The Philosophy of Mathematics: A Study of Indispensability and Inconsistency

This thesis examines possible philosophies to account for the practice of mathematics, exploring the metaphysical, ontological, and epistemological outcomes of each possible theory. Through a study of the two most probable ideas, mathematical platonism and fictionalism, I focus on the compelling argument for platonism given by an appeal to the sciences. The Indispensability Argument establishes the power of explanation seen in the relationship between mathematics and empirical science. Cases of this explanatory power illustrate how we might have reason to believe in the existence of mathematical entities present within our best scientific theories. The second half of this discussion surveys Newtonian Cosmology and other inconsistent theories as they pose issues that have received insignificant attention within the philosophy of mathematics. The application of these inconsistent theories raises questions about the effectiveness of mathematics to model physical systems

Improving the TanDEM-X Digital Elevation Model for flood modelling using flood extents from Synthetic Aperture Radar images

The topography of many floodplains in the developed world has now been surveyed with high resolution sensors such as airborne LiDAR (Light Detection and Ranging), giving accurate Digital Elevation Models (DEMs) that facilitate accurate flood inundation modelling. This is not always the case for remote rivers in developing countries. However, the accuracy of DEMs produced for modelling studies on such rivers should be enhanced in the near future by the high resolution TanDEM-X WorldDEM. In a parallel development, increasing use is now being made of flood extents derived from high resolution Synthetic Aperture Radar (SAR) images for calibrating, validating and assimilating observations into flood inundation models in order to improve these. This paper discusses an additional use of SAR flood extents, namely to improve the accuracy of the TanDEM-X DEM in the floodplain covered by the flood extents, thereby permanently improving this DEM for future flood modelling and other studies. The method is based on the fact that for larger rivers the water elevation generally changes only slowly along a reach, so that the boundary of the flood extent (the waterline) can be regarded locally as a quasi-contour. As a result, heights of adjacent pixels along a small section of waterline can be regarded as samples with a common population mean. The height of the central pixel in the section can be replaced with the average of these heights, leading to a more accurate estimate. While this will result in a reduction in the height errors along a waterline, the waterline is a linear feature in a two-dimensional space. However, improvements to the DEM heights between adjacent pairs of waterlines can also be made, because DEM heights enclosed by the higher waterline of a pair must be at least no higher than the corrected heights along the higher waterline, whereas DEM heights not enclosed by the lower waterline must in general be no lower than the corrected heights along the lower waterline. In addition, DEM heights between the higher and lower waterlines can also be assigned smaller errors because of the reduced errors on the corrected waterline heights. The method was tested on a section of the TanDEM-X Intermediate DEM (IDEM) covering an 11km reach of the Warwickshire Avon, England. Flood extents from four COSMO-SKyMed images were available at various stages of a flood in November 2012, and a LiDAR DEM was available for validation. In the area covered by the flood extents, the original IDEM heights had a mean difference from the corresponding LiDAR heights of 0.5 m with a standard deviation of 2.0 m, while the corrected heights had a mean difference of 0.3 m with standard deviation 1.2 m. These figures show that significant reductions in IDEM height bias and error can be made using the method, with the corrected error being only 60% of the original. Even if only a single SAR image obtained near the peak of the flood was used, the corrected error was only 66% of the original. The method should also be capable of improving the final TanDEM-X DEM and other DEMs, and may also be of use with data from the SWOT (Surface Water and Ocean Topography) satellite

Satellite-supported flood forecasting in river networks: a real case study

Satellite-based (e.g., Synthetic Aperture Radar [SAR]) water level observations (WLOs) of the floodplain can be sequentially assimilated into a hydrodynamic model to decrease forecast uncertainty. This has the potential to keep the forecast on track, so providing an Earth Observation (EO) based flood forecast system. However, the operational applicability of such a system for floods developed over river networks requires further testing. One of the promising techniques for assimilation in this field is the family of ensemble Kalman (EnKF) filters. These filters use a limited-size ensemble representation of the forecast error covariance matrix. This representation tends to develop spurious correlations as the forecast-assimilation cycle proceeds, which is a further complication for dealing with floods in either urban areas or river junctions in rural environments. Here we evaluate the assimilation of WLOs obtained from a sequence of real SAR overpasses (the X-band COSMO-Skymed constellation) in a case study. We show that a direct application of a global Ensemble Transform Kalman Filter (ETKF) suffers from filter divergence caused by spurious correlations. However, a spatially-based filter localization provides a substantial moderation in the development of the forecast error covariance matrix, directly improving the forecast and also making it possible to further benefit from a simultaneous online inflow error estimation and correction. Additionally, we propose and evaluate a novel along-network metric for filter localization, which is physically-meaningful for the flood over a network problem. Using this metric, we further evaluate the simultaneous estimation of channel friction and spatially-variable channel bathymetry, for which the filter seems able to converge simultaneously to sensible values. Results also indicate that friction is a second order effect in flood inundation models applied to gradually varied flow in large rivers. The study is not conclusive regarding whether in an operational situation the simultaneous estimation of friction and bathymetry helps the current forecast. Overall, the results indicate the feasibility of stand-alone EO-based operational flood forecasting

