Boolean functions with small spectral norm

Suppose that f is a boolean function from F_2^n to {0,1} with spectral norm (that is the sum of the absolute values of its Fourier coefficients) at most M. We show that f may be expressed as +/- 1 combination of at most 2^(2^(O(M^4))) indicator functions of subgroups of F_2^n.Comment: 17 pp. Updated references

Monochromatic sums and products

Suppose that $\mathbb{F}_p$ is coloured with $r$ colours. Then there is some colour class containing at least $c_r p^2$ quadruples of the form $(x, y , x + y, xy)$.Comment: 48 pages, accepted for publication in Discrete Analysis. Second version has minor changes arising from the referee report. Third version updated to DAJ format. in Discrete Analysis 2016:

A quantitative version of the idempotent theorem in harmonic analysis

Suppose that G is a locally compact abelian group, and write M(G) for the algebra of bounded, regular, complex-valued measures under convolution. A measure \mu in M(G) is said to be idempotent if \mu * \mu = \mu, or alternatively if the Fourier-Stieltjes transform \mu^ takes only the values 0 and 1. The Cohen-Helson-Rudin idempotent theorem states that a measure \mu is idempotent if and only if the set {r in G^ : \mu^(r) = 1} belongs to the coset ring of G^, that is to say we may write \mu^ as a finite plus/minus 1 combination of characteristic functions of cosets r_j + H_j, where the H_j are open subgroups of G^. In this paper we show that the number L of such cosets can be bounded in terms of the norm ||\mu||, and in fact one may take L <= \exp\exp(C||\mu||^4). In particular our result is non-trivial even for finite groups.Comment: 28 page

An own goal in sport for development: Time to change the playing field

Sport for Development and Peace (SDP) refers to the use of sport to promote varied outcomes beyond the playing field and has been defined as ‘the intentional use of sport, physical activity and play to attain specific development objectives in low- and middle-income countries and disadvantaged communities in high-income settings.’ Stakeholders working in the field for the last two decades include the United Nations, the public sector, the private sector and civil society with an increasing number of SDP initiatives across the globe. While other disciplines such as health and education have engendered a more critical perspective on the factors causing and constraining development, certain SDP programmes do exhibit an ongoing gap between evidence and practice. In the most pronounced cases this is reflected with somewhat naïve and idealistic notions of the power of sport. Even if sport is applied in the right manner and results in the intended change, there are deeper structural issues that may negate such well-intentioned work. While a focus of many SDP organisations is to develope the individual to realise his/her capacity, there appears to be a genuine lack of initiatives that seek to challenge or reform the societal structures and conditions that caused this ‘underdevelopment' to occur in the first place

Traditioning Blackness: A Theo-Ethical Analysis of Black Identity in Black Theological Discourse

The emergence of James Cone\u27s black liberation theology in the late-1960s and early 1970s marked both a radical challenge to and a historical transformation of the fields of religious and theological studies. Building on Cone\u27s work, black theological discourse has developed a rich tradition of religious and academic inquiry characterized by its commitment to interpreting Christianity in particular, and religious experience more broadly, from the vantage point of oppressed black people. This dissertation shows that James Cone developed a particular understanding of black identity in his early works and, furthermore, that various scholars have critically engaged this conception of black identity in both explicit and implicit ways. I argue that retaining and developing black theology\u27s commitment to the lived experiences of oppressed black people requires clarifying the meaning of black identity in light of the complex socio-economic realities that characterize black life in the 21st-century. Borrowing from the work of Latin American theologian Orlando Espìn, this dissertation identifies and interprets outstanding examples of critical engagement with Cone\u27s coneption of blackness as moments of traditioning. Traditioning marks the ongoing and inevitable process of contesting and reshaping theological realities. This dissertation, then, analyzes the ongoing contestation and reshaping - traditioning - of black identity in black theological discourse. Through this analysis, this dissertation seeks to maintain and develop black theology\u27s revolutionary commitment to the oppressed by refracting this commitment through the lens of the historic socio-economic stratification that characterizes black life in the 21st century

An analysis on the relation between users' online social networks addiction and users security concerns

Use of online social network platforms has increased over last decades. There are various activities that users can do on those platforms such as, making friends, enjoying time, making business, and education. Given activities make online social network platforms more attractive and users want to spend more time on those platforms. Although there is a massive increment in their use, they are not secure enough to fully protect their users' data and privacy. Some users are not aware of the security settings (i.e. privacy settings) since most users focus on spending time on those platforms which brings online social networks addiction into the consideration. Addiction is defined with time dependency in most of the literature works, however, calling a person as an addicted person depends on various factors. This work provides three main contributions; 1-) It clarifies the definition of addiction with a quantitative model. 2-) It provides an analysis on online social networks addiction; answers the question "whom could be called as an addicted user to those platforms" 3-)It provides an analysis on users' trusts to online social networks platforms