Localized energy for wave equations with degenerate trapping

Localized energy estimates have become a fundamental tool when studying wave equations in the presence of asymptotically at background geometry. Trapped rays necessitate a loss when compared to the estimate on Minkowski space. A loss of regularity is a common way to incorporate such. When trapping is sufficiently weak, a logarithmic loss of regularity suffices. Here, by studying a warped product manifold introduced by Christianson and Wunsch, we encounter the first explicit example of a situation where an estimate with an algebraic loss of regularity exists and this loss is sharp. Due to the global-in-time nature of the estimate for the wave equation, the situation is more complicated than for the Schr\"{o}dinger equation. An initial estimate with sub-optimal loss is first obtained, where extra care is required due to the low frequency contributions. An improved estimate is then established using energy functionals that are inspired by WKB analysis. Finally, it is shown that the loss cannot be improved by any power by saturating the estimate with a quasimode.Comment: 18 page

Response to comment on "solid recovered fuel: Materials flow analysis and fuel property development during the mechanical processing of biodried waste"

Laner and Cencic1 comment on Velis et al. (2013)2 clarifying certain points on the use of the material flow analysis (MFA) software STAN3. We welcome the correspondence and the opportunity this exchange provides to discuss optimal approaches to using STAN. In keeping with Velis et al.2 these physically impossible, and otherwise insignificant, negative flows have enabled improvements to STAN. Here, we elaborate on the practicalities of using STAN in our research and on the correctness and validation of our results, notwithstanding the inclusion of negative flows. We explain the contribution of our approach to solid waste management and resource recovery

Enabling the informal recycling sector to prevent plastic pollution and deliver an inclusive circular economy

Recycling by the informal sector provides a rapid, inexpensive solution to plastic pollution, whilst supporting the livelihoods via their inclusion and empowerment. This solution will have the greatest benefit to the environment if supporting interventions are targeted at types of plastic pollution that are the most damaging from an ecological and wider risk perspective. Interventions should target three aspects of the pollution: reducing barriers to collection, improving the revenue from the materials and wider informal recycler remuneration, and increasing the quality of the materials. Done well, these interventions will increase the collection rate, reduce pollution from plastics, and help millions of people escape poverty. They present a scalable international solution to a global challenge; and are likely the only viable solution to the widespread lack of solid waste services and infrastructure across low- and middle-income countries

Technical properties of biomass and solid recovered fuel (SRF) co-fired with coal: Impact on multi-dimensional resource recovery value

The power plant sector is adopting the co-firing of biomass and solid recovered fuel (SRF) with coal in an effort to reduce its environmental impact and costs. Whereas this intervention contributes to reducing carbon emissions and those of other pollutants related with the burning of fossil fuel, it may also result in hidden impacts that are often overlooked. When co-firing, the physical and chemical properties of the mixed fuels and the subsequent technical implications on the process performance and by-products are significant. Interconnections between multiple values nested within four domains of value, i.e. environmental, economic, technical and social, mean that changes in the one domain (in the co-firing case, the technical one) can have considerable implications in the other domains as well. In this study, using a systematic and flexible approach to conceptualising multi-dimensional aspects associated with the co-firing of biomass and SRF with coal, we unveil examples of such interconnections and implications on overall value delivered through the use and recovery of waste resources. Such an analysis could underpin the selection of useful metrics (quantitative or semi-quantitative descriptors) for enabling a systemic multi-dimensional value assessment, and value’s distribution amongst interconnected parts of resource recovery systems; key in enabling sound analysis and decision-making.UK Natural Environment Research Council (NERC) ;UK Economic and Social Research Council (ESRC

The Lesioned Brain: Still a Small-World?

The intra-arterial amobarbital procedure (IAP or Wada test) is used to determine language lateralization and contralateral memory functioning in patients eligible for neurosurgery because of pharmaco-resistant epilepsy. During unilateral sedation, functioning of the contralateral hemisphere is assessed by means of neuropsychological tests. We use the IAP as a reversible model for the effect of lesions on brain network topology. Three artifact-free epochs (4096 samples) were selected from each electroencephalogram record before and after amobarbital injection. Functional connectivity was assessed by means of the synchronization likelihood. The resulting functional connectivity matrices were constructed for all six epochs per patient in four frequency bands, and weighted network analysis was performed. The clustering coefficient, average path length, small-world index, and edge weight correlation were calculated. Recordings of 33 patients were available. Network topology changed significantly after amobarbital injection: clustering decreased in all frequency bands, while path length decreased in the theta and lower alpha band, indicating a shift toward a more random network topology. Likewise, the edge weight correlation decreased after injection of amobarbital in the theta and beta bands. Network characteristics after injection of amobarbital were correlated with memory score: higher theta band small-world index and increased upper alpha path length were related to better memory score. The whole-brain network topology in patients eligible for epilepsy surgery becomes more random and less optimally organized after selective sedation of one hemisphere, as has been reported in studies with brain tumor patients. Furthermore, memory functioning after injection seems related to network topology, indicating that functional performance is related to topological network properties of the brain

