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Investigating the mathematical and geometric principles embedded in ancient classic architecture is a significant tradition in the history of architectural development. Drawing inspiration from the modular design and creative ideology based on the geometric proportions of squareness and roundness in ancient Chinese architecture, we propose a new mode of squareness and roundness composition based on scale proportion specifically for the design of multi-story buildings. Taking Yingxian Wooden Pagoda as the case study, we not only re-evaluate the modular system and proportional rules followed in the design of the entire pagoda, but also reveal the technical approaches and geometric rules for effectively controlling the form of multi-story buildings. In particular, the mode of squareness and roundness composition based on scale proportion, utilizing a modular grid combined with squareness and roundness drawings as decision-making tools, can control the scale and proportion of buildings across different design dimensions and organically coordinate the design of multi-story buildings’ plans and elevations. Thus, it can achieve an effective balance of multi-story architectural forms. This study has potential applications in the creation of traditional multi-story buildings and heritage restoration projects, and offers valuable insights for future research on ancient multi-story buildings.

Using the synchronization mechanism developed in the previous work on the Potts spin glass model, we obtain the analogue of the Parisi formula for the free energy in the mixed even p-spin models with vector spins, which include the Sherrington–Kirkpatrick model with vector spins interacting through their scalar product. As a special case, this also establishes the sharpness of Talagrand’s upper bound for the free energy of multiple mixed p-spin systems coupled by constraining their overlaps.

The development of the digital economy has become a new way to respond to the epidemic impact effectively. With the innovative breakthrough of information and communication technology, the digital and real economies are deeply integrated. The digital economy has become an important driving force for the transformation of economic momentum and development. Panel data from 31 provinces in China from 2010 to 2019 were selected for analysis. In the first stage, the study constructed the evaluation index system of digital economy development. Then, the quality development index of the digital economy is calculated by using the entropy method. Finally, the main factors of digital economy development are analysed by spatial measurement. The research results prove that: (1) the development of China’s digital economy in 2010–2019 has gradually increased; (2) the development of the digital economy has a positive correlation between regions and has a spatial spillover effect; (3) the level of economic development, urbanisation, government support, industrial structure, and the level of opening will promote the development of the digital economy. First published online 30 November 2022

We study the Potts spin glass model, which generalizes the Sherrington–Kirkpatrick model to the case when spins take more than two values but their interactions are counted only if the spins are equal. We obtain the analogue of the Parisi variational formula for the free energy, with the order parameter now given by a monotone path in the set of positive-semidefinite matrices. The main idea of the paper is a novel synchronization mechanism for blocks of overlaps. This mechanism can be used to solve a more general version of the Sherrington–Kirkpatrick model with vector spins interacting through their scalar product, which includes the Potts spin glass as a special case. As another example of application, one can show that Talagrand’s bound for multiple copies of the mixed p-spin model with constrained overlaps is asymptotically sharp. We will consider these problems in the subsequent paper and illustrate the main new idea on the technically more transparent case of the Potts spin glass.

Peer-to-peer (P2P) energy trading could help address grid management challenges in a decentralizing electricity system, as well as provide other social and environmental benefits. Many existing and proposed trading schemes are enabled by blockchain, a distributed ledger technology (DLT) relying on cryptographic proof of ownership rather than human intermediaries to establish energy transactions. This study used an online survey experiment (n = 2064) to investigate how consumer demand for blockchain-enabled peer-to-peer energy trading schemes in the United Kingdom varies depending on how the consumer proposition is designed and communicated. The analysis provides some evidence of a preference for schemes offering to meet a higher proportion of participants’ energy needs and for those operating at the city/region (as compared to national or neighbourhood) level. People were more likely to say they would participate when the scheme was framed as being run by their local council, followed by an energy supplier, community energy organization, and social media company. Anonymity was the most valued DLT characteristic and mentioning blockchain’s association with Bitcoin led to a substantial decrease in intended uptake. We highlight a range of important questions and implications suggested by these findings for the introduction and operation of P2P trading schemes.

