A motif building process for simulating random networks

Polansky, Alan M.; Pramanik, Paramahansa

doi:10.1016/j.csda.2021.107263

Cited by 11 publications

(10 citation statements)

References 36 publications

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“…Here edges are selected randomly for updating assuming that time has some passage between each update. Firstly, the updating function starts with a list of objects that would be used to store an updated network (Luke, 2015;Polansky and Pramanik, 2021). Then inside a loop a random node is selected, and the update function is called when an existing edge is removed, and a new edge is added.…”

Section: Spread Of the Pandemicmentioning

confidence: 99%

Stochastic Control of a SIR Model with Non-linear Incidence Rate Through Euclidean Path Integral

Pramanik¹

2022

Preprint

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This paper utilizes a stochastic Susceptible-Infected-recovered (SIR) model with a non-linear incidence rate to perform a detailed mathematical study of optimal lock-down intensity and vaccination rate under the COVID-19 pandemic environment. We use a Feynman-type path integral control approach to determine a Fokker-Plank type equation of this system. Since we assume the availability of information on the COVID-19 pandemic is complete and perfect, we can show a unique fixed point. A nonlinear incidence rate is used because, it can be raised from saturation effects that if the proportion of infected agents is very high so that exposure to the pandemic is inevitable, then the transmission rate responds slower than linearity to the increase in the number of infections. The simulation study shows that with higher diffusion coefficients susceptible and recovery curves keep the downward trends while the infection curve becomes ergodic. Finally, we perform a data analysis using UK data at the beginning of 2021 and compare it with our theoretical results.

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Section: Spread Of the Pandemicmentioning

confidence: 99%

Stochastic Control of a SIR Model with Non-linear Incidence Rate Through Euclidean Path Integral

Pramanik¹

2022

Preprint

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“…This surface is continuous but not differentiable. Furthermore, at 8/3 this behaves like a Brownian surface Sheffield, 2015, 2016;Hua, Polansky and Pramanik, 2019;Polansky, 2019, 2020b;Polansky and Pramanik, 2021;Pramanik and Polansky, 2021;Pramanik, 2021d). Furthermore, this approach can be used to obtain a solution for stability of an economy after pandemic crisis (Ahamed, 2021a), determine an optimal bank profitability (Islam, Alam and Chowdhury;Alam, Sultan and Afrin;Mohammad and Mohammad, 2010;Alam, Khondker and Molla, 2013;Hossain and Ahamed, 2015;Pramanik, 2016;ALAM and HOSSAIN, 2018;Ahamed, 2021b;Alam, 2021a,b).…”

Section: Introductionmentioning

confidence: 99%

Scoring a Goal optimally in a Soccer game under Liouville-like quantum gravity action

Pramanik¹,

Polansky²

2021

Preprint

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In this paper we present a new theoretical model to find out an optimal weight associated with a soccer player under the presence of a stochastic goal dynamics by using Feynman path integral method, where the action of a player is on 8/3-Liouville Quantum Gravity surface. Before determine the optimal weight we first establish an Infinitary logic which can deal with infinite variables on the strategy space then, a quantum formula of this logic has been developed and finally, based on this we are able show the existence of a Lefschetz-Hopf fixed point of this game. As in a competitive tournament, all possible standard strategies to score goals are known to the opposition team, a player's action is stochastic in nature and they would have some comparative advantage to score goals. Furthermore, conditions like uncertainties due to rain, dribbling and passing skill of a player, whether the match is a day match or a day-night match, advantages of having home crowd and asymmetric information of action profiles have been considered on the way to determine the optimal weight.

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“…Based on the grouping, I classify the social network directed graph and determine the adjacency matrix without existence of a loop. Furthermore, an undirected network graph leads to a symmetric adjacency matrix (Pramanik 2016;Hua et al 2019;Polansky and Pramanik 2021). The diagonal terms of this matrix are zero, and the off-diagonal terms have different values based on their weight in relation to the other persons in a community.…”

Section: Introductionmentioning

confidence: 99%

“…The statistical analysis of network formation goes dates back to the seminal work by Erdös and Rényi (1959) where a random graph is based on independent links with a fixed probability (Sheng 2020). Beyond Erdös-Rényi model, many methods have been designed to simulate graphs with characteristics like degree distributions, small world, and Markov type properties (Polansky and Pramanik 2021;Pramanik 2021c).…”

Section: Introductionmentioning

confidence: 99%

Path integral control of a stochastic multi-risk SIR pandemic model

Pramanik

2023

Theory Biosci.

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In this paper a Feynman-type path integral control approach is used for a recursive formulation of a health objective function subject to a fatigue dynamics, a forward-looking stochastic multi-risk susceptible-infective-recovered (SIR) model with riskgroup's Bayesian opinion dynamics toward vaccination against COVID-19. My main interest lies in solving a minimization of a policy-maker's social cost which depends on some deterministic weight. I obtain an optimal lock-down intensity from a Wick-rotated Schrödinger-type equation which is analogous to a Hamiltonian-Jacobi-Bellman (HJB) equation. My formulation is based on path integral control and dynamic programming tools facilitates the analysis and permits the application of algorithm to obtain numerical solution for pandemic control model.

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A motif building process for simulating random networks

Cited by 11 publications

References 36 publications

Stochastic Control of a SIR Model with Non-linear Incidence Rate Through Euclidean Path Integral

Stochastic Control of a SIR Model with Non-linear Incidence Rate Through Euclidean Path Integral

Scoring a Goal optimally in a Soccer game under Liouville-like quantum gravity action

Path integral control of a stochastic multi-risk SIR pandemic model

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