Academic literature on the topic 'Gillespie simulations'

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Journal articles on the topic "Gillespie simulations"

1

Rajput, Nikhil Kumar. "Gillespie algorithm and diffusion approximation based on Monte Carlo simulation for innovation diffusion: A comparative study." Monte Carlo Methods and Applications 25, no. 3 (2019): 209–15. http://dx.doi.org/10.1515/mcma-2019-2040.

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Abstract Monte Carlo simulations have been utilized to make a comparative study between diffusion approximation (DA) and the Gillespie algorithm and its dependence on population in the information diffusion model. Diffusion approximation is one of the widely used approximation methods which have been applied in queuing systems, biological systems and other fields. The Gillespie algorithm, on the other hand, is used for simulating stochastic systems. In this article, the validity of diffusion approximation has been studied in relation to the Gillespie algorithm for varying population sizes. It is found that diffusion approximation results in large fluctuations which render forecasting unreliable particularly for a small population. The relative fluctuations in relation to diffusion approximation, as well as to the Gillespie algorithm have been analyzed. To carry out the study, a nonlinear stochastic model of innovation diffusion in a finite population has been considered. The nonlinearity of the problem necessitates use of approximation methods to understand the dynamics of the system. A stochastic differential equation (SDE) has been used to model the innovation diffusion process, and corresponding sample paths have been generated using Monte Carlo simulation methods.
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2

Kierzek, A. M. "STOCKS: STOChastic Kinetic Simulations of biochemical systems with Gillespie algorithm." Bioinformatics 18, no. 3 (2002): 470–81. http://dx.doi.org/10.1093/bioinformatics/18.3.470.

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3

Alfonso, L., G. B. Raga, and D. Baumgardner. "Monte Carlo simulations of two-component drop growth by stochastic coalescence." Atmospheric Chemistry and Physics Discussions 8, no. 2 (2008): 7289–313. http://dx.doi.org/10.5194/acpd-8-7289-2008.

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Abstract. The evolution of two-dimensional drop distributions is simulated in this study using a Monte Carlo method.~The stochastic algorithm of Gillespie (1976) for chemical reactions in the formulation proposed by Laurenzi et al. (2002) was used to simulate the kinetic behavior of the drop population. Within this framework species are defined as droplets of specific size and aerosol composition. The performance of the algorithm was checked by comparing the numerical with the analytical solutions found by Lushnikov (1975). Very good agreement was observed between the Monte Carlo simulations and the analytical solution. Simulation results are presented for bi-variate constant and hydrodynamic kernels. The algorithm can be easily extended to incorporate various properties of clouds such as including several crystal habits, different types of soluble CCN, particle charging and drop breakup.
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4

Martinecz, Antal, Fabrizio Clarelli, Sören Abel, and Pia Abel zur Wiesch. "Reaction Kinetic Models of Antibiotic Heteroresistance." International Journal of Molecular Sciences 20, no. 16 (2019): 3965. http://dx.doi.org/10.3390/ijms20163965.

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Bacterial heteroresistance (i.e., the co-existence of several subpopulations with different antibiotic susceptibilities) can delay the clearance of bacteria even with long antibiotic exposure. Some proposed mechanisms have been successfully described with mathematical models of drug-target binding where the mechanism’s downstream of drug-target binding are not explicitly modeled and subsumed in an empirical function, connecting target occupancy to antibiotic action. However, with current approaches it is difficult to model mechanisms that involve multi-step reactions that lead to bacterial killing. Here, we have a dual aim: first, to establish pharmacodynamic models that include multi-step reaction pathways, and second, to model heteroresistance and investigate which molecular heterogeneities can lead to delayed bacterial killing. We show that simulations based on Gillespie algorithms, which have been employed to model reaction kinetics for decades, can be useful tools to model antibiotic action via multi-step reactions. We highlight the strengths and weaknesses of current models and Gillespie simulations. Finally, we show that in our models, slight normally distributed variances in the rates of any event leading to bacterial death can (depending on parameter choices) lead to delayed bacterial killing (i.e., heteroresistance). This means that a slowly declining residual bacterial population due to heteroresistance is most likely the default scenario and should be taken into account when planning treatment length.
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5

Chen-Charpentier, Benito. "Stochastic Modeling of Plant Virus Propagation with Biological Control." Mathematics 9, no. 5 (2021): 456. http://dx.doi.org/10.3390/math9050456.

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Plants are vital for man and many species. They are sources of food, medicine, fiber for clothes and materials for shelter. They are a fundamental part of a healthy environment. However, plants are subject to virus diseases. In plants most of the virus propagation is done by a vector. The traditional way of controlling the insects is to use insecticides that have a negative effect on the environment. A more environmentally friendly way to control the insects is to use predators that will prey on the vector, such as birds or bats. In this paper we modify a plant-virus propagation model with delays. The model is written using delay differential equations. However, it can also be expressed in terms of biochemical reactions, which is more realistic for small populations. Since there are always variations in the populations, errors in the measured values and uncertainties, we use two methods to introduce randomness: stochastic differential equations and the Gillespie algorithm. We present numerical simulations. The Gillespie method produces good results for plant-virus population models.
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6

Alfonso, L., G. B. Raga, and D. Baumgardner. "Monte Carlo simulations of two-component drop growth by stochastic coalescence." Atmospheric Chemistry and Physics 9, no. 4 (2009): 1241–51. http://dx.doi.org/10.5194/acp-9-1241-2009.

