanktons of all the five dams of Ajodhya hills viz. Upper dam, Lower dam, Marvel Lake, Kestobazar lake and Murguma dam was carried out. During the systematic investigations on morphotaxonomy of green algal flora of Ajodhya hills and forest area altogether 15 taxa of green algae were studied. These taxa belong to Volvocales, Chlorococcales and Zygnematales. These taxa come under the genera Eudorina, Gonium, Pandorina (Volvocales), Hydrodictyon, Pediastrum, Scenedesmus (Chlorococcales), Spirogyra, and Zygnema, (Zygnematales). Out of these members of Zygnematales were found to be abundant reflecting the optimum nutrient and atmospheric condition supporting their growth. The collections of algal samples were made periodically (during 2020 to 2022) and characteristic features were studied and identification was done based on standard literatures. However, the part of the Murguma dam which is affected by anthropogenic activity. The algal population showed the abundance of pollution tolerant taxa and the water quality of that particular part of dam showed organic pollution in physicochemical analysis of the water taken up during the studies.

Thematisch-systematisches Verzeichnis der musikalischen Werke von Johann Sebastian Bach ed. by Christine Blanken, Christoph Wolff, and Peter Wollny (review)

Reviewed by: Thematisch-systematisches Verzeichnis der musikalischen Werke von Johann Sebastian Bached. by Christine Blanken, Christoph Wolff, and Peter Wollny Daniel F. Boomhower Thematisch-systematisches Verzeichnis der musikalischen Werke von Johann Sebastian Bach. 3rded. Edited by Christine Blanken, Christoph Wolff, and Peter Wollny. Wiesbaden: Breitkopf & Härtel, 2022. [xliv, 835 p. ISBN 9783765104008 (hardback), €410.] Music examples, bibliography, index. The systematic enumeration of the musical output of individual, primarily European, composers has proven captivating and confounding for generations. While the utility of a logically arranged presentation of any repertory seems to make immediate sense, the method of organization itself has often proven a complication. The chronological presentation of compositions often does not offer space for new discoveries, as seen with Ludwig von Köchel's catalog of the works of Wolfgang Amadeus Mozart ( Chronologisch-thematisches Verzeichnis sämtlicher Tonwerke Wolf-gang Amadé Mozarts[Leipzig: Breitkopf und Härtel, 1862]), a reliable new edition of which has endured a protracted gestation. A more schematic approach, such as by genre, tends to yield rather opaque numbering schemes, as seen with Anthony van Hoboken's Joseph Haydn: Thematisch-bibliographisches Werkverzeichnis(Mainz: B. Schott's Söhne, 1957) and the Bach Compendium: Analytisch-bibliographisches Repertorium der Werke Johann Sebastian Bachsby Hans-Joachim Schulze and Christoph Wolff (Frankfurt: C. F. Peters, 1985; hereafter BC). The definition and operability of the concept of a musical work represents an equally significant challenge with consequences for scholars, performers, and audiences interested in the music of Johann Sebastian Bach. The compilers of this new third edition of the Bach Werke Verzeichnis(hereafter BWV 3) admirably address the challenges of concisely integrating vast expanses of knowledge about the corpus of Bach compositions while deftly navigating the pitfalls of this enterprise. The well-known and now firmly entrenched BWV numbering scheme, which originated with Wolfgang Schmieder's catalog of Bach's works, Thematisch-systematisches Verzeichnis der musikalischen Werke von Johann Sebastian Bach: Bach-Werke-Verzeichnis (BWV)(Leipzig: Breitkopf & Härtel, 1950; hereafter BWV 1), represents the first significant challenge of BWV 3. This ordering reflects the sequence in which the composer's music appeared in the edition prepared by the Bach Gesellschaft and published by Breitkopf & Härtel ( J. S. Bach Werke[Leipzig, 1851–99]; hereafter BG). In the BG, the ten sacred cantatas published in the first volume of the edition bear the designations "Cantata 1," Cantata 2," and so forth. Hence, "Wie schön leuchtet der Morgenstern" from March 1725 for the Feast of the Annunciation (Cantata 1) preceded "Ach Gott, vom Himmel sieh darein" from June 1724 for the [End Page 602]second Sunday after Trinity (Canata 2) and "Ach Gott, wie manches Herzeleid" from January 1725 for the second Sunday after Epiphany (Cantata 3). As seen in these examples, the BGordering relies neither on the chronology of the compositions nor their place in the liturgical calendar. BWV 1also applies numbers to instrumental works based on the order in which they appeared in BG. Moreover, the BGcreates a static, even monolithic, identity to compositions, informed in no small part by nineteenth-century interpretations of the religious and artistic conception of Bach's compositions, that remains at odds with the reality documented in the sources containing Bach's output. Attempts have arisen to develop more intuitive numerical references to the cantatas, including alphabetical order based on text (e.g., Carl Tamme, Thematisches Verzeichniss der Vokalwerke Joh. Seb. Bachs[Leipzig: C. F. Peters, 1889]) and the Lutheran liturgical calendar (e.g., J. S. Bach: Neue Ausgabe sämtlicher Werke (Neue Bach-Ausgabe), ed. Johann-Sebastian-Bach-Institut, Göttingen, and Bach-Archiv, Leipzig [Kassel: Bärenreiter, 1954–]; hereafter NBA). To their credit, the compilers of BWV 3have embraced the firmly entrenched numbering scheme and adapted it as gracefully as possible, differentiating the distinct compositional phases of, for instance, BWV 36 as: Weltliche Fassungen (Glückwunschkantate): 36.1 Schwingt freudig euch empor (1725) 36.2 Steigt freudig in die Luft (um 1725–26) 36.3 Die Freude reget sich (um 1737–1738) Geistliche Fassungen (Adventskantate): 36.4 Schwingt freudig euch empor (um 1726–1730) 36.5 Schwingt freudig euch empor (1731) Subsequent entries for...

