Constraints on pure point diffraction on aperiodic point patterns of finite local complexity

We consider the pure point part of the diffraction on families of aperiodic point sets obeying common local rules. It is shown that imposing such rules results in linear constraints on the partial diffraction amplitudes. These relations can be explicitly derived from the geometry of the prototile space representing the local rules.

Unravel the Local Complexity of Biological Environments by MALDI Mass Spectrometry Imaging

Classic metabolomic methods have proven to be very useful to study functional biology and variation in the chemical composition of different tissues. However, they do not provide any information in terms of spatial localization within fine structures. Matrix-assisted laser desorption ionization mass spectrometry imaging (MALDI MSI) does and reaches at best a spatial resolution of 0.25 μm depending on the laser setup, making it a very powerful tool to analyze the local complexity of biological samples at the cellular level. Here, we intend to give an overview of the diversity of the molecules and localizations analyzed using this method as well as to update on the latest adaptations made to circumvent the complexity of samples. MALDI MSI has been widely used in medical sciences and is now developing in research areas as diverse as entomology, microbiology, plant biology, and plant–microbe interactions, the rhizobia symbiosis being the most exhaustively described so far. Those are the fields of interest on which we will focus to demonstrate MALDI MSI strengths in characterizing the spatial distributions of metabolites, lipids, and peptides in relation to biological questions.

Emergent simplicity despite local complexity in eroding fluvial landscapes

Much of our current understanding of continental topographic evolution is rooted in measuring and predicting the rates at which rivers erode the landscape. Flume tank and field observations indicate that stochasticity and local conditions play important roles in determining rates at small scales (e.g., <10 km, thousands of years). Obversely, preserved river profiles and common shapes of rivers atop uplifting topography indicate that erosion rates are predictable at larger scales. These observations indicate that the response of rivers to forcing can be scale dependent. I demonstrate that erosional thresholds can provide an explanation for why profile evolution can be very complicated and unique at small scales yet simple and predictable at large scales.

Emergent simplicity despite local complexity in eroding fluvial landscapes

Much understanding of continental topographic evolution is rooted in measuring and predicting rates at which rivers erode. Flume tank and field observations indicate that stochasticity and local conditions play important roles in determining rates at small scales (e.g. < 10 km, thousands of years). Obversely, preserved river profiles and common shapes of rivers atop uplifting topography indicate that erosion rates are predictable at larger scales. These observations indicate that the response of rivers to forcing can be scale dependent. Here I demonstrate that erosional thresholds can provide an explanation for why profile evolution can be very complicated and unique at small scales yet simple and predictable at large scales.

Supplemental Material: Emergent simplicity despite local complexity in eroding fluvial landscapes

Movies S1 and S2 (showing examples of the time dependent behavior of the threshold model), and a simple mathematical explanation for how models of physical erosion can be simplified to few parameters.<br>

Supplemental Material: Emergent simplicity despite local complexity in eroding fluvial landscapes

Movies S1 and S2 (showing examples of the time dependent behavior of the threshold model), and a simple mathematical explanation for how models of physical erosion can be simplified to few parameters.<br>

A dichotomy for bounded displacement equivalence of Delone sets

We prove that in every compact space of Delone sets in ${\mathbb {R}}^d$ , which is minimal with respect to the action by translations, either all Delone sets are uniformly spread or continuously many distinct bounded displacement equivalence classes are represented, none of which contains a lattice. The implied limits are taken with respect to the Chabauty–Fell topology, which is the natural topology on the space of closed subsets of ${\mathbb {R}}^d$ . This topology coincides with the standard local topology in the finite local complexity setting, and it follows that the dichotomy holds for all minimal spaces of Delone sets associated with well-studied constructions such as cut-and-project sets and substitution tilings, whether or not finite local complexity is assumed.

Heart of Wetness: Living, narrating, and representing ancient memories and new water rhythms in the Venetian Lagoon

The natural and human ensemble of Venice and its lagoon, with its peculiar island features, is among one of the most studied urban and environmental systems in the world. This introduction to Shima’s special issue on Venice and its lagoon provides a brief historical and environmental context to this space and a possible platform whereby the local complexity and liminality of wetlands, lagoons and islands gesture to and evoke global themes, conceptual views, and transdisciplinary opportunities. Focusing on key topics like the theatricality of water engineering, the understanding of water rhythms and the recovery of water memories, we introduce the articles presented herein, providing a geo-historical framework for the various interpretations of living, narrating and representing Venice and its lagoon.

Lattice Bounded Distance Equivalence for 1D Delone Sets with Finite Local Complexity

Spectra of suitably chosen Pisot-Vijayaraghavan numbers represent non-trivial examples of self-similar Delone point sets of finite local complexity, indispensable in quasicrystal modeling. For the case of quadratic Pisot units we characterize, dependingly on digits in the corresponding numeration systems, the spectra which are bounded distance to an average lattice. Our method stems in interpretation of the spectra in the frame of the cut-and-project method. Such structures are coded by an infinite word over a finite alphabet which enables us to exploit combinatorial notions such as balancedness, substitutions and the spectrum of associated incidence matrices.