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Subject and purpose of work: The aim of the work is to present and compare the results of selected procedures for assessing linear ordering methods. The considerations were carried out on the example of taxonomic measures of the security of cryptocurrency exchanges. Materials and methods: Publicly available data published on internet portals were used to assess the security of cryptocurrency exchanges. Composite indicators were created using the standardized sum method. The selection of the final representative was made on the basis of the similarity of rankings, the choice of the measure from the so-called efficient frontier, aggregate measure of the correctness of linear ordering methods and the PROMETHEE II method. Results: According to the values of all selected composite indicators, the Gemini exchange was the best in terms of the adopted criteria. Conclusions: Each of the analyzed procedures for selecting the final linear ordering method has its own logic, advantages and disadvantages

Subject and purpose of work: The aim of the work is to present and compare the results of selected procedures for assessing linear ordering methods. The considerations were carried out on the example of taxonomic measures of the security of cryptocurrency exchanges.Materials and methods: Publicly available data published on internet portals were used to assess the security of cryptocurrency exchanges. Composite indicators were created using the standardized sum method. The selection of the final representative was made on the basis of the similarity of rankings, the choice of the measure from the so-called efficient frontier, aggregate measure of the correctness of linear ordering methods and the PROMETHEE II method.Results: According to the values of all selected composite indicators, the Gemini exchange was the best in terms of the adopted criteria.Conclusions: Each of the analyzed procedures for selecting the final linear ordering method has its own logic, advantages and disadvantages.

We examine the efficacy of two linear programming models for optimizing the linear ordering problem (LOP) of ranking teams in major American sports, whether measured by head-to-head win counts or by collective victory margins. Using standard solution software, both models are tested over 42 problems involving full seasons from the National Football League, the National Basketball Association, the National Hockey League, and Major League Baseball, as well as major college football, baseball, and men’s basketball. We find that optimal solutions can be achieved rapidly for all four professional sports from either model, regardless of whether victory margins or win counts are used. However, solution speeds were much slower for the collegiate sports, particularly for baseball and men’s basketball where the number of teams were the largest, and especially when win counts were the performance measure. Such problems have a large and sparse pairwise comparison matrix with low values and variation in its non-zero elements, characteristics that have been found to be challenging in the general LOP literature. However, a modified minimum violations model demonstrated dramatic efficiency advantages when solving the collegiate cases, and illustrated that optimal solutions are largely achievable in reasonable time frames even for those sports.

The 2030 Agenda with 17 Sustainable Development Goals (SDGs) is a challenge for all countries in the world. Their implementation may turn out to be a compromise or the creation of effective interactions that dynamize sustainable development. To achieve the SDGs, it is essential to understand how they interact with each other. It seems that in the times of the climate and health crisis caused by the COVID-19 pandemic, caring for the environment and ensuring a healthy life and promoting well-being at all ages is the basis for environmental, economic and social sustainable development. The aim of the study is to compare the degree of implementation of the goals of sustainable development in the scope of goal 13 “Climate action” and goal 3 “Good health and well-being” in the EU countries. In addition, we analyze how trade-offs and synergies between these goals have developed. Data from the Eurostat database were used to achieve the goal. The study used the method of multivariate comparative analysis—linear ordering of objects. The technique for order preference by similarity to an ideal solution (TOPSIS) method was used to measure the studied phenomenon. The results indicate a different degree of implementation of the sustainable development goals related to climate change and the improvement of health and social well-being. Only a few countries have synergy in achieving these goals, most of them compromise, manifesting themselves in improving one goal over another. In the group of analyzed EU countries, a simultaneous deterioration in the effectiveness of achieving both objectives were also noted. Our research also shows that energy policy is an important attribute in improving the achievement of these goals. The conducted analysis fills the gap in the research on the implementation of selected sustainable development goals and their interactions. It contributes to the discussion on increasing the links between them, in particular with regard to emerging compromises. This research can provide a basis for re-prioritizing and intensifying the actions where individual EU countries are lagging most behind.

This paper advances novel theory and evidence on the emergence of informal leadership networks in groups that feature no formally designated leaders or authority hierarchies. We integrate insights from relational schema and network theory to develop and empirically test a three-step process model. The model’s first hypothesis is that people use a “linear ordering schema” to process information about leadership relations. The second hypothesis argues that when an individual experiences a particular leadership attribution to be inconsistent with the linear ordering schema, that individual will tend to reduce the ensuing cognitive inconsistency by modifying that leadership attribution. Finally, the third hypothesis builds on this inconsistency-reduction mechanism to derive implications about a set of network structural features (asymmetry, acyclicity, transitivity, popularity, and inverse popularity) that are predicted to emerge endogenously as a group’s informal leadership network evolves. We find broad support for our proposed theoretical model using a multi-method, multi-study approach combining experimental and observational data. Our study contributes to the organizational literature by illuminating a socio-cognitive dynamics underpinning the evolution of informal leadership structures in groups where formal authority plays a limited role. The e-companion is available at https://doi.org/10.1287/orsc.2017.1171 .

