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 ...

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 probabili...

Among the six classes of pro-2-groups of finite and fixed co-classes and trivial Schur Multiplicator which studied by Abdolzadeh and Eick in 2009, there are two classes $$S_5=langle a,bmid [b,a^2]=1, a^2=[b,a]^2, (b^2)^{[b,a]}b^2=1rangle$$ and $$S_6=langle a,t,bmid a^2=b^2,[b,a]^2=1, t^a=t^{-1}[b,a], b^t=abarangle$$that have been conjectured to have deficiency zero presentations. In this paper ...

This paper provides a necessary and sufficient condition for detectability, and an explicit construction of observers when this condition is satisfied, for chemical reaction networks of the Feinberg-Horn-Jackson zero deficiency type.

among the six classes of pro-2-groups of finite and fixed co-classes and trivial schur multiplicator which studied by abdolzadeh and eick in 2009, there are two classes $$s_5=langle a,bmid [b,a^2]=1, a^2=[b,a]^2, (b^2)^{[b,a]}b^2=1rangle$$ and $$s_6=langle a,t,bmid a^2=b^2,[b,a]^2=1, t^a=t^{-1}[b,a], b^t=abarangle$$that have been conjectured to have deficiency zero presentations. in this paper ...

Twenty-one Nigerian rice landraces were screened for tolerance to phosphate deficiency in nutrient medium using selected morphological indices from which Phosphate Deficiency Tolerance Index (PDTI) was evaluated. All analyzed the presence of four uptake 1 (Pup-1) gene-linked markers while relative expression levels two Pup-1 genes evaluated under zero, normal and excess phosphate. PDTI analysis...

the bulk of our knowledge on immunosuppression in malnutrition comes from the experiments done on cell-mediated immunity. however, malnutrition-induced modifications of humoral immunity have been less understood. the objective of this study was to determine the effects of acute protein-energy malnutrition on serum levels of immunoglobulins and their subclasses in murine models. male and female ...

The impact of random fluctuations on the dynamical behavior a complex biological systems is a longstanding issue, whose understanding would shed light on the evolutionary pressure that nature imposes on the intrinsic noise levels and would allow rationally designing synthetic networks with controlled noise. Using the Itō stochastic differential equation formalism, we performed both analytic and...

We consider both deterministically and stochastically modeled chemical reaction systems and prove that a product-form stationary distribution exists for each closed, irreducible subset of the state space of a stochastically modeled system (with quite general kinetics) if the corresponding deterministically modeled system (with mass-action kinetics) admits a complex balanced equilibrium. Feinber...