A hybrid spatiotemporal model of PCa dynamics and insights into optimal therapeutic strategies.

Using a hybrid cellular automaton with stochastic elements, we investigate the effectiveness of multiple drug therapies on prostate cancer (PCa) growth. The ability of Androgen Deprivation Therapy to reduce PCa growth represents a milestone in prostate cancer treatment, nonetheless most patients eventually become refractory and develop castration-resistant prostate cancer. In recent years, a "second generation" drug called enzalutamide has been used to treat advanced PCa, or patients already exposed to chemotherapy that stopped responding to it.

PCa dynamics with neuroendocrine differentiation and distributed delay.

Prostate cancer is the fifth most common cause of death from cancer, and the second most common diagnosed cancer in men. In the last few years many mathematical models have been proposed to describe the dynamics of prostate cancer under treatment. So far one of the major challenges has been the development of mathematical models that would represent conditions and therefore be suitable for clinical applications, while being mathematically treatable.

Microscopic superfluidity in 4He clusters stirred by a rotating impurity molecule.

The effective moment of inertia of a CO impurity molecule in 4HeN and p-(H2)N solvent clusters initially increases with N but then commences a nonclassical decrease at N=4 (4He) or N=6 (p-H2). This suggests molecule-solvent decoupling and a transition to microscopic superfluidity. However, the quantum decoupling mechanism has not been elucidated.

Efficient procedure to compute the microcanonical volume of initial conditions that lead to escape trajectories from a multidimensional potential well.

A procedure is presented for computing the phase space volume of initial conditions for trajectories that escape or "react" from a multidimensional potential well. The procedure combines a phase space transition state theory, which allows one to construct dividing surfaces that are free of local recrossing and that minimize the directional flux, and a classical spectral theorem. The procedure gives the volume of reactive initial conditions in terms of a sum over each entrance channel of the well of the product of the phase space flux across the dividing surface associated with the channel and the mean residence time in the well of trajectories which enter through the channel.

Phase space conduits for reaction in multidimensional systems: HCN isomerization in three dimensions.

The three-dimensional hydrogen cyanide/isocyanide isomerization problem is taken as an example to present a general theory for computing the phase space structures which govern classical reaction dynamics in systems with an arbitrary (finite) number of degrees of freedom. The theory, which is algorithmic in nature, comprises the construction of a dividing surface of minimal flux which is locally a "surface of no return." The theory also allows for the computation of the global phase space transition pathways that trajectories must follow in order to react.

Chaos-assisted capture of irregular moons.

It has been thought that the capture of irregular moons--with non-circular orbits--by giant planets occurs by a process in which they are first temporarily trapped by gravity inside the planet's Hill sphere (the region where planetary gravity dominates over solar tides). The capture of the moons is then made permanent by dissipative energy loss (for example, gas drag) or planetary growth. But the observed distributions of orbital inclinations, which now include numerous newly discovered moons, cannot be explained using current models.