526 research outputs found
Volumes transverses aux feuilletages définissables dans des structures o-minimales
Let be a family of codimension foliations defined on a family of manifolds and let be a family of compact subsets of . Suppose that , and are definable in an o-minimal structure and that all leaves of are closed. Given a definable family of differential -forms satisfaying for any vector field tangent to , we prove that there exists a constant A >0 such that the integral of on any transversal of intersecting each leaf in at most one point is bounded by . We apply this result to prove that -volumes of transverse sections of 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 arithmetic operations, where 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
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