Recidivism and rehabilitation of criminal offenders: a carrot and stick evolutionary game.

Motivated by recent efforts by the criminal justice system to treat and rehabilitate nonviolent offenders rather than focusing solely on their punishment, we introduce an evolutionary game theoretic model to study the effects of "carrot and stick" intervention programs on criminal recidivism. We use stochastic simulations to study the evolution of a population where individuals may commit crimes depending on their past history, surrounding environment and, in the case of recidivists, on any counseling, educational or training programs available to them after being punished for their previous crimes. These sociological factors are embodied by effective parameters that determine the decision making probabilities. Players may decide to permanently reform or continue engaging in criminal activity, eventually reaching a state where they are considered incorrigible. Depending on parameter choices, the outcome of the game is a society with a majority of virtuous, rehabilitated citizens or incorrigibles. Since total resources may be limited, we constrain the combined punishment and rehabilitation costs per crime to be fixed, so that increasing one effort will necessarily decrease the other. We find that the most successful strategy in reducing crime is to optimally allocate resources so that after being punished, criminals experience impactful intervention programs, especially during the first stages of their return to society. Excessively harsh or lenient punishments are less effective. We also develop a system of coupled ordinary differential equations with memory effects to give a qualitative description of our simulated societal dynamics. We discuss our findings and sociological implications.

Combinatoric analysis of heterogeneous stochastic self-assembly.

We analyze a fully stochastic model of heterogeneous nucleation and self-assembly in a closed system with a fixed total particle number M, and a fixed number of seeds Ns. Each seed can bind a maximum of N particles. A discrete master equation for the probability distribution of the cluster sizes is derived and the corresponding cluster concentrations are found using kinetic Monte-Carlo simulations in terms of the density of seeds, the total mass, and the maximum cluster size. In the limit of slow detachment, we also find new analytic expressions and recursion relations for the cluster densities at intermediate times and at equilibrium. Our analytic and numerical findings are compared with those obtained from classical mass-action equations and the discrepancies between the two approaches analyzed.

A tracer kinetic model for 18F-FHBG for quantitating herpes simplex virus type 1 thymidine kinase reporter gene expression in living animals using PET.

UNLABELLED: Reporter probe 9-(4-18F-fluoro-3-[hydroxymethyl]butyl)guanine (18F-FHBG) and reporter gene mutant herpes simplex virus type 1 thymidine kinase (HSV1-sr39tk) have been used for imaging reporter gene expression with PET. Current methods for quantitating the images using the percentage injected dose per gram of tissue do not distinguish between the effects of probe transport and subsequent phosphorylation. We therefore investigated tracer kinetic models for 18F-FHBG dynamic microPET data and noninvasive methods for determining blood time-activity curves in an adenoviral gene delivery model in mice. METHODS: 18F-FHBG (approximately 7.4 MBq [approximately 200 microCi]) was injected into 4 mice; 18F-FHBG concentrations in plasma and whole blood were measured from mouse heart left ventricle (LV) direct sampling. Replication-incompetent adenovirus (0-2 x 10(9) plaque-forming units) with the E1 region deleted (n = 8) or replaced by HSV1-sr39tk (n = 18) was tail-vein injected into mice. Mice were dynamically scanned using microPET (approximately 7.4 MBq [approximately 200 microCi] 18F-FHBG) over 1 h; regions of interest were drawn on images of the heart and liver. Serial whole blood 18F-FHBG concentrations were measured in 6 of the mice by LV sampling, and 1 least-squares ratio of the heart image to the LV time-activity curve was calculated for all 6 mice. For 2 control mice and 9 mice expressing HSV1-sr39tk, heart image (input function) and liver image time-activity curves (tissue curves) were fit to 2- and 3-compartment models using Levenberg-Marquardt nonlinear regression. The models were compared using an F statistic. HSV1-sr39TK enzyme activity was determined from liver samples and compared with model parameter estimates. For another 3 control mice and 6 HSV1-sr39TK-positive mice, the model-predicted relative percentage of metabolites was compared with high-performance liquid chromatography analysis. RESULTS: The ratio of 18F-FHBG in plasma to whole blood was 0.84 +/- 0.05 (mean +/- SE) by 30 s after injection. The least-squares ratio of the heart image time-activity curve to the LV time-activity curve was 0.83 +/- 0.02, consistent with the recovery coefficient for the partial-volume effect (0.81) based on independent measures of heart geometry. A 3-compartment model best described 18F-FHBG kinetics in mice expressing HSV1-sr39tk in the liver; a 2-compartment model best described the kinetics in control mice. The 3-compartment model parameter, k3, correlated well with the HSV1-sr39TK enzyme activity (r2 = 0.88). CONCLUSION: 18F-FHBG equilibrates rapidly between plasma and whole blood in mice. Heart image time-activity curves corrected for partial-volume effects well approximate LV time-activity curves and can be used as input functions for 2- and 3-compartment models. The model parameter k3 from the 3-compartment model can be used as a noninvasive estimate for HSV1-sr39TK reporter protein activity and can predict the relative percentage of metabolites.