scholarly journals Constructing sequences with high nonlinear complexity using the Weierstrass semigroup of a pair of distinct points of a Hermitian curve

2018 ◽  
Vol 98 (3) ◽  
pp. 543-555
Author(s):  
Olav Geil ◽  
Ferruh Özbudak ◽  
Diego Ruano
Keyword(s):  
Weierstrass Semigroup ◽  
Hermitian Curve ◽  
Nonlinear Complexity

Nonlinear complexity of human biodynamics engine

2010 ◽  
Vol 61 (1-2) ◽  
pp. 123-139 ◽  
Author(s):  
Vladimir G. Ivancevic
Keyword(s):  
Nonlinear Complexity

scholarly journals Using Bidimensional Multiscale Entropy Analysis of Ultrasound Images to Assess the Effect of Various Walking Intensities on Plantar Soft Tissues

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 264
Author(s):  
Ben-Yi Liau ◽  
Fu-Lien Wu ◽  
Keying Zhang ◽  
Chi-Wen Lung ◽  
Chunmei Cao ◽  
...  
Keyword(s):  
Soft Tissues ◽  
Linear Analysis ◽  
Multiscale Entropy ◽  
Ultrasound Images ◽  
Entropy Analysis ◽  
Nonlinear Complexity ◽  
Human Movements ◽  
Before And After ◽  
Walking Performance ◽  
Linear And Nonlinear

Walking performance is usually assessed by linear analysis of walking outcome measures. However, human movements consist of both linear and nonlinear complexity components. The purpose of this study was to use bidimensional multiscale entropy analysis of ultrasound images to evaluate the effects of various walking intensities on plantar soft tissues. Twelve participants were recruited to perform six walking protocols, consisting of three speeds (slow at 1.8 mph, moderate at 3.6 mph, and fast at 5.4 mph) for two durations (10 and 20 min). A B-mode ultrasound was used to assess plantar soft tissues before and after six walking protocols. Bidimensional multiscale entropy (MSE2D) and the Complexity Index (CI) were used to quantify the changes in irregularity of the ultrasound images of the plantar soft tissues. The results showed that the CI of ultrasound images after 20 min walking increased when compared to before walking (CI4: 0.39 vs. 0.35; CI5: 0.48 vs. 0.43, p < 0.05). When comparing 20 and 10 min walking protocols at 3.6 mph, the CI was higher after 20 min walking than after 10 min walking (CI4: 0.39 vs. 0.36, p < 0.05; and CI5: 0.48 vs. 0.44, p < 0.05). This is the first study to use bidimensional multiscale entropy analysis of ultrasound images to assess plantar soft tissues after various walking intensities.

scholarly journals The source of discrepancies in aerosol–cloud–precipitation interactions between GCM and A-Train retrievals

2016 ◽  
Vol 16 (23) ◽  
pp. 15413-15424 ◽  
Author(s):  
Takuro Michibata ◽  
Kentaroh Suzuki ◽  
Yousuke Sato ◽  
Toshihiko Takemura
Keyword(s):  
General Circulation ◽  
Climate Models ◽  
Circulation Model ◽  
Cloud Droplet ◽  
Systematic Difference ◽  
Liquid Water Path ◽  
Light Rain ◽  
Aerosol Cloud ◽  
Nonlinear Complexity ◽  
Aerosol Cloud Interactions

Abstract. Aerosol–cloud interactions are one of the most uncertain processes in climate models due to their nonlinear complexity. A key complexity arises from the possibility that clouds can respond to perturbed aerosols in two opposite ways, as characterized by the traditional “cloud lifetime” hypothesis and more recent “buffered system” hypothesis. Their importance in climate simulations remains poorly understood. Here we investigate the response of the liquid water path (LWP) to aerosol perturbations for warm clouds from the perspective of general circulation model (GCM) and A-Train remote sensing, through process-oriented model evaluations. A systematic difference is found in the LWP response between the model results and observations. The model results indicate a near-global uniform increase of LWP with increasing aerosol loading, while the sign of the response of the LWP from the A-Train varies from region to region. The satellite-observed response of the LWP is closely related to meteorological and/or macrophysical factors, in addition to the microphysics. The model does not reproduce this variability of cloud susceptibility (i.e., sensitivity of LWP to perturbed aerosols) because the parameterization of the autoconversion process assumes only suppression of rain formation in response to increased cloud droplet number, and does not consider macrophysical aspects that serve as a mechanism for the negative responses of the LWP via enhancements of evaporation and precipitation. Model biases are also found in the precipitation microphysics, which suggests that the model generates rainwater readily even when little cloud water is present. This essentially causes projections of unrealistically frequent and light rain, with high cloud susceptibilities to aerosol perturbations.

𝔽 p 2 -maximal curves with many automorphisms are Galois-covered by the Hermitian curve

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Daniele Bartoli ◽  
Maria Montanucci ◽  
Fernando Torres
Keyword(s):  
Finite Field ◽  
Prime Numbers ◽  
Hermitian Curve ◽  
Maximal Curve ◽  
Maximal Curves

Abstract Let 𝔽 be the finite field of order q 2. It is sometimes attributed to Serre that any curve 𝔽-covered by the Hermitian curve H q + 1 : y q + 1 = x q + x ${{\mathcal{H}}_{q+1}}:{{y}^{q+1}}={{x }^{q}}+x$ is also 𝔽-maximal. For prime numbers q we show that every 𝔽-maximal curve x $\mathcal{x}$ of genus g ≥ 2 with | Aut(𝒳) | > 84(g − 1) is Galois-covered by H q + 1 . ${{\mathcal{H}}_{q+1}}.$ The hypothesis on | Aut(𝒳) | is sharp, since there exists an 𝔽-maximal curve x $\mathcal{x}$ for q = 71 of genus g = 7 with | Aut(𝒳) | = 84(7 − 1) which is not Galois-covered by the Hermitian curve H 72 . ${{\mathcal{H}}_{72}}.$

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