A Dense Packing of Regular Tetrahedra

We construct a dense packing of regular tetrahedra, with packing density $D > >.7786157$.Comment: full color versio

Outbreak of tropical rat mite (Ornithonyssus bacoti) dermatitis in a home for disabled persons

Five mentally handicapped individuals living in a home for disabled persons in Southern Germany were seen in our outpatient department with pruritic, red papules predominantly located in groups on the upper extremities, neck, upper trunk and face. Over several weeks 40 inhabitants and 5 caretakers were affected by the same rash. Inspection of their home and the sheds nearby disclosed infestation with rat populations and mites. Finally the diagnosis of tropical rat mite dermatitis was made by the identification of the arthropod Ornithonyssus bacoti or so-called tropical rat mite. The patients were treated with topical corticosteroids and antihistamines. After elimination of the rats and disinfection of the rooms by a professional exterminator no new cases of rat mite dermatitis occurred. The tropical rat mite is an external parasite occurring on rats, mice, gerbils, hamsters and various other small mammals. When the principal animal host is not available, human beings can become the victim of mite infestation. Copyright (c) 2007 S. Karger AG, Base

HGaze Typing: head-gesture assisted gaze typing

This paper introduces a bi-modal typing interface, HGaze Typing, which combines the simplicity of head gestures with the speed of gaze inputs to provide efficient and comfortable dwell-free text entry. HGaze Typing uses gaze path information to compute candidate words and allows explicit activation of common text entry commands, such as selection, deletion, and revision, by using head gestures (nodding, shaking, and tilting). By adding a head-based input channel, HGaze Typing reduces the size of the screen regions for cancel/deletion buttons and the word candidate list, which are required by most eye-typing interfaces. A user study finds HGaze Typing outperforms a dwell-time-based keyboard in efficacy and user satisfaction. The results demonstrate that the proposed method of integrating gaze and head-movement inputs can serve as an effective interface for text entry and is robust to unintended selections.https://dl.acm.org/doi/pdf/10.1145/3448017.3457379Published versio

Using collision cones to assess biological deconfliction methods

Biological systems consistently outperform autonomous systems governed by engineered algorithms in their ability to reactively avoid collisions. To better understand this discrepancy, a collision avoidance algorithm was applied to frames of digitized video trajectory data from bats, swallows and fish (Myotis velifer, Petrochelidon pyrrhonota and Danio aequipinnatus). Information available from visual cues, specifically relative position and velocity, was provided to the algorithm which used this information to define collision cones that allowed the algorithm to find a safe velocity requiring minimal deviation from the original velocity. The subset of obstacles provided to the algorithm was determined by the animal's sensing range in terms of metric and topological distance. The algorithmic calculated velocities showed good agreement with observed biological velocities, indicating that the algorithm was an informative basis for comparison with the three species and could potentially be improved for engineered applications with further study

Crystalline Assemblies and Densest Packings of a Family of Truncated Tetrahedra and the Role of Directional Entropic Forces

Polyhedra and their arrangements have intrigued humankind since the ancient Greeks and are today important motifs in condensed matter, with application to many classes of liquids and solids. Yet, little is known about the thermodynamically stable phases of polyhedrally-shaped building blocks, such as faceted nanoparticles and colloids. Although hard particles are known to organize due to entropy alone, and some unusual phases are reported in the literature, the role of entropic forces in connection with polyhedral shape is not well understood. Here, we study thermodynamic self-assembly of a family of truncated tetrahedra and report several atomic crystal isostructures, including diamond, {\beta}-tin, and high- pressure lithium, as the polyhedron shape varies from tetrahedral to octahedral. We compare our findings with the densest packings of the truncated tetrahedron family obtained by numerical compression and report a new space filling polyhedron, which has been overlooked in previous searches. Interestingly, the self-assembled structures differ from the densest packings. We show that the self-assembled crystal structures can be understood as a tendency for polyhedra to maximize face-to-face alignment, which can be generalized as directional entropic forces.Comment: Article + supplementary information. 23 pages, 10 figures, 2 table

