Shifting : one-inclusion mistake bounds and sample compression

We present new expected risk bounds for binary and multiclass prediction, and resolve several recent conjectures on sample compressibility due to Kuzmin and Warmuth. By exploiting the combinatorial structure of concept class F, Haussler et al. achieved a VC(F)/n bound for the natural one-inclusion prediction strategy. The key step in their proof is a d=VC(F) bound on the graph density of a subgraph of the hypercube—one-inclusion graph. The first main result of this report is a density bound of n∙choose(n-1,≤d-1)/choose(n,≤d) < d, which positively resolves a conjecture of Kuzmin and Warmuth relating to their unlabeled Peeling compression scheme and also leads to an improved one-inclusion mistake bound. The proof uses a new form of VC-invariant shifting and a group-theoretic symmetrization. Our second main result is an algebraic topological property of maximum classes of VC-dimension d as being d-contractible simplicial complexes, extending the well-known characterization that d=1 maximum classes are trees. We negatively resolve a minimum degree conjecture of Kuzmin and Warmuth—the second part to a conjectured proof of correctness for Peeling—that every class has one-inclusion minimum degree at most its VC-dimension. Our final main result is a k-class analogue of the d/n mistake bound, replacing the VC-dimension by the Pollard pseudo-dimension and the one-inclusion strategy by its natural hypergraph generalization. This result improves on known PAC-based expected risk bounds by a factor of O(log n) and is shown to be optimal up to a O(log k) factor. The combinatorial technique of shifting takes a central role in understanding the one-inclusion (hyper)graph and is a running theme throughout

Are low CO2 emitters in rural areas also socially excluded? An empirical investigation of travel diary data from rural Northern Ireland

The reduction of CO2 emissions and social exclusion are two key elements of UK transport strategy. Despite intensive research on each theme, little effort has so far been made linking the relationship between emissions and social exclusion. In addition, current knowledge on each theme is limited to urban areas; little research is available on these themes for rural areas. This research contributes to this gap in the literature by analysing 157 weekly activity-travel diary data collected from three case study areas with differential levels of area accessibility and area mobility options, located in rural Northern Ireland. Individual weekly CO2 emission levels from personal travel diaries (both hot exhaust emission and cold-start emission) were calculated using average speed models for different modes of transport. The socio-spatial patterns associated with CO2 emissions were identified using a general linear model whereas binary logistic regression analyses were conducted to identify mode choice behaviour and activity patterns. This research found groups that emitted a significantly lower level of CO2 included individuals living in an area with a higher level of accessibility and mobility, non-car, non-working, and low-income older people. However, evidence in this research also shows that although certain groups (e.g. those working, and residing in an area with a lower level of accessibility) emitted higher levels of CO2, their rate of participation in activities was however found to be significantly lower compared to their counterparts. Based on the study findings, this research highlights the need for both soft (e.g. teleworking) and physical (e.g. accessibility planning) policy measures in rural areas in order to meet government’s stated CO2 reduction targets while at the same time enhancing social inclusion.

Numerical methods for second-order stochastic differential equations

We seek numerical methods for second‐order stochastic differential equations that reproduce the stationary density accurately for all values of damping. A complete analysis is possible for scalar linear second‐order equations (damped harmonic oscillators with additive noise), where the statistics are Gaussian and can be calculated exactly in the continuous‐time and discrete‐time cases. A matrix equation is given for the stationary variances and correlation for methods using one Gaussian random variable per timestep. The only Runge–Kutta method with a nonsingular tableau matrix that gives the exact steady state density for all values of damping is the implicit midpoint rule. Numerical experiments, comparing the implicit midpoint rule with Heun and leapfrog methods on nonlinear equations with additive or multiplicative noise, produce behavior similar to the linear case.

The differential recognition of children’s cultural practices in middle primary literacy classrooms

This paper argues that teachers’ recognition of children’s cultural practices is an important positive step in helping socio-economically disadvantaged children engage with school literacies. Based on twenty-one longitudinal case studies of children’s literacy development over a three-year period, the authors demonstrate that when children’s knowledges and practices assembled in home and community spheres are treated as valuable material for school learning, children are more likely to invest in the work of acquiring school literacies. However they show also that whilst some children benefit greatly from being allowed to draw on their knowledge of popular culture, sports and the outdoors, other children’s interests may be ignored or excluded. Some differences in teachers’ valuing of home and community cultures appeared to relate to gender dimensions.

