We prove a precise relationship between the threshold state of the fixed-energy sandpile and the stationary state of Dhar’s abelian sandpile: In the limit as the initial condition s0 tends to −∞, the former is obtained by size-biasing the latter according to burst size, an avalanche statistic. The question of whether and how these two states are related has been a subject of some controversy si...

We study the limit theory of large threshold graphs and apply this to a variety of models for random threshold graphs. The results give a nice set of examples for the emerging theory of graph limits.

9. REFERENCES Abu-Hilal AH, Khordagui HK. 1993. Assessment of tar pollution on the United Arab Emirates beaches. Environ Int 19:589-596. ACGIH. 1986. Documentation of the threshold limit values and biological exposure indices. American Conference of Governmental Industrial Hygienists, Cincinnati, OH. ACGIH. 1992. Threshold limit values for chemical substances and physical agents and biological ...

To examine the relationship between the defibrillation threshold and the strength of shocks that induce ventricular fibrillation during the vulnerable period, we determined the defibrillation threshold in 22 open-chest dogs using epicardial defibrillation electrodes with the cathode at the ventricular apex and the anode at the right atrium. We also determined whether there was an upper limit of...

In the pharmaceutical industry, genotoxic drug substances are developed for life-threatening indications such as cancer. Healthy employees handle these substances during research, development, and manufacturing; therefore, safe handling of genotoxic substances is essential. When an adequate preclinical dataset is available, a risk-based decision related to exposure controls for manufacturing is...

Somatic cells, including immune cells such as T-cells have a limited capacity for proliferation and can only replicate for a finite number of generations (known as the Hayflick limit) before dying. In this paper we use mathematical models to investigate the consequences of introducing a Hayflick limit on the dynamics of T-cells stimulated with specific antigen. We show that while the Hayflick l...