Robust Network Routing under Cascading Failures

We propose a dynamical model for cascading failures in single-commodity network flows. In the proposed model, the network state consists of flows and activation status of the links. Network dynamics is determined by a, possibly state-dependent and adversarial, disturbance process that reduces flow capacity on the links, and routing policies at the nodes that have access to the network state, but are oblivious to the presence of disturbance. Under the proposed dynamics, a link becomes irreversibly inactive either due to overload condition on itself or on all of its immediate downstream links. The coupling between link activation and flow dynamics implies that links to become inactive successively are not necessarily adjacent to each other, and hence the pattern of cascading failure under our model is qualitatively different than standard cascade models. The magnitude of a disturbance process is defined as the sum of cumulative capacity reductions across time and links of the network, and the margin of resilience of the network is defined as the infimum over the magnitude of all disturbance processes under which the links at the origin node become inactive. We propose an algorithm to compute an upper bound on the margin of resilience for the setting where the routing policy only has access to information about the local state of the network. For the limiting case when the routing policies update their action as fast as network dynamics, we identify sufficient conditions on network parameters under which the upper bound is tight under an appropriate routing policy. Our analysis relies on making connections between network parameters and monotonicity in network state evolution under proposed dynamics

After the Fall: Legacy Effects of Biogenic Structure on Wind-Generated Ecosystem Processes Following Mussel Bed Collapse

Blue mussels (Mytilus edulis) are ecosystem engineers with strong effects on species diversity and abundances. Mussel beds appear to be declining in the Gulf of Maine, apparently due to climate change and predation by the invasive green crab, Carcinus maenas. As mussels die, they create a legacy of large expanses of shell biogenic structure. In Maine, USA, we used bottom traps to examine effects of four bottom cover types (i.e., live mussels, whole shells, fragmented shells, bare sediment) and wind condition (i.e., days with high, intermediate, and low values) on flow-related ecosystem processes. Significant differences in transport of sediment, meiofauna, and macrofauna were found among cover types and days, with no significant interaction between the two factors. Wind condition had positive effects on transport. Shell hash, especially fragmented shells, had negative effects, possibly because it acted as bed armor to reduce wind-generated erosion and resuspension. Copepods had the greatest mobility and shortest turnover times (0.15 d), followed by nematodes (1.96 d) and the macrofauna dominant, Tubificoides benedeni (2.35 d). Shell legacy effects may play an important role in soft-bottom system responses to wind-generated ecosystem processes, particularly in collapsed mussel beds, with implications for recolonization, connectivity, and the creation and maintenance of spatial pattern

Information and Control in Networks

Information and Control in Networks demonstrates the way in which system dynamics and information flows intertwine as they evolve, and the central role played by information in the control of complex networked systems. It is a milestone on the road to that convergence from traditionally independent development of control theory and information theory which has emerged strongly in the last fifteen years, and is now a very active research field. In addition to efforts in control and information theory, the text is witness to strong research in such diverse fields as computer science, mathematics, and statistics. Aspects that are given specialist treatment include: ·                 data-rate theorems; ·                 computation and control over communication networks; ·                 decentralized stochastic control; ·                 Gaussian networks and Gaussian–Markov random fields; and ·                 routability in information networks. Information and Control in Networks collects contributions from world-leading researchers in the area who came together for the Lund Center for Control of Complex Engineering Systems Workshop in Information and Control in Networks from 17th–19th October 2012; the workshop being the centrepiece of a five-week-long focus period on the same theme. A source of exciting cross-fertilization and new ideas for extensive future research, this volume will be of great interest to any researcher or graduate student interested in the interaction of control and information theory

Robust Distributed Routing in Dynamical Networks - Part II: Strong Resilience, Equilibrium Selection and Cascaded Failures