Stochastic models and simulation of ion channel dynamics

The behaviour of ion channels within cardiac and neuronal cells is intrinsically stochastic in nature. When the number of channels is small this stochastic noise is large and can have an impact on the dynamics of the system which is potentially an issue when modelling small neurons and drug block in cardiac cells. While exact methods correctly capture the stochastic dynamics of a system they are computationally expensive, restricting their inclusion into tissue level models and so approximations to exact methods are often used instead. The other issue in modelling ion channel dynamics is that the transition rates are voltage dependent, adding a level of complexity as the channel dynamics are coupled to the membrane potential. By assuming that such transition rates are constant over each time step, it is possible to derive a stochastic differential equation (SDE), in the same manner as for biochemical reaction networks, that describes the stochastic dynamics of ion channels. While such a model is more computationally efficient than exact methods we show that there are analytical problems with the resulting SDE as well as issues in using current numerical schemes to solve such an equation. We therefore make two contributions: develop a different model to describe the stochastic ion channel dynamics that analytically behaves in the correct manner and also discuss numerical methods that preserve the analytical properties of the model.

Young children’s beliefs about including others in their play: Social and moral reasoning about inclusion and exclusion

Previous research has emphasised the importance of active citizenship in the early years for the development of a tolerant and cohesive Australian society. This paper presents findings related to young children’s beliefs about exclusion based on gender and race. The findings draw from a larger study exploring the development of children’s moral and social values and teachers’ beliefs and practices related to teaching for moral development, in the early years of school in Australia. This current study examined reasoning about exclusion in early childhood with children aged 5-8 years. One hundred children from seven schools (Preparatory to Grade 3) answered questions relating to two scenarios in which the children had to make a decision about whether to include others of different gender or race in their play. The majority of children believed that others should be included in their play, regardless of their gender or race. When asked to explain, the children primarily gave reasons related to moral concern and fairness. Children were then asked whether they would continue to include or exclude if their friends (social consensus) or teachers (authority) suggested otherwise. The majority of children maintained their beliefs when beliefs to the contrary were voiced by their peers and teachers. The implications of these responses are discussed.

Supplement : Efficient weak second-order stochastic Runge-Kutta methods for non-commutative Stratonvich stochastic differential equations

This paper gives a modification of a class of stochastic Runge–Kutta methods proposed in a paper by Komori (2007). The slight modification can reduce the computational costs of the methods significantly.

Multiculturalism, education for sustainable development (ESD) and the shifting discursive landscape of social inclusion

Australia has a long and sometimes turbulent relationship with the migrant Other. This paper examines a component of this relationship via the window of contemporary multicultural policy. The paper begins with an analysis of the political and social conditions that enabled a national and bipartisan policy of multiculturalism to emerge as formalised federal policy during the late 1960s and early 1970s. The paper re-problematises the influences that helped shape Australia's articulation of race and ethnicity and argues that multiculturalism, within a post-September 11 environment, can no longer be framed solely within its traditional framework of social justice. The paper positions education for sustainable development (ESD) as an emerging discursive field that provides educators with an alternative road map for critiquing Australia's fluid relationship with the migrant Other. By linking the tenets of multiculturalism with ESD, this paper suggests pre-service teacher educators are presented with a productive, and at the same time politically palatable, means for regaining pedagogical traction for a semi-dormant agenda of social inclusion.

Academic faculty’s teaching social networks : what is the extent of library faculty’s inclusion?

Collaboration between academic and library faculty is an important topic of discussion and research among academic librarians. Partnerships are vital for developing effective information literacy education. The research reported in this paper aims to develop an understanding of academic collaborators by analyzing academic faculty’s teaching social network. Academic faculty teaching social networks have not been previously described through the lens of social network analysis. A teaching social network is comprised of people and their communication channels that affect academic faculty when they design and deliver their courses. Social network analysis was the methodology used to describe the teaching social networks. The preliminary results show academic faculty were more affected by the channels of communication in how they taught (pedagogy) than what they taught (course content). This study supplements the existing research on collaboration and information literacy. It provides both academic and library faculty with added insight into their relationships.