Final nanoparticle size distribution under unusual parameter regimes.

We explore the large-scale behavior of a stochastic model for nanoparticle growth in an unusual parameter regime. This model encompasses two types of reactions: nucleation, where n monomers aggregate to form a nanoparticle, and growth, where a nanoparticle increases its size by consuming a monomer. Reverse reactions are disregarded.

Transition graph decomposition for complex balanced reaction networks with non-mass-action kinetics.

Reaction networks are widely used models to describe biochemical processes. Stochastic fluctuations in the counts of biological macromolecules have amplified consequences due to their small population sizes. This makes it necessary to favor stochastic, discrete population, continuous time models.

A hidden integral structure endows absolute concentration robust systems with resilience to dynamical concentration disturbances.

Biochemical systems that express certain chemical species of interest at the same level at any positive steady state are called 'absolute concentration robust' (ACR). These species behave in a stable, predictable way, in the sense that their expression is robust with respect to sudden changes in the species concentration, provided that the system reaches a (potentially new) positive steady state. Such a property has been proven to be of importance in certain gene regulatory networks and signaling systems.

Addition of flow reactions preserving multistationarity and bistability.

We consider the question whether a chemical reaction network preserves the number and stability of its positive steady states upon inclusion of inflow and outflow reactions. Often a model of a reaction network is presented without inflows and outflows, while in fact some of the species might be degraded or leaked to the environment, or be synthesized or transported into the system. We provide a sufficient and easy-to-check criterion based on the stoichiometry of the reaction network alone and discuss examples from systems biology.

Discrepancies between extinction events and boundary equilibria in reaction networks.

Reaction networks are mathematical models of interacting chemical species that are primarily used in biochemistry. There are two modeling regimes that are typically used, one of which is deterministic and one that is stochastic. In particular, the deterministic model consists of an autonomous system of differential equations, whereas the stochastic system is a continuous-time Markov chain.

Non-explosivity of Stochastically Modeled Reaction Networks that are Complex Balanced.

We consider stochastically modeled reaction networks and prove that if a constant solution to the Kolmogorov forward equation decays fast enough relatively to the transition rates, then the model is non-explosive. In particular, complex-balanced reaction networks are non-explosive.

Node balanced steady states: Unifying and generalizing complex and detailed balanced steady states.

We introduce a unifying and generalizing framework for complex and detailed balanced steady states in chemical reaction network theory. To this end, we generalize the graph commonly used to represent a reaction network. Specifically, we introduce a graph, called a reaction graph, that has one edge for each reaction but potentially multiple nodes for each complex.

Comparison of embolic load in femoropopliteal interventions: percutaneous transluminal angioplasty versus stenting.

Purpose: To compare the incidence of distal emboli occurring during percutaneous transluminal angioplasty (PTA) and primary stent on the superficial femoral artery (SFA) METHODS: A total of 50 consecutive patients were entered in a prospective, randomized trial. Inclusion criteria were the presence of symptomatic limb ischemia due to stenosis or occlusion of the SFA. An embolic protection device was placed in the popliteal artery.