ASU Scholarship Showcase

Nonhyperbolicity, as characterized by the coexistence of Kolmogorov-Arnold-Moser (KAM) tori and chaos in the phase space, is generic in classical Hamiltonian systems. An open but fundamental question in physics concerns the relativistic quantum manifestations of nonhyperbolic dynamics. We choose the mushroom billiard that has been mathematically proven to be nonhyperbolic, and study the resonant tunneling dynamics of a massless Dirac fermion. We find that the tunneling rate as a function of the energy exhibits a striking "clustering" phenomenon, where the majority of the values of the rate concentrate on a narrow region, as a result of the chaos component in the classical phase space. Relatively few values of the tunneling rate, however, spread outside the clustering region due to the integrable component. Resonant tunneling of electrons in nonhyperbolic chaotic graphene systems exhibits a similar behavior. To understand these numerical results, we develop a theoretical framework by combining analytic solutions of the Dirac equation in certain integrable domains and physical intuitions gained from current understanding of the quantum manifestations of chaos. In particular, we employ a theoretical formalism based on the concept of self-energies to calculate the tunneling rate and analytically solve the Dirac equation in one dimension as well as in two dimensions for a circular-ring-type of tunneling systems exhibiting integrable dynamics in the classical limit. Because relatively few and distinct classical periodic orbits are present in the integrable component, the corresponding relativistic quantum states can have drastically different behaviors, leading to a wide spread in the values of the tunneling rate in the energy-rate plane. In contrast, the chaotic component has embedded within itself an infinite number of unstable periodic orbits, which provide far more quantum states for tunneling. Due to the nature of chaos, these states are characteristically similar, leading to clustering of the values of the tunneling rate in a narrow band. The appealing characteristic of our work is a demonstration and physical understanding of the "mixed" role played by chaos and regular dynamics in shaping relativistic quantum tunneling dynamics.

Investigation into the causes underlying the rapid, global amphibian decline provides critical insight into the effects of changing ecosystems. Hypothesized and confirmed links between amphibian declines, disease, and environmental changes are increasingly represented in published literature. However, there are few long-term amphibian studies that include data on population size, abnormality/injury rates, disease, and habitat variables to adequately assess changes through time. We cultured and identified microorganisms isolated from abnormal/injured and repressed tissue regeneration sites of the endangered Ozark Hellbender, Cryptobranchus alleganiensis bishopi, to discover potential causative agents responsible for their significant decline in health and population. This organism and our study site were chosen because the population and habitat of C. a. bishopi have been intensively studied from 1969–2009, and the abnormality/injury rate and apparent lack of regeneration were established.

Although many bacterial and fungal isolates recovered were common environmental organisms, several opportunistic pathogens were identified in association with only the injured tissues of C.a. bishopi. Bacterial isolates included Aeromonas hydrophila, a known amphibian pathogen, Granulicetella adiacens, Gordonai terrae, Stenotrophomonas maltophilia, Aerococcus viridans, Streptococcus pneumoniae and a variety of Pseudomonads, including Pseudomonas aeruginosa, P. stutzeri, and P. alcaligenes. Fungal isolates included species in the genera Penicillium, Acremonium, Cladosporium, Curvularia, Fusarium, Streptomycetes, and the Class Hyphomycetes. Many of the opportunistic pathogens identified are known to form biofilms. Lack of isolation of the same organism from all wounds suggests that the etiological agent responsible for the damage to C. a. bishopi may not be a single organism. To our knowledge, this is the first study to profile the external microbial consortia cultured from a Cryptobranchid salamander. The incidence of abnormalities/injury and retarded regeneration in C. a. bishopi may have many contributing factors including disease and habitat degradation. Results from this study may provide insight into other amphibian population declines.

A distinct pathovar of Salmonella enterica serovar Typhimurium, ST313, has emerged in sub-Saharan Africa as a major cause of fatal bacteremia in young children and HIV-infected adults. D23580, a multidrug resistant clinical isolate of ST313, was previously shown to have undergone genome reduction in a manner that resembles that of the more human-restricted pathogen, Salmonella enterica serovar Typhi. It has since been shown through tissue distribution studies that D23580 is able to establish an invasive infection in chickens. However, it remains unclear whether ST313 can cause lethal disease in a non-human host following a natural course of infection. Herein we report that D23580 causes lethal and invasive disease in a murine model of infection following peroral challenge. The LD⁵⁰ of D23580 in female BALB/c mice was 4.7 x 10⁵ CFU. Tissue distribution studies performed 3 and 5 days post-infection confirmed that D23580 was able to more rapidly colonize the spleen, mesenteric lymph nodes and gall bladder in mice when compared to the well-characterized S. Typhimurium strain SL1344. D23580 exhibited enhanced resistance to acid stress relative to SL1344, which may lend towards increased capability to survive passage through the gastrointestinal tract as well as during its intracellular lifecycle. Interestingly, D23580 also displayed higher swimming motility relative to SL1344, S. Typhi strain Ty2, and the ST313 strain A130. Biochemical tests revealed that D23580 shares many similar metabolic features with SL1344, with several notable differences in the Voges-Proskauer and catalase tests, as well alterations in melibiose, and inositol utilization. These results represent the first full duration infection study using an ST313 strain following the entire natural course of disease progression, and serve as a benchmark for ongoing and future studies into the pathogenesis of D23580.

