Behaviour of the reference measure on $\mathsf{RCD}$ spaces under charts

2021 ◽  
Vol 29 (6) ◽  
pp. 1391-1414
Author(s):  
Nicola Gigli ◽  
Enrico Pasqualetto
Keyword(s):  
Reference Measure

scholarly journals Conditional Rényi Entropy and the Relationships between Rényi Capacities

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 526
Author(s):  
Gautam Aishwarya ◽  
Mokshay Madiman
Keyword(s):  
Mutual Information ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Basic Properties ◽  
Reference Measure ◽  
Definition Of ◽  
Discrete Setting

The analogues of Arimoto’s definition of conditional Rényi entropy and Rényi mutual information are explored for abstract alphabets. These quantities, although dependent on the reference measure, have some useful properties similar to those known in the discrete setting. In addition to laying out some such basic properties and the relations to Rényi divergences, the relationships between the families of mutual informations defined by Sibson, Augustin-Csiszár, and Lapidoth-Pfister, as well as the corresponding capacities, are explored.

scholarly journals The Holy Grail

2015 ◽  
Vol 27 (5) ◽  
pp. 714-738 ◽  
Author(s):  
Jorge Pereira-Moliner ◽  
Xavier Font ◽  
Juan José Tarí ◽  
Jose F. Molina-Azorin ◽  
Maria D. Lopez-Gamero ◽  
...  
Keyword(s):  
Environmental Management ◽  
Business Performance ◽  
Competitive Advantages ◽  
Performance Levels ◽  
Content Type ◽  
Reference Measure ◽  
Environmental Capability ◽  
And Performance ◽  
Hotel Managers ◽  
The Relationship

Purpose – This paper aims to analyse the influence of environmental proactivity on cost and differentiation competitive advantages, and to explore the double relationship between environmental proactivity and business performance. Design/methodology/approach – The population consists of all three- to five-star hotels in Spain. A sample of 350 hotels was classified according to environmental proactivity and performance levels, employing a two-step cluster analysis. Significant differences between groups were examined. Findings – The results show two types of environmental behaviour (reactive and proactive), with proactive hotels developing significantly better on both cost and differentiation competitive advantage and achieving significantly higher performance levels. Hotels which achieve above average business performance levels are significantly more environmentally proactive. Research limitations/implications – The present paper demonstrates that environmental management is related to competitive advantages and business performance. Environmental management systems are more developed in higher category, chain-affiliated and larger hotels. This could be due to having more resources to develop their environmental capability. The environmental proactivity scale employed in this study is presented as a reference measure for hotel managers to benchmark their current practices and implement environmental improvements. Originality/value – First, measuring environmental proactivity using four managerial systems (operative, information, strategic and technical) is innovative and provides a more detailed approach to measuring environmental proactivity. Second, demonstrating a double association between environmental proactivity and performance provides fresh insights into the relationship between these variables.

Cyber Space Security Assessment Case Study

2018 ◽  
pp. 1060-1092
Author(s):  
Hanaa. M. Said ◽  
Rania El Gohary ◽  
Mohamed Hamdy ◽  
Abdelbadeeh M. Salem
Keyword(s):  
Data Mining ◽  
Cyber Security ◽  
Cyber Attacks ◽  
Assessment Procedure ◽  
Security Assessment ◽  
Reference Measure ◽  
Decision Tress ◽  
Cyber Space ◽  
Reference Measurements

Cyberspace is known as the digital electronic medium for the knowing range of securing in the cyberspace. Therefore the importance of inferring the reference measure in the form of assessment procedure to improve the knowledge and making the decision for the e- government services. A series of the standards build on the application of data mining methods specifically represented as decision tress model, Logistic regression, association rules model, Bayesian network for making reference measurements, to measure the extent of securing the data, and the provided services. The authors discuss various types of cyber-attacks describing how data mining helps in detection and prevention of these attacks. A comparative analysis between a set of selected frameworks is presented. Finally this chapter imparts numbers of applications for the data mining Methodologies in Cyber Security. Results applied on the site of the authority for cleaning and beautifying Cairo governorate in Egypt.

scholarly journals On the optimal importance process for piecewise deterministic Markov process

2019 ◽  
Vol 23 ◽  
pp. 893-921
Author(s):  
H. Chraibi ◽  
A. Dutfoy ◽  
T. Galtier ◽  
J. Garnier
Keyword(s):  
Importance Sampling ◽  
Simulation Study ◽  
Variance Reduction ◽  
Sampling Method ◽  
Piecewise Deterministic Markov Process ◽  
Importance Sampling Method ◽  
Markovian Processes ◽  
Component Systems ◽  
Reference Measure ◽  
Reduction Methods

In order to assess the reliability of a complex industrial system by simulation, and in reasonable time, variance reduction methods such as importance sampling can be used. We propose an adaptation of this method for a class of multi-component dynamical systems which are modeled by piecewise deterministic Markovian processes (PDMP). We show how to adapt the importance sampling method to PDMP, by introducing a reference measure on the trajectory space. This reference measure makes it possible to identify the admissible importance processes. Then we derive the characteristics of an optimal importance process, and present a convenient and explicit way to build an importance process based on theses characteristics. A simulation study compares our importance sampling method to the crude Monte-Carlo method on a three-component systems. The variance reduction obtained in the simulation study is quite spectacular.

