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

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

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

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

Appeal No. 0873: Stonebridge Operating Co., LLC. v. Division of Oil & Gas Resources Management

Chief\u27s Orders 2014-39 (suspension of operations); 2014-236, 2014-238,2014-239, 2014-241 (denials of plug-back permits); 2014-253, 2014-256 thru 2014-262 & 2014-264 thru 2014-266 (plug orders

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

Categorification of persistent homology

We redevelop persistent homology (topological persistence) from a categorical point of view. The main objects of study are diagrams, indexed by the poset of real numbers, in some target category. The set of such diagrams has an interleaving distance, which we show generalizes the previously-studied bottleneck distance. To illustrate the utility of this approach, we greatly generalize previous stability results for persistence, extended persistence, and kernel, image and cokernel persistence. We give a natural construction of a category of interleavings of these diagrams, and show that if the target category is abelian, so is this category of interleavings.Comment: 27 pages, v3: minor changes, to appear in Discrete & Computational Geometr

The Theory of the Interleaving Distance on Multidimensional Persistence Modules

In 2009, Chazal et al. introduced $\epsilon$-interleavings of persistence modules. $\epsilon$-interleavings induce a pseudometric $d_I$ on (isomorphism classes of) persistence modules, the interleaving distance. The definitions of $\epsilon$-interleavings and $d_I$ generalize readily to multidimensional persistence modules. In this paper, we develop the theory of multidimensional interleavings, with a view towards applications to topological data analysis. We present four main results. First, we show that on 1-D persistence modules, $d_I$ is equal to the bottleneck distance $d_B$. This result, which first appeared in an earlier preprint of this paper, has since appeared in several other places, and is now known as the isometry theorem. Second, we present a characterization of the $\epsilon$-interleaving relation on multidimensional persistence modules. This expresses transparently the sense in which two $\epsilon$-interleaved modules are algebraically similar. Third, using this characterization, we show that when we define our persistence modules over a prime field, $d_I$ satisfies a universality property. This universality result is the central result of the paper. It says that $d_I$ satisfies a stability property generalizing one which $d_B$ is known to satisfy, and that in addition, if $d$ is any other pseudometric on multidimensional persistence modules satisfying the same stability property, then $d\leq d_I$. We also show that a variant of this universality result holds for $d_B$, over arbitrary fields. Finally, we show that $d_I$ restricts to a metric on isomorphism classes of finitely presented multidimensional persistence modules.Comment: Major revision; exposition improved throughout. To appear in Foundations of Computational Mathematics. 36 page

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