Given a complex geospatial network with nodes distributed in a two-dimensional region of physical space, can the locations of the nodes be determined and their connection patterns be uncovered based solely on data? We consider the realistic situation where time series/signals can be collected from a single location. A key challenge is that the signals collected are necessarily time delayed, due to the varying physical distances from the nodes to the data collection centre. To meet this challenge, we develop a compressive-sensing-based approach enabling reconstruction of the full topology of the underlying geospatial network and more importantly, accurate estimate of the time delays. A standard triangularization algorithm can then be employed to find the physical locations of the nodes in the network. We further demonstrate successful detection of a hidden node (or a hidden source or threat), from which no signal can be obtained, through accurate detection of all its neighbouring nodes. As a geospatial network has the feature that a node tends to connect with geophysically nearby nodes, the localized region that contains the hidden node can be identified.

We develop a framework to uncover and analyse dynamical anomalies from massive, nonlinear and non-stationary time series data. The framework consists of three steps: preprocessing of massive datasets to eliminate erroneous data segments, application of the empirical mode decomposition and Hilbert transform paradigm to obtain the fundamental components embedded in the time series at distinct time scales, and statistical/scaling analysis of the components. As a case study, we apply our framework to detecting and characterizing high-frequency oscillations (HFOs) from a big database of rat electroencephalogram recordings. We find a striking phenomenon: HFOs exhibit on–off intermittency that can be quantified by algebraic scaling laws. Our framework can be generalized to big data-related problems in other fields such as large-scale sensor data and seismic data analysis.

Recent works revealed that the energy required to control a complex network depends on the number of driving signals and the energy distribution follows an algebraic scaling law. If one implements control using a small number of drivers, e.g. as determined by the structural controllability theory, there is a high probability that the energy will diverge. We develop a physical theory to explain the scaling behaviour through identification of the fundamental structural elements, the longest control chains (LCCs), that dominate the control energy. Based on the LCCs, we articulate a strategy to drastically reduce the control energy (e.g. in a large number of real-world networks). Owing to their structural nature, the LCCs may shed light on energy issues associated with control of nonlinear dynamical networks.

A challenging problem in network science is to control complex networks. In existing frameworks of structural or exact controllability, the ability to steer a complex network toward any desired state is measured by the minimum number of required driver nodes. However, if we implement actual control by imposing input signals on the minimum set of driver nodes, an unexpected phenomenon arises: due to computational or experimental error there is a great probability that convergence to the final state cannot be achieved. In fact, the associated control cost can become unbearably large, effectively preventing actual control from being realized physically. The difficulty is particularly severe when the network is deemed controllable with a small number of drivers. Here we develop a physical controllability framework based on the probability of achieving actual control. Using a recently identified fundamental chain structure underlying the control energy, we offer strategies to turn physically uncontrollable networks into physically controllable ones by imposing slightly augmented set of input signals on properly chosen nodes. Our findings indicate that, although full control can be theoretically guaranteed by the prevailing structural controllability theory, it is necessary to balance the number of driver nodes and control cost to achieve physical control.

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.

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.

The process of cell fate determination has been depicted intuitively as cells travelling and resting on a rugged landscape, which has been probed by various theoretical studies. However, few studies have experimentally demonstrated how underlying gene regulatory networks shape the landscape and hence orchestrate cellular decision-making in the presence of both signal and noise. Here we tested different topologies and verified a synthetic gene circuit with mutual inhibition and auto-activations to be quadrastable, which enables direct study of quadruple cell fate determination on an engineered landscape. We show that cells indeed gravitate towards local minima and signal inductions dictate cell fates through modulating the shape of the multistable landscape. Experiments, guided by model predictions, reveal that sequential inductions generate distinct cell fates by changing landscape in sequence and hence navigating cells to different final states. This work provides a synthetic biology framework to approach cell fate determination and suggests a landscape-based explanation of fixed induction sequences for targeted differentiation.