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

Smoothness of continuous state branching with immigration semigroups

In this work we develop an original and thorough analysis of the (non)-smoothness properties of the semigroups, and their heat kernels, associated to a large class of continuous state branching processes with immigration. Our approach is based on an in-depth analysis of the regularity of the absolutely continuous part of the invariant measure combined with a substantial refinement of Ogura's spectral expansion of the transition kernels. In particular, we find new representations for the eigenfunctions and eigenmeasures that allow us to derive delicate uniform bounds that are useful for establishing the uniform convergence of the spectral representation of the semigroup acting on linear spaces that we identify. We detail several examples which illustrate the variety of smoothness properties that CBI transition kernels may enjoy and also reveal that our results are sharp. Finally, our technique enables us to provide the (eventually) strong Feller property as well as the rate of convergence to equilibrium in the total variation norm

Low energy neutron propagation in MCNPX and GEANT4

Simulations of neutron background from rock for underground experiments are presented. Neutron propagation through two types of rock, lead and hydrocarbon material is discussed. The results show a reasonably good agreement between GEANT4, MCNPX and GEANT3 in transporting low-energy neutrons.Comment: 9 Figure

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

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

The persistence landscape and some of its properties

Persistence landscapes map persistence diagrams into a function space, which may often be taken to be a Banach space or even a Hilbert space. In the latter case, it is a feature map and there is an associated kernel. The main advantage of this summary is that it allows one to apply tools from statistics and machine learning. Furthermore, the mapping from persistence diagrams to persistence landscapes is stable and invertible. We introduce a weighted version of the persistence landscape and define a one-parameter family of Poisson-weighted persistence landscape kernels that may be useful for learning. We also demonstrate some additional properties of the persistence landscape. First, the persistence landscape may be viewed as a tropical rational function. Second, in many cases it is possible to exactly reconstruct all of the component persistence diagrams from an average persistence landscape. It follows that the persistence landscape kernel is characteristic for certain generic empirical measures. Finally, the persistence landscape distance may be arbitrarily small compared to the interleaving distance.Comment: 18 pages, to appear in the Proceedings of the 2018 Abel Symposiu

Heartbeat Classification in Wearables Using Multi-layer Perceptron and Time-Frequency Joint Distribution of ECG

Heartbeat classification using electrocardiogram (ECG) data is a vital assistive technology for wearable health solutions. We propose heartbeat feature classification based on a novel sparse representation using time-frequency joint distribution of ECG. Fundamental to this is a multi-layer perceptron, which incorporates these signatures to detect cardiac arrhythmia. This approach is validated with ECG data from MIT-BIH arrhythmia database. Results show that our approach has an average 95.7% accuracy, an improvement of 22% over state-of-the-art approaches. Additionally, ECG sparse distributed representations generates only 3.7% false negatives, reduction of 89% with respect to existing ECG signal classification techniques.Comment: 6 pages, 7 figures, published in IEEE/ACM International Conference on Connected Health: Applications, Systems and Engineering Technologies (CHASE

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

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