Componentwise linearity of ideals arising from graphs

Let $G$ be a simple undirected graph on $n$ vertices. Francisco and Van Tuyl have shown that if $G$ is chordal, then $\bigcap_{\{x_i,x_j\}\in E_G} < x_i,x_j>$ is componentwise linear. A natural question that arises is for which $t_{ij}>1$ the ideal $\bigcap_{\{x_i,x_j\}\in E_G}^{t_{ij}}$ is componentwise linear, if $G$ is chordal. In this report we show that $\bigcap_{\{x_i,x_j\}\in E_G} ^{t}$ is componentwise linear for all $n\geq 3$ and positive $t$, if $G$ is a complete graph. We give also an example where $G$ is chordal, but the intersection ideal is not componentwise linear for any $t>1$.Comment: 5 page

Predictive spatial network analysis for high resolution transport modelling, applied to cyclist flows, mode choice and targeting investment

Betweenness is a measure long used in spatial network analysis (SpNA) to predict flows of pedestrians and vehicles, and more recently in public health research. We improve on this approach with a methodology for combining multiple betweenness computations using cross-validated ridge regression to create wide-scale, high-resolution transport models. This enables computationally efficient calibration of distance decay, agglomeration effects, and multiple trip purposes. Together with minimization of the Geoffrey E. Havers (GEH) statistic commonly used to evaluate transport models, this bridges a gap between SpNA and mainstream transport modeling practice. The methodology is demonstrated using models of bicycle transport, where the higher resolution of the SpNA models compared to mainstream (four-step) models is of particular use. Additional models are developed incorporating heterogeneous user preferences (cyclist aversion to motor traffic). Based on network shape and flow data alone the best model gives reasonable correlation against cyclist flows on individual links, weighted to optimize GEH (r2 = 0.78, GEH = 1.9). As SpNA models use a single step rather than four, and can be based on flow data alone rather than demographics and surveys, the cost of calibration is lower, ensuring suitability for small-scale infrastructure projects as well as large-scale studies

Quantitative models of well-being to inform policy: Problems and opportunities

Subjective well-being, in contrast to other commonly used performance metrics such as gross domestic product, appears to offer a way to directly measure what society aims to achieve. Subjective well-being modeling to date has been restricted to regression analysis. This paper synthesizes and critiques existing literature and case studies to examine the challenges and opportunities presented by more advanced computations of well-being, including spatial, optimizing and spatial-optimizing models, which may well be created by researchers in the future if current policy level interest in well-being continues to grow. Subjective well-being is a promising measure, especially in light of recent research that shows reliable correlations with objective measures. However, the issue of individual adaptation means that excessive focus on subjective well-being may discriminate against groups with lower expectations and higher ability and/or willingness to adapt. Alternative approaches such as equivalent income may address this issue, at the expense of being harder to measure. Through an examination of four case studies and one thought experiment, we find that modeling challenges include nonlinearity, interaction, spatial sorting and extrapolation beyond valid limits. A significant research gap is found in how individual well-being scores should be aggregated to a collective one; this is a normative question although descriptive ethics would appear to offer a practical approach

Surface Acoustic Wave Single-Electron Interferometry

We propose an experiment to observe interference of a single electron as it is transported along two parallel quasi-one-dimensional channels trapped in a single minimum of a travelling periodic electric field. The experimental device is a modification of the surface acoustic wave (SAW) based quantum processor. Interference is achieved by creating a superposition of spatial wavefunctions between the two channels and inducing a relative phase shift via either a transverse electric field or a magnetic field. The interference can be used to estimate the decoherence time of an electron in this type of solid-state device

Bayesian inference of elevation to reduce large interpolation errors in 2-d road features draped over digital elevation models

The usual approach for adding elevation data to two dimensional (2-d) vector features in a Geographic Information System (GIS) is to infer heights from a Digital Elevation Model (DEM), either through traditional (naïve) interpolation, Kriging, or deep learning. Where the terrain contains steep slopes, however, any of these approaches can generate large errors due to the limited resolution of the DEM, and model error in the DEM concept itself. In the case of road networks, these errors have a severe and nonlinear effect on cycling route planners and transport models, especially those based on open elevation data. This paper introduces a Bayesian maximum likelihood approach to correcting interpolated heights, by combining a DEM with prior expectations of feature gradient. The topological network defined by feature shapes is used as auxiliary information. Correcting the output of naïve interpolation shows reduction of mean errors, and reduced overprediction of elevation change outliers, compared to both naïve interpolation and Kriging

Using spatial network analysis to model pedal cycle flows, risk and mode choice.

