Oppia Quadrangle Av-10 (288–360°E, ±22°) is a junction of key geologic features that preserve a rough history of Asteroid (4) Vesta and serves as a case study of using geologic mapping to define a relative geologic timescale. Clear filter images, stereo-derived topography, slope maps, and multispectral color-ratio images from the Framing Camera on NASA’s Dawn spacecraft served as basemaps to create a geologic map and investigate the spatial and temporal relationships of the local stratigraphy. Geologic mapping reveals the oldest map unit within Av-10 is the cratered highlands terrain which possibly represents original crustal material on Vesta that was then excavated by one or more impacts to form the basin Feralia Planitia. Saturnalia Fossae and Divalia Fossae ridge and trough terrains intersect the wall of Feralia Planitia indicating that this impact basin is older than both the Veneneia and Rheasilvia impact structures, representing Pre-Veneneian crustal material. Two of the youngest geologic features in Av-10 are Lepida (∼45 km diameter) and Oppia (∼40 km diameter) impact craters that formed on the northern and southern wall of Feralia Planitia and each cross-cuts a trough terrain. The ejecta blanket of Oppia is mapped as ‘dark mantle’ material because it appears dark orange in the Framing Camera ‘Clementine-type’ color-ratio image and has a diffuse, gradational contact distributed to the south across the rim of Rheasilvia. Mapping of surface material that appears light orange in color in the Framing Camera ‘Clementine-type’ color-ratio image as ‘light mantle material’ supports previous interpretations of an impact ejecta origin. Some light mantle deposits are easily traced to nearby source craters, but other deposits may represent distal ejecta deposits (emplaced >5 crater radii away) in a microgravity environment.

The Dawn Framing Camera (FC) has imaged the northern hemisphere of the Asteroid (4) Vesta at high spatial resolution and coverage. This study represents the first investigation of the overall geology of the northern hemisphere (22–90°N, quadrangles Av-1, 2, 3, 4 and 5) using these unique Dawn mission observations. We have compiled a morphologic map and performed crater size–frequency distribution (CSFD) measurements to date the geologic units. The hemisphere is characterized by a heavily cratered surface with a few highly subdued basins up to ∼200 km in diameter. The most widespread unit is a plateau (cratered highland unit), similar to, although of lower elevation than the equatorial Vestalia Terra plateau. Large-scale troughs and ridges have regionally affected the surface. Between ∼180°E and ∼270°E, these tectonic features are well developed and related to the south pole Veneneia impact (Saturnalia Fossae trough unit), elsewhere on the hemisphere they are rare and subdued (Saturnalia Fossae cratered unit). In these pre-Rheasilvia units we observed an unexpectedly high frequency of impact craters up to ∼10 km in diameter, whose formation could in part be related to the Rheasilvia basin-forming event. The Rheasilvia impact has potentially affected the northern hemisphere also with S–N small-scale lineations, but without covering it with an ejecta blanket. Post-Rheasilvia impact craters are small (<60 km in diameter) and show a wide range of degradation states due to impact gardening and mass wasting processes. Where fresh, they display an ejecta blanket, bright rays and slope movements on walls. In places, crater rims have dark material ejecta and some crater floors are covered by ponded material interpreted as impact melt.

Dynamical processes occurring on the edges in complex networks are relevant to a variety of real-world situations. Despite recent advances, a framework for edge controllability is still required for complex networks of arbitrary structure and interaction strength. Generalizing a previously introduced class of processes for edge dynamics, the switchboard dynamics, and exploit- ing the exact controllability theory, we develop a universal framework in which the controllability of any node is exclusively determined by its local weighted structure. This framework enables us to identify a unique set of critical nodes for control, to derive analytic formulas and articulate efficient algorithms to determine the exact upper and lower controllability bounds, and to evaluate strongly structural controllability of any given network. Applying our framework to a large number of model and real-world networks, we find that the interaction strength plays a more significant role in edge controllability than the network structure does, due to a vast range between the bounds determined mainly by the interaction strength. Moreover, transcriptional regulatory networks and electronic circuits are much more strongly structurally controllable (SSC) than other types of real-world networks, directed networks are more SSC than undirected networks, and sparse networks are typically more SSC than dense networks.

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.

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.

Locating sources of diffusion and spreading from minimum data is a significant problem in network science with great applied values to the society. However, a general theoretical framework dealing with optimal source localization is lacking. Combining the controllability theory for complex networks and compressive sensing, we develop a framework with high efficiency and robustness for optimal source localization in arbitrary weighted networks with arbitrary distribution of sources. We offer a minimum output analysis to quantify the source locatability through a minimal number of messenger nodes that produce sufficient measurement for fully locating the sources. When the minimum messenger nodes are discerned, the problem of optimal source localization becomes one of sparse signal reconstruction, which can be solved using compressive sensing. Application of our framework to model and empirical networks demonstrates that sources in homogeneous and denser networks are more readily to be located. A surprising finding is that, for a connected undirected network with random link weights and weak noise, a single messenger node is sufficient for locating any number of sources. The framework deepens our understanding of the network source localization problem and offers efficient tools with broad applications.

Evolutionary games model a common type of interactions in a variety of complex, networked, natural systems and social systems. Given such a system, uncovering the interacting structure of the underlying network is key to understanding its collective dynamics. Based on compressive sensing, we develop an efficient approach to reconstructing complex networks under game-based interactions from small amounts of data. The method is validated by using a variety of model networks and by conducting an actual experiment to reconstruct a social network. While most existing methods in this area assume oscillator networks that generate continuous-time data, our work successfully demonstrates that the extremely challenging problem of reverse engineering of complex networks can also be addressed even when the underlying dynamical processes are governed by realistic, evolutionary-game type of interactions in discrete time.

There is a need for indicators of transportation-land use system quality that are understandable to a wide range of stakeholders, and which can provide immediate feedback on the quality of interactively designed scenarios. Location-based accessibility indicators are promising candidates, but indicator values can vary strongly depending on time of day and transfer wait times. Capturing this variation increases complexity, slowing down calculations. We present new methods for rapid yet rigorous computation of accessibility metrics, allowing immediate feedback during early-stage transit planning, while being rigorous enough for final analyses. Our approach is statistical, characterizing the uncertainty and variability in accessibility metrics due to differences in departure time and headway-based scenario specification. The analysis is carried out on a detailed multi-modal network model including both public transportation and streets. Land use data are represented at high resolution. These methods have been implemented as open-source software running on commodity cloud infrastructure. Networks are constructed from standard open data sources, and scenarios are built in a map-based web interface. We conclude with a case study, describing how these methods were applied in a long-term transportation planning process for metropolitan Amsterdam.

Accessibility is increasingly used as a metric when evaluating changes to public transport systems. Transit travel times contain variation depending on when one departs relative to when a transit vehicle arrives, and how well transfers are coordinated given a particular timetable. In addition, there is necessarily uncertainty in the value of the accessibility metric during sketch planning processes, due to scenarios which are underspecified because detailed schedule information is not yet available. This article presents a method to extend the concept of "reliable" accessibility to transit to address the first issue, and create confidence intervals and hypothesis tests to address the second.

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.