Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences最新文献

Perhaps the best-known result from neoclassical economics is the 'law of supply and demand'. This depicts markets using curves of supply and demand that intersect at a unique equilibrium, whose value represents a kind of aggregate market decision about price. However, because it is impossible to separate supply and demand in practice, the model has little in the way of empirical backing. In finance, in contrast, the related question of price impact, where a large transaction results in a changed price, has been widely studied. This paper uses a probabilistic approach to obtain a model of price impact in the context of asset pricing. A model based on classical probability is first used to simulate economic decisions to buy or sell, and a quantum version is then developed that better captures the response of the system to perturbations. The result is then extended to the general question of supply and demand. The formula is used to obtain a relationship between price change and volatility which is illustrated using empirical stock market data, and implications for other areas such as option pricing and real estate are discussed.This article is part of the theme issue 'Quantum theory and topology in models of decision making (Part 1)'.

In this work, we introduce a quantum-inspired epidemic model to study the dynamics of an infectious disease in a population divided into compartments. By treating the healthy population as a large reservoir, we construct a framework based on open quantum systems and a Hilbert space formalism to model the spread of the infection. This approach allows for a mathematical framework that captures both Markovian and semi-Markovian dynamics in the evolution equations. Through numerical experiments, we examine the effect of varying memory parameters on the epidemic evolution, focusing in particular on the conditions under which the model remains physically admissible.This article is part of the theme issue 'Quantum theory and topology in models of decision making (Part 1)'.

We characterize the class of quantum measurements that matches the applications of quantum theory to cognition (and decision-making)-quantum-like modelling. Projective measurements describe the canonical measurements of the basic observables of quantum physics. However, the combinations of the basic cognitive effects, such as the question order and response replicability effects (RREs), cannot be described by projective measurements. We motivate the use of the special class of quantum measurements, namely, sharp repeatable non-projective measurements-[Formula: see text] This class is practically unused in quantum physics. Thus, physics and cognition explore different parts of quantum measurement theory. Quantum-like modelling is not the automatic borrowing of the quantum formalism. Exploring the class [Formula: see text] highlights the role of non-commutativity of the state-update maps generated by measurement back action. Thus, 'non-classicality' in quantum physics as well as quantum-like modelling for cognition is based on two different types of non-commutativity, of operators (observables) and instruments (state-update maps): observable non-commutativity versus state-update-non-commutativity. We speculate that distinguishing quantum-like properties of the cognitive effects is the expression of the latter, or possibly both.This article is part of the theme issue 'Quantum theory and topology in models of decision making (Part 1)'.

In this paper, we investigate deliberation procedures that invite citizens with contextual opinions to explore alternative thinking frames. Contextuality is captured in a simple quantum cognitive model. We show how disagreeing citizens endowed with contextual opinions can reach consensus in a binary collective decision problem with no improvement in their information. A necessary condition is that they are willing to (mentally) experience their fellow citizens' way of thinking. The diversity of thinking frames is what makes it possible to overcome initial disagreement. Consensus does not emerge spontaneously from deliberations: it requires facilitation.This article is part of the theme issue 'Quantum theory and topology in models of decision making (Part 1)'.

Urban areas are renowned for their intricate atmospheric dynamics, influenced by diverse building configurations. Understanding the implications of urban morphology for flow patterns, ventilation and heat dissipation is crucial for urban climate management. However, comprehending the interplay between thermal-driven buoyancy flow and urban morphology remains a challenge. To address this gap, we measured heat transport and fluid flow around three-dimensional parametric urban models resembling Singapore's urban morphology accounting for buoyancy effects, using simultaneous Particle Image Velocimetry (PIV) and Laser-Induced Fluorescence (LIF) measurements. Our study meticulously documents the development of non-isothermal urban flow, highlighting heat plume generation from the ground, buoyant updraft development and temperature variations along the flow. The variations in urban morphologies have a profound impact on these developmental processes, resulting in substantial differences in heat and flow mechanisms, ventilation efficiency and heat removal performance. For example, significant differences are observed in ventilation rates and their fluctuations, with values reaching up to approximately 10.5 times and 12.2 times, respectively. These findings of the fluid flow and heat spreading above the ground contribute to the broader understanding of urban heat dynamics by demonstrating how localized thermal effects propagate through urban environments, influencing microclimatic conditions.This article is part of the theme issue 'Urban heat spreading above and below ground'.

Anthropogenic heat (AH) emissions in urban environments alter the surface energy budget and significantly influence urban climates. However, these emissions vary spatiotemporally, leading to considerable uncertainty in their estimation. As remote sensing in the urban environment advances, the remotely sensed urban surface temperatures are becoming increasingly available. Yet, assimilating these observations into surface energy modelling for AH estimation has not been fully explored. In this study, a model for AH estimation based on the Kalman filter-surface energy balance (KF-SEB) is developed. Urban meteorological data, including air temperature and building surface temperature, are assimilated into the Kalman filter (KF), yielding sensible heat flux, building heat storage and estimated AH using the surface energy balance (SEB) equation. The KF-SEB model is evaluated using two forward models with predefined AH emissions. The first model is a simple slab model, and the second one is a more complex single-layer urban canopy model (UCM). The results show that the KF-SEB model accurately captures the magnitude and temporal variation of AH, with reduced uncertainties compared to previous studies. This study offers a novel approach to AH estimation based on urban meteorological data and provides important insights into the feedback between urban microclimates and anthropogenic energy use.This article is part of the theme issue 'Urban heat spreading above and below ground'.

