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Capturing Multiple Timescales of Adaptation to Second-Order Statistics With Generalized Linear Models: Gain Scaling and Fractional Differentiation [PDF]
Frontiers in Systems Neuroscience, 2020 Single neurons can dynamically change the gain of their spiking responses to take into account shifts in stimulus variance. Moreover, gain adaptation can occur across multiple timescales.
Kenneth W. Latimer, Adrienne L. Fairhall
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The PLSR-ML fusion strategy for high-accuracy leaf potassium inversion in karst region of Southwest China [PDF]
Frontiers in Plant SciencePotassium is a critical macronutrient for plant growth, yet accurately and rapidly estimating its content in karst regions remains challenging due to complex terrestrial conditions.
Zhihao Song +7 more
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Fractional Integration and Differentiation by new Transformation
Wasit Journal for Pure Sciences, 2023 In opposite to differentiation and integration of integer order, an important type of differentiation and integration is the so - called “ Fractional Calculus (FC) ” in which the differentiation and integration is of non-integer order.
Anfal khalil, Basim Albuohimad
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Hyperspectral Remote Sensing Images Feature Extraction Based on Spectral Fractional Differentiation
Remote Sensing, 2023 To extract effective features for the terrain classification of hyperspectral remote-sensing images (HRSIs), a spectral fractional-differentiation (SFD) feature of HRSIs is presented, and a criterion for selecting the fractional-differentiation order is ...
Jing Liu, Yang Li, Feng Zhao, Yi Liu
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Axioms, 2022 The paper presents an analytical solution of a partial differential equation of hyperbolic-type, containing both second-order partial derivatives and fractional derivatives of order below the second.
Ludmila Vladimirovna Kirianova
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Predicting the Long-Term Dependencies in Time Series Using Recurrent Artificial Neural Networks
Machine Learning and Knowledge Extraction, 2023 Long-term dependence is an essential feature for the predictability of time series. Estimating the parameter that describes long memory is essential to describing the behavior of time series models.
Cristian Ubal +3 more
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Fractional differential forms [PDF]
Journal of Mathematical Physics, 2001 A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector spaces of finite and infinite dimension, fractional differential form spaces. The definitions of closed and exact forms
Cottrill-Shepherd, Kathleen, Naber, Mark
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Fractals, 2021 A new differentiation technique, fractional pseudospectral shifted Legendre differentiation matrices (FSL D-matrices), was introduced. It depends on shifted Legendre polynomials (SLPs) as a base function. We take into consideration its extreme points and inner product. The technique was used to solve fractional ordinary differential equations (FODEs).
Abdelhakem, Mohamed +3 more
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Depth Image Enhancement Algorithm Based on Fractional Differentiation
Fractal and Fractional, 2023 Depth image enhancement techniques can help to improve image quality and facilitate computer vision tasks. Traditional image-enhancement methods, which are typically based on integer-order calculus, cannot exploit the textural information of an image ...
Tingsheng Huang +4 more
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FRACTIONAL DIFFERENTIATION MATRICES FOR SOLVING FRACTIONAL ORDERS DIFFERENTIAL EQUATIONS [PDF]
International Journal of Pure and Apllied Mathematics, 2013 This paper gives a new formula for the fractional differentiation matrix based on shifted Chebyshev polynomials for solving fractional order ordinary differential equations (FODEs). In addition, we will estimate the error bound of the in the largest element of that matrix.
M. El-Kady, A. El-Sayed
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