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The aim of this paper is to analyze the formative and evaluative activities involving statistical graphs in the new textbooks for Chilean rural multigrade education. The methodology is qualitative, at a descriptive level and uses the content analysis technique. The sample is made up of the six primary education textbooks distributed by the Ministry of Education for rural multigrade schools. The results show the predominance of the bar chart, semiotic level 3, the task of calculating and the personal context in both types of activities, although with respect to the reading level, it is evident that level 4 predominates in the formative activities and level 2 in the evaluative ones. According to the results, it is recommended to incorporate graphs proposed by the curricular guidelines of the Ministry of Education, which are absent in textbooks as well as to include evaluative activities that require reflection on the nature of the data, context, representation and conclusions obtained from them.

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Löwenstein's avoidance rule in aluminosilicates is reinterpreted on the basis of the fourth Pauling rule. It is shown that avoidance of Si-O-Si bridges may account for avoidance of Al-O-Al bridges. In view of this interpretation, it is proposed that the most favourable distributions of cations entering in substitution of silicon in the framework are associated to maximal independent sets of the respective 3-periodic nets. Among all possible solutions, only those with maximal symmetry are realized. The applicability of the concept is demonstrated for a few natural tectosilicates, which have been analysed through the prism of their labelled quotient graph.

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This article proposes a benchmark instance generator for the Hop-Constrained Minimum Spanning Tree problem, the Delay-Constrained Minimum Spanning Tree problem, and their bi-objective variants. The generator is developed in C++ and does not uses external libraries, being understandable, easy-to-read, and easy-to-use. Furthermore, the generator employs five parameters that makes possible to generate personalized benchmark instances for these problems. We also describe 640 benchmark instances that were previously used in computational experiments in the literature. Lastly, we include raw results obtained from computational experiments with the described benchmark instances. We hope that the data introduced in this article can foster the development and the evaluation of new algorithms for solving constrained minimum spanning tree problems.

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This paper introduces a new method of determining the independence ratio of periodic nets, based on the observation that, in any maximum independent set of the whole net, be it periodic or not, the vertices of every unit cell should constitute an independent set, called here a configuration. For 1-periodic graphs, a configuration digraph represents possible sequences of configurations of the unit cell along the periodic line. It is shown that maximum independent sets of the periodic graph are based on directed cycles with the largest ratio. In the case of 2-periodic nets, it is necessary to draw a different configuration digraph for each crystallographic direction defining a linkage between neighbouring cells, a concept known as a binary relational system. The two possible systems are analysed in this paper: \overrightarrow{\bf{sql}} is associated to nets displaying linkages between unit cells along the directions 10 and 01, and \overrightarrow{\bf{hxl}} is associated to nets also displaying linkages between cells along the direction 11. For both kinds of nets, a maximum independent set is obtained as a homomorphic image from \overrightarrow{\bf{sql}} or \overrightarrow{\bf{hxl}} to the respective configuration system. The method is illustrated with some of the 2-periodic nets listed on the Reticular Chemistry Structure Resource site; it is shown that it provides a rigorous solution to the case of the net sdh that was not satisfactorily solved in Part II [Moreira de Oliveira, de Abreu Mendes & Eon (2022). Acta Cryst. A78, 115-127]. The method is extended to relational systems based on non-translational symmetry operations. The successive steps are then summarized and a simple application to the 3-periodic net qtz is discussed; analysis of zeolites and aluminosilicates may proceed along the same lines. It is shown that the new method enables the analysis of disordered distributions in periodic nets.

