scholarly journals Generalization of the Winfree model to the high-dimensional sphere and its emergent dynamics

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Hansol Park
Keyword(s):  
Influence Function ◽  
Equilibrium Solution ◽  
Phase Locking ◽  
Small Diameter ◽  
High Dimensional ◽  
Dimensional Sphere ◽  
Sphere Model ◽  
Dirac Delta ◽  
Delta Distribution ◽  
Winfree Model

<p style='text-indent:20px;'>We present a high-dimensional Winfree model in this paper. The Winfree model is a mathematical model for synchronization on the unit circle. We generalize this model compare to the high-dimensional sphere and we call it the Winfree sphere model. We restricted the support of the influence function in the neighborhood of the attraction point to a small diameter to mimic the influence function as the Dirac delta distribution. We can obtain several new conditions of the complete phase-locking states for the identical Winfree sphere model from restricting the support of the influence function. We also prove the complete oscillator death(COD) state from the exponential <inline-formula><tex-math id="M1">\begin{document}$ \ell^1 $\end{document}</tex-math></inline-formula>-stability and the existence of the equilibrium solution.</p>

Role of phase-dependent influence function in the Winfree model of coupled oscillators

2021 ◽  
Vol 104 (6) ◽  
Author(s):  
M. Manoranjani ◽  
R. Gopal ◽  
D. V. Senthilkumar ◽  
V. K. Chandrasekar
Keyword(s):  
Influence Function ◽  
Coupled Oscillators ◽  
Winfree Model

scholarly journals Topology of Chromosomes 18 and X in Human Blastomeres from 3- to 4-Day-old Embryos

2005 ◽  
Vol 53 (3) ◽  
pp. 273-276 ◽  
Author(s):  
Jan Diblík ◽  
Milan Macek ◽  
Maria-Cristina Magli ◽  
Roman Krejčí ◽  
Luca Gianaroli
Keyword(s):  
Three Dimensional ◽  
Dimensional Sphere ◽  
Chromosome X ◽  
Sphere Model ◽  
Chromosome 18 ◽  
Vitro Fertilization ◽  
Signal Distribution ◽  
Human In Vitro Fertilization

The positions of chromosomes 18 and X fluorescence in situ hybridization signals were analyzed in blastomeres generated from human in vitro fertilization 3- to 4-day-old embryos after preimplantation screening of aneuploidy of chromosomes 13, 16, 18, 21, 22, X, and Y. Fluorescent signal localization compared with a three-dimensional sphere model of random signal distribution revealed significant differences, providing evidence of peripheral localization of chromosome 18 in aneuploid ( p=0.0013) and aneuploid/euploid blastomeres ( p=0.0011). No differences were found in localization of chromosome 18 in euploid and in chromosome X in euploid and aneuploid blastomeres.

Multi-channel laser system with phase locking by holographic gain gratings and small diameter deep hole drilling

2007 ◽  
Author(s):  
Alexander V. Fedin ◽  
Andrey V. Gavrilov ◽  
Sergey N. Smetanin ◽  
Sergey A. Solokhin
Keyword(s):  
Phase Locking ◽  
Laser System ◽  
Small Diameter ◽  
Hole Drilling ◽  
Deep Hole ◽  
Deep Hole Drilling

scholarly journals Three simple scenarios for high-dimensional sphere packings

2021 ◽  
Vol 104 (6) ◽  
Author(s):  
Patrick Charbonneau ◽  
Peter K. Morse ◽  
Will Perkins ◽  
Francesco Zamponi
Keyword(s):  
High Dimensional ◽  
Dimensional Sphere ◽  
Sphere Packings

scholarly journals On the Convolution Equation Related to the Diamond Klein-Gordon Operator

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Amphon Liangprom ◽  
Kamsing Nonlaopon
Keyword(s):  
Convolution Equation ◽  
Dirac Delta ◽  
Delta Distribution ◽  
Singular Distribution ◽  
Klein Gordon ◽  
The Relationship

We study the distributioneαx(♢+m2)kδform≥0, where(♢+m2)kis the diamond Klein-Gordon operator iteratedktimes,δis the Dirac delta distribution,x=(x1,x2,…,xn)is a variable inℝn, andα=(α1,α2,…,αn)is a constant. In particular, we study the application ofeαx(♢+m2)kδfor solving the solution of some convolution equation. We find that the types of solution of such convolution equation, such as the ordinary function and the singular distribution, depend on the relationship betweenkandM.

