Matching Points with Things

Given an ordered set of points and an ordered set of geometric objects in the plane, we are interested in finding a non-crossing matching between point-object pairs. We show that when the objects we match the points to are finite point sets, the problem is NP-complete in general, and polynomial when the objects are on a line or when their number is at most 2. When the objects are line segments, we show that the problem is NP-complete in general, and polynomial when the segments form a convex polygon or are all on a line. Finally, for objects that are straight lines, we show that the problem of finding a min-max non-crossing matching is NP-complete

Multidimensional Scaling of Varietal Data in Sedimentary Provenance Analysis

Varietal studies of sedimentary provenance use the properties of individual minerals or mineral groups. These are recorded as lists of numerical tables that can be difficult to interpret. Multidimensional Scaling (MDS) is a popular multivariate ordination technique for analyzing other types of provenance data based on, for example, detrital geochronology or petrography. Applying MDS to varietal data would allow them to be treated on an equal footing with those other provenance proxies. MDS requires a method to quantify the dissimilarity between two samples. This paper introduces three ways to do so. The first method (“treatment-by-row”) turns lists of (compositional) data tables into lists of vectors, using principal component analysis. These lists of vectors can then be treated as “distributional” data and subjected to MDS analysis using dissimilarity measures such as the Kolmogorov-Smirnov statistic. The second method (“treatment-by-column”) turns lists of compositional data tables into multiple lists of vectors, each representing a single component of the varietal data. These multiple distributional data sets are subsequently subjected to Procrustes analysis or 3-way MDS. The third method uses the Wasserstein-2 distance to jointly compare the rows and columns of varietal data. This arguably makes the best use of the data but acts more like a “black box” than the other two methods. Applying the three methods to a detrital titanite data set from Colombia yields similar results. After converting varietal data to dissimilarity matrices, they can be combined with other types of provenance data, again using Procrustes analysis or 3-way MDS

Grating-coupled excitation of multiple surface plasmon-polariton waves

The excitation of multiple surface-plasmon-polariton (SPP) waves of different linear polarization states and phase speeds by a surface-relief grating formed by a metal and a rugate filter, both of finite thickness, was studied theoretically, using rigorous coupled-wave-analysis. The incident plane wave can be either p or s polarized. The excitation of SPP waves is indicated by the presence of those peaks in the plots of absorbance vs. the incidence angle that are independent of the thickness of the rugate filter. The absorbance peaks representing the excitation of s-polarized SPP waves are narrower than those representing p-polarized SPP waves. Two incident plane waves propagating in different directions may excite the same SPP wave. A line source could excite several SPP waves simultaneously

Effectiveness of an online intervention for parents/guardians of children aged 4-7 years who are concerned about their child's emotional and behavioural development: protocol for an online randomised controlled trial (EMERGENT study).

The demand for resources to support emotional and behavioural development in early childhood is ever increasing. However, conventional interventions are lacking in resources and have significant barriers. The Embers the Dragon programme helps address the growing unmet need of children requiring support. The delivery of the current project seeks to help support parents, reduce the burden placed on pressed services (eg, Child and Adolescent Mental Health Services) and to help improve the emotional and behavioural development of children. This project aims to investigate the efficacy and acceptability of Embers on parenting and children's psychosocial outcomes. 364 parents/guardians of children aged between 4 and 7 will be recruited via the internet, schools and general practitioners (GPs). This is an online waitlist-controlled trial with three arms: (1) control arm, (2) access to Embers arm and (3) access to Embers+school. Participants will be randomised (1:1) into (1) or (2) to evaluate the use of Embers at home. To evaluate scalability in schools, (3) will be compared with (2), and (1) to test efficacy against treatment as usual (not receiving the intervention). Qualitative interviews will also be conducted. Primary outcomes are the Parental Self-efficacy Scale, Strengths and Difficulties Questionnaire and qualitative interviews. Outcomes will be compared between the three groups at baseline, 8, 16 and 24 weeks. Ethical approval has been granted by the London South Bank University ethics panel (ETH2324-0004). To recruit via GPs, NHS ethical approval has been applied for, and the IRAS (331410) application is under consideration by the Central Bristol REC. The results of the project will be submitted for publication in a peer-reviewed journal. Parents/guardians will provide informed consent online prior to taking part in the study. For the interviews, assent will be taken from children by the researchers on the day. ISRCTN58327872. [Abstract copyright: © Author(s) (or their employer(s)) 2024. Re-use permitted under CC BY-NC. No commercial re-use. See rights and permissions. Published by BMJ.

