剑桥大学圣约翰学院

We prove that the maximal graph-density of an independent set in a Penrose P3 tiling considered as a planar non-directed graph is equal to (57 - 25 √(5))/2 ≈ 0.54915 despite the fact that the graph is bipartite. Accordingly, the extreme Gibbs measure of the nearest-neighbor hard core particle model on this graph is unique for sufficiently large values of the particle activity. This invalidates a natural expectation to observe the coexistence of even and odd phases.

In this paper we use the Pirogov–Sinai theory to analyze a class of particle models of Statistical Mechanics on the unit triangular lattice 𝔸_2. The models are specified by two parameters: the particle activity u∈(0,1) and a positive Löschian number t interpreted as a maximal squared clearing radius. Admissible configurations are those in which every empty lattice site has an occupied site within squared distance at most t, thereby forbidding empty disks of radius exceeding or equal t. The Hamiltonian favors configurations with as few occupied sites as possible, while the admissibility condition enforces a positive density of particles. We prove that the periodic ground states of the model, i.e., the configurations achieving an optimal balance of two tendencies, are the ones whose occupied sites form triangular sublattices of explicitly determined squared side-length d_*(t). Furthermore, for sufficiently small values of the activity parameter u, some (but not necessarily all) periodic ground states generate extreme Gibbs (DLR) measures. We describe the resulting phase structure and characterize the pure phases associated with stable ground states.

The importance of the visual system to birds for behaviours from feeding, mate choice, flying, navigation and determination of seasons, together with the presence of photoreceptors in the retina, the pineal and the brain, render the avian visual system a particularly fruitful model for understanding of eye-brain interactions. In this review we will particularly focus on the pigeon, since here we have a brain stereotactically mapped and a genome fully sequenced, together with a particular bird, the homing pigeon, with remarkable ability to navigate over hundreds of miles and return to exactly the same roosting site with exceptional precision. We might denigrate the avian species by the term bird brained, but here are animals with phenomenal abilities to use their exceptional vision, their eagle eyedness, to best advantage.

Recent research on collective memory and war commemoration highlights the ‘conspicuous silence’ of war veterans in Chinese history. Studies of the War of Resistance against Japan (1937–1945) typically reflect either a state-centred approach, which emphasises the official history constructed by the Chinese Communist Party (CCP), or the alternative narratives constructed by intellectual elites in post-socialist China. In response to these top-down narratives, this essay focuses instead on a historical redress movement led by ex-servicemen of the People’s Liberation Army (PLA) in the People’s Republic of China (PRC). The former PLA members, the participant volunteers of this movement, devote themselves into seeking and supporting a group of forgotten Kuomintang (KMT) veterans who fought against the Japanese invaders in the Second World War but now struggle with impoverished living conditions. Drawing on ethnographic fieldwork from 2013 to 2015, I will show how the daily interactions between these two groups of veterans embody a more private and internalised sense of commemorative yearning for a lost past, highlighting in the process the value of ethnographic research in breaking through the wall of silence constructed by hegemonic histories around veteran communities and their role in making war history.