scholarly journals A new weighted metric: the relative metric II

2005 ◽  
Vol 301 (2) ◽  
pp. 336-353 ◽  
Author(s):  
Peter A. Hästö
Keyword(s):  
Relative Metric

scholarly journals Deep relative metric learning for visual tracking

2018 ◽  
Vol 48 (1) ◽  
pp. 60-78
Author(s):  
Wen GUO ◽  
Sisi YOU ◽  
Junyu GAO ◽  
Xiaoshan YANG ◽  
Tianzhu ZHANG ◽  
...  
Keyword(s):  
Visual Tracking ◽  
Metric Learning ◽  
Relative Metric

Reproducibility and diurnal variation of the directional sensitivity of the cerebral pressure-flow relationship in men and women

2021 ◽  
Author(s):  
Lawrence Labrecque ◽  
Joel S. Burma ◽  
Marc-Antoine Roy ◽  
Jonathan David Smirl ◽  
Patrice Brassard
Keyword(s):  
Sex Differences ◽  
Diurnal Variation ◽  
Cerebral Arteries ◽  
Intraclass Correlation ◽  
Time Of Day ◽  
Effect Sizes ◽  
Directional Sensitivity ◽  
Pressure Flow ◽  
Biological Sex ◽  
Relative Metric

The cerebral pressure-flow relationship has directional sensitivity, meaning the augmentation in cerebral blood flow is attenuated when mean arterial pressure (MAP) increases vs MAP decreases. We employed repeated squat-stands (RSS) to quantify it using a novel metric. However, its within-day reproducibility and the impacts of diurnal variation and biological sex are unknown. Study aims were to evaluate this metric for: 1) within-day reproducibility and diurnal variation in middle (MCA; ∆MCAvT/∆MAPT) and posterior cerebral arteries (PCA; ∆PCAvT/∆MAPT); 2) sex differences. ∆MCAvT/∆MAPT and ∆PCAvT/∆MAPT were calculated at seven time-points (08:00-17:00) in 18 participants (8 women; 24 ± 3 yrs) using the minimum-to-maximum MCAv or PCAv and MAP for each RSS at 0.05 Hz and 0.10 Hz. Relative metric values were also calculated (%MCAvT/%MAPT, %PCAvT/%MAPT). Intraclass correlation coefficient (ICC) evaluated reproducibility, which was good (0.75-0.90) to excellent (>0.90). Time-of-day impacted ∆MCAvT/∆MAPT (0.05 Hz: p = 0.002; 0.10 Hz: p = 0.001), %MCAvT/%MAPT (0.05 Hz: p = 0.035; 0.10 Hz: p = 0.009), and ∆PCAvT/∆MAPT (0.05 Hz: p = 0.024), albeit with small/negligible effect sizes. MAP direction impacted both arteries' metric at 0.10 Hz (all p < 0.024). Sex differences in the MCA only (p = 0.003) vanished when reported in relative terms. These findings demonstrate this metric is reproducible throughout the day in the MCA and PCA and is not impacted by biological sex.

RELATIVE EQUILIBRIUM STATES AND DIMENSIONS OF FIBERWISE INVARIANT MEASURES FOR RANDOM DISTANCE EXPANDING MAPS

2013 ◽  
Vol 14 (01) ◽  
pp. 1350015 ◽  
Author(s):  
DAVID SIMMONS ◽  
MARIUSZ URBAŃSKI
Keyword(s):  
Invariant Measure ◽  
Invariant Measures ◽  
Gibbs State ◽  
Relative Equilibrium ◽  
Equilibrium States ◽  
Expanding Maps ◽  
Hölder Continuous ◽  
Random Maps ◽  
Full Dimension ◽  
Relative Metric

