Weighted-function based algorithm for retrieving handwriting trajectory from off-line data

Some weighted-type classes of holomorphic function spaces were introduced in the current study. Moreover, as an application of the new defined classes, the specific growth of certain entire-solutions of a linear-type differential equation by the use of concerned coefficients of certain analytic-type functions, that is the equation h(k)+Kk−1(υ)h(k−1)+…+K1(υ)h′+K0(υ)h=0, will be discussed in this current research, whereas the considered coefficients K0(υ),…,Kk−1(υ) are holomorphic in the disc ΓR={υ∈C:|υ|<R},0<R≤∞. In addition, some non-trivial specific examples are illustrated to clear the roles of the obtained results with some sharpness sense. Hence, the obtained results are strengthen to some previous interesting results from the literature.

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Spectral invariance for pseudodifferential operators on weighted function spaces

manuscripta mathematica ◽

10.1007/bf02567616 ◽

1994 ◽

Vol 83 (1) ◽

pp. 315-325 ◽

Cited By ~ 4

Author(s):

Hans-Gerd Leopold ◽

Hans Triebel

Keyword(s):

Pseudodifferential Operators ◽

Function Spaces ◽

Weighted Function ◽

Spectral Invariance ◽

Weighted Function Spaces

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Phase Transition in Elementary Cellular Automata with Memory

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127414501168 ◽

2014 ◽

Vol 24 (09) ◽

pp. 1450116 ◽

Cited By ~ 3

Author(s):

Shigeru Ninagawa ◽

Andrew Adamatzky ◽

Ramón Alonso-Sanz

Keyword(s):

Cellular Automata ◽

State Transition ◽

Time Interval ◽

Complex Behavior ◽

Weighted Function ◽

Transition Functions ◽

Elementary Cellular Automata ◽

Computational Universality ◽

With Memory ◽

Time Automaton

We study elementary cellular automata with memory. The memory is a weighted function averaged over cell states in a time interval, with a varying factor which determines how strongly a cell's previous states contribute to the cell's present state. We classify selected cell-state transition functions based on Lempel–Ziv compressibility of space-time automaton configurations generated by these functions and the spectral analysis of their transitory behavior. We focus on rules 18, 22, and 54 because they exhibit the most intriguing behavior, including computational universality. We show that a complex behavior is observed near the nonmonotonous transition to null behavior (rules 18 and 54) or during the monotonic transition from chaotic to periodic behavior (rule 22).

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Percolation phase transition of static and growing networks under a weighted function

International Journal of Modern Physics C ◽

10.1142/s0129183116500820 ◽

2016 ◽

Vol 27 (07) ◽

pp. 1650082 ◽

Cited By ~ 1

Author(s):

Xiao Jia ◽

Jin-Song Hong ◽

Ya-Chun Gao ◽

Hong-Chun Yang ◽

Chun Yang ◽

...

Keyword(s):

Phase Transition ◽

Continuous Phase ◽

Weighted Function ◽

Percolation Process ◽

Practical Applications ◽

Network Intervention ◽

Growing Networks ◽

Discontinuous Phase ◽

And Control ◽

Growing Network

We investigate the percolation phase transitions in both the static and growing networks where the nodes are sampled according to a weighted function with a tunable parameter [Formula: see text]. For the static network, i.e. the number of nodes is constant during the percolation process, the percolation phase transition can evolve from continuous to discontinuous as the value of [Formula: see text] is tuned. Based on the properties of the weighted function, three typical values of [Formula: see text] are analyzed. The model becomes the classical Erdös–Rényi (ER) network model at [Formula: see text]. When [Formula: see text], it is shown that the percolation process generates a weakly discontinuous phase transition where the order parameter exhibits an extremely abrupt transition with a significant jump in large but finite system. For [Formula: see text], the cluster size distribution at the lower pseudo-transition point does not obey the power-law behavior, indicating a strongly discontinuous phase transition. In the case of growing network, in which the collection of nodes is increasing, a smoother continuous phase transition emerges at [Formula: see text], in contrast to the weakly discontinuous phase transition of the static network. At [Formula: see text], on the other hand, probability modulation effect shows that the nature of strongly discontinuous phase transition remains the same with the static network despite the node arrival even in the thermodynamic limit. These percolation properties of the growing networks could provide useful reference for network intervention and control in practical applications in consideration of the increasing size of most actual networks.

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A Regularized Weighted Smoothed L0 Norm Minimization Method for Underdetermined Blind Source Separation

Sensors ◽

10.3390/s18124260 ◽

2018 ◽

Vol 18 (12) ◽

pp. 4260 ◽

Cited By ~ 8

Author(s):

Linyu Wang ◽

Xiangjun Yin ◽

Huihui Yue ◽

Jianhong Xiang

Keyword(s):

Blind Source Separation ◽

Signal Reconstruction ◽

Source Separation ◽

Minimization Method ◽

Underdetermined Blind Source Separation ◽

Weighted Function ◽

Performance Simulation ◽

Linear System Of Equations ◽

Norm Minimization ◽

Magnetic Resonance Imaging Mri

Compressed sensing (CS) theory has attracted widespread attention in recent years and has been widely used in signal and image processing, such as underdetermined blind source separation (UBSS), magnetic resonance imaging (MRI), etc. As the main link of CS, the goal of sparse signal reconstruction is how to recover accurately and effectively the original signal from an underdetermined linear system of equations (ULSE). For this problem, we propose a new algorithm called the weighted regularized smoothed L 0 -norm minimization algorithm (WReSL0). Under the framework of this algorithm, we have done three things: (1) proposed a new smoothed function called the compound inverse proportional function (CIPF); (2) proposed a new weighted function; and (3) a new regularization form is derived and constructed. In this algorithm, the weighted function and the new smoothed function are combined as the sparsity-promoting object, and a new regularization form is derived and constructed to enhance de-noising performance. Performance simulation experiments on both the real signal and real images show that the proposed WReSL0 algorithm outperforms other popular approaches, such as SL0, BPDN, NSL0, and L p -RLSand achieves better performances when it is used for UBSS.

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