Solving Non-homogeneous Nested Recursions Using Trees

The solutions to certain nested recursions, such as Conolly's C(n) = C(n-C(n-1))+C(n-1-C(n-2)), with initial conditions C(1)=1, C(2)=2, have a well-established combinatorial interpretation in terms of counting leaves in an infinite binary tree. This tree-based interpretation, which has a natural generalization to a k-term nested recursion of this type, only applies to homogeneous recursions, and only solves each recursion for one set of initial conditions determined by the tree. In this paper, we extend the tree-based interpretation to solve a non-homogeneous version of the k-term recursion that includes a constant term. To do so we introduce a tree-grafting methodology that inserts copies of a finite tree into the infinite k-ary tree associated with the solution of the corresponding homogeneous k-term recursion. This technique can also be used to solve the given non-homogeneous recursion with various sets of initial conditions.Comment: 14 page

Children’s experiences of domestic violence and abuse: siblings’ accounts of relational coping

This article explores how young people see their relationships, particularly their sibling relationships, in families affected by domestic violence, and how relationality emerges in their accounts as a resource to build an agentic sense of self. The ‘voice’ of children is largely absent from domestic violence literature, which typically portrays them as passive, damaged and relationally incompetent. Children’s own understandings of their relational worlds are often overlooked, and consequently existing models of children’s social interactions give inadequate accounts of their meaning-making-in-context. Drawn from a larger study of children’s experiences of domestic violence and abuse, this paper uses two case studies of sibling relationships to explore young people’s use of relational resources, for coping with violence in the home. The paper explores how relationality and coping intertwine in young people’s accounts, and disrupts the taken for granted assumption that children’s ‘premature caring’ or ‘parentification’ is (only) pathological in children’s responses to domestic violence. This has implications for understanding young people’s experiences in the present, and supporting their capacity for relationship building in the future

Towards the Physical Instantiation of Virtual People and Components in Physical Mixed-Reality Tele-Presence Environments

Interaction between virtual and physical worlds is an area of growing importance as technology increases the amount of virtualization in our lives. However, to-date, most of this work has focused on translating the physical world into a virtual representation, with little attention being paid to instantiating the virtual in the physical world. This paper addresses this latter issue. In particular we examine how a virtual student can be given a presence in a real smart classroom in order to have better interaction with local students within a shared environment. In this 'work-in-progress' (concept) paper, we propose a novel augmented-reality based approach that identifies and synchronises the remote and local environmental states (people and environment) so as to provide a more naturalistic mixed reality shared environment

Field dependence of the vortex core size in a multi-band superconductor

The magnetic field dependence of the vortex core size in the multi-band superconductor NbSe2 has been determined from muon spin rotation measurements. The spatially extended nature of the quasiparticle core states associated with the smaller gap leads to a rapid field-induced shrinkage of the core size at low fields, while the more tightly bound nature of the states associated with the larger gap leads to a field-independent core size for fields greater than 4 kOe. A simple model is proposed for the density of delocalized core states that establishes a direct relationship between the field-induced reduction of the vortex core size and the corresponding enhancement of the electronic thermal conductivity. We show that this model accurately describes both NbSe2 and the single-band superconductor V3Si.Comment: 4 pages, 4 figures. Version accepted for publication in Physical Review Letter

Multi-filter spectrophotometry simulations

To complement both the multi-filter observations of quasar environments described in these proceedings, as well as the proposed UBC 2.7 m Liquid Mirror Telescope (LMT) redshift survey, we have initiated a program of simulated multi-filter spectrophotometry. The goal of this work, still very much in progress, is a better quantitative assessment of the multiband technique as a viable mechanism for obtaining useful redshift and morphological class information from large scale multi-filter surveys

Towards Measuring Learning Effectiveness considering Presence, Engagement and Immersion in a Mixed and Augmented Reality Learning Environment

The current era of advanced display technologies, such as a head mounted displays, smart glasses and handheld devices, have supported the usage of mixed-reality and augmented reality concepts in smart educational classrooms. These advanced technologies have enabled enhanced collaboration and an interactive communication between distance learners and local learners. Being present' is a key factor in both worlds (real and virtual) as it plays an important role in increasing the students' collaborative engagement during the learning activity. However, few studies have considered how much using such immersive interfaces with various learning scenarios may ultimately affect learning outcomes, and whether students feel fully engaged or not in such environments. This work-in-progress paper will demonstrate a MiRTLE+ prototype of how remote students can collaborate within mixed-reality environments by using an augmented reality approach. Secondly, it will explore the learning effectiveness based on the following factors: students' presence, engagement, and immersion in smart environments. With regard to the learning task, we will consider a card game task to measure the learners' progress as they progress from novice to expert player. To evaluate these factors, we utilise several existing frameworks which have been applied to our mixed-reality worlds that help us to examine the learning outcomes from using these environments

Hfq binding changes the structure of Escherichia coli small noncoding RNAs OxyS and RprA, which are involved in the riboregulation of rpoS

OxyS and RprA are two small noncoding RNAs (sRNAs) that modulate the expression of rpoS, encoding an alternative sigma factor that activates transcription of multiple Escherichia coli stress-response genes. While RprA activates rpoS for translation, OxyS down-regulates the transcript. Crucially, the RNA binding protein Hfq is required for both sRNAs to function, although the specific role played by Hfq remains unclear. We have investigated RprA and OxyS interactions with Hfq using biochemical and biophysical approaches. In particular, we have obtained the molecular envelopes of the Hfq–sRNA complexes using small-angle scattering methods, which reveal key molecular details. These data indicate that Hfq does not substantially change shape upon complex formation, whereas the sRNAs do. We link the impact of Hfq binding, and the sRNA structural changes induced, to transcript stability with respect to RNase E degradation. In light of these findings, we discuss the role of Hfq in the opposing regulatory functions played by RprA and OxyS in rpoS regulation

Investigation into use of double-layer grid structures as frequency selective surfaces for buildings

A simple Double–Layer Grid plane wave filter structure is proposed that can provide multiple transmission bands for cellular phone frequencies but with a reflection band for WLAN signals. The approach offers ease of construction making it applicable to building applications. A parametric study using simulation supported by simple experimental data investigates the proposed, novel desig