Spatial network analysis (SpNA) provides a promising alternative to traditional transport models for the modelling of active travel, because walking and cycling behaviour is influenced by features smaller than the scale of zones in a traditional model. There is currently a need for link-level, city wide modelling of cycling, both to ensure the needs of existing cyclists are catered for in planning, and to model the effects of changing infrastructure in shaping cyclist behaviour. Existing SpNA models treat cyclists and car drivers as if they make navigational decisions in a similar way, which in reality is not the case. This paper presents an SpNA model using hybrid betweenness, which fits cyclist flows in Cardiff, Wales using distance, angular distance, motor vehicle traffic and slope as predictors of route choice. SpNA betweenness is also shown to implicitly capture the effect of urban density on mode choice. As it handles route finding decisions of drivers and cyclists separately, the model presented is also applicable to road safety models examining the interaction between the two classes of road user. The model has low cost of data collection and is reproducible using publicly available network analysis software and open mapping data. Further avenues for modelling the effect of infrastructure on cycling are discussed

Spatial localization of closeness and betweenness measures: a self-contradictory but useful form of network analysis

Closeness and betweenness are forms of spatial network analysis grounded in a long-standing tradition of measuring accessibility and flow potential. More recently, these measures have been enhanced by the concept of spatial localization, producing effective models for the prediction of pedestrian and vehicle driver behaviour. A contradiction arises where the distance metric used to define locality does not match the distance metric used to define shortest paths for closeness and betweenness. A typical case is the use of angular shortest paths within a Euclidean buffer as a pedestrian flow model. Such a model assumes that people make a mode choice based on distance, but a route choice based on least angular change – even when this results in an excessively long ‘problem route’, which conflicts with their criterion for mode choice. This study examines the prevalence of problem routes and the magnitude of their effect on some pedestrian and vehicle models. We show that while in a weighted analysis, pathological cases could invalidate an entire model, in the models presented the effect of this contradiction is minor. We do this by comparing model predictions to real flow data, using four strategies for handling problem routes: ignore, discard, reroute and strict locality. Strict locality is justified on the grounds of bounded rationality. We find all strategies to give broadly similar results, although the reroute and strict strategies give marginally better simulation accuracy. We also present a discussion of the characteristics of each strategy, and findings on computational efficiency. We conclude that it is prudent in any computation of localized closeness and betweenness to consider the impact of problem routes; however, they do not necessarily invalidate these forms of analysis, which remain useful

The structure of epitaxial V2O3 films and their surfaces : a medium energy ion scattering study

Medium energy ion scattering, using 100 keV H+ incident ions, has been used to investigate the growth of epitaxial films, up to thicknesses of ~200 Å, of V2O3 on both Pd(111) and Au(111). Scattered-ion energy spectra provide a measure of the average film thickness and the variations in this thickness, and show that, with suitable annealing, the crystalline quality is good. Plots of the scattering yield as a function of scattering angle, so-called blocking curves, have been measured for two different incidence directions and have been used to determine the surface structure. Specifically, scattering simulations for a range of different model structures show poor agreement with experiment for half-metal (….V’O3V) and vanadyl (….V’O3V=O) terminations, with and without surface interlayer relaxations. However, good agreement with experiment is found for the modified oxygen-termination structure, first proposed by Kresse et al., in which a subsurface V half-metal layer is moved up into the outermost V buckled metal layer to produce a VO2 overlayer on the underlying V2O3, with an associated layer structure of ….O3VV’’V’O3

Spatial Network Analysis as a tool for measuring change in accessibility over time: limits of transport investment as a driver for UK regional development.

This paper develops spatial network metrics that contribute to analysis of regional development. We use the sDNA software to derive longitudinal road network density and efficiency measures based on the network within a 1-hr travel time buffer. We estimate this travel time itself from network shape and show it to be comparable to Google Maps travel time data. Economic analysis of 374 Local Administrative Units in the UK mainland shows cross-sectional association between our network density and efficiency measures and Gross Value Added per capita (GVApc), whether measured in bivariate correlation or in multiple regression controlling for population, education, economic activity rate and rail stations. This is however both mediated and moderated by the proportion of knowledge-based businesses; regions lacking a strong knowledge-based sector show only weak correspondence between GVApc and accessibility. Looking at change over time, increase in network accessibility is linked to growth in the knowledge-based sector, but inversely linked to economic performance during the 8-year period studied, a finding which remains unexplained. Although further substantiation is needed, results suggest that the policy of transport investment as a driver of UK economic growth may be less effective in areas lacking potential to develop a strong knowledge-based sector