Valuations on lattice polytopes

This survey is on classification results for valuations defined on lattice polytopes that intertwine the special linear group over the integers. The basic real valued valuations, the coefficients of the Ehrhart polynomial, are introduced and their characterization by Betke and Kneser is discussed. More recent results include classification theorems for vector and convex body valued valuations. © Springer International Publishing AG 2017

More efficient periodic traversal in anonymous undirected graphs

We consider the problem of periodic graph exploration in which a mobile entity with constant memory, an agent, has to visit all n nodes of an arbitrary undirected graph G in a periodic manner. Graphs are supposed to be anonymous, that is, nodes are unlabeled. However, while visiting a node, the robot has to distinguish between edges incident to it. For each node v the endpoints of the edges incident to v are uniquely identified by different integer labels called port numbers. We are interested in minimisation of the length of the exploration period. This problem is unsolvable if the local port numbers are set arbitrarily. However, surprisingly small periods can be achieved when assigning carefully the local port numbers. Dobrev et al. described an algorithm for assigning port numbers, and an oblivious agent (i.e. agent with no memory) using it, such that the agent explores all graphs of size n within period 10n. Providing the agent with a constant number of memory bits, the optimal length of the period was previously proved to be no more than 3.75n (using a different assignment of the port numbers). In this paper, we improve both these bounds. More precisely, we show a period of length at most 4 1/3 n for oblivious agents, and a period of length at most 3.5n for agents with constant memory. Moreover, we give the first non-trivial lower bound, 2.8n, on the period length for the oblivious case

Majorations explicites de fonctions de Hilbert-Samuel géométrique et arithmétique

International audienceBy using the $\mathbb R$-filtration approach of Arakelov geometry, one establishes explicit upper bounds for geometric and arithmetic Hilbert-Samuel function for line bundles on projective varieties and hermitian line bundles on arithmetic projective varieties

Diffusion of peroxides through dentine in vitro with and without prior use of a desensitizing varnish

Different bleaching regimens are used in dentistry possibly penetrating the dentine and affecting the pulp. The aim of the present study was to investigate peroxide diffusion through dentine pre-treated with a desensitizing varnish (Vivasens®) in a standardized in vitro setup during application of different bleaching materials. The penetration was tested using 1.3-mm-thick bovine dentine slabs. The following bleaching materials were tested with and without prior application of the desensitizing varnish on the external side of the dentine slabs: Vivastyle, Whitestrips, Simply White, Opalescence (external bleaching), and sodium perborate (internal bleaching, only tested without varnish; n = 8 samples per subgroup). The penetration of peroxides was measured photometrically using 4-aminoantipyrin as a substrate, the penetration of peroxides was monitored over 240 min. All bleaching agents yielded a diffusion of peroxides through the dentine, the kinetics of penetration were approximately linear for all materials tested. The significantly highest diffusion of peroxides was observed with Opalescence, the lowest with sodium perborate. The adoption of the desensitizing varnish reduced the diffusion of peroxides significantly for all external bleaching materials. Peroxides penetrated the dentine during application of bleaching materials; the penetration of peroxides can be reduced by application of a desensitizing agent

Interactive models of communication at the nanoscale using nanoparticles that talk to one another

[EN] 'Communication' between abiotic nanoscale chemical systems is an almost-unexplored field with enormous potential. Here we show the design and preparation of a chemical communication system based on enzyme-powered Janus nanoparticles, which mimics an interactive model of communication. Cargo delivery from one nanoparticle is governed by the biunivocal communication with another nanoparticle, which involves two enzymatic processes and the interchange of chemical messengers. The conceptual idea of establishing communication between nanodevices opens the opportunity to develop complex nanoscale systems capable of sharing information and cooperating.A. L.-L. is grateful to 'La Caixa' Banking Foundation for his PhD fellowship. We wish to thank the Spanish Government (MINECO Projects MAT2015-64139-C4-1, CTQ2014-58989-P and CTQ2015-71936-REDT and AGL2015-70235-C2-2-R) and the Generalitat Valenciana (Project PROMETEOII/2014/047) for support. 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