Volumes transverses aux feuilletages définissables dans des structures o-minimales

Let $\mathcal{F}_\lambda$ be a family of codimension $p$ foliations defined on a family $M_\lambda$ of manifolds and let $X_\lambda$ be a family of compact subsets of $M_\lambda$. Suppose that $\mathcal{F}_\lambda$, $M_\lambda$ and $X_\lambda$ are definable in an o-minimal structure and that all leaves of $\mathcal{F}_\lambda$ are closed. Given a definable family $\Omega_\lambda$ of differential $p$-forms satisfaying $i_Z\Omega_\lambda = 0$ for any vector field $Z$ tangent to $\mathcal{F}_\lambda$, we prove that there exists a constant A >0 such that the integral of $|\Omega_\lambda|$ on any transversal of $\mathcal{F}_\lambda$ intersecting each leaf in at most one point is bounded by $A$. We apply this result to prove that $p$-volumes of transverse sections of $\mathcal{F}_\lambda$ are uniformly bounded

Investigations of fast neutron production by 190 GeV/c muon interactions on different targets

The production of fast neutrons (1 MeV - 1 GeV) in high energy muon-nucleus interactions is poorly understood, yet it is fundamental to the understanding of the background in many underground experiments. The aim of the present experiment (CERN NA55) was to measure spallation neutrons produced by 190 GeV/c muons scattering on carbon, copper and lead targets. We have investigated the energy spectrum and angular distribution of spallation neutrons, and we report the result of our measurement of the neutron production differential cross section.Comment: 19 pages, 11 figures ep

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

An advanced 3D multi-body system model for the human lumbar spine

Series : Mechanisms and machine science, ISSN 2211-0984, vol. 24A novel 3D multi-body system model of the human lumbar spine is presented, allowing the dynamic study of the all set but also to access mechanical demands, characteristics and performance under work of the individual intervertebral discs. An advanced FEM analysis was used for the most precise characterization of the disc 6DOF mechanical behavior, in order to build up a tool capable of predicting and assist in the design of disc recovery strategies – namely in the development of replace-ment materials for the degenerated disc nucleus – as well as in the analysis of variations in the me-chanical properties (disorders) at disc level or kinematic structure (e.g. interbody fusion, pedicle fixa-tion, etc.), and its influence in the overall spine dynamics and at motion segments individual level. Preliminary results of the model, at different levels of its development, are presented

Good covers are algorithmically unrecognizable

A good cover in R^d is a collection of open contractible sets in R^d such that the intersection of any subcollection is either contractible or empty. Motivated by an analogy with convex sets, intersection patterns of good covers were studied intensively. Our main result is that intersection patterns of good covers are algorithmically unrecognizable. More precisely, the intersection pattern of a good cover can be stored in a simplicial complex called nerve which records which subfamilies of the good cover intersect. A simplicial complex is topologically d-representable if it is isomorphic to the nerve of a good cover in R^d. We prove that it is algorithmically undecidable whether a given simplicial complex is topologically d-representable for any fixed d \geq 5. The result remains also valid if we replace good covers with acyclic covers or with covers by open d-balls. As an auxiliary result we prove that if a simplicial complex is PL embeddable into R^d, then it is topologically d-representable. We also supply this result with showing that if a "sufficiently fine" subdivision of a k-dimensional complex is d-representable and k \leq (2d-3)/3, then the complex is PL embeddable into R^d.Comment: 22 pages, 5 figures; result extended also to acyclic covers in version

Sub MeV Particles Detection and Identification in the MUNU detector ((1)ISN, IN2P3/CNRS-UJF, Grenoble, France, (2)Institut de Physique, Neuch\^atel, Switzerland, (3) INFN, Padova Italy, (4) Physik-Institut, Z\"{u}rich, Switzerland)

We report on the performance of a 1 m$^{3}$ TPC filled with CF$_{4}$ at 3 bar, immersed in liquid scintillator and viewed by photomultipliers. Particle detection, event identification and localization achieved by measuring both the current signal and the scintillation light are presented. Particular features of $\alpha$ particle detection are also discussed. Finally, the ${54}$Mn photopeak, reconstructed from the Compton scattering and recoil angle is shown.Comment: Latex, 19 pages, 20 figure

Impact of thymidine phosphorylase surexpression on fluoropyrimidine activity and on tumour angiogenesis

Tumoral thymidine phosphorylase (TP) appears to play a dual role by being involved in neoangiogenesis and by activating 5FU prodrugs at the tumoral target site. The aim of the study was to investigate more thoroughly these potential physiological and pharmacological roles of TP. A rat carcinoma cell line (PROb) was transfected with TP/PD-ECGF in order to study the effect of the overexpression of this enzyme (1) on the sensitivity of cells to 5′DFUR and 5FU in vitro and (2) on tumour growth in vivo by using a syngenic tumour model in the BDIX rat (hepatic tumours, sub-cutaneous tumours). Cytotoxic effects of 5′DFUR, and to a lesser extent those of 5FU, were enhanced in TP clones as compared to control cells: there was a highly significant correlation between TP activity and in vitro sensitivity to 5’DFUR (r2= 0.91, P = 0.0002, n = 8) and, to a lesser extent, to 5FU (r2= 0.49, P = 0.053, n = 8). The impact of TP transfection on tumour growth was relatively modest and concerned only the initial stages of tumour expansion. Staining of TP tumours for endothelial (factor VIII) cells was always higher than controls. The staining ratio (TP/controls) tended to be reduced as tumours increased in size. The stability of TP expression was checked both in vitro (TP activity measurement) and in vivo (RT-PCR determinations) and there was no loss of TP expression over time which could be advanced to explain the progressive weakening of the impact of TP overexpression on both tumour growth and neoangiogenesis. © 2001 Cancer Research Campaign http://www.bjcancer.co

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

Biomechanical experimental data curation: an example for main lumbar spine ligaments characterization for a MBS spine model

Series : Mechanisms and machine science, ISSN 2211-0984, vol. 24This work overviews an extensive analysis in the context of mechanical characterization of human biomaterials, carried out over a broad set of published experimental data. Focused on main lumbar spine ligaments, several test procedures are exhaustively analyzed, in order to identify possible causes for divergences that have been found in some results. Moreover, guidelines are proposed for da-ta filtering and selection. The main objective of the task was to retrieve trustworthy inputs to a hybrid Finite Element Analysis / Multibody System dynamic simulation model of the human intervertebral disc, which can be used on the prediction of nucleus prosthetics working performance