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Abstract. The evolution of two-dimensional drop distributions is simulated in this study using a Monte Carlo method. The stochastic algorithm of Gillespie (1976) for chemical reactions in the formulation proposed by Laurenzi et al. (2002) was used to simulate the kinetic behavior of the drop population. Within this framework, species are defined as droplets of specific size and aerosol composition. The performance of the algorithm was checked by a comparison with the analytical solutions found by Lushnikov (1975) and Golovin (1963) and with finite difference solutions of the two-component kinetic collection equation obtained for the Golovin (sum) and hydrodynamic kernels. Very good agreement was observed between the Monte Carlo simulations and the analytical and numerical solutions. A simulation for realistic initial conditions is presented for the hydrodynamic kernel. As expected, the aerosol mass is shifted from small to large particles due to collection process. This algorithm could be extended to incorporate various properties of clouds such several crystals habits, different types of soluble CCN, particle charging and drop breakup.
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7

Chang, Qiang, Yang Lu, and Donghui Quan. "Accelerated Gillespie Algorithm for Gas–Grain Reaction Network Simulations Using Quasi-steady-state Assumption." Astrophysical Journal 851, no. 1 (2017): 68. http://dx.doi.org/10.3847/1538-4357/aa99d9.

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8

Jo, Yeji, Kyusik Mun, Yeonjoo Jeong, et al. "A Poisson Process Generator Based on Multiple Thermal Noise Amplifiers for Parallel Stochastic Simulation of Biochemical Reactions." Electronics 11, no. 7 (2022): 1039. http://dx.doi.org/10.3390/electronics11071039.

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In this paper, we propose a novel Poisson process generator that uses multiple thermal noise amplifiers (TNAs) as a source of randomness and controls its event rate via a frequency-locked loop (FLL). The increase in the number of TNAs extends the effective bandwidth of amplified thermal noise and hence enhances the maximum event rate the proposed architecture can generate. Verilog-A simulation of the proposed Poisson process generator shows that its maximum event rate can be increased by a factor of 26.5 when the number of TNAs increases from 1 to 10. In order to realize parallel stochastic simulations of the biochemical reaction network, we present a fundamental reaction building block with continuous-time multiplication and addition using an AND gate and a 1-bit current-steering digital-to-analog converter, respectively. Stochastic biochemical reactions consisting of the fundamental reaction building blocks are simulated in Verilog-A, demonstrating that the simulation results are consistent with those of conventional Gillespie algorithm. An increase in the number of TNAs to accelerate the Poisson events and the use of digital AND gates for robust reaction rate calculations allow for faster and more accurate stochastic simulations of biochemical reactions than previous parallel stochastic simulators.
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9

Iwuchukwu, Edward Uchechukwu, and Ardson dos Santos Junior Vianna. "Stochastic Modelling and Simulation of Free Radical Polymerization of Styrene in Microchannels using a Hybrid Gillespie Algorithm." Journal of Engineering and Exact Sciences 9, no. 1 (2023): 15327–01. http://dx.doi.org/10.18540/jcecvl9iss1pp15327-01e.

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Most recently, the production of polystyrene by Free Radical Polymerization (FRP) via microchannels has been a subject of core interest due to the efficiency of a micro-or milli-reactor brings. In addition, especially in pilot experimentations, a micro or milli-reactor has been known widely to be efficient in monitoring the microstructural end-use features or properties of the polymer as the chain propagates and ultimately terminates. However, the limitations posed by using micro or milli-reactors in process intensification such as clogging of pores can be a bottleneck when tracking the common phenomena associated with FRP such as cage, gel, and glass effects. In this work, the simulation of the synthesis of polystyrene in FRP via microchannels is computed using a robust and time-efficient hybrid Gillespie Algorithm (GA) or Hybrid Stochastic Simulation Algorithm (HSSA). The obtained results of the end-use properties of polystyrene such as Monomer conversion, Polydispersity Index, Number-Average Molar Mass and Weight Average Molar Mass were compared to experimental data. The simulation results agree well with the experimental results reported in this work. Hence, stochastic simulations prove to be an effective tool in making decisions in the context of process intensification of chain growth polymerization reactions even at a large scale.
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10

Matzko, Richard Oliver, Laurentiu Mierla, and Savas Konur. "Novel Ground-Up 3D Multicellular Simulators for Synthetic Biology CAD Integrating Stochastic Gillespie Simulations Benchmarked with Topologically Variable SBML Models." Genes 14, no. 1 (2023): 154. http://dx.doi.org/10.3390/genes14010154.

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The elevation of Synthetic Biology from single cells to multicellular simulations would be a significant scale-up. The spatiotemporal behavior of cellular populations has the potential to be prototyped in silico for computer assisted design through ergonomic interfaces. Such a platform would have great practical potential across medicine, industry, research, education and accessible archiving in bioinformatics. Existing Synthetic Biology CAD systems are considered limited regarding population level behavior, and this work explored the in silico challenges posed from biological and computational perspectives. Retaining the connection to Synthetic Biology CAD, an extension of the Infobiotics Workbench Suite was considered, with potential for the integration of genetic regulatory models and/or chemical reaction networks through Next Generation Stochastic Simulator (NGSS) Gillespie algorithms. These were executed using SBML models generated by in-house SBML-Constructor over numerous topologies and benchmarked in association with multicellular simulation layers. Regarding multicellularity, two ground-up multicellular solutions were developed, including the use of Unreal Engine 4 contrasted with CPU multithreading and Blender visualization, resulting in a comparison of real-time versus batch-processed simulations. In conclusion, high-performance computing and client–server architectures could be considered for future works, along with the inclusion of numerous biologically and physically informed features, whilst still pursuing ergonomic solutions.
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