Deficiency zero for random reaction networks under a stochastic block model framework
نویسندگان
چکیده
Deficiency zero is an important network structure and has been the focus of many celebrated results within reaction theory. In our previous paper Prevalence deficiency networks in Erdős-Rényi framework, we provided a framework to quantify prevalence among randomly generated networks. Specifically, given binary with n species, edge between two arbitrary vertices occurring independently probability $$p_n$$ , established threshold function $$r(n)=\frac{1}{n^3}$$ such that random being converges 1 if $$\frac{p_n}{r(n)}\rightarrow 0$$ 0 \infty $$ as $$n \rightarrow . With base starting point, current provides significantly more flexible by weighting probabilities via control parameters $$\alpha _{i,j}$$ $$i,j\in \{0,1,2\}$$ enumerating types possible (zeroth, first, or second order). The can be chosen generate specific underlying structure, “closed” very few inflow outflow reactions, “open” abundant outflow. Under this new for each choice $$\{\alpha _{i,j}\}$$ establish $$r(n,\{\alpha _{i,j}\})$$ $$\frac{p_n}{r(n,\{\alpha _{i,j}\})}\rightarrow
منابع مشابه
Product-form stationary distributions for deficiency zero chemical reaction networks.
We consider stochastically modeled chemical reaction systems with mass-action kinetics and prove that a product-form stationary distribution exists for each closed, irreducible subset of the state space if an analogous deterministically modeled system with mass-action kinetics admits a complex balanced equilibrium. Feinberg's deficiency zero theorem then implies that such a distribution exists ...
متن کاملMass Action Reaction Networks and The Deficiency Zero Theorem
Acknowledgments First and foremost, I would like to thank my advisors, Steve Altschuler and Lani Wu. In addition to suggesting to me a rich and interesting thesis topic, and advising me as I wrote about it, Steve and Lani have deeply informed my view of what it is to be a mathematician and a scientist. My work with them, both during the summer and on this thesis, has influenced my academic and ...
متن کاملan investigation about the appropriate stochastic modeling framework for agricultural insurance pricing
با توجه به اینکه بیمه محصولات کشاورزی در ایران بیشتر جنبه ای حمایتی دارد و خسارات گزارش شده عموما بیش از حق بیمه های دریافت شده است، در این پایان نامه به جهت تعیین قیمت بیمه محصولات کشاورزی (گندم دیم) از فرآیندهای نوفه شلیک به عنوان مدلی مناسب استفاده شده است. بر اساس داده های صندوق بیمه کشاورزی از خسارات اعلام شده در سال زراعی 1388-1389 گندم دیم، در این پایان نامه حق بیمه خالص و ناخالص این محص...
ذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Chemistry
سال: 2021
ISSN: ['1572-8897', '0259-9791']
DOI: https://doi.org/10.1007/s10910-021-01278-8