Rough sets in graphs using similarity relations

<abstract><p>In this paper, we investigate the theory of rough set to study graphs using the concept of orbits. Rough sets are based on a clustering criterion and we use the idea of similarity of vertices under automorphism as a criterion. We introduce indiscernibility relation in terms of orbits and prove necessary and sufficient conditions under which the indiscernibility partitions remain the same when associated with different attribute sets. We show that automorphisms of the graph $ \mathcal{G} $ preserve the indiscernibility partitions. Further, we prove that for any graph $ \mathcal{G} $ with $ k $ orbits, any reduct $ \mathcal{R} $ consists of one element from $ k-1 $ orbits of the graph. We also study the rough membership functions for paths, cycles, complete and complete bipartite graphs. Moreover, we introduce essential sets and discernibility matrices induced by orbits of graphs and study their relationship. We also prove that every essential set consists of union of any two orbits of the graph.</p></abstract>

Markov Chain Monte Carlo in Practice

Markov chain Monte Carlo (MCMC) is an essential set of tools for estimating features of probability distributions commonly encountered in modern applications. For MCMC simulation to produce reliable outcomes, it needs to generate observations representative of the target distribution, and it must be long enough so that the errors of Monte Carlo estimates are small. We review methods for assessing the reliability of the simulation effort, with an emphasis on those most useful in practically relevant settings. Both strengths and weaknesses of these methods are discussed. The methods are illustrated in several examples and in a detailed case study. Expected final online publication date for the Annual Review of Statistics, Volume 9 is March 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Bigrassmannian permutations and Verma modules

We show that bigrassmannian permutations determine the socle of the cokernel of an inclusion of Verma modules in type A. All such socular constituents turn out to be indexed by Weyl group elements from the penultimate two-sided cell. Combinatorially, the socular constituents in the cokernel of the inclusion of a Verma module indexed by $$w\in S_n$$ w ∈ S n into the dominant Verma module are shown to be determined by the essential set of w and their degrees in the graded picture are shown to be computable in terms of the associated rank function. As an application, we compute the first extension from a simple module to a Verma module.

THE PRESERVATION OF WORLD ARCHAEOLOGICAL SITES AND PROMOTION OF TOURISM: QALA'AT BANI HAMMAD (M'SILA) ALGERIA

Archaeological sites are currently considered as one of the most important tourism industry drivers, becoming an autonomous economy. Among the most outstanding archaeological sites in Algeria is the fort of Bani Hammad. This site is the first archaeological site classified by UNESCO in 1980, located in central Algeria in M'sila province. Given its importance, we conducted a scientific study to highlight its beautiful archaeological tourism components and national and international tourist attractions. Then, we revealed the tourism challenges and the physical and moral deterioration affecting this site. Also, we propose a preservation plan to promote this site’s touristic assets, enabling its transformation into a tourist destination competing with other archaeological sites in Algeria and the Maghreb; through a sustainable development plan of archaeological tourism, while preserving its historical identity and role. To this aim, we used a descriptive and quantitative analytical approach, starting with a theoretical and analytical analysis of various studies, plans, and documents related to this archaeological site's components. Then, we analyzed the geographical and statistical data of the tourist traffic over five years using the SPSS statistical program. Finally, we presented the results, developed a rehabilitation plan for the site, and suggested an essential set of recommendations.

Implications of Supply Chain Management on the Connection between Business Performance and Enterprise Resource Planning Framework

Enterprise Resource Planning (ERP) and Supply Chain Management (SCM) are the two fundamental Information Technology (IT) investment advancements that businesses are resorting to in the modern age. These are the advancements and options which are known to be essential in literature as a contributing fact to the enhancement of Business Performance (BP). In that regard, the main purpose of this contribution is to evaluate the adoption of ERP and its effects of BP through the option of SCM. This paper presents a novel model that applies enterprise resource planning with the option of SCM to effectively optimize BP in the competitive world. The structural equation framework is thus fundamental for testing of the model and how its fits the level of the four projected research hypotheses. The essential set of data for this analysis was gathered from companies in Malaysia. The findings in this research have been supported using empirical evidences, availability of positive factors of ERP for the option of supply chain ultimately amounts to enhanced BP.

Charaterizing RDF graphs through graph-based measures – framework and assessment

The topological structure of RDF graphs inherently differs from other types of graphs, like social graphs, due to the pervasive existence of hierarchical relations (TBox), which complement transversal relations (ABox). Graph measures capture such particularities through descriptive statistics. Besides the classical set of measures established in the field of network analysis, such as size and volume of the graph or the type of degree distribution of its vertices, there has been some effort to define measures that capture some of the aforementioned particularities RDF graphs adhere to. However, some of them are redundant, computationally expensive, and not meaningful enough to describe RDF graphs. In particular, it is not clear which of them are efficient metrics to capture specific distinguishing characteristics of datasets in different knowledge domains (e.g., Cross Domain vs. Linguistics). In this work, we address the problem of identifying a minimal set of measures that is efficient, essential (non-redundant), and meaningful. Based on 54 measures and a sample of 280 graphs of nine knowledge domains from the Linked Open Data Cloud, we identify an essential set of 13 measures, having the capacity to describe graphs concisely. These measures have the capacity to present the topological structures and differences of datasets in established knowledge domains.

An Efficient Explorative Sampling Considering the Generative Boundaries of Deep Generative Neural Networks

Deep generative neural networks (DGNNs) have achieved realistic and high-quality data generation. In particular, the adversarial training scheme has been applied to many DGNNs and has exhibited powerful performance. Despite of recent advances in generative networks, identifying the image generation mechanism still remains challenging. In this paper, we present an explorative sampling algorithm to analyze generation mechanism of DGNNs. Our method efficiently obtains samples with identical attributes from a query image in a perspective of the trained model. We define generative boundaries which determine the activation of nodes in the internal layer and probe inside the model with this information. To handle a large number of boundaries, we obtain the essential set of boundaries using optimization. By gathering samples within the region surrounded by generative boundaries, we can empirically reveal the characteristics of the internal layers of DGNNs. We also demonstrate that our algorithm can find more homogeneous, the model specific samples compared to the variations of ϵ-based sampling method.

Medicaid’s EPSDT Benefit: An Opportunity to Improve Pediatric Screening for Social Determinants of Health

The Early and Periodic Screening, Diagnostic, and Treatment (EPSDT) benefit is a key component of Medicaid policy intended to define an essential set of services provided to patients younger than age 21. Given increasing attention to social determinants of health in pediatric health care, this qualitative review examines the extent to which EPSDT might be used to implement structured screening to identify environmental and social factors affecting children’s health. Themes derived from semistructured interviews conducted in 2017 were triangulated with a review of the recent literature to describe how states currently consider the EPSDT benefit with respect to social determinants of health screening. Our findings suggest that, with sufficient stakeholder advocacy given the evidence supporting social determinants of health screening as “medically necessary,” EPSDT benefits could be considered as a funding source to incentivize the incorporation of social determinants of health screening into the basic package of well-child care.