On the odd girth and the circular chromatic number of generalized Petersen graphs

A class \(\mathcal{G}\) of simple graphs is said to be girth-closed (odd-girth-closed) if for any positive integer g there exists a graph \(\mathrm {G} \in \mathcal{G}\) such that the girth (odd-girth) of \(\mathrm {G}\) is \(\ge g\). A girth-closed (odd-girth-closed) class \(\mathcal{G}\) of graphs is said to be pentagonal (odd-pentagonal) if there exists a positive integer \(g^*\) depending on \(\mathcal{G}\) such that any graph \(\mathrm {G} \in \mathcal{G}\) whose girth (odd-girth) is greater than \(g^*\) admits a homomorphism to the five cycle (i.e. is \(\mathrm {C}_{_{5}}\)-colourable). Although, the question “Is the class of simple 3-regular graphs pentagonal?” proposed by Ne?et?il (Taiwan J Math 3:381–423, 1999) is still a central open problem, Gebleh (Theorems and computations in circular colourings of graphs, 2007) has shown that there exists an odd-girth-closed subclass of simple 3-regular graphs which is not odd-pentagonal. In this article, motivated by the conjecture that the class of generalized Petersen graphs is odd-pentagonal, we show that finding the odd girth of generalized Petersen graphs can be transformed to an integer programming problem, and using the combinatorial and number theoretic properties of this problem, we explicitly compute the odd girth of such graphs, showing that the class is odd-girth-closed. Also, we obtain upper and lower bounds for the circular chromatic number of these graphs, and as a consequence, we show that the subclass containing generalized Petersen graphs \(\mathrm {Pet}(n,k)\) for which either k is even, n is odd and \(n\mathop {\equiv }\limits ^{k-1}\pm 2\) or both n and k are odd and \(n\ge 5k\) is odd-pentagonal. This in particular shows the existence of nontrivial odd-pentagonal subclasses of 3-regular simple graphs.     

Alterations in IGF-I affect elderly: role of physical activity

The growth hormone–insulin-like growth factor I (IGF-I) axis is an important physiological regulator muscle for development. Although there is evidence that aging muscle retains the ability to synthesize IGF-I, there is also evidence that aging may be associated with attenuation of the ability of exercise to induce an isoform of IGF-I that promotes satellite cell proliferation. However, it is clear that overexpression of IGF-I in the muscle can protect against age-related sarcopenia. Strength training appears to be the intervention of choice for the prevention and treatment of sarcopenia. IGF-I has been implicated in the loss of the muscle with age, and IGF-I expression levels change as a consequence of strength training in older adults. However, it seems that advancing age, rather than declining serum levels of IGF-I, appears to be a major determinant of life-time changes in body composition in women and men. We concluded that resistive exercise is a significant determinant of muscle mass and function. Elevated levels of IGF-I have been found in physically active compared to sedentary individuals. Recent work suggests that IGF-I as a mediator plays an important role in muscle hypertrophy and angiogenesis, both of which characterize the anabolic adaptation of muscles to exercise.     

Media, Racism and Islamophobia: The Representation of Islam and Muslims in the Media

This article examines the representation of Islam and Muslims in the British press. It suggests that British Muslims are portrayed as an 'alien other' within the media. It suggests that this misrepresenatation can be linked to the development of a 'racism', namely, Islamphobia that has its roots in cultural representations of the 'other'. In order to develop this arguement, the article provies a summary/overview of how ethnic minorities have been represented in the British press and argues that the treatment of British Muslims and Islam follows these themes of 'deviance' and 'un-Britishness'.     

Pluralistic media ignorance: Presence and causes

This study examines the presence and causes of pluralistic media ignorance - incorrect estimation of media content in a way that creates the impression that popular broadcasting is overabundant with morally controversial material. Using the appearance of sexual content in television advertising in Israel as a case study, we compare survey estimates (N = 305) of the prevalence of this material with its actual level according to the findings of a content analysis of commercials (N = 752). Pluralistic media ignorance emerges as a predominant norm, when viewers are requested to estimate the prevalence of “soft core” content like kissing and partial nudity, but it is a minor phenomenon, when estimating the share of more explicit material such as intercourse, homosexuality and rape. The most prominent predictors of pluralistic media ignorance are disapproval of the inclusion of objectionable content in popular media and extended recall of media exemplars that contain such content. Religiosity, ethnicity and sex are only partly predicting the emergence of pluralistic media ignorance. Media consumption, fear of media influence and other demographics are not predicting it at all. Public policy implications are discussed and suggestions for future research are given.