Proposal for witnessing non-classical light with the human eye

We give a complete proposal showing how to detect the non-classical nature of photonic states with naked eyes as detectors. The enabling technology is a sub-Poissonian photonic state that is obtained from single photons, displacement operations in phase space and basic non-photon-number-resolving detectors. We present a detailed statistical analysis of our proposal including imperfect photon creation and detection and a realistic model of the human eye. We conclude that a few tens of hours are sufficient to certify non-classical light with the human eye with a p-value of 10%.Comment: 9 pages, 5 figures, accepted versio

Learning Surfaces by Probing

We consider the problem of discovering a smooth unknown surface S bounding an object O in R^3. The discovery process consists of moving a point probing device in the free space around O so that it repeatedly comes in contact with S. We propose a probing strategy for generating a sequence of surface samples on S from which a triangulated surface can be generated which approximates S within any desired accuracy. We bound the number of probes and the number of elementary moves of the probing device. Our solution is an extension of previous work on Delaunay refinement techniques for surface meshing. The approximating surface we generate enjoys the many nice properties of the meshes obtained by those techniques, e.g. exact topological type, nomal approximation, etc

Manifold Reconstruction in Arbitrary Dimensions using Witness Complexes

A preliminary version of this paper has been presented at the ACM Symp. on Computational Geometry 2007International audienceIt is a well-established fact that the witness complex is closely related to the restricted Delaunay triangulation in low dimensions. Specifically, it has been proved that the witness complex coincides with the restricted Delaunay triangulation on curves, and is still a subset of it on surfaces, under mild sampling conditions. In this paper, we prove that these results do not extend to higher-dimensional manifolds, even under strong sampling conditions such as uniform point density. On the positive side, we show how the sets of witnesses and landmarks can be enriched, so that the nice relations that exist between restricted Delaunay triangulation and witness complex hold on higher-dimensional manifolds as well. We derive from our structural results an algorithm that reconstructs manifolds of any arbitrary dimension or co-dimension at different scales. The algorithm combines a farthest-point refinement scheme with a vertex pumping strategy. It is very simple conceptually, and it does not require the input point sample to be sparse. Its running time is bounded by c(d)n2, where n is the size of the input point cloud, and c(d) is a constant depending solely (yet exponentially) on the dimension d of the ambient space. Although this running time makes our reconstruction algorithm rather theoretical, recent work has shown that a variant of our approach can be made tractable in arbitrary dimensions, by building upon the results of this paper

Persistent Homology Over Directed Acyclic Graphs

We define persistent homology groups over any set of spaces which have inclusions defined so that the corresponding directed graph between the spaces is acyclic, as well as along any subgraph of this directed graph. This method simultaneously generalizes standard persistent homology, zigzag persistence and multidimensional persistence to arbitrary directed acyclic graphs, and it also allows the study of more general families of topological spaces or point-cloud data. We give an algorithm to compute the persistent homology groups simultaneously for all subgraphs which contain a single source and a single sink in $O(n^4)$ arithmetic operations, where $n$ is the number of vertices in the graph. We then demonstrate as an application of these tools a method to overlay two distinct filtrations of the same underlying space, which allows us to detect the most significant barcodes using considerably fewer points than standard persistence.Comment: Revised versio

Persistence-Based Clustering in Riemannian Manifolds

We present a novel clustering algorithm that combines a mode-seeking phase with a cluster merging phase. While mode detection is performed by a standard graph-based hill-climbing scheme, the novelty of our approach resides in its use of {\em topological persistence} theory to guide the merges between clusters. An interesting feature of our algorithm is to provide additional feedback in the form of a finite set of points in the plane, called a {\em persistence diagram}, which provably reflects the prominence of each of the modes of the density. Such feedback is an invaluable tool in practice, as it enables the user to determine a set of parameter values that will make the algorithm compute a relevant clustering on the next run. In terms of generality, our approach requires the sole knowledge of (approximate) pairwise distances between the data points, as well as of rough estimates of the density at these points. It is therefore virtually applicable in any arbitrary metric space. In the meantime, its complexity remains reasonable: although the size of the input distance matrix may be up to quadratic in the number of data points, a careful implementation only uses a linear amount of main memory and barely takes more time to run than the one spent reading the input. Taking advantage of recent advances in topological persistence theory, we are able to give a theoretically sound notion of what the {\em correct} number $k$ of clusters is, and to prove that under mild sampling conditions and a relevant choice of parameters (made possible in practice by the persistence diagram) our clustering scheme computes a set of $k$ clusters whose spatial locations are bound to the ones of the basins of attraction of the peaks of the density. These guarantess hold in a large variety of contexts, including when data points are distributed along some unknown Riemannian manifold

In Silico Survey of the Mitochondrial Protein Uptake and Maturation Systems in the Brown Alga Ectocarpus siliculosus

The acquisition of mitochondria was a key event in eukaryote evolution. The aim of this study was to identify homologues of the components of the mitochondrial protein import machinery in the brown alga Ectocarpus and to use this information to investigate the evolutionary history of this fundamental cellular process. Detailed searches were carried out both for components of the protein import system and for related peptidases. Comparative and phylogenetic analyses were used to investigate the evolution of mitochondrial proteins during eukaryote diversification. Key observations include phylogenetic evidence for very ancient origins for many protein import components (Tim21, Tim50, for example) and indications of differences between the outer membrane receptors that recognize the mitochondrial targeting signals, suggesting replacement, rearrangement and/or emergence of new components across the major eukaryotic lineages. Overall, the mitochondrial protein import components analysed in this study confirmed a high level of conservation during evolution, indicating that most are derived from very ancient, ancestral proteins. Several of the protein import components identified in Ectocarpus, such as Tim21, Tim50 and metaxin, have also been found in other stramenopiles and this study suggests an early origin during the evolution of the eukaryotes

CSRP3 mediates polyphenols-induced cardioprotection in hypertension

Berries contain bioactive polyphenols, whose capacity to prevent cardiovascular diseases has been established recently in animal models as well in human clinical trials. However, cellular processes and molecular targets of berries polyphenols remain to be identified. The capacity of a polyphenol-enriched diet (i.e., blueberries, blackberries, raspberries, strawberry tree fruits and Portuguese crowberries berries mixture) to promote animal survival and protect cardiovascular function from salt-induced hypertension was evaluated in a chronic salt-sensitive Dahl rat model. The daily consumption of berries improved survival of Dahl/salt-sensitive rats submitted to high-salt diet and normalized their body weight, renal function and blood pressure. In addition, a prophylactic effect was observed at the level of cardiac hypertrophy and dysfunction, tissue cohesion and cardiomyocyte hypertrophy. Berries also protected the aorta from fibrosis and modulated the expression of aquaporin-1, a channel involved in endothelial water and nitric oxide permeability. Left ventricle proteomics analysis led to the identification of berries and salt metabolites targets, including cystein and glycin-rich protein 3 (CSRP3), a protein involved in myocyte cytoarchitecture. In neonatal rat ventricular cardiomyocytes, CSRP3 was validated as a target of a berries-derived polyphenol metabolite, 4-methylcatechol sulfate, at micromolar concentrations, mimicking physiological conditions of human plasma circulation. Accordingly, siRNA silencing of CSRP3 and 4-methylcatechol sulfate pretreatment reversed cardiomyocyte hypertrophy and CSRP3 overexpression induced by phenylephrine. Our systemic study clearly supports the modulation of CSRP3 by a polyphenol-rich berries diet as an efficient cardioprotective strategy in hypertension-induced heart failure