Long-Term Effects of Temporal Lobe Epilepsy on Local Neural Networks: A Graph Theoretical Analysis of Corticography Recordings

Purpose: Pharmaco-resistant temporal lobe epilepsy (TLE) is often treated with surgical intervention at some point. As epilepsy surgery is considered a last resort by most physicians, a long history of epileptic seizures prior to surgery is not uncommon. Little is known about the effects of ongoing TLE on neural functioning. A better understanding of these effects might influence the moment of surgical intervention. Functional connectivity (interaction between spatially distributed brain areas) and network structure (integration and segregation of information processing) are thought to be essential for optimal brain functioning. We report on the impact of TLE duration on temporal lobe functional connectivity and network characteristics. Methods: Functional connectivity of the temporal lobe at the time of surgery was assessed by means of interictal electrocorticography (ECoG) recordings of 27 TLE patients by using the phase lag index (PLI). Graphs (abstract network representations) were reconstructed from the PLI matrix and characterized by the clustering coefficient C (local clustering), the path length L (overall network interconnectedness), and the ‘‘small world index’ ’ S (network configuration). Results: Functional connectivity (average PLI), clustering coefficients, and the small world index were negatively correlated with TLE duration in the broad frequency band (0.5–48 Hz). Discussion: Temporal lobe functional connectivity is lower in patients with longer TLE history, and longer TLE duration i

Waste sorting social technology in Brazilian informal Materials Recovery Facilities

It is commonly accepted that the recycling and reuse of solid waste materials in developing countries has the potential to create many social, environmental and financial benefits. Given that the majority of recycling in these locations is carried out informally by waste pickers, it is also recognised that their inclusion into formal service provision could be the most efficient way of maintaining and increasing the recycling rates of a city. In the absence of sophisticated equipment, the informal recycling sector (IRS) has developed a wealth of self-taught knowledge and skills for manually identifying and processing waste materials. Using primary and secondary data gathered from a materials recovery facility (MRF) in Belo Horizonte, Brazil, this study describes the so called ‘social technology’ techniques used to sort municipal waste materials by a cooperative of informal sector recycling workers. This involves identifying and separating 17types of plastic polymers by visual and tactile sorting skills. The methods presented are compared and contrasted with manual sorting techniques used mainly in the near past in the UK. To conclude, the study discusses whether these techniques provide a viable method for increasing recycling rates at scale in the Global South

Localization of the Epileptogenic Zone Using Interictal MEG and Machine Learning in a Large Cohort of Drug-Resistant Epilepsy Patients

Objective: Epilepsy surgery results in seizure freedom in the majority of drug-resistant patients. To improve surgery outcome we studied whether MEG metrics combined with machine learning can improve localization of the epileptogenic zone, thereby enhancing the chance of seizure freedom.Methods: Presurgical interictal MEG recordings of 94 patients (64 seizure-free >1y post-surgery) were analyzed to extract four metrics in source space: delta power, low-to-high-frequency power ratio, functional connectivity (phase lag index), and minimum spanning tree betweenness centrality. At the group level, we estimated the overlap of the resection area with the five highest values for each metric and determined whether this overlap differed between surgery outcomes. At the individual level, those metrics were used in machine learning classifiers (linear support vector machine (SVM) and random forest) to distinguish between resection and non-resection areas and between surgery outcome groups.Results: The highest values, for all metrics, overlapped with the resection area in more than half of the patients, but the overlap did not differ between surgery outcome groups. The classifiers distinguished the resection areas from non-resection areas with 59.94% accuracy (95% confidence interval: 59.67–60.22%) for SVM and 60.34% (59.98–60.71%) for random forest, but could not differentiate seizure-free from not seizure-free patients [43.77% accuracy (42.08–45.45%) for SVM and 49.03% (47.25–50.82%) for random forest].Significance: All four metrics localized the resection area but did not distinguish between surgery outcome groups, demonstrating that metrics derived from interictal MEG correspond to expert consensus based on several presurgical evaluation modalities, but do not yet localize the epileptogenic zone. Metrics should be improved such that they correspond to the resection area in seizure-free patients but not in patients with persistent seizures. It is important to test such localization strategies at an individual level, for example by using machine learning or individualized models, since surgery is individually tailored