Seasonal benefits of farmland pond management for birds

Capsule: There is seasonal variation in the benefits that birds can take from restored farmland ponds. Aims: To evaluate season-specific benefits of farmland pond restoration for local bird communities. Methods: Bird communities were recorded at unmanaged overgrown and managed open-canopy farmland ponds over the breeding, post-breeding and winter seasons. Results were compared and related to seasonal variation in environmental conditions of within-pond and marginal habitats to identify predictors of local bird communities. Results: Bird communities at managed open-canopy ponds showed a higher abundance and species richness over all seasons and displayed pronounced seasonal shifts in composition. Warblers and other specialised bird species were frequently observed at open-canopy sites over the breeding and post-breeding seasons but were generally absent from overgrown ponds. While pond management and landscape connectivity had a consistent positive influence on bird communities over all seasons, the importance of other predictors such as bramble area varied seasonally. Conclusions: Our study highlights a key role of pond management for farmland bird conservation. In addition, the identified seasonal predictors of bird assemblages provide valuable lessons for the design of agri-environment prescriptions for farmland ponds, highlighting the importance of bramble-dominated patches and pond marginal habitat over the breeding season and of a strong connectivity between pond margins and surrounding semi-natural habitats throughout the year

Face, body and speech cues independently predict judgments of attractiveness

Research on human attraction frequently makes use of single-modality stimuli such as neutral-expression facial photographs as proxy indicators of an individual’s attractiveness. However, we know little about how judgments of these single-modality stimuli correspond to judgments of stimuli that incorporate multi-modal cues of face, body and speech. In the present study, ratings of attractiveness judged from videos of participants introducing themselves were independently predicted by judgments of the participant’s facial attractiveness (a neutral-expression facial photograph masked to conceal the hairstyle), body attractiveness (a photograph of the upper body), and speech attractiveness (the soundtrack to the video). We also found that ratings of the face, body and speech were positively related to each other. Our results support the assumption that the single-modality stimuli used in much attractiveness research are valid proxy indicators of overall attractiveness in ecologically valid contexts, and complement literature showing cross-modality concordance of trait attractiveness, but also recommend that research relying on assessments of individual attractiveness take account of both visual and vocal attractiveness where possible

Training future generations to deliver evidence-based conservation and ecosystem management

1. To be effective, the next generation of conservation practitioners and managers need to be critical thinkers with a deep understanding of how to make evidence-based decisions and of the value of evidence synthesis. 2. If, as educators, we do not make these priorities a core part of what we teach, we are failing to prepare our students to make an effective contribution to conservation practice. 3. To help overcome this problem we have created open access online teaching materials in multiple languages that are stored in Applied Ecology Resources. So far, 117 educators from 23 countries have acknowledged the importance of this and are already teaching or about to teach skills in appraising or using evidence in conservation decision-making. This includes 145 undergraduate, postgraduate or professional development courses. 4. We call for wider teaching of the tools and skills that facilitate evidence-based conservation and also suggest that providing online teaching materials in multiple languages could be beneficial for improving global understanding of other subject areas.Peer reviewe

Elective cancer surgery in COVID-19-free surgical pathways during the SARS-CoV-2 pandemic: An international, multicenter, comparative cohort study