Degenerate curves and harmonic analysis

1990 ◽  
Vol 108 (1) ◽  
pp. 89-96 ◽  
Author(s):  
S. W. Drury
Keyword(s):  
Harmonic Analysis ◽  
Correct Choice ◽  
Degenerate Case ◽  
Point Of View ◽  
Affine Geometry ◽  
The Poor ◽  
Reference Measure ◽  
Affine Arclength

This article deals with several related questions in harmonic analysis which are well understood for non-degenerate curves in ℝn, but poorly understood in the degenerate case. These questions invariably involve a positive ‘reference’ measure on the curve. In the non-degenerate case the choice of measure is not particularly critical and it is usually taken to be the Euclidean arclength measure. Since the questions considered here are invariant under the group of affine motions (of determinant 1), the correct choice of reference measure is the affine arclength measure. We refer the reader to Guggenheimer [8] for information on affine geometry. When the curve has degeneracies, the choice of measure becomes critical and it is the affine arclength measure which yields the most powerful results. From the Euclidean point of view the affine arclength measure has correspondingly little mass near the degeneracies and thus compensates automatically for the poor behaviour there. This principle should also be valid for general submanifolds of ℝn but alas the affine geometry of submanifolds is itself not well understood in general.

scholarly journals Influence of Ionizing Radiation on Two Generations of Cochlear Implants

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Nicolas Guevara ◽  
Anaïs Gérard ◽  
Jeanne Dupré ◽  
Delphine Goursonnet ◽  
Michel Hoen ◽  
...  
Keyword(s):  
Cochlear Implant ◽  
Cochlear Implants ◽  
Radiation Doses ◽  
Output Current ◽  
Single Measurement ◽  
Stereotactic Irradiation ◽  
Reference Measure ◽  
Two Generations ◽  
Clinical Radiotherapy

The purpose of the present study was to test the behavior of two different generations of cochlear implant systems subjected to a clinical radiotherapy scheme and to determine the maximal acceptable cumulative radiation levels at which the devices show out-of-specification behaviors. Using stereotactic irradiation (Cyberknife, 6 MV photon beam), three Digisonic SP and three Neuro devices were submitted to 5 Gy doses that cumulated to 60 Gy (12 sessions) and 80 Gy (16 sessions), respectively. A follow-up series of irradiation was then applied, in which Digisonic SP devices received two additional fractions of 50 Gy each, cumulating to 160 Gy, and Neuro devices three additional fractions of 20, 40, and 150 Gy, cumulating to 290 Gy. Output current values were monitored during the treatment. At clinical doses, with 60 or 80 Gy cumulative radiation exposure, no single measurement showed more than 10% divergence from the reference measure. The cochlear implants tested in this study showed high resistance to clinically relevant cumulative radiation doses and showed no out-of-bounds behavior up to cumulative doses of 140 or 160 Gy. These observations suggest that cochlear implant users can undergo radiotherapy up to cumulative doses well above those currently used in clinical situations without risk of failure.

scholarly journals SYMPHYSIS MORPHOLOGY AND DIMENSIONS IN DIFFERENT VERTICAL FACIAL PATTERNS (CBCT SCAN STUDY)

2015 ◽  
Vol 61 (3) ◽  
pp. 217-226
Author(s):  
Mohamad Mahfoud ◽  
◽  
Hazem Hassan ◽  
Keyword(s):  
Orthodontic Treatment ◽  
Growth Direction ◽  
Cone Beam ◽  
Planning Tool ◽  
Mandibular Symphysis ◽  
Mandibular Growth ◽  
Mandibular Plane ◽  
Reference Measure ◽  
The Face ◽  
Highly Correlated

Mandibular symphysis (MS) morphology is a valuable diagnostic and treatment-planning tool in orthodontics. It is utilised as a reference measure for esthetic purposes, specifically in the lower part of the face, as well as to predict the direction of the mandibular growth rotation as the vertical growth direction. The aim of the presenting study is to use cone beam computed tomography (CBCT) to evaluate the MS morphology and dimensions of adults with different vertical facial patterns and had no previous orthodontic treatment. The study consisted of 100 subjects (42 males and 58 females). Mean age of subjects is 27.6 years (average age of men 29.2 years, average age of women 26.4 years). The CBCT images were obtained by Scanora 3D. The evaluation of the different vertical facial patterns was carried out according to Björk and Jarabak. Six lines, four angles and one area were used in the mandibular symphysis study. The study revealed varying correlations between the parameters of the mandibular symphysis and those of the vertical facial patterns. It was found that the convexity of the mandibular symphysis (B-POG-Me) and the distance from POG to the z-axis (POG-Z Axis) are highly correlated to the parameters evaluating the vertical facial patterns. The angle between the Gonion-Nasion line and the mandibular plane (GO2-Angle) and the angle between the palatal and mandibular planes (B-Angle) were highly correlated to the measurements used on the mandibular symphysis.

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