ASU Scholarship Showcase

We recommend using backward design to develop course-based undergraduate research experiences (CUREs). The defining hallmark of CUREs is that students in a formal lab course explore research questions with unknown answers that are broadly relevant outside the course. Because CUREs lead to novel research findings, they represent a unique course design challenge, as the dual nature of these courses requires course designers to consider two distinct, but complementary, sets of goals for the CURE: 1) scientific discovery milestones (i.e., research goals) and 2) student learning in cognitive, psychomotor, and affective domains (i.e., pedagogical goals). As more undergraduate laboratory courses are re-imagined as CUREs, how do we thoughtfully design these courses to effectively meet both sets of goals? In this Perspectives article, we explore this question and outline recommendations for using backward design in CURE development.

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.

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.

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.

Integrating research experiences into undergraduate life sciences curricula in the form of course-based undergraduate research experiences (CUREs) can meet national calls for education reform by giving students the chance to “do science.” In this article, we provide a step-by-step practical guide to help instructors assess their CUREs using best practices in assessment. We recommend that instructors first identify their anticipated CURE learning outcomes, then work to identify an assessment instrument that aligns to those learning outcomes and critically evaluate the results from their course assessment. To aid instructors in becoming aware of what instruments have been developed, we have also synthesized a table of “off-the-shelf” assessment instruments that instructors could use to assess their own CUREs. However, we acknowledge that each CURE is unique and instructors may expect specific learning outcomes that cannot be assessed using existing assessment instruments, so we recommend that instructors consider developing their own assessments that are tightly aligned to the context of their CURE.

Women who start college in one of the natural or physical sciences leave in greater proportions than their male peers. The reasons for this difference are complex, and one possible contributing factor is the social environment women experience in the classroom. Using social network analysis, we explore how gender influences the confidence that college-level biology students have in each other’s mastery of biology. Results reveal that males are more likely than females to be named by peers as being knowledgeable about the course content. This effect increases as the term progresses, and persists even after controlling for class performance and outspokenness. The bias in nominations is specifically due to males over-nominating their male peers relative to their performance. The over-nomination of male peers is commensurate with an overestimation of male grades by 0.57 points on a 4 point grade scale, indicating a strong male bias among males when assessing their classmates. Females, in contrast, nominated equitably based on student performance rather than gender, suggesting they lacked gender biases in filling out these surveys. These trends persist across eleven surveys taken in three different iterations of the same Biology course. In every class, the most renowned students are always male. This favoring of males by peers could influence student self-confidence, and thus persistence in this STEM discipline.