PURPOSE As cancer surgery restarts after the first COVID-19 wave, health care providers urgently require data to determine where elective surgery is best performed. This study aimed to determine whether COVID-19–free surgical pathways were associated with lower postoperative pulmonary complication rates compared with hospitals with no defined pathway. PATIENTS AND METHODS This international, multicenter cohort study included patients who underwent elective surgery for 10 solid cancer types without preoperative suspicion of SARS-CoV-2. Participating hospitals included patients from local emergence of SARS-CoV-2 until April 19, 2020. At the time of surgery, hospitals were defined as having a COVID-19–free surgical pathway (complete segregation of the operating theater, critical care, and inpatient ward areas) or no defined pathway (incomplete or no segregation, areas shared with patients with COVID-19). The primary outcome was 30-day postoperative pulmonary complications (pneumonia, acute respiratory distress syndrome, unexpected ventilation). RESULTS Of 9,171 patients from 447 hospitals in 55 countries, 2,481 were operated on in COVID-19–free surgical pathways. Patients who underwent surgery within COVID-19–free surgical pathways were younger with fewer comorbidities than those in hospitals with no defined pathway but with similar proportions of major surgery. After adjustment, pulmonary complication rates were lower with COVID-19–free surgical pathways (2.2% v 4.9%; adjusted odds ratio [aOR], 0.62; 95% CI, 0.44 to 0.86). This was consistent in sensitivity analyses for low-risk patients (American Society of Anesthesiologists grade 1/2), propensity score–matched models, and patients with negative SARS-CoV-2 preoperative tests. The postoperative SARS-CoV-2 infection rate was also lower in COVID-19–free surgical pathways (2.1% v 3.6%; aOR, 0.53; 95% CI, 0.36 to 0.76). CONCLUSION Within available resources, dedicated COVID-19–free surgical pathways should be established to provide safe elective cancer surgery during current and before future SARS-CoV-2 outbreaks

Elective Cancer Surgery in COVID-19-Free Surgical Pathways During the SARS-CoV-2 Pandemic: An International, Multicenter, Comparative Cohort Study.

PURPOSE: As cancer surgery restarts after the first COVID-19 wave, health care providers urgently require data to determine where elective surgery is best performed. This study aimed to determine whether COVID-19-free surgical pathways were associated with lower postoperative pulmonary complication rates compared with hospitals with no defined pathway. PATIENTS AND METHODS: This international, multicenter cohort study included patients who underwent elective surgery for 10 solid cancer types without preoperative suspicion of SARS-CoV-2. Participating hospitals included patients from local emergence of SARS-CoV-2 until April 19, 2020. At the time of surgery, hospitals were defined as having a COVID-19-free surgical pathway (complete segregation of the operating theater, critical care, and inpatient ward areas) or no defined pathway (incomplete or no segregation, areas shared with patients with COVID-19). The primary outcome was 30-day postoperative pulmonary complications (pneumonia, acute respiratory distress syndrome, unexpected ventilation). RESULTS: Of 9,171 patients from 447 hospitals in 55 countries, 2,481 were operated on in COVID-19-free surgical pathways. Patients who underwent surgery within COVID-19-free surgical pathways were younger with fewer comorbidities than those in hospitals with no defined pathway but with similar proportions of major surgery. After adjustment, pulmonary complication rates were lower with COVID-19-free surgical pathways (2.2% v 4.9%; adjusted odds ratio [aOR], 0.62; 95% CI, 0.44 to 0.86). This was consistent in sensitivity analyses for low-risk patients (American Society of Anesthesiologists grade 1/2), propensity score-matched models, and patients with negative SARS-CoV-2 preoperative tests. The postoperative SARS-CoV-2 infection rate was also lower in COVID-19-free surgical pathways (2.1% v 3.6%; aOR, 0.53; 95% CI, 0.36 to 0.76). CONCLUSION: Within available resources, dedicated COVID-19-free surgical pathways should be established to provide safe elective cancer surgery during current and before future SARS-CoV-2 outbreaks

Towards ecological science for all by all

Editorial for the special issue on Citizen Science

Safeguarding the nation’s digital memory : towards a Bayesian model of digital preservation risk

Preservation of digital material is a challenge for which many archives feel underprepared and ill equipped. The National Archives (UK) has been working in collaboration with statisticians from the University of Warwick and partners from across the UK archives sector to develop a decision-support system which quantifies the risks involved in digital preservation. Through interdisciplinary collaboration, this partnership has developed an interactive tool for managing risks to digital material, based on a Bayesian statistical network. The tool provides archivists with a different way of thinking about digital preservation, supported by an evidence base they can use to advocate for action. The project illustrates the potential benefit of a collaborative approach, combining insight from different disciplines