A comparison of continuous and discrete foreign gas VA/Q distributions

1980 ◽  
Vol 49 (4) ◽  
pp. 684-692 ◽  
Author(s):  
R. Teplick ◽  
M. T. Snider ◽  
J. P. Gilbert
Keyword(s):  
Discrete Model ◽  
Continuous Model ◽  
Lung Model ◽  
Logarithmic Scale ◽  
Linear Scale ◽  
Similar Shape ◽  
Distribution Moments ◽  
Ventilation Perfusion Ratio ◽  
Q Values

Estimates of ventilation-perfusion ratio (VA/Q) distributions from foreign gas infusions have utilized a discrete lung model that constrains all alveoli to have 1 of 50 specified VA/Q. In contrast, distribution estimates based on a continuous model allow alveoli to have any VA/Q and can be derived directly from foreign gas data or by transforming distributions derived using the discrete model. We have compared analytically and empirically the properties of distributions based on these two models. Unlike the discrete model, the shape of distributions obtained from the continuous model are insensitive to changes in the VA/Q used in their calculation. Perfusion distributions found from the discrete model using VA/Q values evenly spaced on a logarithmic scale resemble ventilation distributions derived from the continuous model. In contrast, by use of VA/Q evenly spaced on a linear scale, perfusion distributions derived from either model have a similar shape. We concluded that physiological inferences derived from distribution shapes may vary according to the model employed. However, those based upon cumulative perfusion or distribution moments are invariant.

scholarly journals Spatiotemporal Patterns Formed by a Discrete Nutrient-Phytoplankton Model with Time Delay

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Feifan Zhang ◽  
Wenjiao Zhou ◽  
Lei Yao ◽  
Xuanwen Wu ◽  
Huayong Zhang
Keyword(s):  
Steady State ◽  
Time Delay ◽  
Numerical Simulations ◽  
Functional Response ◽  
Bifurcation Analysis ◽  
Discrete Model ◽  
Continuous Model ◽  
Spatiotemporal Patterns ◽  
Homogeneous Steady State ◽  
Simulation Results

In this research, a continuous nutrient-phytoplankton model with time delay and Michaelis–Menten functional response is discretized to a spatiotemporal discrete model. Around the homogeneous steady state of the discrete model, Neimark–Sacker bifurcation and Turing bifurcation analysis are investigated. Based on the bifurcation analysis, numerical simulations are carried out on the formation of spatiotemporal patterns. Simulation results show that the diffusion of phytoplankton and nutrients can induce the formation of Turing-like patterns, while time delay can also induce the formation of cloud-like pattern by Neimark–Sacker bifurcation. Compared with the results generated by the continuous model, more types of patterns are obtained and are compared with real observed patterns.

scholarly journals Logarithmic Axis Graphs Distort Lay Judgment

2020 ◽  
Author(s):  
William Ryan ◽  
Ellen Riemke Katrien Evers
Keyword(s):  
Logarithmic Scale ◽  
Linear Scale ◽  
Policy Interventions ◽  
Linear Graphs

COVID-19 data is often presented using graphs with either a linear or logarithmic scale. Given the importance of this information, understanding how choice of scale changes interpretations is critical. To test this, we presented laypeople with the same data plotted using differing scales. We found that graphs with a logarithmic, as opposed to linear, scale resulted in laypeople making less accurate predictions of growth, viewing COVID-19 as less dangerous, and expressing both less support for policy interventions and less intention to take personal actions to combat COVID-19. Education reduces, but does not eliminate these effects. These results suggest that public communications should use logarithmic graphs only when necessary, and such graphs should be presented alongside education and linear graphs of the same data whenever possible.

scholarly journals Stability Analysis of an Alcoholism Model with Public Health Education and NSFD Scheme

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Zhaofeng An ◽  
Suxia Zhang ◽  
Jinhu Xu
Keyword(s):  
Public Health ◽  
Health Education ◽  
Differential Equations ◽  
Discrete Model ◽  
Public Health Education ◽  
Continuous Model ◽  
Basic Reproductive Number ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Nsfd Scheme

In this paper, an alcoholism model of SEAR type with different susceptibilities due to public health education is investigated, with the form of continuous differential equations as well as discrete differential equations by applying the Mickens nonstandard finite difference (NSFD) scheme to the continuous equations. Threshold dynamics of the continuous model are performed by constructing Lyapunov functions. The analysis of a discrete model indicates that the alcohol-free equilibrium is globally asymptotically stable if the basic reproductive number R0<1, and conversely, the alcohol-present equilibrium is globally asymptotically stable if R0>1, revealing the consistency and efficiency of the discrete model to preserve the dynamical properties of the corresponding continuous model. In addition, stability preserving and the impact of the parameters related with public health education are conducted by numerical simulations.

scholarly journals A Discrete Model for HIV Infection with Distributed Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Brahim EL Boukari ◽  
Khalid Hattaf ◽  
Noura Yousfi
Keyword(s):  
Hiv Infection ◽  
Global Stability ◽  
Time Delays ◽  
Discrete Model ◽  
Distributed Delay ◽  
Continuous Model ◽  
Distributed Time Delays ◽  
A Cell ◽  
The Times ◽  
Theoretical Results

