A Complete Characterization of the One-Dimensional Intrinsic Čech Persistence Diagrams for Metric Graphs

2018 ◽  
pp. 33-56 ◽  
Author(s):  
Ellen Gasparovic ◽  
Maria Gommel ◽  
Emilie Purvine ◽  
Radmila Sazdanovic ◽  
Bei Wang ◽  
...  
Keyword(s):  
Complete Characterization ◽  
Metric Graphs ◽  
One Dimensional ◽  
The One ◽  
Persistence Diagrams

Stability of a thermoelastic mixture with second sound

2018 ◽  
Vol 24 (6) ◽  
pp. 1692-1706 ◽  
Author(s):  
Margareth S. Alves ◽  
Marcio V. Ferreira ◽  
Jaime E. Muñoz Rivera ◽  
O. Vera Villagrán
Keyword(s):  
Initial Data ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Complete Characterization ◽  
Second Sound ◽  
Dimensional Model ◽  
One Dimensional ◽  
The One ◽  
Necessary And Sufficient

We consider the one-dimensional model of a thermoelastic mixture with second sound. We give a complete characterization of the asymptotic properties of the model in terms of the coefficients of the model. We establish the necessary and sufficient conditions for the model to be exponential or polynomial stable and also the conditions for which there exist initial data for where the energy is conserved.

scholarly journals Complete characterization of a class of privacy-preserving tracking problems

2018 ◽  
Vol 38 (2-3) ◽  
pp. 299-315 ◽  
Author(s):  
Yulin Zhang ◽  
Dylan A Shell
Keyword(s):  
Privacy Preserving ◽  
Complete Characterization ◽  
Dimensional Model ◽  
Strategy Space ◽  
Initial Information ◽  
One Dimensional ◽  
Higher Dimensional ◽  
The One ◽  
Tracking Strategy

We examine the problem of target tracking whilst simultaneously preserving the target’s privacy as epitomized by the robotic panda-tracking scenario, which O’Kane introduced at the 2008 Workshop on the Algorithmic Foundations of Robotics to elegantly illustrate the utility of ignorance. The present paper reconsiders his formulation and the tracking strategy he proposed, along with its completeness. We explore how the capabilities of the robot and panda affect the feasibility of tracking with a privacy stipulation, uncovering intrinsic limits, no matter the strategy employed. This paper begins with a one-dimensional setting and, putting the trivially infeasible problems aside, analyzes the strategy space as a function of problem parameters. We show that it is not possible to actively track the target as well as protect its privacy for every non-trivial pair of tracking and privacy stipulations. Secondly, feasibility can be sensitive, in several cases, to the information available to the robot initially. Quite naturally in the one-dimensional model, one may quantify sensing power by the number of perceptual (or output) classes available to the robot. The robot’s power to achieve privacy-preserving tracking is bounded, converging asymptotically with increasing sensing power. We analyze the entire space of possible tracking problems, characterizing every instance as either achievable, constructively by giving a policy where one exists (some of which depend on the initial information), or proving that the instance is impossible. Finally, to relate some of the impossibility results in one dimension to their higher-dimensional counterparts, including the planar panda-tracking problem studied by O’Kane, we establish a connection between tracking dimensionality and the sensing power of a one-dimensional robot.

A Note on Hidden Transient Chaos in the Lorenz System

2017 ◽  
Vol 18 (5) ◽  
pp. 427-434 ◽  
Author(s):  
Quan Yuan ◽  
Fang-Yan Yang ◽  
Lei Wang
Keyword(s):  
Rayleigh Number ◽  
Lorenz System ◽  
Critical Value ◽  
Transient Chaos ◽  
Topological Horseshoe ◽  
One Dimensional ◽  
Dynamical Behaviors ◽  
The Lorenz System ◽  
The One

AbstractIn this paper, the classic Lorenz system is revisited. Some dynamical behaviors are shown with the Rayleigh number $\rho $ somewhat smaller than the critical value 24.06 by studying the basins characterization of attraction of attractors and tracing the one-dimensional unstable manifold of the origin, indicating some interesting clues for detecting the existence of hidden transient chaos. In addition, horseshoes chaos is verified in the famous system for some parameters corresponding to the hidden transient chaos by the topological horseshoe theory.

scholarly journals Lipoarabinomannans: characterization of the multiacylated forms of the phosphatidyl-myo-inositol anchor by NMR spectroscopy

1999 ◽  
Vol 337 (3) ◽  
pp. 453-460 ◽  
Author(s):  
Jérôme NIGOU ◽  
Martine GILLERON ◽  
Germain PUZO
Keyword(s):  
Molecular Basis ◽  
Quantum Correlation ◽  
Analytical Approach ◽  
31P Nmr ◽  
Multiple Quantum ◽  
Double Negative ◽  
Bacillus Calmette Guerin ◽  
One Dimensional ◽  
The One

