Cluster solutions in networks of weakly coupled oscillators on a 2D square torus

Mathematics in Applied Sciences and Engineering ◽

10.5206/mase/14147 ◽

2021 ◽

Author(s):

Jordan Michael Culp

Keyword(s):

Matrix Theory ◽

Circulant Matrix ◽

Von Neumann ◽

Novel Approach ◽

Weakly Coupled ◽

Cluster Solutions ◽

Lattice Network ◽

The Stability ◽

Model Reduction Technique ◽

Phase Differences

We consider a model for an N × N lattice network of weakly coupled neural oscilla- tors with periodic boundary conditions (2D square torus), where the coupling between neurons is assumed to be within a von Neumann neighborhood of size r, denoted as von Neumann r-neighborhood. Using the phase model reduction technique, we study the existence of cluster solutions with constant phase differences (Ψh, Ψv) between adjacent oscillators along the horizontal and vertical directions in our network, where Ψh and Ψv are not necessarily to be identical. Applying the Kronecker production representation and the circulant matrix theory, we develop a novel approach to analyze the stability of cluster solutions with constant phase difference (i.e., Ψh,Ψv are equal). We begin our analysis by deriving the precise conditions for stability of such cluster solutions with von Neumann 1-neighborhood and 2 neighborhood couplings, and then we generalize our result to von Neumann r-neighborhood coupling for arbitrary neighborhood size r ≥ 1. This developed approach for the stability analysis indeed can be extended to an arbitrary coupling in our network. Finally, numerical simulations are used to validate the above analytical results for various values of N and r by considering an inhibitory network of Morris-Lecar neurons.

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Unbounded Linear Operators

10.1093/oso/9780198812050.003.0003 ◽

2018 ◽

Author(s):

D. E. Edmunds ◽

W. D. Evans

Keyword(s):

Hilbert Spaces ◽

Linear Operators ◽

Von Neumann ◽

Limit Circle ◽

Sectorial Operators ◽

Closed Operators ◽

The Stability ◽

Symmetric Operators ◽

Unbounded Linear Operators ◽

Special Case

This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.

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A Novel Approach to Fabricate Foam Ceramics from Steel Slag

Advances in Materials Science and Engineering ◽

10.1155/2020/4649082 ◽

2020 ◽

Vol 2020 ◽

pp. 1-7

Author(s):

Yu Zheng ◽

Xudong Luo ◽

Jinlong Yang ◽

Wenlong Huo ◽

Chi Kang

Keyword(s):

Compressive Strength ◽

Ph Value ◽

Steel Slag ◽

Raw Material ◽

Solid Loading ◽

Insulation Material ◽

Ceramic Foams ◽

Novel Approach ◽

The Stability ◽

First Time

A novel approach is used for fabricating steel slag foam ceramics based on the particle-stabilized foaming method. In this work, steel slag was used as the raw material and propyl gallate (PG) was used as the surface modifier. For the first time, steel slag ceramic foams were successfully fabricated based on particle-stabilized foams. The results show that the stability of the ceramic foams was closely related to the pH value and PG concentration. The porosity and compressive strength could be controlled by changing the solid loading of steel slag and sintering temperature. The porosity of steel slag foam ceramics ranged from 85.6% to 62.53%, and the compressive strength was from 1.74 MPa to 10.42 MPa. The thermal conductivity of steel slag foam ceramics was only 0.067 W (m·K)−1, which shows that it could be used as a thermal insulation material.

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A novel approach for the stability problem in non-linear dynamical systems

Computer Physics Communications ◽

10.1016/s0010-4655(03)00295-9 ◽

2003 ◽

Vol 155 (1) ◽

pp. 21-30 ◽

Cited By ~ 5

Author(s):

Tarcı́sio M. Rocha Filho ◽

Iram M. Gléria ◽

Annibal Figueiredo

Keyword(s):

Dynamical Systems ◽

Stability Problem ◽

Linear Dynamical Systems ◽

Novel Approach ◽

Non Linear ◽

The Stability

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Asymptotic Stability of Caputo Type Fractional Neutral Dynamical Systems with Multiple Discrete Delays

Abstract and Applied Analysis ◽

10.1155/2014/138124 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Hai Zhang ◽

Daiyong Wu ◽

Jinde Cao

Keyword(s):

Asymptotic Stability ◽

Matrix Theory ◽

Sufficient Conditions ◽

Algebraic Approach ◽

Stability Criteria ◽

Differential Systems ◽

Discrete Delays ◽

Transcendental Equations ◽

The Stability ◽

Theoretical Results

We discuss the delay-independent asymptotic stability of Caputo type fractional-order neutral differential systems with multiple discrete delays. Based on the algebraic approach and matrix theory, the sufficient conditions are derived to ensure the asymptotic stability for all time-delay parameters. By applying the stability criteria, one can avoid solving the roots of transcendental equations. The results obtained are computationally flexible and convenient. Moreover, an example is provided to illustrate the effectiveness and applicability of the proposed theoretical results.