We give a consistent discretization of a continuous model of HIV infection, with distributed time delays to express the lag between the times when the virus enters a cell and when the cell becomes infected. The global stability of the steady states of the model is determined and numerical simulations are presented to illustrate our theoretical results.

scholarly journals Elastic-viscous properties of acrylic acid 2-propenamide gel

2021 ◽  
pp. 79-88
Author(s):  
A.K. Dorosh ◽  
N.M. Bilko ◽  
D.I. Bilko
Keyword(s):  
Elastic Modulus ◽  
Acrylic Acid ◽  
Modulus Of Elasticity ◽  
Deformation Temperature ◽  
Complex Viscosity ◽  
Equilibrium Structure ◽  
Relative Deformation ◽  
Logarithmic Scale ◽  
Linear Scale ◽  
Biophysical Properties

The rheological properties of the gel-like material, the monomer of which is a crosslinked and modified 2-propenamide of acrylic acid, were determined by relaxation rheometry methods. The values of its elastic modulus and modulus of losses and complex viscosity depending on: deforming stress and its frequency are determined; relative deformation; temperature in the range (20-100) ° C and the regularities of these dependences are noted. It is established that: 1) the dependence of the modulus of elasticity (G'); modulus of loss (G'') and complex viscosity from: relative deformation; voltage; temperature; frequencies indicate that in the linear scale they change according to nonlinear dependencies, and in the transition to the logarithmic scale contain plateau-like areas; 2) analytical dependences of the above parameters on stress, strain rate and temperature are complex and difficult to establish; 3) in the range (20-80) ° C and relative deformations (10-100)% hydrogel has a virtually unchanged value of the modulus (G ') ten times greater than the modulus (G' '), whichdetermines the uniqueness of its rheological and biophysical properties ;  4) in the region (20-80) ° C hydrogel in terms of modulus of elasticity and tangent of the angle of loss is close to a completely elastic body; 5) when the frequency of the deforming voltage is more than 15.8 Hz and the relative deformation ≥100%, the gel is brittlely deformed; while the modulus of its elasticity decreases abruptly and the modulus of losses increases rapidly with increasing frequency of the deforming stress. 6) the dependence of the elastic-viscosity characteristics of the samples washed and unwashed in saline gel in the temperature range (20-80) ° C differ little and indicate that the equilibrium structure of the hydrogel 2-propenamide acrylic acid belongs to the typical colloidal dispersed structure of gelatinous substances.

scholarly journals Simulation of Discrete Predator-Prey Model

2020 ◽  
Vol 55 (1) ◽  
Author(s):  
Adel A. Abed Al Wahab ◽  
Nihad Mahmoud Nasir ◽  
Adil I. Khalil
Keyword(s):  
Discrete Model ◽  
Initial Conditions ◽  
Current Model ◽  
Continuous Model ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Computerized Simulation ◽  
Theoretical Results ◽  
Over Time

It is well known that dynamical systems deal with situations in which the system transforms over time. In fact, undertaking a manual simulation of such systems is a difficult task due to the complexity of the computations. Therefore, a computerized simulation is frequently required for accurate results and fast execution time. Nowadays, computer programs have become an important tool to confirm the theoretical results obtained from the study of models. This paper aims to employ new MATLAB codes to examine a discrete predator–prey model using a difference equations system. The paper discusses the existences and stabilities of each possible fixed point appearing in the current model. Furthermore, numerical simulations fixed by a certain parameter to plot the diagrams are presented. Our results confirm that the systems sensitive to initial conditions are chaotic. Furthermore, the theoretical results as well as numerical examples illustrated that the discrete model exhibits complex behavior compared to a continuous model. The conclusion drawn is that the numerical simulation is an important tool to confirm theoretical results.

scholarly journals Logarithmic encoding of ensemble time intervals

2020 ◽  
Author(s):  
Yue Ren ◽  
Fredrik Allenmark ◽  
Hermann J. Müller ◽  
Zhuanghua Shi
Keyword(s):  
Time Perception ◽  
Geometric Mean ◽  
Internal Representation ◽  
Internal Clock ◽  
Time Range ◽  
Subjective Time ◽  
Logarithmic Scale ◽  
Linear Scale ◽  
Ensemble Averaging ◽  
Time Intervals

AbstractAlthough time perception is based on the internal representation of time, whether the subjective timeline is scaled linearly or logarithmically remains an open issue. Evidence from previous research is mixed: while the classical internal-clock model assumes a linear scale with scalar variability, there is evidence that logarithmic timing provides a better fit to behavioral data. A major challenge for investigating the nature of the internal scale is that the retrieval process required for time judgments may involve a remapping of the subjective time back to the objective scale, complicating any direct interpretation of behavioral findings. Here, we used a novel approach, requiring rapid intuitive ‘ensemble’ averaging of a whole set of time intervals, to probe the subjective timeline. Specifically, observers’ task was to average a series of successively presented, auditory or visual, intervals in the time range 300-1300 ms. Importantly, the intervals were taken from three sets of durations, which were distributed such that the arithmetic mean (from the linear scale) and the geometric mean (from the logarithmic scale) were clearly distinguishable. Consistently across the three sets and the two presentation modalities, our results revealed subjective averaging to be close to the geometric mean, indicative of a logarithmic timeline underlying time perception.