A cause is proportional to its effect when, roughly speaking, it is at the right level of detail. There is a lively debate about whether proportionality is a necessary condition for causation. One of the main arguments against a proportionality constraint on causation is that many ordinary and seemingly perfectly acceptable causal claims cite causes that are not proportional to their effects. In this paper, I suggest that proponents of a proportionality constraint can respond to this objection by developing an idea that is present in Yablo’s early work on proportionality, but which has strangely been ignored by both Yablo and others in the subsequent debate. My suggestion is that proportionality—and, indeed, causation itself—is relative to a domain of events. At the metaphysical level, this means that the causal relation has an extra relatum—namely, a domain of events. At the level of language, it introduces a new way in which causal claims are context-sensitive: what is expressed by a causal claim depends on the contextually relevant domain of events. As I argue, this suggestion allows us to accommodate the truth of ordinary causal claims while extending the explanatory benefits of a proportionality constraint.

Between 1876 and 1882, Brazilian photographer Marc Ferrez produced a series of photographs documenting the construction and completion of dams, reservoirs, and various engineering projects for Rio de Janeiro’s new water supply systems. While the titled subject of each image is infrastructure, an unacknowledged presence marks many of the compositions: the human body. People constellate the series, captured by accident or intentionally posed by Ferrez as tools by which size can be made sense of, setting monumental constructions to scale. The use of the body as an informal scale legend signals unintended tensions in Ferrez’s photographs. In concert with the imperial constructions, Brazil’s government completed a tumultuous process of implementing new metric guidelines that redefined the country’s measurement system, enabled large-scale civil infrastructure projects, and sparked popular protest. More than a marker, the human body—a fundamentally inexact tool of measurement—renders a distinct ambiguity to the modernity and scientific rationality Ferrez’s images champion, returning to embodied modes of knowledge.

Philosophers writing about proportionality in self-defense and war will often assume that defensive agents have full knowledge about the threat that they face and the defensive options available to them. But no actual defensive agents possess this kind of knowledge. How, then, should we make proportionality decisions under uncertainty? The natural answer is that we should move from comparing the harm we will do with the good we will achieve to comparing expected harm with expected good. I argue that this simple calculation is flawed, and I begin to develop a more sophisticated account of \"subjective proportionality.\"

Parametric design stands out in contemporary landscape facilities design with its distinctive beauty sense. However, understanding this beauty sense and establishing an aesthetic design method is one of the problems needed to be solved. In this context, this study integrates the Stimulus-Organism-Response (SOR) model and hybrid Kansei Engineering establish the aesthetic design method for parametric landscape facilities from the perspectives of cognition and positivist design. Firstly, the SOR model is used to reveal the aesthetic cognitive mechanism of parametric landscape facilities. Secondly, the forward Kansei Engineering is used to extract design features. Thirdly, the extracted design features are combined with shape grammar for parametric modeling in the Grasshopper platform. Fourthly, backward Kansei Engineering is used to evaluate design schemes and analyze their data of beauty sense. Finally, this study takes the landscape corridor as a case to illustrate the proposed method. The results show that (1) in aesthetic cognition, dynamic visual forms, transparency of spatial feeling, and abstract style have a significant positive impact on the beauty perception of parametric landscape facilities, and the beauty perception of parametric design has a unique appeal to the general public. (2) The design case verified the effectiveness of this method, and this study can provide a valuable reference for parametric landscape facilities.

Wim Wenders’ Perfect Days explores the intersection of cinema and architecture through a phenomenological lens. The film examines public restrooms in Tokyo, each with unique architectural characteristics, delving into how these spaces are perceived and how they enhance the viewer’s spatial experience. In the film, spaces transcend their traditional role as mere backdrops to become central components of the narrative. The restrooms featured in the film stand out as significant elements that shape individuals’ sensory awareness, social contexts, and personal experiences from both architectural and phenomenological viewpoints. Architectural design integrates phenomenological qualities of space, such as the interplay of light, shadow, sound, and textures, enriching the viewer’s experience of these locations. This study investigates how these restrooms are conveyed to the audience through the film’s structure and narrative and how they shape sensory and emotional experiences. Qualitative research methods were employed, using document analysis and content analysis to frame the conceptual foundation of the study. It was found that these spaces form layers of both individual and collective meaning through their design elements and relationships with the urban context. The study demonstrates how the concept of phenomenological space can be interpreted through cinema.