Superstatistics of the Klein–Gordon equation in deformed formalism for modified Dirac delta distribution

2018 ◽  
Vol 33 (10n11) ◽  
pp. 1850060 ◽  
Author(s):  
S. Sargolzaeipor ◽  
H. Hassanabadi ◽  
W. S. Chung
Keyword(s):  
Deformation Parameter ◽  
Gordon Equation ◽  
Wave Functions ◽  
Boltzmann Factor ◽  
Dirac Delta ◽  
Cornell Potential ◽  
Delta Distribution ◽  
Klein Gordon ◽  
Aharonov Bohm ◽  
Klein Gordon Equation

The Klein–Gordon equation is extended in the presence of an Aharonov–Bohm magnetic field for the Cornell potential and the corresponding wave functions as well as the spectra are obtained. After introducing the superstatistics in the statistical mechanics, we first derived the effective Boltzmann factor in the deformed formalism with modified Dirac delta distribution. We then use the concepts of the superstatistics to calculate the thermodynamics properties of the system. The well-known results are recovered by the vanishing of deformation parameter and some graphs are plotted for the clarity of our results.

scholarly journals Massively Parallel Tree Search for High-Dimensional Sphere Decoders

2019 ◽  
Vol 30 (10) ◽  
pp. 2309-2325 ◽  
Author(s):  
Konstantinos Nikitopoulos ◽  
Georgios Georgis ◽  
Chathura Jayawardena ◽  
Daniil Chatzipanagiotis ◽  
Rahim Tafazolli
Keyword(s):  
Massively Parallel ◽  
High Dimensional ◽  
Dimensional Sphere ◽  
Tree Search ◽  
Parallel Tree Search

scholarly journals A NOVEL FAST FRACTAL IMAGE COMPRESSION METHOD BASED ON DISTANCE CLUSTERING IN HIGH DIMENSIONAL SPHERE SURFACE

Fractals ◽  
2017 ◽  
Vol 25 (04) ◽  
pp. 1740004 ◽  
Author(s):  
SHUAI LIU ◽  
ZHENG PAN ◽  
XIAOCHUN CHENG
Keyword(s):  
Image Compression ◽  
High Dimensional ◽  
Dimensional Sphere ◽  
Compression Method ◽  
Sphere Surface ◽  
Fractal Image Compression ◽  
Fractal Compression ◽  
Fractal Image ◽  
Speed Up ◽  
Encoding Method

Fractal encoding method becomes an effective image compression method because of its high compression ratio and short decompressing time. But one problem of known fractal compression method is its high computational complexity and consequent long compressing time. To address this issue, in this paper, distance clustering in high dimensional sphere surface is applied to speed up the fractal compression method. Firstly, as a preprocessing strategy, an image is divided into blocks, which are mapped on high dimensional sphere surface. Secondly, a novel image matching method is presented based on distance clustering on high dimensional sphere surface. Then, the correctness and effectiveness properties of the mentioned method are analyzed. Finally, experimental results validate the positive performance gain of the method.

scholarly journals On regularizations of the Dirac delta distribution

2016 ◽  
Vol 305 ◽  
pp. 423-447 ◽  
Author(s):  
Bamdad Hosseini ◽  
Nilima Nigam ◽  
John M. Stockie
Keyword(s):  
Dirac Delta ◽  
Delta Distribution
Sign in / Sign up

Export Citation Format

Share Document