Hilbert series, the Higgs mechanism, and HEFT

We expand Hilbert series technologies in effective field theory for the inclusion of massive particles, enabling, among other things, the enumeration of operator bases for non-linearly realized gauge theories. We find that the Higgs mechanism is manifest at the level of the Hilbert series, as expected for the partition function of an S-matrix that is subject to the Goldstone equivalence theorem. In addition to massive vectors, we detail how other massive, spinning particles can be studied with Hilbert series; in particular, we spell out the ingredients for massive gravity in general spacetime dimensions. Further methodology is introduced to enable Hilbert series to capture the effect of spurion fields acquiring vevs. We apply the techniques to the Higgs Effective Field Theory (HEFT), providing a systematic enumeration of its operator basis. This is achieved both from a direct and a custodial symmetry spurion-based approach; we compare and contrast the two approaches, and our results to those appearing in previous literature.

Models of configurationally-complex alloys made simple

We present a Python package for the efficient generation of special quasi-random structures (SQS) for atomic-scale calculations of disordered systems. Both, a Monte-Carlo approach or a systematic enumeration of structures can be used to carry out optimizations to ensure the best optimal configuration is found for given cell size and composition. We present a measure of randomness based on Warren-Cowley short-range order parameters allowing for fast analysis of atomic structures. Hence, optimal structures are found in a reasonable time for several dozens or even hundreds of atoms. Both SQS optimizations and analysis of structures can be carried out via a command-line interface or a Python API. Additional features, such as optimization towards partial ordering or independent sublattices allow the generation of atomistic models of modern complex materials. Moreover, hybrid parallelization, as well as distribution of vacancies, are supported. The output data format is compatible with ase, pymatgen and pyiron packages to be easily embeddable in complex simulation workflows. Program summaryProgram title: sqsgeneratorCPC Library link to program files:https://doi.org/10.17632/m2sb3wzcvc.1Developer's repository link:https://github.com/dgehringer/sqsgeneratorLicensing provisions: MITProgramming language: Python, C++Supplementary material:https://sqsgenerator.readthedocs.ioNature of problem: Many technological relevant materials, exhibit a crystalline disorder. Within atomistic modelling approaches such as Density Functional Theory (DFT) or Molecular Dynamics, disorder is modelled with a cell containing a (small) finite set of atoms. Such an atomic configuration is usually found by enumerating structures. However, since configurational space is growing exponentially efficient tools are needed to sample it properly.Solution method: Efficient quantification of disorder using a generalization of Warren-Cowley Short Range Order (WC-SRO) parameters [1,2]. By either a Monte-Carlo approach or systematic enumeration, optimal structures can be found. The software is distributed as a Python package offering a command line interface. Core parts are written in C++ and exhibit shared (OpenMP) and distributed (MPI) memory parallelism. For embedding into complex simulation workflows, the tool exposes a Python API to integrate into popular packages such as ase [3], pymatgen [4] or pyiron [5].