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On the exact and numerical solutions to a nonlinear model arising in mathematical biology

ITM Web of Conferences ◽

10.1051/itmconf/20182201061 ◽

2018 ◽

Vol 22 ◽

pp. 01061 ◽

Cited By ~ 5

Author(s):

Asif Yokus ◽

Tukur Abdulkadir Sulaiman ◽

Haci Mehmet Baskonus ◽

Sibel Pasali Atmaca

Keyword(s):

Analytical Solutions ◽

Numerical Solutions ◽

Soliton Solutions ◽

Hyperbolic Function ◽

Von Neumann ◽

Convection Diffusion Equation ◽

Wolfram Mathematica ◽

Forward Difference ◽

Von Neumann Analysis ◽

The Stability

This study acquires the exact and numerical approximations of a reaction-convection-diffusion equation arising in mathematical bi- ology namely; Murry equation through its analytical solutions obtained by using a mathematical approach; the modified exp(-Ψ(η))-expansion function method. We successfully obtained the kink-type and singular soliton solutions with the hyperbolic function structure to this equa- tion. We performed the numerical simulations (3D and 2D) of the obtained analytical solutions under suitable values of parameters. We obtained the approximate numerical and exact solutions to this equa- tion by utilizing the finite forward difference scheme by taking one of the obtained analytical solutions into consideration. We investigate the stability of the finite forward difference method with the equation through the Fourier-Von Neumann analysis. We present the L2 and L∞ error norms of the approximations. The numerical and exact approx- imations are compared and the comparison is supported by a graphic plot. All the computations and the graphics plots in this study are car- ried out with help of the Matlab and Wolfram Mathematica softwares. Finally, we submit a comprehensive conclusion to this study.

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Analysis of dengue model with fractal-fractional Caputo–Fabrizio operator

Advances in Difference Equations ◽

10.1186/s13662-020-02881-w ◽

2020 ◽

Vol 2020 (1) ◽

Cited By ~ 1

Author(s):

Fatmawati ◽

Muhammad Altaf Khan ◽

Cicik Alfiniyah ◽

Ebraheem Alzahrani

Keyword(s):

Statistical Data ◽

Dengue Infection ◽

Fractional Operator ◽

Novel Approach ◽

Reduction Number ◽

Best Fitting ◽

The Stability ◽

Parameter Values ◽

Graphical Illustration ◽

Stability Results

AbstractIn this work, we study the dengue dynamics with fractal-factional Caputo–Fabrizio operator. We employ real statistical data of dengue infection cases of East Java, Indonesia, from 2018 and parameterize the dengue model. The estimated basic reduction number for this dataset is $\mathcal{R}_{0}\approx2.2020$ R 0 ≈ 2.2020 . We briefly show the stability results of the model for the case when the basic reproduction number is $\mathcal{R}_{0} <1$ R 0 < 1 . We apply the fractal-fractional operator in the framework of Caputo–Fabrizio to the model and present its numerical solution by using a novel approach. The parameter values estimated for the model are used to compare with fractal-fractional operator, and we suggest that the fractal-fractional operator provides the best fitting for real cases of dengue infection when varying the values of both operators’ orders. We suggest some more graphical illustration for the model variables with various orders of fractal and fractional.

