ASU Scholarship Showcase

The electronic structure of eight zinc-centered porphyrin macrocyclic molecules are investigated using density functional theory for ground-state properties, time-dependent density functional theory (TDDFT) for excited states, and Franck-Condon (FC) analysis for further characterization of the UV-vis spectrum. Symmetry breaking was utilized to find the lowest energy of the excited states for many states in the spectra. To confirm the theoretical modeling, the spectroscopic result from zinc phthalocyanine (ZnPc) is used to compare to the TDDFT and FC result. After confirmation of the modeling, five more planar molecules are investigated: zinc tetrabenzoporphyrin (ZnTBP), zinc tetrabenzomonoazaporphyrin (ZnTBMAP), zinc tetrabenzocisdiazaporphyrin (ZnTBcisDAP), zinc tetrabenzotransdiazaporphyrin (ZnTBtransDAP), and zinc tetrabenzotriazaporphyrin (ZnTBTrAP). The two latter molecules are then compared to their phenylated sister molecules: zinc monophenyltetrabenzotriazaporphyrin (ZnMPTBTrAP) and zinc diphenyltetrabenzotransdiazaporphyrin (ZnDPTBtransDAP). The spectroscopic results from the synthesis of ZnMPTBTrAP and ZnDPTBtransDAP are then compared to their theoretical models and non-phenylated pairs. While the Franck-Condon results were not as illuminating for every B-band, the Q-band results were successful in all eight molecules, with a considerable amount of spectral analysis in the range of interest between 300 and 750 nm. The π-π^* transitions are evident in the results for all of the Q bands, while satellite vibrations are also visible in the spectra. In particular, this investigation finds that, while ZnPc has a D_4h symmetry at ground state, a C_4v symmetry is predicted in the excited-state Q band region. The theoretical results for ZnPc found an excitation energy at the Q-band 0-0 transition of 1.88 eV in vacuum, which is in remarkable agreement with published gas-phase spectroscopy, as well as our own results of ZnPc in solution with Tetrahydrofuran that are provided in this paper.

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.

Controlling complex networks has become a forefront research area in network science and engineering. Recent efforts have led to theoretical frameworks of controllability to fully control a network through steering a minimum set of driver nodes. However, in realistic situations not every node is accessible or can be externally driven, raising the fundamental issue of control efficacy: if driving signals are applied to an arbitrary subset of nodes, how many other nodes can be controlled? We develop a framework to determine the control efficacy for undirected networks of arbitrary topology. Mathematically, based on non-singular transformation, we prove a theorem to determine rigorously the control efficacy of the network and to identify the nodes that can be controlled for any given driver nodes. Physically, we develop the picture of diffusion that views the control process as a signal diffused from input signals to the set of controllable nodes. The combination of mathematical theory and physical reasoning allows us not only to determine the control efficacy for model complex networks and a large number of empirical networks, but also to uncover phenomena in network control, e.g., hub nodes in general possess lower control centrality than an average node in undirected networks.

Successful identification of directed dynamical influence in complex systems is relevant to significant problems of current interest. Traditional methods based on Granger causality and transfer entropy have issues such as difficulty with nonlinearity and large data requirement. Recently a framework based on nonlinear dynamical analysis was proposed to overcome these difficulties. We find, surprisingly, that noise can counterintuitively enhance the detectability of directed dynamical influence. In fact, intentionally injecting a proper amount of asymmetric noise into the available time series has the unexpected benefit of dramatically increasing confidence in ascertaining the directed dynamical influence in the underlying system. This result is established based on both real data and model time series from nonlinear ecosystems. We develop a physical understanding of the beneficial role of noise in enhancing detection of directed dynamical influence.

In spite of the recent interest and advances in linear controllability of complex networks, controlling nonlinear network dynamics remains an outstanding problem. Here we develop an experimentally feasible control framework for nonlinear dynamical networks that exhibit multistability. The control objective is to apply parameter perturbation to drive the system from one attractor to another, assuming that the former is undesired and the latter is desired. To make our framework practically meaningful, we consider restricted parameter perturbation by imposing two constraints: it must be experimentally realizable and applied only temporarily. We introduce the concept of attractor network, which allows us to formulate a quantifiable controllability framework for nonlinear dynamical networks: a network is more controllable if the attractor network is more strongly connected. We test our control framework using examples from various models of experimental gene regulatory networks and demonstrate the beneficial role of noise in facilitating control.

Our ability to uncover complex network structure and dynamics from data is fundamental to understanding and controlling collective dynamics in complex systems. Despite recent progress in this area, reconstructing networks with stochastic dynamical processes from limited time series remains to be an outstanding problem. Here we develop a framework based on compressed sensing to reconstruct complex networks on which stochastic spreading dynamics take place. We apply the methodology to a large number of model and real networks, finding that a full reconstruction of inhomogeneous interactions can be achieved from small amounts of polarized (binary) data, a virtue of compressed sensing. Further, we demonstrate that a hidden source that triggers the spreading process but is externally inaccessible can be ascertained and located with high confidence in the absence of direct routes of propagation from it. Our approach thus establishes a paradigm for tracing and controlling epidemic invasion and information diffusion in complex networked systems.