Using the Framework for Reporting Adaptations and Modifications-Expanded (FRAME) to study adaptations in lung cancer screening delivery in the Veterans Health Administration: a cohort study

BackgroundLung cancer screening is a complex clinical process that includes identification of eligible individuals, shared decision-making, tobacco cessation, and management of screening results. Adaptations to the delivery process for lung cancer screening in situ are understudied and underreported, with the potential loss of important considerations for improved implementation. The Framework for Reporting Adaptations and Modifications-Expanded (FRAME) allows for a systematic enumeration of adaptations to implementation of evidence-based practices. We applied FRAME to study adaptations in lung cancer screening delivery processes implemented by lung cancer screening programs in a Veterans Health Administration (VHA) Enterprise-Wide Initiative.MethodsWe prospectively conducted semi-structured interviews at baseline and 1-year intervals with lung cancer screening program navigators at 10 Veterans Affairs Medical Centers (VAMCs) between 2019 and 2021. Using this data, we developed baseline (1st) process maps for each program. In subsequent years (year 1 and year 2), each program navigator reviewed the process maps. Adaptations in screening processes were identified, documented, and mapped to FRAME categories.ResultsWe conducted a total of 16 interviews across 10 VHA lung cancer screening programs (n=6 in year 1, n=10 in year 2) to collect adaptations. In year 1 (2020), six programs were operational and eligible. Of these, three reported adaptations to their screening process that were planned or in response to COVID-19. In year 2 (2021), all 10 programs were operational and eligible. Programs reported 14 adaptations in year 2. These adaptations were planned and unplanned and often triggered by increased workload; 57% of year 2 adaptations were related to the identification and eligibility of Veterans and 43% were related to follow-up with Veterans for screening results. Throughout the 2 years, adaptations related to data management and patient tracking occurred in 60% of programs to improve the data collection and tracking of Veterans in the screening process.ConclusionsUsing FRAME, we found that adaptations occurred primarily in the areas of patient identification and communication of results due to increased workload. These findings highlight navigator time and resource considerations for sustainability and scalability of existing and future lung cancer screening programs as well as potential areas for future intervention.

An account of parasitic angiosperms of Purulia District, West Bengal

The present work is a systematic enumeration of parasitic angiosperm diversity of Purulia district, the western most part of West Bengal and last step of Chhotanagpur plateau. A total of 16 species of parasitic angiosperms under 13 genera and 5 families are so far recorded during the survey. Orobanchaceae with 6 species stand for the most dominant family followed by Santalaceae (4 spp), Loranthaceae (3 spp), Convolvuaceae (2 spp) and Lauraceae (1 sp). Habitat wise, 9 species are stem parasites and rest 7 species are root parasites among the 16 species of recorded parasitic plants. The flowering and fruiting time, host range and nature of parasitism are also recorded during the study.

Molecular Framework Analysis of the Generated Database GDB-13s.

The generated databases (GDBs) list billions of possible molecules from systematic enumeration following simple rules of chemical stability and synthetic feasibility. To assess the originality of GDB molecules, we compared their Bemis and Murcko molecular frameworks (MFs) with those in public databases. MFs result from molecules by converting all atoms to carbons, all bonds to single bonds, and removing terminal atoms iteratively until none remain. We compared GDB-13s (99,394,177 molecules up to 13 atoms containing simplified functional groups, 22,130 MFs) with ZINC (885,905,524 screening compounds, 1,016,597 MFs), PubChem50 (100,852,694 molecules up to 50 atoms, 1,530,189 MFs), and COCONUT (401,624 natural products, 42,734 MFs). While MFs in public databases mostly contained linker bonds and six-membered rings, GDB-13s MFs had diverse ring sizes and ring systems without linker bonds. Most GDB-13s MFs were exclusive to this database, and many were relatively simple, representing attractive targets for synthetic chemistry aiming at innovative molecules.

