Visual assessment of matrix-variate normality

In recent years, the analysis of three-way data has become ever more prevalent in the literature. It is becoming increasingly common to analyse such data by means of matrix-variate distributions, the most prevalent of which is the matrix-variate normal distribution. Although many methods exist for assessing multivariate normality, there is a relative paucity of approaches for assessing matrix-variate normality. Herein, a new visual method is proposed for assessing matrix-variate normality by means of a distance–distance plot. In addition, a testing procedure is discussed to be used in tandem with the proposed visual method. The proposed approach is illustrated via simulated data as well as an application on analysing handwritten digits.     

AFFINE‐EQUIVARIANT SPATIAL MEDIAN AND ITS USE IN THE MULTIVARIATE MULTI‐SAMPLE LOCATION PROBLEM

The classical spatial median is not affine‐equivariant, which often turns out to be an unfavourable property. In this paper, the asymptotic properties of an affine‐equivariant modification of the spatial median are investigated. It is shown that under some weak regularity conditions, the modified spatial median computed by means of the sample norming matrix is asymptotically equivalent to the one computed by means of the population norming matrix, which yields its asymptotic normality. A consistent estimate of the asymptotic covariance matrix of the modified spatial median is also presented. These results are implemented in a scheme, where the sample norm is determined by means of the sample Dümbgen scatter matrix. The results are utilized in the construction of affine‐invariant test statistics for testing the multi‐sample hypothesis of equality of location parameters. The performance of the proposed tests is demonstrated through a simulation study.     

Embeddings into almost self-centered graphs of given radius

A graph is almost self-centered (ASC) if all but two of its vertices are central. An almost self-centered graph with radius r is called an r-ASC graph. The r-ASC index \(\theta _r(G)\) of a graph G is the minimum number of vertices needed to be added to G such that an r-ASC graph is obtained that contains G as an induced subgraph. It is proved that \(\theta _r(G)\le 2r\) holds for any graph G and any \(r\ge 2\) which improves the earlier known bound \(\theta _r(G)\le 2r+1\). It is further proved that \(\theta _r(G)\le 2r-1\) holds if \(r\ge 3\) and G is of order at least 2. The 3-ASC index of complete graphs is determined. It is proved that \(\theta _3(G)\in \{3,4\}\) if G has diameter 2 and for several classes of graphs of diameter 2 the exact value of the 3-ASC index is obtained. For instance, if a graph G of diameter 2 does not contain a diametrical triple, then \(\theta _3(G) = 4\). The 3-ASC index of paths of order \(n\ge 1\), cycles of order \(n\ge 3\), and trees of order \(n\ge 10\) and diameter \(n-2\) are also determined, respectively, and several open problems proposed.     

Public relations and the rise of hypermodern values: Exploring the profession in Europe

This article raises the question of whether European public relations (PR) and communications professionals perceive a cultural transformation in the direction of hypermodernity, and if so, attempts to assess how this influences their organizations and their work. Questions were asked in the European Communication Monitor 2017, an annual survey among communications professionals, and 3387 respondents from 50 European countries filled in the questionnaire. The results indicate that European professionals recognize a cultural transformation in the direction of hyper consumption, hyper modernization and hyper narcissism that influences the communication between their organizations and their stakeholders. A cluster analysis shows that less than half of the respondents perceive a transformation of their organization in the direction of hypermodern characteristics and values. Organizations with post/hypermodern characteristics have superior communications departments compared to modern organizations. Post/hypermodern organizations and excellent communications departments also engage more often in societal debates than other types of organizations and departments.     

‘She will know that her mother’s doing something for her’: women with intellectual disabilities assuming the mother identity

This article explores the experiences of women with intellectual disabilities in becoming a mother. The presented findings are from a grounded theory research study with 19 women with intellectual disabilities from the Czech Republic. The findings are organised around external and internal factors affecting the women’s assumption of the mother identity, with the most prominent being poverty of the participating mothers, negative attitudes towards their motherhood, and a lack of preparation for motherhood. There is a need for systemic support for mothers with intellectual disabilities, starting in adolescence with sexual education, and continued throughout adulthood, including programmes focused on skills development.     

Contradictory tendencies in the political culture of Croatian youth: unexpected anomalies or an expected answer to the social crisis?

A successful democratic consolidation of post-socialist societies depends, among other things, on their citizens’ political culture, younger generations included. Moreover, youth civic engagement today and in the future is a guarantee of the continuity and development of democracy, which means that scientists need to gain insight into young people’s political culture. In this paper we look at political values, institutional trust and participation as relevant components of the civic political culture. The analysis is based on quantitative data collected in the empirical studies of Croatian youth, carried out between 1999 and 2013. Based on longitudinal study results, a downward trend is identified regarding selected political culture indicators: acceptance of liberal-democratic values, trust in social and political institutions, interest in politics and party preference. However, there is a simultaneous increase in participation in various types of organizations, especially political parties. The interpretation of established tendencies is placed in a broader context of an inherited democratic deficit, economic recession and social crisis. Current trends are both indicators and consequences of young people’s inadequate political socialization as well as weaknesses of political institutions and various actors during the transition and consolidation period.     

A linear algebra approach to non-transitive expected utility

The purpose of this paper is twofold. One of the aims is to give a view of P. C. Fishburn's non-transitive expected utility through geometric linear algebra. The other is to give an application of these ideas to a social choice problem. Actually, the problem under consideration arises from the theory of dynamical systems of structures in a society as studied in [All] and [Om1]. A variation of this model as presented in [Om2] leads to the problem of how macro structures of a society form coalitions. Their possible irrational behaviour may be treated using non-transitive expected utility. Received: 14 February 1996/Accepted: 22 January 1997