Partitioning the triangles of the cross polytope into surfaces

We present a constructive proof that there exists a decomposition of the 2-skeleton of the k-dimensional cross polytope $\beta^k$ into closed surfaces of genus $g \leq 1$, each with a transitive automorphism group given by the vertex transitive $\mathbb{Z}_{2k}$-action on $\beta^k$. Furthermore we show that for each $k \equiv 1,5(6)$ the 2-skeleton of the (k-1)-simplex is a union of highly symmetric tori and M\"obius strips.Comment: 13 pages, 1 figure. Minor update. Journal-ref: Beitr. Algebra Geom. / Contributions to Algebra and Geometry, 53(2):473-486, 201

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

Rescaled coordinate descent methods for linear programming

We propose two simple polynomial-time algorithms to find a positive solution to Ax=0Ax=0 . Both algorithms iterate between coordinate descent steps similar to von Neumann’s algorithm, and rescaling steps. In both cases, either the updating step leads to a substantial decrease in the norm, or we can infer that the condition measure is small and rescale in order to improve the geometry. We also show how the algorithms can be extended to find a solution of maximum support for the system Ax=0Ax=0 , x≥0x≥0 . This is an extended abstract. The missing proofs will be provided in the full version

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

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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Perspectives on care and communication involving incurably ill Turkish and Moroccan patients, relatives and professionals: a systematic literature review

<p>Abstract</p> <p>Background</p> <p>Our aim was to obtain a clearer picture of the relevant care experiences and care perceptions of incurably ill Turkish and Moroccan patients, their relatives and professional care providers, as well as of communication and decision-making patterns at the end of life. The ultimate objective is to improve palliative care for Turkish and Moroccan immigrants in the Netherlands, by taking account of socio-cultural factors in the guidelines for palliative care.</p> <p>Methods</p> <p>A systematic literature review was undertaken. The data sources were seventeen national and international literature databases, four Dutch journals dedicated to palliative care and 37 websites of relevant national and international organizations. All the references found were checked to see whether they met the structured inclusion criteria. Inclusion was limited to publications dealing with primary empirical research on the relationship between socio-cultural factors and the health or care situation of Turkish or Moroccan patients with an oncological or incurable disease. The selection was made by first reading the titles and abstracts and subsequently the full texts. The process of deciding which studies to include was carried out by two reviewers independently. A generic appraisal instrument was applied to assess the methodological quality.</p> <p>Results</p> <p>Fifty-seven studies were found that reported findings for the countries of origin (mainly Turkey) and the immigrant host countries (mainly the Netherlands). The central themes were experiences and perceptions of family care, professional care, end-of-life care and communication. Family care is considered a duty, even when such care becomes a severe burden for the main female family caregiver in particular. Professional hospital care is preferred by many of the patients and relatives because they are looking for a cure and security. End-of-life care is strongly influenced by the continuing hope for recovery. Relatives are often quite influential in end-of-life decisions, such as the decision to withdraw or withhold treatments. The diagnosis, prognosis and end-of-life decisions are seldom discussed with the patient, and communication about pain and mental problems is often limited. Language barriers and the dominance of the family may exacerbate communication problems.</p> <p>Conclusions</p> <p>This review confirms the view that family members of patients with a Turkish or Moroccan background have a central role in care, communication and decision making at the end of life. This, in combination with their continuing hope for the patient’s recovery may inhibit open communication between patients, relatives and professionals as partners in palliative care. This implies that organizations and professionals involved in palliative care should take patients’ socio-cultural characteristics into account and incorporate cultural sensitivity into care standards and care practices<it>.</it></p

Population growth of Mexican free-tailed bats (Tadarida brasiliensis mexicana) predates human agricultural activity

Background Human activities, such as agriculture, hunting, and habitat modification, exert a significant effect on native species. Although many species have suffered population declines, increased population fragmentation, or even extinction in connection with these human impacts, others seem to have benefitted from human modification of their habitat. Here we examine whether population growth in an insectivorous bat (Tadarida brasiliensis mexicana) can be attributed to the widespread expansion of agriculture in North America following European settlement. Colonies of T. b. mexicana are extremely large (~106 individuals) and, in the modern era, major agricultural insect pests form an important component of their food resource. It is thus hypothesized that the growth of these insectivorous bat populations was coupled to the expansion of agricultural land use in North America over the last few centuries. Results We sequenced one haploid and one autosomal locus to determine the rate and time of onset of population growth in T. b. mexicana. Using an approximate Maximum Likelihood method, we have determined that T. b. mexicana populations began to grow ~220 kya from a relatively small ancestral effective population size before reaching the large effective population size observed today. Conclusions Our analyses reject the hypothesis that T. b. mexicana populations grew in connection with the expansion of human agriculture in North America, and instead suggest that this growth commenced long before the arrival of humans. As T. brasiliensis is a subtropical species, we hypothesize that the observed signals of population growth may instead reflect range expansions of ancestral bat populations from southern glacial refugia during the tail end of the Pleistocene