The pivotal role of digital transformation (DT) in contemporary socio-economic development cannot be overstated. This crucial aspect is highlighted in the Agenda 2030, specifically in goal 9 among the 17 objectives. This article presents the results of a study assessing the level of DT in industry, innovation, and infrastructure in the 27 European Union (EU) countries in 2015 and 2020. Central to this study is the proposition of an aggregated Digital Transformation Assessment Indicator (DTAI), serving as a metric to gauge the progression of EU member states. Utilizing this indicator, the article assesses the advancement status of EU countries and orchestrates a comparative ranking of their achievements in fulfilling Sustainable Development Goal (SDG) 9 between 2015 and 2020. Moreover, a classification of countries into analogous groups based on this criterion for both periods is provided. The DTAI is prepared following the methodology of the linear ordering of objects—countries of the EU 27. The zero unitarization method (ZUM) is used as the main ordering method. To compare the results obtained, the DTAI value and classifications of countries in 2015, and 2020, are also presented using Hellwig’s pattern development method. The findings of this investigation underscore the variances existing among the EU 27 nations concerning the implementation of SDG 9. Furthermore, notable fluctuations in ranking positions are also observed. The research outcomes underscore significant challenges in DT implementation, particularly within Central, Eastern, and Southern European nations. The utilized research methodology bears substantial implications for the effective realization of the 2030 Agenda and its corresponding SDGs, both at the individual nation-state level and within the broader framework of the EU.

The author intended to present the relationship between the standard of living of EU citizens and the level of the development of renewable energy. It is particularly important in the context of the implementation of the sustainable development idea, by ensuring a high standard of living for both current and future generations, with rational use of available natural resources. The first, theoretical part of the article presents the problem related to the impact of renewable energy on the standard of living in a synthetic way. The second part involves empirical research conducted in all countries of the EU. To evaluate the level of renewable energy development and the standard of living, the author constructed original measures based on the TOPSIS method. Variables were selected on the basis of substantive, statistical and formal criteria (primarily the completeness and availability of data in 2019). Within the framework of the conducted study, the author obtained, among other things, a relatively high value of Spearman’s rank correlation coefficient between the constructed synthetic measures (0.47). Canonical analysis was used to identify the relationship between them. Numerous indicators, including canonical correlations, complete redundancy and extracted variances, were determined with the use of canonical analysis. Seven statistically significant canonical variables were identified. The value of the greatest and most statistically significant canonical correlation exceeded 0.94, and for the last statistically significant canonical variable, the value reached over 0.31. Statistical data were primarily obtained from the publicly available EUROSTAT database.

The minimum linear ordering problem (MLOP) generalizes well-known combinatorial optimization problems such as minimum linear arrangement and minimum sum set cover. MLOP seeks to minimize an aggregated cost f ( · ) due to an ordering σ of the items (say [ n ]), i.e., min σ ∑ i ∈ [ n ] f ( E i , σ ) , where E i , σ is the set of items mapped by σ to indices [ i ]. Despite an extensive literature on MLOP variants and approximations for these, it was unclear whether the graphic matroid MLOP was NP-hard. We settle this question through non-trivial reductions from mininimum latency vertex cover and minimum sum vertex cover problems. We further propose a new combinatorial algorithm for approximating monotone submodular MLOP, using the theory of principal partitions. This is in contrast to the rounding algorithm by Iwata et al. (in: APPROX, 2012), using Lovász extension of submodular functions. We show a ( 2 - 1 + ℓ f 1 + | E | ) -approximation for monotone submodular MLOP where ℓ f = f ( E ) max x ∈ E f ( { x } ) satisfies 1 ≤ ℓ f ≤ | E | . Our theory provides new approximation bounds for special cases of the problem, in particular a ( 2 - 1 + r ( E ) 1 + | E | ) -approximation for the matroid MLOP, where f = r is the rank function of a matroid. We further show that minimum latency vertex cover is 4 3 -approximable, by which we also lower bound the integrality gap of its natural LP relaxation, which might be of independent interest.

Airborne organic dust has rarely been subject to immunotoxicological analysis. A pilot study was undertaken to link exposure metrics (respirable crystalline silica (RCS), bacteria, fungi, endotoxins (END), peptidoglycans (PGN), (1 → 3)-β-D-glucans (GLU)) with in vitro cytotoxicity and cytokine responses based on analysis of airborne organic dust samples collected during a single work shift at six different facilities. The A549 and BEAS-2B cell lines were used to assess cytotoxicity and proinflammatory cytokine release. The general linear model (GLM) and taxonomic linear ordering were used to identify key determinants and rank facilities by the hazard level they pose. The highest cytotoxicity of organic dust was observed at the sewage treatment plant, while the lowest was at the poultry farm. The most hazardous agents present in organic dust included RCS, aerobic bacteria, fungi, PGN, and GLU. They significantly affected cytokine release, particularly of IL-6 and IL-8. The use of a synthetic measure showed that inhalable organic dust from the composting plant presented the highest potential to induce adverse effects on human health, while the lowest one was characterized by the biomass-fired power plant samples. The open-ended statistical method can significantly increase awareness of occupational hazards and promote more responsible protection for exposed workers.

Any countable (infinite or not) linear (total) ordering can be represented by displaying all its elements on an axis in increasing order. Such a representation can be generated using only geometrical constructions based on coloured line segment extensions and rules to handle segment intersections. After a bounded time, the construction segments disappear and only the representation remains. The process starts with finitely many segments, so that unbounded acceleration effects are used to generate infinitely many segments for the representation. There is no outside machinery nor operator: any needed computation has to be carried out through the drawing. After providing some illustrative examples with ad hoc constructions, we prove our main results. One rational signal machine (bounded to use only rational coordinates) can generate the representation of any decidable linear ordering (i.e. the order between two elements is decidable by a Turing machine). In the general case, there is a signal machine able to generate the representation of any countable linear ordering (encoded in a real number).