It has recently been observed that wide-sense self-similar processes have a rich linear structure analogous to that of wide-sense stationary processes. In this paper, a reproducing kernel Hilbert space (RKHS) approach is used to characterize this structure. The RKHS associated with a selfsimilar process on a variety of simple index sets has a straightforward description, provided that the scale...

The Cable equation has been one of the most fundamental equations for modeling neuronal dynamics. In this paper, we consider the numerical solution of the fractional Cable equation, which is a generalization of the classical Cable equation by taking into account the anomalous diffusion in the movement of the ions in neuronal system. A schema combining a finite difference approach in the time di...

It is known that if x ∈ [0, 1] is polynomial time random (i.e. no polynomial time computable martingale succeeds on the binary fractional expansion of x) then x is normal in any integer base greater than one. We show that if x is polynomial time random and β > 1 is Pisot, then x is “normal in base β”, in the sense that the sequence (xβ)n∈N is uniformly distributed modulo one. We work with the n...

Diffusion tensor imaging (DTI) has already proven to be a valuable tool when investigating both global and regional microstructural white matter (WM) brain changes in the human aging process. Although subject to many criticisms, voxel-based analysis is currently one of the most common and preferred approaches in such DTI aging studies. In this context, voxel-based DTI analyses have assumed a 'l...

This paper proposes a novel approach for analyzing the stability of polynomial fractional-order systems using frequency-distributed fractional integrator model. There are two types frequency and temporal stabilization methods that global semi-global conditions attain sum-of-squares (SOS) method. Substantiation asymptotical complicated systems. According to recent studies on nonlinear systems, t...

A variable fractional-order equivalent circuit model is proposed to accurately describe the dynamic characteristics of lithium-ion batteries (LIBs). Firstly, a fractional impedance (FIM) established, such that (FO) polynomial function LIB state charge (SOC). Then, chaotic adaptive particle swarm optimization (CAFPSO) method derived identify parameters FIM. Experiments reveal reliability novel a...

conclusions the use of smoothing methods helps us to eliminate non-linear effects but it is more appropriate to use cox proportional hazards model in medical data because of its’ ease of interpretation and capability of modeling both continuous and discrete covariates. also, cox proportional hazards model and smoothing methods analysis identified that age at diagnosis and tumor size were indepe...