Orthogonal nets and Clifford algebras

A Clifford algebra model for M"obius geometry is presented. The notion of Ribaucour pairs of orthogonal systems in arbitrary dimensions is introduced, and the structure equations for adapted frames are derived. These equations are discretized and the geometry of the occuring discrete nets and sphere congruences is discussed in a conformal setting. This way, the notions of ``discrete Ribaucour congruences'' and ``discrete Ribaucour pairs of orthogonal systems'' are obtained --- the latter as a generalization of discrete orthogonal systems in Euclidean space. The relation of a Cauchy problem for discrete orthogonal nets and a permutability theorem for the Ribaucour transformation of smooth orthogonal systems is discussed.Comment: Plain TeX, 16 pages, 4 picture

Modeling pedestrian evacuation movement in a swaying ship

With the advance in living standard, cruise travel has been rapidly expanding around the world in recent years. The transportation of passengers in water has also made a rapid development. It is expected that ships will be more and more widely used. Unfortunately, ship disasters occurred in these years caused serious losses. It raised the concern on effectiveness of passenger evacuation on ships. The present study thus focuses on pedestrian evacuation features on ships. On ships, passenger movements are affected by the periodical water motion and thus are quite different from the characteristic when walking on static horizontal floor. Taking into consideration of this special feature, an agent-based pedestrian model is formulized and the effect of ship swaying on pedestrian evacuation efficiency is investigated. Results indicated that the proposed model can be used to quantify the special evacuation process on ships.Comment: Traffic and Granular Flow'15, At Delft, the Netherland

Directing Selectivity of Electrochemical Carbon Dioxide Reduction Using Plasmonics

Catalysts for electrochemical carbon dioxide reduction in aqueous electrolytes suffer from high energy input requirements, competition with hydrogen evolution from water reduction, and low product selectivity. Theory suggests that plasmonic catalysts can be tuned to selectively lower the energy barrier for a specific reaction in a set of competitive reactions, but there has been little experimental evidence demonstrating plasmon-driven selectivity in complicated multielectron electrochemical processes. Here, the photoactivity at a plasmonically active silver thin film electrode at small cathodic potentials selectively generates carbon monoxide while simultaneously suppressing hydrogen production. At larger cathodic potentials, the photoactivity promotes production of methanol and formate. Methanol production is observed only under illumination, not in dark conditions. The preference of the plasmonic activity for carbon dioxide reduction over hydrogen evolution and the ability to tune plasmonic activity with voltage demonstrates that plasmonics provide a promising approach to promote complex electrochemical reactions over other competing reactions

Subsquares Approach - Simple Scheme for Solving Overdetermined Interval Linear Systems

In this work we present a new simple but efficient scheme - Subsquares approach - for development of algorithms for enclosing the solution set of overdetermined interval linear systems. We are going to show two algorithms based on this scheme and discuss their features. We start with a simple algorithm as a motivation, then we continue with a sequential algorithm. Both algorithms can be easily parallelized. The features of both algorithms will be discussed and numerically tested.Comment: submitted to PPAM 201

On local structures of cubicity 2 graphs

A 2-stab unit interval graph (2SUIG) is an axes-parallel unit square intersection graph where the unit squares intersect either of the two fixed lines parallel to the $X$-axis, distance $1 + \epsilon$ ($0 < \epsilon < 1$) apart. This family of graphs allow us to study local structures of unit square intersection graphs, that is, graphs with cubicity 2. The complexity of determining whether a tree has cubicity 2 is unknown while the graph recognition problem for unit square intersection graph is known to be NP-hard. We present a polynomial time algorithm for recognizing trees that admit a 2SUIG representation

An analytic solution to the Busemann-Petty problem on sections of convex bodies

We derive a formula connecting the derivatives of parallel section functions of an origin-symmetric star body in R^n with the Fourier transform of powers of the radial function of the body. A parallel section function (or (n-1)-dimensional X-ray) gives the ((n-1)-dimensional) volumes of all hyperplane sections of the body orthogonal to a given direction. This formula provides a new characterization of intersection bodies in R^n and leads to a unified analytic solution to the Busemann-Petty problem: Suppose that K and L are two origin-symmetric convex bodies in R^n such that the ((n-1)-dimensional) volume of each central hyperplane section of K is smaller than the volume of the corresponding section of L; is the (n-dimensional) volume of K smaller than the volume of L? In conjunction with earlier established connections between the Busemann-Petty problem, intersection bodies, and positive definite distributions, our formula shows that the answer to the problem depends on the behavior of the (n-2)-nd derivative of the parallel section functions. The affirmative answer to the Busemann-Petty problem for n\le 4 and the negative answer for n\ge 5 now follow from the fact that convexity controls the second derivatives, but does not control the derivatives of higher orders.Comment: 13 pages, published versio

CRISPR evolution and bacteriophage persistence in the context of population bottlenecks

This is the author accepted manuscript. The final version is available from RNA Biology via the DOI in this recordPopulation bottlenecks often cause strong reductions in genetic diversity and alter population structure. In the context of host-parasite interactions, bottlenecks could in theory benefit either the host or the pathogen. We predicted that bottlenecking of bacterial populations that evolve CRISPR immunity against bacteriophages (phage) would benefit the pathogen, because CRISPR spacer diversity can rapidly drive phages extinct. To test this, we bottlenecked populations of bacteria and phage, tracking phage persistence and the evolution of bacterial resistance mechanisms. Contrary to our prediction, bottlenecking worked in the advantage of the host. With some possible exceptions, this effect was not caused by CRISPR immunity. This host benefit is consistent with a dilution effect disproportionately affecting phage. This study provides further insight into how bottlenecking influences bacteria-phage dynamics, the role of dilution in bacteria-phage interactions, and the evolution of host immune systems.South West Biosciences Doctoral Training PartnershipWellcome TrustNatural Environment Research CouncilBBSRCEuropean Research Counci