Noise resilience and entanglement evolution in two nonequivalent classes of quantum algorithms

The speedup provided by quantum algorithms with respect to their classical counterparts is at the origin of scientific interest in quantum computation. However, the fundamental reasons for such a speedup are not yet completely understood and deserve further attention. In this context, the classical simulation of quantum algorithms is a useful tool that can help us in gaining insight. Starting from the study of general conditions for classical simulation, we highlight several important differences between two nonequivalent classes of quantum algorithms. We investigate their performance under realistic conditions by quantitatively studying their resilience with respect to static noise. This latter refers to errors affecting the initial preparation of the register used to run an algorithm. We also compare the evolution of the entanglement involved in the different computational processes.

Novel linkage to chromosome 20p using latent classes of psychotic illness in 270 Irish high-density families

Background: Several lines of evidence suggest that the clinical heterogeneity of schizophrenia is due to genetic heterogeneity. Genetic heterogeneity may decrease the signal-to-noise ratio in linkage and association studies. Therefore, linkage studies of clinically homogeneous classes of psychotic illness may result in greater power to detect at least some loci.

Sharing Classes between Separate Schools: a mechanism for improving inter-group relations in Northern Ireland?

One manifestation of division and the history of conflict in Northern Ireland is the parallel education system that exists for Protestants and Catholics. Although recent decades have seen some advances in the promotion of integrated education, around 95% of children continue to attend schools separated on ethno-religious lines. In 2007 a programme for sharing education was established. Underpinned by intergroup contact theory, and reflecting educational priorities shared by all school sectors, the programme seeks to offer children from different denominational schools an opportunity to engage with each other on a sustained basis. In this article the authors adopt a quantitative approach to examining the impact of participation in the Sharing Education Programme on a range of outcomes (out-group attitudes, positive action tendencies and out-group trust) via, first, intergroup contact (cross-group friendships) and, second, intergroup anxiety. Their findings confirm the value of contact as a mechanism for promoting more harmonious relationships, and affirm the Sharing Education Programme as an initiative that can help promote social cohesion in a society that remains deeply divided.

What is being taught in Religious Education classes in Northern Ireland and to what extent should states be concerned about regulation, quality and control of the subject?

This paper reports on a research project designed to discover what schools are teaching in Religious Education in Northern Ireland and what procedures are in place to maintain standards in the delivery of the subject. A search through literature shows that little research has been carried out to determine what is being taught in Religious Education in Northern Ireland. It also indicates that there are very weak systems of control to measure the effectiveness or quality of what is delivered. A survey of the websites of all Post-Primary schools in the region was used to provide some answers to the basic question of what is being taught in RE. Using content and discourse analysis of these alongside supporting documentary sources (textbooks and exam specifications), it is possible to get a clearer picture of how the Northern Ireland Core Syllabus for Religious Education and any additional curricular elements are delivered in schools. The findings show that a significant minority of schools do not publicly articulate what pupils do in religious education. In situations where the content of religious education is made clear, some definite trends are evident. Despite the existence of a statutory core syllabus, there is significant variation in what is taught in schools. The content is most divergent from the syllabus in relation to the teaching of World Religions at Key Stage 3 and at Key Stage 4 whole elements of the syllabus are neglected due to limited conformity between the syllabus and exam specifications. These results raise important questions about the systems of regulation and control of the subject in the region. In law the subject is exempt from formal inspection by the local inspection authority; instead, a form of inspection is allowed for by the Christian churches who design the syllabus, but it is a process that is either entirely neglected or entirely unreported in situations where it does occur. It is argued that these findings raise questions of more general concern for this and other regions in Europe where the teaching of religious education is largely unregulated. For example, to what extent should states take an interest in what is taught in religious education, how it is delivered, what values it promotes and how standards of teaching and learning in the subject are upheld?

Patterns of co‑occurrence and interactions between age classes of the common triplefin, Forsterygion lapillum

Many marine organisms have pelagic larval stages that settle into benthic habitats occupied by older individuals; however, a mechanistic understanding of inter cohort interactions remains elusive for most species. Patterns of spatial covariation in the densities of juvenile and adult age classes of a small temperate reef fish, the common triplefin (Forsterygion lapillum), were evaluated during the recruitment season (Feb–Mar, 2011) in Wellington, New Zealand (41°17′S, 174°46′E). The relationship between juvenile and adult density among sites was best approximated by a dome-shaped curve, with a negative correlation between densities of juveniles and adults at higher adult densities. The curve shape was temporally variable, but was unaffected by settlement habitat type (algal species). A laboratory experiment using a “multiple-predator effects”design tested the hypothesis that increased settler mortality in the presence of adults (via enhanced predation risk or cannibalism) contributed to the observed negative relationship between juveniles and adults. Settler mortality did not differ between controls and treatments that contained either one (p = 0.08) or two (p = 0.09) adults. However, post hoca analyses revealed a significant positive correlation between the mean length of juveniles used in experimental trials and survival of juveniles in these treatments, suggesting that smaller juveniles may be vulnerable to cannibalism. There was no evidence for risk enhancement or predator interference when adults were present alongside a hetero specific predator (F. varium). These results highlight the complex nature of intercohort relationships in shaping recruitment patterns and add to the growing body of literature recognizing the importance of age class interactions.

Multiplicity results for some classes of Schrödinger-Poisson systems

In this thesis, we study the existence and multiplicity of solutions of the following class of Schr odinger-Poisson systems: u + u + l(x) u = (x; u) in R3; = l(x)u2 in R3; where l 2 L2(R3) or l 2 L1(R3). And we consider that the nonlinearity satis es the following three kinds of cases: (i) a subcritical exponent with (x; u) = k(x)jujp 2u + h(x)u (4 p < 2 ) under an inde nite case; (ii) a general inde nite nonlinearity with (x; u) = k(x)g(u) + h(x)u; (iii) a critical growth exponent with (x; u) = k(x)juj2 2u + h(x)jujq 2u (2 q < 2 ). It is worth mentioning that the thesis contains three main innovations except overcoming several di culties, which are generated by the systems themselves. First, as an unknown referee said in his report, we are the rst authors concerning the existence of multiple positive solutions for Schr odinger- Poisson systems with an inde nite nonlinearity. Second, we nd an interesting phenomenon in Chapter 2 and Chapter 3 that we do not need the condition R R3 k(x)ep 1dx < 0 with an inde nite noncoercive case, where e1 is the rst eigenfunction of +id in H1(R3) with weight function h. A similar condition has been shown to be a su cient and necessary condition to the existence of positive solutions for semilinear elliptic equations with inde nite nonlinearity for a bounded domain (see e.g. Alama-Tarantello, Calc. Var. PDE 1 (1993), 439{475), or to be a su cient condition to the existence of positive solutions for semilinear elliptic equations with inde nite nonlinearity in RN (see e.g. Costa-Tehrani, Calc. Var. PDE 13 (2001), 159{189). Moreover, the process used in this case can be applied to study other aspects of the Schr odinger-Poisson systems and it gives a way to study the Kirchho system and quasilinear Schr odinger system. Finally, to get sign changing solutions in Chapter 5, we follow the spirit of Hirano-Shioji, Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), 333, but the procedure is simpler than that they have proposed in their paper.

Factorização de algumas classes de funções matriciais e suas aplicações

Tese dout., Matemática, Universidade do Algarve, 2007,