Stochastic chemical reaction networks (CRNs) are complex systems that combine the features of concurrent transformation of multiple variables in each elementary reaction event and nonlinear relations between states and their rates of change. Most general results concerning CRNs are limited to restricted cases where a topological characteristic known as deficiency takes a value 0 or 1, implying ...

Mass-action kinetics is frequently used in systems biology to model the behavior of interacting chemical species. Many important dynamical properties are known to hold for such systems if their underlying networks are weakly reversible and have a low deficiency. In particular, the Deficiency Zero and Deficiency One Theorems guarantee strong regularity with regards to the number and stability of...

Abstract We consider geometry theorems whose premises and statement comprise a set of bisector conditions. Each premise the can be represented as rows “bisector matrix”: one with three non zero elements per row, element value -2 others 1. The existence theorem corresponds to rank deficiency in this matrix. Our method discovery starts identification deficient matrices. Some such matrices graphs ...

We describe sufficient conditions for persistence of dynamical systems given by chemical reaction networks with mass-action kinetics. These conditions are expressed in terms of properties of special subnetworks of the original network. Under additional assumptions, such as deficiency zero or the existence of a complex balanced equilibrium, we conclude global asymptotic stability of the mass-act...

This paper presents a novel approach to compute the rank-deficiency locus of non-square Jacobian matrices. This algorithm is based on the computation of the singular vectors associated to zero singular values of the Jacobian. Examples are provided to illustrate the application of the algorithm. Results are shown for a four degree-of-freedom and a seven degree-of-freedom manipulator.

It is well known that occurrence counts of words in documents are often modeled poorly by standard distributions like the binomial or Poisson. Observed counts vary more than simple models predict, prompting the use of overdispersed models like Gamma-Poisson or Beta-binomial mixtures as robust alternatives. Another deficiency of standard models is due to the fact that most words never occur in a...