Rabi oscillations of two-photon states in nonlinear optical resonators

We demonstrate that four-wave mixing processes in high-quality non-linear resonators can lead to Rabi-like oscillations in photon occupation numbers and second-order correlation functions, being a characteristic feature of the presence of entangled photon pairs in the optical signal. In the case of a system driven by a continuous coherent pump, the oscillations occur in the transient regime. We show that driving the system with pulsed coherent pumping would generate strongly anti-bunched photon states.Comment: 5 pages, 6 figure

Zappa-Sz\'ep product groupoids and C*-blends

We study the external and internal Zappa-Sz\'ep product of topological groupoids. We show that under natural continuity assumptions the Zappa-Sz\'ep product groupoid is \'etale if and only if the individual groupoids are \'etale. In our main result we show that the C*-algebra of a locally compact Hausdorff \'etale Zappa-Sz\'ep product groupoid is a C*-blend, in the sense of Exel, of the individual groupoid C*-algebras. We finish with some examples, including groupoids built from *-commuting endomorphisms, and skew product groupoids.Comment: Updated to agree with published versio

An Exploratory, Cross-Cultural Study of SocioPsychological variables (OPI) Comparing Selective American, Canadian, Hawaiian and Philippine College Students in Education Faculties

To the psychologist interested in cross-cultural studies and higher education in general, and college students more specifically, attitudes and belief systems can be seen as being fundamental in order to appreciate and understand any person, subculture or society. Attitudes denote the way in which people feel about aspects of the world in which they live, and beliefs the way they think about them. These terms are. of course, hypothetical constructs - as is personality under which they are subsumed. How such variables are defined, the theoretical traditions on which they are based, and the conceptualisations of personality which is adopted particularly complicates cross-cultural, psychological research and interpretation. This paper explores a possible approach

Zappa-Sz\'ep products of semigroups and their C*-algebras

Zappa-Sz\'ep products of semigroups encompass both the self-similar group actions of Nekrashevych and the quasi-lattice-ordered groups of Nica. We use Li's construction of semigroup $C^*$-algebras to associate a $C^*$-algebra to Zappa-Sz\'ep products and give an explicit presentation of the algebra. We then define a quotient $C^*$-algebra that generalises the Cuntz-Pimsner algebras for self-similar actions. We indicate how known examples, previously viewed as distinct classes, fit into our unifying framework. We specifically discuss the Baumslag-Solitar groups, the binary adding machine, the semigroup $\mathbb{N}\rtimes\mathbb{N}^\times$, and the $ax+b$-semigroup $\mathbb{Z}\rtimes\mathbb{Z}^\times$

Topological spaces associated to higher-rank graphs

We investigate which topological spaces can be constructed as topological realisations of higher-rank graphs. We describe equivalence relations on higher-rank graphs for which the quotient is again a higher-rank graph, and show that identifying isomorphic co-hereditary subgraphs in a disjoint union of two rank-$k$ graphs gives rise to pullbacks of the associated $C^*$-algebras. We describe a combinatorial version of the connected-sum operation and apply it to the rank-2-graph realisations of the four basic surfaces to deduce that every compact 2-manifold is the topological realisation of a rank-2 graph. We also show how to construct $k$-spheres and wedges of $k$-spheres as topological realisations of rank-$k$ graphs.Comment: Updated to agree with published versio

Doing child-protection social work with parents: what are the barriers in practice?

For many social workers, participatory practice may seem an unachievable goal, particularly in the field of child protection. In this paper, we discuss a significant programme of change in one London local authority, as part of which we undertook 110 observations of practice and provided more than eighty follow-up coaching sessions for workers. Through these observations, we saw many examples of key participatory practice skills such as empathy, collaboration and involvement in decision making. We also saw many examples of reducing autonomy and excluding parents from decision making. Often, we found the same worker would adopt a participatory approach with one family and a non-participatory approach with another. Through coaching sessions, we explored how and why workers used different approaches and discussed the barriers to adopting a more consistently participatory approach. These discussions led us to reflect on fundamental questions relating to the purpose of child-protection social work, how social workers can best help families and what the limits might be of participation in situations of high risk. We argue that truly participatory child-protection social work requires not simply better training or different tools, but an innovation in the value base of children’s services