Symmetry-surfing the moduli space of Kummer K3s.

A maximal subgroup of the Mathieu group M24 arises as the combined holomorphic symplectic automorphism group of all Kummer surfaces whose Kaehler class is induced from the underlying complex torus. As a subgroup of M24, this group is the stabilizer group of an octad in the Golay code. To meaningfully combine the symmetry groups of distinct Kummer surfaces, we introduce the concepts of Niemeier markings and overarching maps between pairs of Kummer surfaces. The latter induce a prescription for symmetry-surfing the moduli space, while the former can be seen as a first step towards constructing a vertex algebra that governs the elliptic genus of K3 in an M24-compatible fashion. We thus argue that a geometric approach from K3 to Mathieu Moonshine may bear fruit.Comment: 20 pages; minor changes; accepted for publication in the Proceedings Volume of String-Math 201

DNA duplex cage structures with icosahedral symmetry

A construction method for duplex cage structures with icosahedral symmetry made out of single-stranded DNA molecules is presented and applied to an icosidodecahedral cage. It is shown via a mixture of analytic and computer techniques that there exist realisations of this graph in terms of two circular DNA molecules. These blueprints for the organisation of a cage structure with a noncrystallographic symmetry may assist in the design of containers made from DNA for applications in nanotechnology

Dynamical implications of Viral Tiling Theory

The Caspar–Klug classification of viruses whose protein shell, called viral capsid, exhibits icosahedral symmetry, has recently been extended to incorporate viruses whose capsid proteins are exclusively organised in pentamers. The approach, named ‘Viral Tiling Theory’, is inspired by the theory of quasicrystals, where aperiodic Penrose tilings enjoy 5-fold and 10-fold local symmetries. This paper analyses the extent to which this classification approach informs dynamical properties of the viral capsids, in particular the pattern of Raman active modes of vibrations, which can be observed experimentally

Infections associated with eating seed sprouts: an international concern.

Recent outbreaks of Salmonella and Escherichia coli O157:H7 infections associated with raw seed sprouts have occurred in several countries. Subjective evaluations indicate that pathogens can exceed 107 per gram of sprouts produced from inoculated seeds during sprout production without adversely affecting appearance. Treating seeds and sprouts with chlorinated water or other disinfectants fails to eliminate the pathogens. A comprehensive approach based on good manufacturing practices and principles of hazard analysis and critical control points can reduce the risk of sprout-associated disease. Until effective measures to prevent sprout-associated illness are identified, persons who wish to reduce their risk of foodborne illness from raw sprouts are advised not to eat them; in particular, persons at high risk for severe complications of infections with Salmonella or E. coli O157:H7, such as the elderly, children, and those with compromised immune systems, should not eat raw sprouts

A Quadrupole/Time-of-Flight Mass Spectrometry Study of Trp-Cage’s Conformation

Trp-cage is a synthetic 20-residue miniprotein that uses tertiary contacts to stabilize its native conformation. NMR, circular dichroism (CD), and UV-resonance Raman spectroscopy were used to probe its energy landscape. In this quadrupole/time-of-flight study, electrospray ionization charge state distribution (CSD) and solution-phase H/D exchange are used to probe Trp-cage’s tertiary structure. The CSDs of Trp-cage and its mutant provide spectra showing a pH-dependent conformation change. Solution-phase H/D exchange in 30% deuterated trifluoroethanol solution of the wild type shows increased protection of one labile hydrogen in the native state. Together, CSDs and solution-phase H/D exchange are demonstrated to constitute a simple but effective means to follow conformation changes in a small tertiary protein

Free field representations for the affine superalgebra sl(2|1)

Free field representations of the affine superalgebra $A(1,0)^{(1)}$ at level $k$ are needed in the description of the noncritical $N=2$ string. The superalgebra admits two inequivalent choices of simple roots. We give the Wakimoto representations corresponding to each of these and derive the relation between the two at the quantum level.Comment: Latex file, 12 page

Rapid spatio-temporal flood modelling via hydraulics-based graph neural networks

Numerical modelling is a reliable tool for flood simulations, but accurate solutions are computationally expensive. In recent years, researchers have explored data-driven methodologies based on neural networks to overcome this limitation. However, most models are only used for a specific case study and disregard the dynamic evolution of the flood wave. This limits their generalizability to topographies that the model was not trained on and in time-dependent applications. In this paper, we introduce shallow water equation–graph neural network (SWE–GNN), a hydraulics-inspired surrogate model based on GNNs that can be used for rapid spatio-temporal flood modelling. The model exploits the analogy between finite-volume methods used to solve SWEs and GNNs. For a computational mesh, we create a graph by considering finite-volume cells as nodes and adjacent cells as being connected by edges. The inputs are determined by the topographical properties of the domain and the initial hydraulic conditions. The GNN then determines how fluxes are exchanged between cells via a learned local function. We overcome the time-step constraints by stacking multiple GNN layers, which expand the considered space instead of increasing the time resolution. We also propose a multi-step-ahead loss function along with a curriculum learning strategy to improve the stability and performance. We validate this approach using a dataset of two-dimensional dike breach flood simulations in randomly generated digital elevation models generated with a high-fidelity numerical solver. The SWE–GNN model predicts the spatio-temporal evolution of the flood for unseen topographies with mean average errors in time of 0.04 m for water depths and 0.004 m2 s−1 for unit discharges. Moreover, it generalizes well to unseen breach locations, bigger domains, and longer periods of time compared to those of the training set, outperforming other deep-learning models. On top of this, SWE–GNN has a computational speed-up of up to 2 orders of magnitude faster than the numerical solver. Our framework opens the doors to a new approach to replace numerical solvers in time-sensitive applications with spatially dependent uncertainties.</p