Quantum Iterated Function Systems

Iterated functions system (IFS) is defined by specifying a set of functions in a classical phase space, which act randomly on an initial point. In an analogous way, we define a quantum iterated functions system (QIFS), where functions act randomly with prescribed probabilities in the Hilbert space. In a more general setting a QIFS consists of completely positive maps acting in the space of density operators. We present exemplary classical IFSs, the invariant measure of which exhibits fractal structure, and study properties of the corresponding QIFSs and their invariant states.Comment: 12 pages, 1 figure include

DW-MRI as a Biomarker to Compare Therapeutic Outcomes in Radiotherapy Regimens Incorporating Temozolomide or Gemcitabine in Glioblastoma

The effectiveness of the radiosensitizer gemcitabine (GEM) was evaluated in a mouse glioma along with the imaging biomarker diffusion-weighted magnetic resonance imaging (DW-MRI) for early detection of treatment effects. A genetically engineered murine GBM model [Ink4a-Arf−/− PtenloxP/loxP/Ntv-a RCAS/PDGF(+)/Cre(+)] was treated with gemcitabine (GEM), temozolomide (TMZ) +/− ionizing radiation (IR). Therapeutic efficacy was quantified by contrast-enhanced MRI and DW-MRI for growth rate and tumor cellularity, respectively. Mice treated with GEM, TMZ and radiation showed a significant reduction in growth rates as early as three days post-treatment initiation. Both combination treatments (GEM/IR and TMZ/IR) resulted in improved survival over single therapies. Tumor diffusion values increased prior to detectable changes in tumor volume growth rates following administration of therapies. Concomitant GEM/IR and TMZ/IR was active and well tolerated in this GBM model and similarly prolonged median survival of tumor bearing mice. DW-MRI provided early changes to radiosensitization treatment warranting evaluation of this imaging biomarker in clinical trials