Original manuscript: March 25, 2011Strong resilience properties of dynamical networks are analyzed for distributed routing policies. The latter are characterized by the property that the way the outflow at a non-destination node gets split among its outgoing links is allowed to depend only on local information about the current particle densities on the outgoing links. The strong resilience of the network is defined as the infimum sum of link-wise flow capacity reductions making the asymptotic total inflow to the destination node strictly less than the total outflow at the origin. A class of distributed routing policies that are responsive to local information is shown to yield the maximum possible strong resilience under such local information constraints for an acyclic dynamical network with a single origin-destination pair. The maximal achievable strong resilience is shown to be equal to the minimum node residual capacity of the network. The latter depends on the limit flow of the unperturbed network and is defined as the minimum, among all the non-destination nodes, of the sum, over all the links outgoing from the node, of the differences between the maximum flow capacity and the limit flow of the unperturbed network. We propose a simple convex optimization problem to solve for equilibrium flows of the unperturbed network that minimize average delay subject to strong resilience guarantees, and discuss the use of tolls to induce such an equilibrium flow in traffic networks. Finally, we present illustrative simulations to discuss the connection between cascaded failures and the resilience properties of the network.National Science Foundation (U.S.). Office of Emerging Frontiers in Research and Innovation (Grant 0735956)United States. Air Force Office of Scientific Research (Grant FA9550-09-1-0538

Robust distributed routing in dynamical networks-part II: Strong resilience, equilibrium selection and cascaded failures

Original manuscript: March 25, 2011Strong resilience properties of dynamical networks are analyzed for distributed routing policies. The latter are characterized by the property that the way the outflow at a non-destination node gets split among its outgoing links is allowed to depend only on local information about the current particle densities on the outgoing links. The strong resilience of the network is defined as the infimum sum of link-wise flow capacity reductions making the asymptotic total inflow to the destination node strictly less than the total outflow at the origin. A class of distributed routing policies that are responsive to local information is shown to yield the maximum possible strong resilience under such local information constraints for an acyclic dynamical network with a single origin-destination pair. The maximal achievable strong resilience is shown to be equal to the minimum node residual capacity of the network. The latter depends on the limit flow of the unperturbed network and is defined as the minimum, among all the non-destination nodes, of the sum, over all the links outgoing from the node, of the differences between the maximum flow capacity and the limit flow of the unperturbed network. We propose a simple convex optimization problem to solve for equilibrium flows of the unperturbed network that minimize average delay subject to strong resilience guarantees, and discuss the use of tolls to induce such an equilibrium flow in traffic networks. Finally, we present illustrative simulations to discuss the connection between cascaded failures and the resilience properties of the network.National Science Foundation (U.S.). Office of Emerging Frontiers in Research and Innovation (Grant 0735956)United States. Air Force Office of Scientific Research (Grant FA9550-09-1-0538

Robust Distributed Routing in Dynamical Networks - Part I: Locally Responsive Policies and Weak Resilience

Original manuscript March 25, 2011Robustness of distributed routing policies is studied for dynamical networks, with respect to adversarial disturbances that reduce the link flow capacities. A dynamical network is modeled as a system of ordinary differential equations derived from mass conservation laws on a directed acyclic graph with a single origin-destination pair and a constant total outflow at the origin. Routing policies regulate the way the total outflow at each nondestination node gets split among its outgoing links as a function of the current particle density, while the outflow of a link is modeled to depend on the current particle density on that link through a flow function. The dynamical network is called partially transferring if the total inflow at the destination node is asymptotically bounded away from zero, and its weak resilience is measured as the minimum sum of the link-wise magnitude of disturbances that make it not partially transferring. The weak resilience of a dynamical network with arbitrary routing policy is shown to be upper bounded by the network's min-cut capacity and, hence, is independent of the initial flow conditions. Moreover, a class of distributed routing policies that rely exclusively on local information on the particle densities, and are locally responsive to that, is shown to yield such maximal weak resilience. These results imply that locality constraints on the information available to the routing policies do not cause loss of weak resilience. Fundamental properties of dynamical networks driven by locally responsive distributed routing policies are analyzed in detail, including global convergence to a unique limit flow. The derivation of these properties exploits the cooperative nature of these dynamical systems, together with an additional stability property implied by the assumption of monotonicity of the flow as a function of the density on each link.National Science Foundation (U.S.). Office of Emerging Frontiers in Research and Innovation (ARES Grant 0735956)United States. Air Force Office of Scientific Research (Grant FA9950-09-1-0538