Screening for important unwarranted variation in clinical practice: a triple-test of processes of care, costs and patient outcomes

Objective: Unwarranted variation in clinical practice is a target for quality improvement in health care, but there is no consensus on how to identify such variation or to assess the potential value of initiatives to improve quality in these areas. This study illustrates the use of a triple test, namely the comparative analysis of processes of care, costs and outcomes, to identify and assess the burden of unwarranted variation in clinical practice. Methods: Routinely collected hospital and mortality data were linked for patients presenting with symptoms suggestive of acute coronary syndromes at the emergency departments of four public hospitals in South Australia. Multiple regression models analysed variation in re-admissions and mortality at 30 days and 12 months, patient costs and multiple process indicators. Results: After casemix adjustment, an outlier hospital with statistically significantly poorer outcomes and higher costs was identified. Key process indicators included admission patterns, use of invasive diagnostic procedures and length of stay. Performance varied according to patients’ presenting characteristics and time of presentation. Conclusions: The joint analysis of processes, outcomes and costs as alternative measures of performance inform the importance of reducing variation in clinical practice, as well as identifying specific targets for quality improvement along clinical pathways. Such analyses could be undertaken across a wide range of clinical areas to inform the potential value and prioritisation of quality improvement initiatives.Andrew Partington, Derek P. Chew, David Ben-Tovim, Matthew Horsfall, Paul Hakendorf and Jonathan Karno

\pi N scattering in relativistic baryon chiral perturbation theory revisited

We have analyzed pion-nucleon scattering using the manifestly relativistic covariant framework of Infrared Regularization up to {\cal O}(q^3) in the chiral expansion, where q is a generic small momentum. We describe the low-energy phase shifts with a similar quality as previously achieved with Heavy Baryon Chiral Perturbation Theory, \sqrt{s}\lesssim1.14 GeV. New values are provided for the {\cal O}(q^2) and {\cal O}(q^3) low-energy constants, which are compared with previous determinations. This is also the case for the scattering lengths and volumes. Finally, we have unitarized the previous amplitudes and as a result the energy range where data are reproduced increases significantly.Comment: 26 pages, 5 figures, 5 table

Resonances from meson-meson scattering in U(3) CHPT

In this work, the complete one loop calculation of meson-meson scattering amplitudes within U(3)\otimes U(3) chiral perturbation theory with explicit resonance states is carried out for the first time. Partial waves are unitarized from the perturbative calculation employing a non-perturbative approach based on the N/D method. Once experimental data are reproduced in a satisfactory way we then study the resonance properties, such as the pole positions, corresponding residues and their N_C behaviors. The resulting N_C dependence is the first one in the literature that takes into account the fact that the \eta_1 becomes the ninth Goldstone boson in the chiral limit for large N_C. Within this scheme the vector resonances studied, \rho(770), K^*(892) and \phi(1020), follow an N_C trajectory in agreement with their standard \bar{q}q interpretation. The scalars f_0(1370), a_0(1450) and K^*(1430) also have for large N_C a \bar{q}q pole position trajectory and all of them tend to a bare octet of scalar resonances around 1.4 GeV. The f_0(980) tends asymptotically to the bare pole position of a singlet scalar resonance around 1 GeV. The \sigma, \kappa and a_0(980) scalar resonances have a very different N_C behavior. The case of the \sigma resonance is analyzed with special detail.Comment: 50 pages, 15 figures, 1 table. Enlarged version with more detail comparisons with previous results in the literature. To match with accepted version for publicatio

A Self-Organized Method for Computing the Epidemic Threshold in Computer Networks

In many cases, tainted information in a computer network can spread in a way similar to an epidemics in the human world. On the other had, information processing paths are often redundant, so a single infection occurrence can be easily "reabsorbed". Randomly checking the information with a central server is equivalent to lowering the infection probability but with a certain cost (for instance processing time), so it is important to quickly evaluate the epidemic threshold for each node. We present a method for getting such information without resorting to repeated simulations. As for human epidemics, the local information about the infection level (risk perception) can be an important factor, and we show that our method can be applied to this case, too. Finally, when the process to be monitored is more complex and includes "disruptive interference", one has to use actual simulations, which however can be carried out "in parallel" for many possible infection probabilities