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BACKGROUND: Research on the effect of adverse childhood experiences (ACEs) on adult outcomes has typically relied on retrospective assessment of ACEs and cumulative scores. However, this approach raises methodological challenges that can limit the validity of findings. OBJECTIVE: The aims of this paper are 1) to present the value of directed acyclic graphs (DAGs) to identify and mitigate potential problems related to confounding and selection bias, and 2) to question the meaning of a cumulative ACE score. RESULTS: Adjusting for variables that post-date childhood could block mediated pathways that are part of the total causal effect while conditioning on adult variables, which often serve as proxies for childhood variables, can create collider stratification bias. Because exposure to ACEs can affect the likelihood of reaching adulthood or study entry, selection bias could be introduced via restricting selection on a variable affected by ACEs in the presence of unmeasured confounding. In addition to challenges regarding causal structure, using a cumulative score of ACEs assumes that each type of adversity will have the same effect on a given outcome, which is unlikely considering differing risk across adverse experiences. CONCLUSIONS: DAGs provide a transparent approach of the researchers' assumed causal relationships and can be used to overcome issues related to confounding and selection bias. Researchers should be explicit about their operationalization of ACEs and how it is to be interpreted in the context of the research question they are trying to answer.

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Several important topological indices studied in mathematical chemistry are expressed in the following way $ \sum_{uv \in E(G)} F(d_u, d_v) $, where $ F $ is a two variable function that satisfies the condition $ F(x, y) = F(y, x) $, $ uv $ denotes an edge of the graph $ G $ and $ d_u $ is the degree of the vertex $ u $. Among them, the variable inverse sum deg index $ IS\!D_a $, with $ F(d_u, d_v) = 1/(d_u^a+d_v^a) $, was found to have several applications. In this paper, we solve some problems posed by Vukicevic [1], and we characterize graphs with maximum and minimum values of the $ IS\!D_a $ index, for $ a < 0 $, in the following sets of graphs with $ n $ vertices: graphs with fixed minimum degree, connected graphs with fixed minimum degree, graphs with fixed maximum degree, and connected graphs with fixed maximum degree. Also, we performed a QSPR analysis to test the predictive power of this index for some physicochemical properties of polyaromatic hydrocarbons.

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Introduction: Clustering is usually the first exploratory analysis step in empirical data. When the data set comprises graphs, the most common approaches focus on clustering its vertices. In this work, we are interested in grouping networks with similar connectivity structures together instead of grouping vertices of the graph. We could apply this approach to functional brain networks (FBNs) for identifying subgroups of people presenting similar functional connectivity, such as studying a mental disorder. The main problem is that real-world networks present natural fluctuations, which we should consider. Methods: In this context, spectral density is an exciting feature because graphs generated by different models present distinct spectral densities, thus presenting different connectivity structures. We introduce two clustering methods: k-means for graphs of the same size and gCEM, a model-based approach for graphs of different sizes. We evaluated their performance in toy models. Finally, we applied them to FBNs of monkeys under anesthesia and a dataset of chemical compounds. Results: We show that our methods work well in both toy models and real-world data. They present good results for clustering graphs presenting different connectivity structures even when they present the same number of edges, vertices, and degree of centrality. Discussion: We recommend using k-means-based clustering for graphs when graphs present the same number of vertices and the gCEM method when graphs present a different number of vertices.

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Functional enrichment analysis is a cornerstone in bioinformatics as it makes possible to identify functional information by using a gene list as source. Different tools are available to compare gene ontology (GO) terms, based on a directed acyclic graph structure or content-based algorithms which are time-consuming and require a priori information of GO terms. Nevertheless, quantitative procedures to compare GO terms among gene lists and species are not available. Here we present a computational procedure, implemented in R, to infer functional information derived from comparative strategies. GOCompare provides a framework for functional comparative genomics starting from comparable lists from GO terms. The program uses functional enrichment analysis (FEA) results and implement graph theory to identify statistically relevant GO terms for both, GO categories and analyzed species. Thus, GOCompare allows finding new functional information complementing current FEA approaches and extending their use to a comparative perspective. To test our approach GO terms were obtained for a list of aluminum tolerance-associated genes in Oryza sativa subsp. japonica and their orthologues in Arabidopsis thaliana. GOCompare was able to detect functional similarities for reactive oxygen species and ion binding capabilities which are common in plants as molecular mechanisms to tolerate aluminum toxicity. Consequently, the R package exhibited a good performance when implemented in complex datasets, allowing to establish hypothesis that might explain a biological process from a functional perspective, and narrowing down the possible landscapes to design wet lab experiments.

