Theoretical modeling of prion disease incubation.

We apply a theoretical aggregation model to laboratory and epidemiological prion disease incubation time data. In our model, slow growth of misfolded protein aggregates from small initial seeds controls the latent or lag phase; aggregate fissioning and subsequent spreading leads to an exponential growth phase. Our model accounts for the striking reproducibility of incubation times for high dose inoculation of lab animals. In particular, low dose yields broad incubation time distributions, and increasing dose narrows distributions and yields sharply defined onset times. We also explore how incubation time statistics depend upon aggregate morphology. We apply our model to fit the experimental dose-incubation curves for distinct strains of scrapie, and explain logarithmic variation at high dose and deviations from logarithmic behavior at low dose. We use this to make testable predictions for infectivity time-course experiments.

Reversal-field memory in the hysteresis of spin glasses.

We report a novel singularity in the hysteresis of spin glasses, the reversal-field memory effect, which creates a nonanalyticity in the magnetization curves at a particular point related to the history of the sample. The origin of the effect is due to the existence of a macroscopic number of "symmetric clusters" of spins associated with a local spin-reversal symmetry of the Hamiltonian. We use first order reversal curve (FORC) diagrams to characterize the effect and compare to experimental results on thin magnetic films. We contrast our results on spin glasses to random magnets and show that the FORC technique is an effective "magnetic fingerprinting" tool.

Using hysteresis for optimization.

We propose a new optimization method based on a demagnetization procedure well known in magnetism. We show how this procedure can be applied as a general tool to search for optimal solutions in any system where the configuration space is endowed with a suitable "distance." We test the new algorithm on frustrated magnetic models and the traveling salesman problem. We find that the new method successfully competes with similar basic algorithms such as simulated annealing.

Statistical mechanics of prion diseases.

We present a two-dimensional, lattice based, protein-level statistical mechanical model for prion diseases (e.g., mad cow disease) with concomitant prion protein misfolding and aggregation. Our studies lead us to the hypothesis that the observed broad incubation time distribution in epidemiological data reflect fluctuation dominated growth seeded by a few nanometer scale aggregates, while much narrower incubation time distributions for innoculated lab animals arise from statistical self-averaging. We model "species barriers" to prion infection and assess a related treatment protocol.

Disorder averaging and finite-size scaling

We propose a new picture of the renormalization group (RG) approach in the presence of disorder, which considers the RG trajectories of each random sample (realization) separately instead of the usual renormalization of the averaged free energy. The main consequence of the theory is that the average over randomness has to be taken after finding the critical point of each realization. To demonstrate these concepts, we study the finite-size scaling properties of the two-dimensional random-bond Ising model. We find that most of the previously observed finite-size corrections are due to the sample-to-sample fluctuation of the critical temperature and scaling predictions are fulfilled only by the new average.