ASU Scholarship Showcase

Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to be no signature of classical chaos whatsoever in the corresponding quantum system, generating a paradox. We find that transient chaos, besides being a physically meaningful phenomenon by itself, provides a resolution. Using the method of quantum state diffusion to simulate the system dynamics subject to continuous homodyne detection, we uncover transient chaos associated with quantum trajectories. The transient behavior is consistent with chaos in the classical limit, while the long term evolution of the quantum system is regular. Transient chaos thus serves as a bridge for the quantum-classical transition (QCT). Strikingly, as the system transitions from the quantum to the classical regime, the average chaotic transient lifetime increases dramatically (faster than the Ehrenfest time characterizing the QCT for isolated quantum systems). We develop a physical theory to explain the scaling law.

Network reconstruction is a fundamental problem for understanding many complex systems with unknown interaction structures. In many complex systems, there are indirect interactions between two individuals without immediate connection but with common neighbors. Despite recent advances in network reconstruction, we continue to lack an approach for reconstructing complex networks with indirect interactions. Here we introduce a two-step strategy to resolve the reconstruction problem, where in the first step, we recover both direct and indirect interactions by employing the Lasso to solve a sparse signal reconstruction problem, and in the second step, we use matrix transformation and optimization to distinguish between direct and indirect interactions. The network structure corresponding to direct interactions can be fully uncovered. We exploit the public goods game occurring on complex networks as a paradigm for characterizing indirect interactions and test our reconstruction approach. We find that high reconstruction accuracy can be achieved for both homogeneous and heterogeneous networks, and a number of empirical networks in spite of insufficient data measurement contaminated by noise. Although a general framework for reconstructing complex networks with arbitrary types of indirect interactions is yet lacking, our approach opens new routes to separate direct and indirect interactions in a representative complex system.

Improved tools for providing specific intraoperative diagnoses could improve patient care. In neurosurgery, intraoperatively differentiating non-operative lesions such as CNS B-cell lymphoma from operative lesions can be challenging, often necessitating immunohistochemical (IHC) procedures which require up to 24-48 hours. Here, we evaluate the feasibility of generating rapid ex vivo specific labeling using a novel lymphoma-specific fluorescent switchable aptamer. Our B-cell lymphoma-specific switchable aptamer produced only low-level fluorescence in its unbound conformation and generated an 8-fold increase in fluorescence once bound to its target on CD20-positive lymphoma cells. The aptamer demonstrated strong binding to B-cell lymphoma cells within 15 minutes of incubation as observed by flow cytometry. We applied the switchable aptamer to ex vivo xenograft tissue harboring B-cell lymphoma and astrocytoma, and within one hour specific visual identification of lymphoma was routinely possible. In this proof-of-concept study in human cell culture and orthotopic xenografts, we conclude that a fluorescent switchable aptamer can provide rapid and specific labeling of B-cell lymphoma, and that developing aptamer-based labeling approaches could simplify tissue staining and drastically reduce time to histopathological diagnoses compared with IHC-based methods. We propose that switchable aptamers could enhance expeditious, accurate intraoperative decision-making.

Background:
Data assimilation refers to methods for updating the state vector (initial condition) of a complex spatiotemporal model (such as a numerical weather model) by combining new observations with one or more prior forecasts. We consider the potential feasibility of this approach for making short-term (60-day) forecasts of the growth and spread of a malignant brain cancer (glioblastoma multiforme) in individual patient cases, where the observations are synthetic magnetic resonance images of a hypothetical tumor.

Results:
We apply a modern state estimation algorithm (the Local Ensemble Transform Kalman Filter), previously developed for numerical weather prediction, to two different mathematical models of glioblastoma, taking into account likely errors in model parameters and measurement uncertainties in magnetic resonance imaging. The filter can accurately shadow the growth of a representative synthetic tumor for 360 days (six 60-day forecast/update cycles) in the presence of a moderate degree of systematic model error and measurement noise.

Conclusions:
The mathematical methodology described here may prove useful for other modeling efforts in biology and oncology. An accurate forecast system for glioblastoma may prove useful in clinical settings for treatment planning and patient counseling.