Quadrilateral-octagon coordinates for almost normal surfaces

Normal and almost normal surfaces are essential tools for algorithmic 3-manifold topology, but to use them requires exponentially slow enumeration algorithms in a high-dimensional vector space. The quadrilateral coordinates of Tollefson alleviate this problem considerably for normal surfaces, by reducing the dimension of this vector space from 7n to 3n (where n is the complexity of the underlying triangulation). Here we develop an analogous theory for octagonal almost normal surfaces, using quadrilateral and octagon coordinates to reduce this dimension from 10n to 6n. As an application, we show that quadrilateral-octagon coordinates can be used exclusively in the streamlined 3-sphere recognition algorithm of Jaco, Rubinstein and Thompson, reducing experimental running times by factors of thousands. We also introduce joint coordinates, a system with only 3n dimensions for octagonal almost normal surfaces that has appealing geometric properties.Comment: 34 pages, 20 figures; v2: Simplified the proof of Theorem 4.5 using cohomology, plus other minor changes; v3: Minor housekeepin

Complementarity, quantum erasure and delayed choice with modified Mach-Zehnder interferometers

Often cited dictums in Quantum Mechanics include "observation disturbance causes loss of interference" and "ignorance is interference". In this paper we propose and describe a series of experiments with modified Mach-Zehnder interferometers showing that one has to be careful when applying such dictums. We are able to show that without interacting in any way with the light quantum (or quanta) expected to behave "wave-like", interference fringes can be lost by simply gaining (or having the potential to gain) the which-path knowledge. Erasing this information may revive the interference fringes. Delayed choice can be added, arriving to an experiment in line with Wheeler's original proposal. We also show that ignorance is not always synonym with having the interference fringes. The often-invoked "collapse of the wavefunction" is found to be a non-necessary ingredient to describe our experiments.Comment: 8 pages, 3 figures; to appear in EPJ

A Delayed Choice Quantum Eraser

This paper reports a "delayed choice quantum eraser" experiment proposed by Scully and Dr\"{u}hl in 1982. The experimental results demonstrated the possibility of simultaneously observing both particle-like and wave-like behavior of a quantum via quantum entanglement. The which-path or both-path information of a quantum can be erased or marked by its entangled twin even after the registration of the quantum.Comment: twocolumn, 4pages, submitted to PR

Beyond representing orthology relations by trees

Reconstructing the evolutionary past of a family of genes is an important aspect of many genomic studies. To help with this, simple relations on a set of sequences called orthology relations may be employed. In addition to being interesting from a practical point of view they are also attractive from a theoretical perspective in that e.\,g.\,a characterization is known for when such a relation is representable by a certain type of phylogenetic tree. For an orthology relation inferred from real biological data it is however generally too much to hope for that it satisfies that characterization. Rather than trying to correct the data in some way or another which has its own drawbacks, as an alternative, we propose to represent an orthology relation $\delta$ in terms of a structure more general than a phylogenetic tree called a phylogenetic network. To compute such a network in the form of a level-1 representation for $\delta$, we formalize an orthology relation in terms of the novel concept of a symbolic 3- dissimilarity which is motivated by the biological concept of a ``cluster of orthologous groups'', or COG for short. For such maps which assign symbols rather that real values to elements, we introduce the novel {\sc Network-Popping} algorithm which has several attractive properties. In addition, we characterize an orthology relation $\delta$ on some set $X$ that has a level-1 representation in terms of eight natural properties for $\delta$ as well as in terms of level-1 representations of orthology relations on certain subsets of $X$

New-particle formation events in a continental boundary layer: first results from the SATURN experiment

International audienceDuring the SATURN experiment, which took place from 27 May to 14 June 2002, new particle formation in the continental boundary layer was investigated. Simultaneous ground-based and tethered-balloon-borne measurements were performed, including meteorological parameters, particle number concentrations and size distributions, gaseous precursor concentrations and SODAR and LIDAR observations. Newly formed particles were observed inside the residual layer, before the break-up process of the nocturnal inversion, and inside the mixing layer throughout the break-up of the nocturnal inversion and during the evolution of the planetary boundary layer.</p