scholarly journals Dynamical analysis of a generalized hepatitis B epidemic model and its dynamically consistent discrete model

2021 ◽  
Author(s):  
Manh Tuan Hoang
Keyword(s):  
Hepatitis B ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Discrete Model ◽  
Reproduction Number ◽  
Continuous Model ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Nsfd Scheme ◽  
The Basic Reproduction Number

The aim of this work is to study qualitative dynamical properties of a generalized hepatitis B epidemic model and its dynamically consistent discrete model. Positivity, boundedness, the basic reproduction number and asymptotic stability properties of the model are analyzed rigorously. By the Lyapunov stability theory and the Poincare-Bendixson theorem in combination with the Bendixson-Dulac criterion, we show that a disease-free equilibrium point is globally asymptotically stable if the basic reproduction number $\mathcal{R}_0 \leq 1$ and a disease-endemic equilibrium point is globally asymptotically stable whenever $\mathcal{R}_0 > 1$. Next, we apply the Mickens’ methodology to propose a dynamically consistent nonstandard finite difference (NSFD) scheme for the continuous model. By rigorously mathematical analyses, it is proved that the constructed NSFD scheme preserves essential mathematical features of the continuous model for all finite step sizes. Finally, numerical experiments are conducted to illustrate the theoretical findings and to demonstrate advantages of the NSFD scheme over standard ones. The obtained results in this work not only improve but also generalize some existing recognized works.

scholarly journals Logarithmic vs. Linear Visualizations of COVID-19 Cases Do Not Affect Citizens’ Support for Confinement

2020 ◽  
Author(s):  
Semra Sevi ◽  
Marco Mendoza Aviña ◽  
Gabrielle Péloquin-Skulski ◽  
Emmanuel Heisbourg ◽  
Paola Vegas ◽  
...  
Keyword(s):  
Causal Effect ◽  
Statistical Information ◽  
Visual Design ◽  
Logarithmic Scale ◽  
Cumulative Number ◽  
Survey Experiment ◽  
Linear Scale ◽  
Design Decisions ◽  
The Public ◽  
The Media

In public health crises, the media and governments routinely share statistical analyses with the public. In the COVID-19 pandemic, the tool most commonly used to convey statistical information about the spread of the virus has been time-series graphs about the cumulative number of cases. When drawing such graphs, analysts have to make design decisions which can have dramatic effects on citizens’ interpretations. Plotting the COVID-19 progression on a linear scale highlights an exponential “explosion” in the number of cases, whereas plotting the number of cases on a logarithmic scale produces a line with a modest-looking slope. Even if the two graphs display the exact same information, differences in visual design may lead people to different substantive conclusions. In this study, we measure the causal effect of different visualization design choices on Canadians’ views about the crisis. We report results from a survey experiment conducted in April 2020 with a sample of 2500 respondents. We find that no matter how the information is presented, Canadians are united in supporting drastic confinement measures and in accepting that these measures will not be removed soon.

scholarly journals Logarithmic encoding of ensemble time intervals

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Yue Ren ◽  
Fredrik Allenmark ◽  
Hermann J. Müller ◽  
Zhuanghua Shi
Keyword(s):  
Time Perception ◽  
Geometric Mean ◽  
Internal Representation ◽  
Internal Clock ◽  
Time Range ◽  
Subjective Time ◽  
Logarithmic Scale ◽  
Linear Scale ◽  
Ensemble Averaging ◽  
Time Intervals

Abstract Although time perception is based on the internal representation of time, whether the subjective timeline is scaled linearly or logarithmically remains an open issue. Evidence from previous research is mixed: while the classical internal-clock model assumes a linear scale with scalar variability, there is evidence that logarithmic timing provides a better fit to behavioral data. A major challenge for investigating the nature of the internal scale is that the retrieval process required for time judgments may involve a remapping of the subjective time back to the objective scale, complicating any direct interpretation of behavioral findings. Here, we used a novel approach, requiring rapid intuitive ‘ensemble’ averaging of a whole set of time intervals, to probe the subjective timeline. Specifically, observers’ task was to average a series of successively presented, auditory or visual, intervals in the time range 300–1300 ms. Importantly, the intervals were taken from three sets of durations, which were distributed such that the arithmetic mean (from the linear scale) and the geometric mean (from the logarithmic scale) were clearly distinguishable. Consistently across the three sets and the two presentation modalities, our results revealed subjective averaging to be close to the geometric mean, indicative of a logarithmic timeline underlying time perception.

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