Robust distributed routing in dynamical networks with cascading failures

We consider a dynamical formulation of network flows, whereby the network is modeled as a switched system of ordinary differential equations derived from mass conservation laws on directed graphs with a single origin-destination pair and a constant inflow at the origin. The rate of change of the density on each link of the network equals the difference between the inflow and the outflow on that link. The inflow to a link is determined by the total flow arriving to the tail node of that link and the routing policy at that tail node. The outflow from a link is modeled to depend on the current density on that link through a flow function. Every link is assumed to have finite capacity for density and the flow function is modeled to be strictly increasing up to the maximum density. A link becomes inactive when the density on it reaches the capacity. A node fails if all its outgoing links become inactive, and such node failures can propagate through the network due to rerouting of flow. We prove some properties of these dynamical networks and study the resilience of such networks under distributed routing policies with respect to perturbations that reduce link-wise flow functions. In particular, we propose an algorithm to compute upper bounds on the maximum resilience over all distributed routing policies, and discuss examples that highlight the role of cascading failures on the resilience of the network.National Science Foundation (U.S.). Office of Emerging Frontiers in Research and Innovation (ARES Grant 0735956)United States. Air Force Office of Scientific Research (Grant FA9550-09-1-0538

Is There a Relationship between Objectively Measured Cognitive Changes in Cancer Patients Undergoing Chemotherapy Treatment and Their Health-related Quality of Life? A Systematic Review

Background/purpose: Many people living with cancer experience depression. Research suggests that the therapeutic effect of exercise on depression is similar to pharmacotherapy or psychological intervention, yet cancer survivors are under-exercising compared to recommended doses. Self-efficacy may be a factor to explain exercise engagement. This cross-sectional study investigated whether exercise task self-efficacy (ETSE) was associated with exercise engagement, further examining differences between cancer survivors with and without elevated depressive symptoms. \ud \ud Methods: Ninety-seven cancer survivors (60.8 ±9.9 years) were mailed self-report questionnaires on ETSE, exercise engagement, and depressive symptoms. A Hospital Anxiety and Depression Scale D cutoff score (≥8) was used to assign participants to a symptomatic (n = 34) or non-symptomatic group (n = 63). An independent t-test was used to examine differences in ETSE between groups. Correlational analyses were used to examine relationships between exercise task self-efficacy and exercise engagement. \ud \ud Results: There was a significant difference in the degree of exercise task self-efficacy between cancer survivors with (M=35.74, SD= 31.47) and without (M=57.30, SD= 26.71) depressive symptoms, t(95) =_3.56, p<0.01, with a large effect size (d =0.74). A positive association was found between ETSE and exercise engagement, r(95)= 0.49, p<0.01, which was similar for both groups. \ud \ud Conclusions: Exercise task self-efficacy appears to influence exercise engagement independently of mood status, but people with higher levels of depression symptoms tend to have lower self-efficacy. Therefore, future research should examine interventions to enhance exercise task self-efficacy, thereby potentially increasing exercise engagement in cancer survivors. Research Implications: These findings demonstrated that cancer survivors with depressive symptoms have low ETSE and that ETSE can predict exercise engagement. This suggests a role for enhancing ETSE to influence exercise engagement in cancer survivors. Future research could investigate causality between ETSE and exercise engagement and interventions to enhance ETSE. The findings of the present study could assist with more definitive research which could aid clinicians interested in behavioral change with regard to exercise engagement and improvement of depressive symptomatology in cancer survivors. Practice Implications: The findings illustrate that exercise self-efficacy predicts exercise engagement, independently of mood. Therefore, clinicians working with depressed or non-depressed cancer survivors should initially target increasing exercise self-efficacy as opposed to reinforcing the positive health benefits of increased physical activity