The simultaneous interaction of lake breeze (LB) flows, complex terrain circulations and urban environments has so far received limited attention in the scientific literature. Here, we use the Weather Research and Forecasting model to investigate the aero- and thermodynamical interaction between Lake Geneva, the Swiss cities of Lausanne and Geneva and their rugged alpine landscape. To better isolate the role of urban areas, we compare results from a set of year-long simulations representing both realistic urban and hypothetical rural landcover scenarios. The results show that the urban areas of Lausanne and Geneva have a negligible effect on the dynamical evolution of LB, mostly consisting of wind deceleration caused by increased surface drag. However, the daytime excess heat over Lausanne results in a shift of the local anabatic wind regime onset time, one hour ahead, and a 1 km spatial displacement northward of the location of opposing flow collision. Urban-induced changes in heat advection can further lead to warmer air temperatures over the lake or cooler urban conditions along the lake shore. Our study shows that, although with due magnitude differences, mid-sized cities may have similar effects on wind and heat dynamics as larger metropolises in different landscapes and climates.This article is part of the theme issue 'Urban heat spreading above and below ground'.

This study investigates the long-term evolution of the subsurface urban heat island (SUHI) effect in Milan, integrating historical records, present observations and future climate projections through a coupled fluid-flow and heat-transport numerical model. A N-S cross-section through the city serves as the domain for this study and boundary conditions were derived from historical maps starting in 1884, long-term air temperature time series starting in 1700, and distributed land surface temperatures from Landsat 8 satellite remote sensing. The research quantifies the temperature variations in the shallow subsurface over the past 150 years (1875-2025), calibrating the model against groundwater temperature measurements, and predicts trends up to 2100. Current estimates indicate urban temperature anomalies up to +5°C at the water table depth, and an expansion of the SUHI along the two-dimensional cross-section from 3 km in 1884 to 9 km in 2025. The findings highlight the heterogeneous distribution of subsurface temperature anomalies, influenced by variations in the groundwater depth, flow patterns, land cover and urban and infrastructure expansion. Future projections suggest a further increase in subsurface temperatures, particularly in areas with shallow groundwater. These results underscore the need to incorporate mitigation strategies into urban planning and policies, such as sustainable urban cooling measures and optimized geothermal energy utilization.This article is part of the theme issue 'Urban heat spreading above and below ground'.

Heatwaves, intensified by climate change and rapid urbanization, pose significant threats to urban systems, particularly in the Global South, where adaptive capacity is constrained. This study investigates the relationship between heatwaves and nighttime light (NTL) radiance, a proxy of nighttime economic activity, in four hyperdense cities: Delhi, Guangzhou, Cairo and São Paulo. We hypothesized that heatwaves increase nighttime activity. Using a double machine learning (DML) framework, we analysed data from 2013 to 2019 to quantify the impact of heatwaves on NTL while controlling for local climatic confounders. The results show a statistically significant increase in NTL radiance for Guangzhou, Cairo and São Paulo when a heatwave event lasts at least 2 days, indicating a rise in nighttime activities. However, when we extend the definition of the heatwave beyond the 2-day threshold, such an increase in the NTL values is reduced. We derive insights to improve resilience to the nighttime effects of heatwaves in urban areas.This article is part of the theme issue 'Urban heat spreading above and below ground'.

Ground-level air temperature maps at the agglomeration scale are vital for assessing hazards from the urban heat island (UHI) effect during extreme heat events. Their prediction is nowadays challenging, requiring models that balance high spatial resolution with scalability. In this study, we develop machine learning (ML) algorithms based on six high-resolution parameters describing topography, geometry and land use of the urban environment. We evaluate two methods-multiple linear regression (MLR) and the convolutional neural network (CNN)-for predicting the UHI effect (and related hazards) in Turin. Models are trained using temperature data from NetAtmo citizen weather stations (CWSs). We also assess the effect of adding a seventh predictor from a numerical weather prediction (NWP) model. The CNN achieves a root-mean-square error (RMSE) below 1.19°C, slightly outperforming the MLR, which reaches an RMSE of up to 1.22°C. Notably, the CNN trained without NWP data performs similarly to the MLR model that includes it, demonstrating CNN robustness with limited input. Temperature maps and parameter analysis reveal the need to better understand spatial drivers of urban temperature variability and confirm the potential of ML tools in urban climate modelling. Leveraging these insights, we discuss key factors to reduce uncertainties in data-driven temperature models.This article is part of the theme issue 'Urban heat spreading above and below ground'.