Lipoarabinomannans, which exhibit a large spectrum of immunological activities, emerge as the major antigens of mycobacterial envelopes. The lipoarabinomannan structure is based on a phosphatidyl-myo-inositol anchor whose integrity has been shown to be crucial for lipoarabinomannan biological activity and particularly for presentation to CD4/CD8 double-negative αβT cells by CD1 molecules. In this report, an analytical approach was developed for high-resolution 31P-NMR analysis of native, i.e. multiacylated, lipoarabinomannans. The one-dimensional 31P spectrum of cellular lipoarabinomannans, from Mycobacterium bovis Bacillus Calmette–Guérin, exhibited four 31P resonances typifying four types of lipoarabinomannans. Two-dimensional 1H-31P heteronuclear multiple-quantum-correlation/homonuclear Hartmann–Hahn analysis of the native molecules showed that these four types of lipoarabinomannan differed in the number and localization of fatty acids (from 1 to 4) esterifying the anchor. Besides the three acylation sites previously described, i.e. positions 1 and 2 of glycerol and 6 of the mannosyl unit linked to the C-2 of myo-inositol, we demonstrate the existence of a fourth acylation position at the C-3 of myo-inositol. We report here the first structural study of native multiacylated lipoarabinomannans, establishing the structure of the intact phosphatidyl-myo-inositol anchor. Our findings would help gain more understanding of the molecular basis of lipoarabinomannan discrimination in the binding process to CD1 molecules.

BORDER COLLISION BIFURCATIONS IN 1D PWL MAP WITH ONE DISCONTINUITY AND NEGATIVE JUMP: USE OF THE FIRST RETURN MAP

2010 ◽  
Vol 20 (11) ◽  
pp. 3529-3547 ◽  
Author(s):  
LAURA GARDINI ◽  
FABIO TRAMONTANA
Keyword(s):  
Parameter Space ◽  
Complete Characterization ◽  
One Dimensional ◽  
Return Map ◽  
Border Collision Bifurcations ◽  
One Dimensional Maps ◽  
Negative Jump

The aim of this work is to study discontinuous one-dimensional maps in the case of slopes and offsets having opposite signs. Such models represent the dynamics of applied systems in several disciplines. We analyze in particular attracting cycles, their border collision bifurcations and the properties of the periodicity regions in the parameter space. The peculiarity of this family is that we can make use of the technical instrument of the first return map. With this, we can rigorously prove properties which were known numerically, as well as prove new ones, giving a complete characterization of the overlapping periodicity regions.

scholarly journals Solutions of the nonlinear paraxial equation due to laser plasma–interactions

2004 ◽  
Vol 22 (1) ◽  
pp. 69-74 ◽  
Author(s):  
F. OSMAN ◽  
R. BEECH ◽  
H. HORA
Keyword(s):  
Laser Plasma ◽  
Theoretical Study ◽  
Semiclassical Limit ◽  
General Setting ◽  
One Dimension ◽  
One Dimensional ◽  
Laser Plasma Interactions ◽  
Weak Limits ◽  
The One

This article presents a numerical and theoretical study of the generation and propagation of oscillation in the semiclassical limit ħ → 0 of the nonlinear paraxial equation. In a general setting of both dimension and nonlinearity, the essential differences between the “defocusing” and “focusing” cases are observed. Numerical comparisons of the oscillations are made between the linear (“free”) and the cubic (defocusing and focusing) cases in one dimension. The integrability of the one-dimensional cubic nonlinear paraxial equation is exploited to give a complete global characterization of the weak limits of the oscillations in the defocusing case.

scholarly journals Observation of broad-band water waveguiding in shallow water: a revival

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Fabián Sepúlveda-Soto ◽  
Diego Guzmán-Silva ◽  
Edgardo Rosas ◽  
Rodrigo A. Vicencio ◽  
Claudio Falcón
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Open Channel ◽  
Fluid Layer ◽  
Broad Band ◽  
Shallow Water Waves ◽  
One Dimensional ◽  
The One ◽  
Complex Phenomena

Abstract We report on the observation and characterization of broad-band waveguiding of surface gravity waves in an open channel, in the shallow water limit. The waveguide is constructed by changing locally the depth of the fluid layer, which creates conditions for surface waves to propagate along the generated guide. We present experimental and numerical results of this shallow water waveguiding, which can be straightforwardly matched to the one-dimensional water wave equation of shallow water waves. Our work revitalizes water waveguiding research as a relevant and controllable experimental setup to study complex phenomena using waveguide geometries.

Equilibrium Distribution of Alloyed Nanowires

2011 ◽  
Vol 172-174 ◽  
pp. 676-681 ◽  
Author(s):  
Emile Maras ◽  
Isabelle Braems ◽  
Fabienne Berthier
Keyword(s):  
Size Distribution ◽  
Equilibrium Distribution ◽  
Canonical Ensemble ◽  
Complete Characterization ◽  
Total Density ◽  
Alloying Effect ◽  
One Dimensional ◽  
Analytical Formulae ◽  
Grand Canonical

The size distribution and the total density of clusters of a one-dimensional pure deposit can be expressed analytically from the Ising model. For a codeposit, the alloying effect and the presence of broken bonds at the cluster edges lead to inhomogeneities of the chemical composition of the clusters. We investigate the influence of codeposition on the size distribution of clusters in the case of an alloy that forms an ideal solution. We obtain the exact solution for the size distribution of clusters while the complete characterization of the system results from coupled analytical formulae in the grand-canonical ensemble. The results of this analytical model are successfully compared with those obtained by Monte Carlo simulations.

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