Lattice Model
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Author(s):  
Agniva Datta ◽  
Muktish Acharyya

The results of Kermack–McKendrick SIR model are planned to be reproduced by cellular automata (CA) lattice model. The CA algorithms are proposed to study the model of an epidemic, systematically. The basic goal is to capture the effects of spreading of infection over a scale of length. This CA model can provide the rate of growth of the infection over the space which was lacking in the mean-field like susceptible-infected-removed (SIR) model. The motion of the circular front of an infected cluster shows a linear behavior in time. The correlation of a particular site to be infected with respect to the central site is also studied. The outcomes of the CA model are in good agreement with those obtained from SIR model. The results of vaccination have been also incorporated in the CA algorithm with a satisfactory degree of success. The advantage of the present model is that it can shed a considerable amount of light on the physical properties of the spread of a typical epidemic in a simple, yet robust way.


2022 ◽  
Vol 105 (4) ◽  
Author(s):  
O. Ndiaye ◽  
D. Dione ◽  
A. Traoré ◽  
A. S. Ndao ◽  
J. P. L. Faye

Semiotica ◽  
2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Vern Poythress

Abstract Tagmemic theory as a semiotic theory can be used to analyze multiple systems of logic and to assess their strengths and weaknesses. This analysis constitutes an application of semiotics and also a contribution to understanding of the nature of logic within the context of human meaning. Each system of logic is best adapted to represent one portion of human rationality. Acknowledging this correlation between systems and their targets helps explain the usefulness of more than one system. Among these systems, the two-valued system of classical logic takes its place. All the systems of logic can be incorporated into a complex mathematical model that has a place for each system and that represents a larger whole in human reasoning. The model can represent why tight formal systems of logic can be applied in some contexts with great success, but in other contexts are not directly applicable. The result suggests that human reasoning is innately richer than any one formal system of logic.


Author(s):  
Margaux Sage ◽  
Jérémie Girardot ◽  
Jean-Benoît Kopp ◽  
Stéphane Morel

AIP Advances ◽  
2022 ◽  
Vol 12 (1) ◽  
pp. 015004
Author(s):  
Sufyan Naji ◽  
Mohammad N. Murshed ◽  
M. A. Ahlam ◽  
Mohamed E. El Sayed ◽  
Ahmed Samir ◽  
...  

2021 ◽  
Author(s):  
R Murugan

We develop a lattice model on the rate of hybridization of the complementary single-stranded DNAs (c-ssDNAs). Upon translational diffusion mediated collisions, c-ssDNAs interpenetrate each other to form correct (cc), incorrect (icc) and trap-correct contacts (tcc) inside the reaction volume. Correct contacts are those with exact registry matches which leads to nucleation and zipping. Incorrect contacts are the mismatch contacts which are less stable compared to tcc which can occur in the repetitive c-ssDNAs. Although tcc possess registry match within the repeating sequences, they are incorrect contacts in the view of the whole c-ssDNAs. The nucleation rate (kN) is directly proportional to the collision rate and the average number of correct-contacts (<ncc>) formed when both the c-ssDNAs interpenetrate each other. Detailed lattice model simulations suggest that 〈n_cc 〉∝L⁄V where L is the length of c-ssDNAs and V is the reaction volume. Further numerical analysis revealed the scaling for the average radius of gyration of c-ssDNAs (Rg) with their length as R_g∝√L. Since the reaction space will be approximately a sphere with radius equals to 2Rg and V∝L^(3⁄2), one obtains k_N∝1/√L. When c-ssDNAs are nonrepetitive, then the overall renaturation rate becomes as k_R∝k_N L and one finally obtains k_R∝√L in line with the experimental observations. When c-ssDNAs are repetitive with a complexity of c, then earlier models suggested the scaling k_R∝√L/c which breaks down at c = L. This clearly suggested the existence of at least two different pathways of renaturation in case of repetitive c-ssDNAs viz. via incorrect contacts and trap correct contacts. The trap correct contacts can lead to the formation of partial duplexes which can keep the complementary strands in the close vicinity for a prolonged timescale. This is essential for the extended 1D slithering, inchworm movements and internal displacement mechanisms which can accelerate the searching for the correct contacts. Clearly, the extent of slithering dynamics will be inversely proportional to the complexity. When the complexity is close to the length of c-ssDNAs, then the pathway via incorrect contacts will dominate. When the complexity is much lesser than the length of c-ssDNA, then pathway via trap correct contacts would be the dominating one.


Author(s):  
Ali Khosravi ◽  
Jorge Augusto Lasave ◽  
Sergio Koval ◽  
Erio Tosatti

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