In one-dimensional disordered wires electronic states are localized at any energy. Correlations of the states at close positive energies and the AC conductivity \sigma(\omega) in the limit of small frequency are described by the Mott-Berezinskii theory. We revisit the instanton approach to the statistics of wave functions and AC transport valid in the tails of the spectrum (large negative energies). Applying our recent results on functional determinants, we calculate exactly the integral over Gaussian fluctuations around the exact two-instanton saddle point. We derive correlators of wave functions at different energies beyond the leading order in the energy difference. This allows us to calculate corrections to the Mott-Berezinskii law (the leading small-frequency asymptotic behavior of \sigma(\omega)) which approximate the exact result in a broad range of \omega. We compare our results with the ones obtained for positive energies.
The liveability of cities worldwide is under threat by the predicted increase in intensity and frequency of heatwaves and the absence of a clear spatial overview of where action to address this. Heat stress impairs vital urban functions (Böcker and Thorsson 2014), hits the local economy (Evers et al. 2020), and brings risks for citizens’ health (Ebi et al. 2021). The ongoing densification of cities may escalate the negative consequences of heat, while rising climate adaptation ambitions require new pathways to (re)design public places for a warmer climate. Currently, policy makers and urban planners rely on remote sensing and modelling to identify potential heat stress locations, but thermal comfort models alone fail to consider socio-environmental vulnerabilities and are often not applicable in different countries (Elnabawi and Hamza 2020).In the Cool Towns Interreg project, researchers collaborated with municipalities and regions to model urban heat stress in nine North-Western European cities, to find vulnerabilities and to measure on the ground (see Spanjar et al. 2020 for methodology) the thermal comfort of residents and the effectiveness of implemented nature-based solutions. Using the Physiological Equivalent Temperature (PET) index, several meteorological scenarios were developed to show the urban areas under threat. The PET maps are complemented by heat vulnerability maps showing key social and environmental indicators. Coupled with local urban planning agendas, the maps allowed partner cities to prioritize neighbourhoods for further investigation. To this end, community amenities and slow traffic routes were mapped on top of the PET maps to identify potential focus areas.A comparative analysis of the collated maps indicates certain spatial typologies, where vital urban activities are often influenced by heat stress, such as shopping areas, mobility hubs, principal bicycle and pedestrian routes. This project has resulted in the development of a multi-level Thermal Comfort Assessment (TCA), highlighting locations where vulnerable user groups are exposed to high temperatures. Standardized for European cities, it is a powerful tool for policy makers and urban planners to strategically identify heat stress risks and prioritize locations for adapting to a changing climate using the appropriate nature-based solutions.
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Gamma-band neuronal synchronization during sentence-level language comprehension has previously been linked with semantic unification. Here, we attempt to further narrow down the functional significance of gamma during language comprehension, by distinguishing between two aspects of semantic unification: successful integration of word meaning into the sentence context, and prediction of upcoming words. We computed eventrelated potentials (ERPs) and frequency band-specific electroencephalographic (EEG) power changes while participants read sentences that contained a critical word (CW) that was (1) both semantically congruent and predictable (high cloze, HC), (2) semantically congruent but unpredictable (low cloze, LC), or (3) semantically incongruent (and therefore also unpredictable; semantic violation, SV). The ERP analysis showed the expected parametric N400 modulation (HC < LC < SV). The time-frequency analysis showed qualitatively different results. In the gamma-frequency range, we observed a power increase in response to the CW in the HC condition, but not in the LC and the SV conditions. Additionally, in the theta frequency range we observed a power increase in the SV condition only. Our data provide evidence that gamma power increases are related to the predictability of an upcoming word based on the preceding sentence context, rather than to the integration of the incoming word's semantics into the preceding context. Further, our theta band data are compatible with the notion that theta band synchronization in sentence comprehension might be related to the detection of an error in the language input.
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