We show that the Gibbs states (known from [10] to be unique) of Hölder continuous potentials and random distance expanding maps coincide with relative equilibrium states of those potentials, proving in particular that the latter exist and are unique. In the realm of conformal expanding random maps, we prove that given an ergodic (globally) invariant measure with a given marginal, for almost every fiber the corresponding conditional measure has dimension equal to the ratio of the relative metric entropy and the Lyapunov exponent. Finally we show that there is exactly one invariant measure whose conditional measures are of full dimension. It is the canonical Gibbs state.

scholarly journals CHOOSING A QUALITY CRITERION FOR EVALUATING THE FORECAST OF NONLINEAR NON-STATIONARY PROCESSES

2021 ◽  
Author(s):  
Andrii O. Belas ◽  
Petro I. Bidyuk
Keyword(s):  
Quality Criterion ◽  
Absolute Error ◽  
Economic Systems ◽  
Nonstationary Processes ◽  
Regression Problem ◽  
Advantages And Disadvantages ◽  
The Given ◽  
Relative Metric ◽  
Selection Of

Background. The problem of forecasting nonlinear nonstationary processes presented in the form of time series is very relevant, since such series can describe dynamics of the processes in both technical and economic systems. To establish the best model, various metrics are used to assess the quality of forecasts, such as R^2, RMSE, MAE, MAPE. However, in many tasks, when optimizing the model according to the selected criterion, the model becomes worse in relation to another criterion. Therefore it is important to understand which metric must be used to optimize and assess the quality of the forecast in the given task. Objective. The aim of the paper is to develop a criteria base for assessing forecasts of nonlinear nonstationary processes, as well as an approach to choosing a metric in accordance to the specificity of the set forecasting problem. Methods. The paper presents a comparative analysis of the basic metrics for the regression problem, their theoretical and practical meaning, advantages and disadvantages in various cases. New approaches are proposed based on the results of the analysis. Results. Based on the analysis of the selected data, it is shown that by optimizing the model according to the selected criterion, the model becomes worse in relation to another criterion. A criterion basis for assessing forecasts of nonlinear nonstationary processes has been formed, as well as an approach to the selection of a quality criterion in accordance with the specifics of the set forecasting problem. To minimize an absolute error, the RMSE (MSE, R^2) and MAE metrics are analysed and recommended, depending on the need to work with outliers. The RMSLE metric is proposed for solving the problems of minimizing the relative metric, for solving the shown problems of the MAPE metric for this class of problems.  Conclusions. The paper shows the importance of choosing a metric that must be used to optimize and assess the quality of the forecasts in the given task. The obtained criterion base and approach can be used in further research to solve practical prob- lems in modelling and forecasting nonlinear nonstationary processes and to develop new methods or general method for solving such problems.

RELATIVE KOLMOGOROV ENTROPY OF A CHAOTIC SYSTEM IN THE PRESENCE OF NOISE

2008 ◽  
Vol 18 (09) ◽  
pp. 2851-2855 ◽  
Author(s):  
VADIM S. ANISHCHENKO ◽  
SERGEY ASTAKHOV
Keyword(s):  
Dynamical Systems ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Stochastic System ◽  
Chaotic Systems ◽  
Metric Entropy ◽  
Kolmogorov Entropy ◽  
Entropy Estimation ◽  
Relative Metric ◽  
Mixing Property

The mixing property is characterized by the metric entropy that is introduced by Kolmogorov for dynamical systems. The Kolmogorov entropy is infinite for a stochastic system. In this work, a relative metric entropy is considered. The relative metric entropy allows to estimate the level of mixing in noisy dynamical systems. An algorithm for calculating the relative metric entropy is described and examples of the metric entropy estimation are provided for certain chaotic systems with various noise intensities. The results are compared to the entropy estimation given by the positive Lyapunov exponents.

Diagnostics of the degree of noise influence on a nonlinear system using relative metric entropy

2010 ◽  
Vol 15 (2-3) ◽  
pp. 261-273 ◽  
Author(s):  
V. S. Anishchenko ◽  
S. V. Astakhov ◽  
T. E. Vadivasova
Keyword(s):  
Nonlinear System ◽  
Metric Entropy ◽  
Relative Metric
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