Systematic enumeration of two-level even-odd designs of strength 3

The first dedicated algorithm to enumerate even-odd designs of strength 3 is presented. Such designs cannot be constructed by folding over smaller designs, but they may permit simultaneous estimation of many more two-factor interactions than designs that can be constructed by folding over. In the algorithm, enumeration is restricted to the computationally convenient class of designs with at least one nonzero correlation between a two-factor and a three-factor interaction contrast vector. All such designs with up to 56 runs, all those with 64 runs and up to 13 factors, and a specific subclass of those with 64 runs and more than 13 factors have been enumerated.1 The best ranked 64-run designs substantially improve on benchmark designs from the literature.

RedDB, a computational database of electroactive molecules for aqueous redox flow batteries

An increasing number of electroactive compounds have recently been explored for their use in high-performance redox flow batteries for grid-scale energy storage. Given the vast and highly diverse chemical space of the candidate compounds, it is alluring to access their physicochemical properties in a speedy way. High-throughput virtual screening approaches, which use powerful combinatorial techniques for systematic enumerations of large virtual chemical libraries and respective property evaluations, are indispensable tools for an agile exploration of the designated chemical space. Herein, RedDB: a computational database that contains 31,618 molecules from two prominent classes of organic electroactive compounds, quinones and aza-aromatics, has been presented. RedDB incorporates miscellaneous physicochemical property information of the compounds that can potentially be employed as battery performance descriptors. RedDB’s development steps, including: (i) chemical library generation, (ii) molecular property prediction based on quantum chemical calculations, (iii) aqueous solubility prediction using machine learning, and (iv) data processing and database creation, have been described.

Systematic enumeration of definitive screening designs

Systematic enumeration of definitive screening designs

Low-resolution description of the conformational space for intrinsically disordered proteins

Intrinsically disordered proteins (IDP) are at the center of numerous biological processes, and attract consequently extreme interest in structural biology. Numerous approaches have been developed for generating sets of IDP conformations verifying a given set of experimental measurements. We propose here to perform a systematic enumeration of protein conformations, carried out using the TAiBP approach based on distance geometry. This enumeration was performed on two proteins, Sic1 and pSic1, corresponding to unphosphorylated and phosphorylated states of an IDP. The relative populations of the obtained conformations were then obtained by fitting SAXS curves as well as Ramachandran probability maps, the original finite mixture approach RamaMix being developed for this second task. The similarity between profiles of local gyration radii provides to a certain extent a converged view of the Sic1 and pSic1 conformational space. Profiles and populations are thus proposed for describing IDP conformations. Different variations of the resulting gyration radius between phosphorylated and unphosphorylated states are observed, depending on the set of enumerated conformations as well as on the methods used for obtaining the populations.

Frustration-induced complexity in order-disorder transitions of the J_{1}-J_{2}-J_{3} Ising model on the square lattice.

We revisit the field-free Ising model on a square lattice with up to third-neighbor (NNNN) interactions, also known as the J_{1}-J_{2}-J_{3} model, in the mean-field approximation. Using a systematic enumeration procedure, we show that the region of phase space in which the high-temperature disordered phase is stable against all modes representing periodic magnetization patterns up to a given size is a convex polytope that can be obtained by solving a standard vertex enumeration problem. Each face of this polytope corresponds to a set of coupling constants for which a single set of modes, equivalent up to a symmetry of the lattice, bifurcates from the disordered solution. While the structure of this polytope is simple in the half-space J_{3}>0, where the NNNN interaction is ferromagnetic, it becomes increasingly complex in the half-space J_{3}<0, where the antiferromagnetic NNNN interaction induces strong frustration. We then pass to the limit N→∞ giving a closed-form description of the order-disorder surface in the thermodynamic limit, which shows that for J_{3}<0, the emergent ordered phases will have a "devil's surface"-like mode structure. Finally, using Monte Carlo simulations, we show that for small periodic systems, the mean-field analysis correctly predicts the dominant modes of the ordered phases that develop for coupling constants associated with the centroid of the faces of the disorder polytope.