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UNIFIED VARIATIONAL PRINCIPLES FOR THE VON NEUMANN, MASTER AND BOLTZMANN-BLOCH EQUATIONS AND THE T-MATRIX

International Journal of Modern Physics B ◽

10.1142/s0217979295000525 ◽

1995 ◽

Vol 09 (10) ◽

pp. 1227-1242

Author(s):

MASUMI HATTORI ◽

HUZIO NAKANO

Keyword(s):

Density Matrix ◽

Variational Principles ◽

Matrix Theory ◽

Bloch Equation ◽

Irreversible Processes ◽

Collision Term ◽

Maximum Condition ◽

Von Neumann ◽

Maximum Problem ◽

T Matrix

The variational principle of irreversible processes, which was previously presented for the von Neumann equation as a stationarity problem and then converted into a maximum problem by contracting the density matrix perturbatively, is reinvestigated w.r.t. the contraction of the density matrix. The present contraction relies on the T-matrix theory of scattering, where no perturbational consideration enters. By taking the electron transport in solids as a typical example, the contraction is performed in two steps: the even component of the density matrix as to time reversal is eliminated first and then the off-diagonal elements in the scheme of diagonalizing the unperturbed Hamiltonian. The maximum problem thus obtained is for the diagonal elements of the odd component of the density matrix. The maximum condition gives the master equation, which is reduced to the Boltzmann-Bloch equation in the scheme of one-body picture. It is noticeable in this equation that the collision term is given in terms of the T-matrix in scattering theory.

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Exploring requirements and detector solutions for FCC-ee

The European Physical Journal Plus ◽

10.1140/epjp/s13360-021-02141-0 ◽

2021 ◽

Vol 136 (11) ◽

Author(s):

Patrizia Azzi ◽

Emmanuel Perez

Keyword(s):

Particle Identification ◽

Detector Performance ◽

Systematic Uncertainties ◽

Weakly Coupled ◽

New Concepts ◽

Statistical Precision ◽

Multiple Interaction ◽

The Stability ◽

The One ◽

Physics Programme

AbstractCircular colliders have the advantage of delivering collisions to multiple interaction points, which allow different detector designs to be studied and optimised—up to four for FCC-ee. On the one hand, the detectors must satisfy the constraints imposed by the invasive interaction region layout. On the other hand, the performance of heavy-flavour tagging, of particle identification, of tracking and particle-flow reconstruction, and of lepton, jet, missing energy and angular resolution, need to match the physics programme and the exquisite statistical precision offered by FCC-ee. During the FCC feasibility study (2021–2025), benchmark physics processes will be used to determine, via appropriate simulations, the requirements on the detector performance or design that must be satisfied to ensure that the systematic uncertainties of the measurements are commensurate with their statistical precision. The usage of the data themselves, in order to reach the challenging goals on the stability and on the alignment of the detector, in particular for the programme at and around the Z peak, will also be studied. In addition, the potential for discovering very weakly coupled new particles, in decays of Z or Higgs bosons, could motivate dedicated detector designs that would increase the efficiency for reconstructing the unusual signatures of such processes. These studies are crucial input to the further optimisation of the two concepts described in the FCC-ee conceptual design report, CLD and IDEA, and to the development of new concepts which might actually prove to be better adapted to the FCC-ee physics programme, or parts thereof.

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A Novel Approach for Robust Perceptual Image Hashing

Computer and Information Science ◽

10.5539/cis.v14n3p38 ◽

2021 ◽

Vol 14 (3) ◽

pp. 38

Author(s):

Azhar Hadmi ◽

Awatif Rouijel

Keyword(s):

Side Information ◽

Main Idea ◽

Jpeg Compression ◽

Image Hashing ◽

Novel Approach ◽

Perceptual Hash ◽

Short Signature ◽

Robust Image ◽

Tampered Image ◽

The Stability

Perceptual image hashing system generates a short signature called perceptual hash attached to an image before transmission and acts as side information for analyzing the trustworthiness of the received image. In this paper, we propose a novel approach to improve robustness for perceptual image hashing scheme for generating a perceptual hash that should be resistant to content-preserving manipulations, such as JPEG compression and Additive white Gaussian noise (AWGN) also should differentiate the maliciously tampered image and its original version. Our algorithm first constructs a robust image, derived from the original input by analyzing the stability of the extracted features and improving their robustness. From the robust image, which does perceptually resemble the original input, we further extract the final robust features. Next, robust features are suitably quantized allowing the generation of the final perceptual hash using the cryptographic hash function SHA1. The main idea of this paper is to transform the original image into a more robust one that allows the extraction of robust features. Generation of the robust image turns out be quite important since it introduces further robustness to the perceptual image hashing system. The paper can be seen as an attempt to propose a general methodology for more robust perceptual image hashing. The experimental results presented in this paper reveal that the proposed scheme offers good robustness against JPEG compression and Additive white Gaussian noise.

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