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Schizophrenia is a severe psychiatric disorder associated with altered connectivity of brain functional networks (BFNs). Researchers have observed a profound disruption in prefrontal-temporal interactions, damage to hub regions in brain networks and modified topological organization of BFNs in schizophrenia (SCZ) individuals. Assessment of BFNs with dynamic approaches allow the characterization of new functional structures, such as topological stability patterns and temporal connectivity, which are not accessible through static methods. In this perspective, the present study investigated the physiological processes of brain connectivity in SCZ. A resting-state EEG dataset of 14 SCZ individuals and 14 healthy controls (HC) was obtained at a sampling rate of 250 Hz. Dynamic BFNs were constructed using time-varying graphs combined with the motifs' synchronization method and the indexes were evaluated in different scales: global averages, by hemispheres, by regions, and by electrodes for both groups. The SCZ group exhibited lower temporal connectivity, lesser hub probability, and fewer number of edges in right and left temporal lobes over time, besides increased temporal connectivity in the central-parietal region. Neither differences for the full synchronization time of BFNs were observed, nor for intra- and inter-hemispheric connections between groups. These results indicate that SCZ BFNs exhibit a dynamic fluctuation pattern with abrupt increases in connectivity over time for the regions studied. This elucidates an attempted interaction of the temporal area with other regions (frontal, central-parietal, and occipital) that is not sufficient to maintain a connectivity pattern in schizophrenia individuals similar to that of healthy subjects. Our results suggest that changes in interaction of dynamic BFNs connections in SCZ can be better approached by dynamic analyses that enable a thorough glance at brain changes over time.

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Resumo Este ensaio trata da questão da causalidade em epidemiologia a partir da década de 1970, cujo marco inicial aqui adotado foi a publicação de The causal thinking in health sciences, por M. Susser, até os dias de hoje, buscando elencar os vários movimentos filosóficos, teóricos e metodológicos que ao longo destes 50 anos buscaram refletir sobre o problema da causalidade na disciplina, tendo em vista o predomínio das pesquisas observacionais no campo. Partindo da contribuição seminal de Susser, foram discutidos vários movimentos, bem como as críticas a eles, tais como a proposta da adoção de lógica popperiana na década de 1980, a crítica aos modelos multicausais e a teoria ecossocial proposta por N. Krieger na década de 1990, as críticas à epidemiologia social também da década de 1990, a influência de J. Pearl e a adoção dos gráficos acíclicos direcionados como nova metodologia na questão da causalidade. A chamada revolução metodológica no início deste século e as críticas de filósofos e epidemiologistas a esta abordagem reducionista também foram revisadas, bem como as alternativas propostas nos últimos 10 anos, incluindo a perspectiva inferencialista, a triangulação de métodos e a defesa da epidemiologia social e de seus modelos de determinação.

Abstract This essay deals with the issue of causality in epidemiology from the 1970s onwards, whose starting point adopted here was the publication of The Causal Thinking in Health Sciences by M. Susser, up to the present day, seeking to list the various philosophical, theoretical and methods that throughout these 50 years have sought to reflect on the problem of causality in the discipline, in view of the predominance of observational research in the field. Starting from Susser's seminal contribution, several movements were discussed as well as their criticisms, such as the proposal to adopt Popperian logic on the 1980s, the criticism of multicausal models and the ecosocial theory proposed by N. Krieger in the 1990s, criticism of social epidemiology also in the 1990s, the influence of J.Pearl and the adoption of directed acyclic graphs as a new tool in the issue of causality. The so-called methodological revolution at the beginning of this century and the criticism of philosophers and epidemiologists to this reductionist approach were also reviewed, as well as the alternatives proposed in the last 10 years, including the inferentialist perspective, the triangulation of methods and the defense of social epidemiology and their determination models.