Three-way symbolic tree-maps and ultrametrics

Three-way dissimilarities are a generalization of (two-way) dissimilarities which can be used to indicate the lack of homogeneity or resemblance between any three objects. Such maps have applications in cluster analysis and have been used in areas such as psychology and phylogenetics, where three-way data tables can arise. Special examples of such dissimilarities are three-way tree-metrics and ultrametrics, which arise from leaf-labelled trees with edges labelled by positive real numbers. Here we consider three-way maps which arise from leaf-labelled trees where instead the interior vertices are labelled by an arbitrary set of values. For unrooted trees, we call such maps three-way symbolic tree-maps; for rooted trees, we call them three-way symbolic ultrametrics since they can be considered as a generalization of the (two-way) symbolic ultrametrics of Bocker and Dress. We show that, as with two- and three-way tree-metrics and ultrametrics, three-way symbolic tree-maps and ultrametrics can be characterized via certain k-point conditions. In the unrooted case, our characterization is mathematically equivalent to one presented by Gurvich for a certain class of edge-labelled hypergraphs. We also show that it can be decided whether or not an arbitrary three-way symbolic map is a tree-map or a symbolic ultrametric using a triplet-based approach that relies on the so-called BUILD algorithm for deciding when a set of 3-leaved trees or triplets can be displayed by a single tree. We envisage that our results will be useful in developing new approaches and algorithms for understanding 3-way data, especially within the area of phylogenetics

Potentiation of thrombus instability: a contributory mechanism to the effectiveness of antithrombotic medications

© The Author(s) 2018The stability of an arterial thrombus, determined by its structure and ability to resist endogenous fibrinolysis, is a major determinant of the extent of infarction that results from coronary or cerebrovascular thrombosis. There is ample evidence from both laboratory and clinical studies to suggest that in addition to inhibiting platelet aggregation, antithrombotic medications have shear-dependent effects, potentiating thrombus fragility and/or enhancing endogenous fibrinolysis. Such shear-dependent effects, potentiating the fragility of the growing thrombus and/or enhancing endogenous thrombolytic activity, likely contribute to the clinical effectiveness of such medications. It is not clear how much these effects relate to the measured inhibition of platelet aggregation in response to specific agonists. These effects are observable only with techniques that subject the growing thrombus to arterial flow and shear conditions. The effects of antithrombotic medications on thrombus stability and ways of assessing this are reviewed herein, and it is proposed that thrombus stability could become a new target for pharmacological intervention.Peer reviewedFinal Published versio

Testing foundations of quantum mechanics with photons

The foundational ideas of quantum mechanics continue to give rise to counterintuitive theories and physical effects that are in conflict with a classical description of Nature. Experiments with light at the single photon level have historically been at the forefront of tests of fundamental quantum theory and new developments in photonics engineering continue to enable new experiments. Here we review recent photonic experiments to test two foundational themes in quantum mechanics: wave-particle duality, central to recent complementarity and delayed-choice experiments; and Bell nonlocality where recent theoretical and technological advances have allowed all controversial loopholes to be separately addressed in different photonics experiments.Comment: 10 pages, 5 figures, published as a Nature Physics Insight review articl

Mathematical Modelling of Optical Coherence Tomography

In this chapter a general mathematical model of Optical Coherence Tomography (OCT) is presented on the basis of the electromagnetic theory. OCT produces high resolution images of the inner structure of biological tissues. Images are obtained by measuring the time delay and the intensity of the backscattered light from the sample considering also the coherence properties of light. The scattering problem is considered for a weakly scattering medium located far enough from the detector. The inverse problem is to reconstruct the susceptibility of the medium given the measurements for different positions of the mirror. Different approaches are addressed depending on the different assumptions made about the optical properties of the sample. This procedure is applied to a full field OCT system and an extension to standard (time and frequency domain) OCT is briefly presented.Comment: 28 pages, 5 figures, book chapte