Data-driven approach to parameterize SCAN+U for an accurate description of 3d transition metal oxide thermochemistry

Semilocal density-functional theory (DFT) methods exhibit significant errors for the phase diagrams of transition-metal oxides that are caused by an incorrect description of molecular oxygen and the large self-interaction error in materials with strongly localized electronic orbitals. Empirical and semiempirical corrections based on the $\mathrm{DFT}+U$ method can reduce these errors, but the parameterization and validation of the correction terms remains an on-going challenge. We develop a systematic methodology to determine the parameters and to statistically assess the results by considering interlinked thermochemical data across a set of transition metal compounds. We consider three interconnected levels of correction terms: (1) a constant oxygen binding correction, (2) Hubbard-$U$ correction, and (3) $\mathrm{DFT}/\mathrm{DFT}+U$ compatibility correction. The parameterization is expressed as a unified optimization problem. We demonstrate this approach for $3d$ transition metal oxides, considering a target set of binary and ternary oxides. With a total of 37 measured formation enthalpies taken from the literature, the dataset is augmented by the reaction energies of 1710 unique reactions that were derived from the formation energies by systematic enumeration. To ensure a balanced dataset across the available data, the reactions were grouped by their similarity using clustering and suitably weighted. The parameterization is validated using leave-one-out cross validation (CV), a standard technique for the validation of statistical models. We apply the methodology to the strongly constrained and appropriately normed (SCAN) density functional. Based on the CV score, the error of binary (ternary) oxide formation energies is reduced by 40% (75%) to 0.10 (0.03) eV/atom. A simplified correction scheme that does not involve $\mathrm{SCAN}/\mathrm{SCAN}+U$ compatibility terms still achieves an error reduction of 30% (25%). The method and tools demonstrated here can be applied to other classes of materials or to parameterize the corrections to optimize $\mathrm{DFT}+U$ performance for other target physical properties.

The bioethical problems of umbilical cord blood: a study of institutional statements

This article aims to explore the bioethical problems that are concentrated around the Umbilical Cord Blood. The publication in the year 2020 in Spain of the new National Umbilical Cord Blood Plan recalls the current status of the issue. The bioethical problems of umbilical cord blood have not been specially studied, rather there are few studies in this regard and above all they have focused on the controversy over its autologous use and its storage in private banks. This work, the result of reading twenty-six institutional statements from the most diverse institutions in different countries, offers a detailed and systematic enumeration of the bioethical problems that arise around the life of umbilical cord blood and proposes, fundamentally, a classification with an evolutionary criterion, that is, following the course of the Umbilical Cord Blood, from its donation to its use, passing through the problems of donors and storage. The sources used cover a period from 1998 to 2019 and are practically all the existing ones. This work offers a conclusive analysis of a synchronic nature, in which the bioethical constants are detected in the 31 years analyzed, specifically the principles of autonomy and solidarity, in addition to the so-called bioethics of expectations; and another of a diachronic nature in which the bioethical nuclei in which the questions are concentrated stand out: the lack of personalistic principles and the conflict between freedom and solidarity.

РАЗРАБОТКА МАТЕМАТИЧЕСКОЙ МОДЕЛИ ДЛЯ ЗАДАЧИ БЕЙПЛАНА С УЧЕТОМ ОЧЕРЕДНОСТИ ЗАГРУЗКИ КОНТЕЙНЕРОВ

Compiling a load plan for a containership, which incorporates the maximum number of factors which requires restrictions on placement, consideration of the structural constraints for containers/ a vessel, segregation rules for dangerous cargoes and container loading sequencу in respect of a discharge port. The proposed approach for solving the task on automation of a load plan compilation aboard a containership implies dividing the task into two stages. At the first stage, one calculates the permissible arrangement of containers taking into consideration the structural limitations, container loading sequence, compatibility of dangerous cargoes, at the second stage – one calculates safety parameters (stability, operating life, etc.). This paper proposes a Boolean mathematical model of integer linear programming, which takes into consideration the structural features of containers, of a vessel, rules for stowage of hazardous cargoes according to the International Maritime Dangerous Cargoes Code, as well as container loading sequence (sequence of loading containers depending on the port of unloading), as well as a modified additive algorithm for solving a problem on compiling a load plan for a containership. Boolean programming methodology is applied to the problem. The usage simplifies calculations as all variables can only have two values: “0” or “1”. To validate the mathematical model, we have chosen a classic algorithm that relies on the ideas from the general method of branches and boundaries. Its calculations are limited to operations of addition and subtraction. The main idea consists of a systematic enumeration of possible candidate solutions, but the enumeration procedure allows to eliminate the solutions which are not proved to be optimal. Taken into account that this mathematical model on loading a containership has a specific form, this algorithmhas been complemented with tests, which make it possible to reject some solutions without direct checking. The paper gives an example of solving the problem on placing cargoes in the hold, which was obtained through the modified additive algorithm.