A Second Order Gradient Flow of p-Elastic Planar Networks

We consider a second order gradient flow of the p-elastic energy for a planar theta-network of three curves with fixed lengths. We construct a weak solution of the flow by means of an implicit variational scheme. We show long-time existence of the evolution and convergence to a critical point of the energy

The use of dynamical networks to detect the hierarchical organization of financial market sectors

Two kinds of filtered networks: minimum spanning trees (MSTs) and planar maximally filtered graphs (PMFGs) are constructed from dynamical correlations computed over a moving window. We study the evolution over time of both hierarchical and topological properties of these graphs in relation to market fluctuations. We verify that the dynamical PMFG preserves the same hierarchical structure as the dynamical MST, providing in addition a more significant and richer structure, a stronger robustness and dynamical stability. Central and peripheral stocks are differentiated by using a combination of different topological measures. We find stocks well connected and central; stocks well connected but peripheral; stocks poorly connected but central; stocks poorly connected and peripheral. It results that the Financial sector plays a central role in the entire system. The robustness, stability and persistence of these findings are verified by changing the time window and by performing the computations on different time periods. We discuss these results and the economic meaning of this hierarchical positioning

Predicting the Condition Evolution of Controlled Infrastructure Components Modeled by Markov Processes

When the operation and maintenance (O&M) of infrastructure components is modeled as a Markov Decision Process (MDP), the stochastic evolution following the optimal policy is completely described by a Markov transition matrix. This paper illustrates how to predict relevant features of the time evolution of these controlled components. We are interested in assessing if a critical state is reachable, in assessing the probability of reaching that state within a time period, of visiting that state before another, and in returning to that state. We present analytical methods to address these questions and discuss their computational complexity. Outcomes of these analyses can provide the decision makers with deeper understanding of the component evolution and suggest revising the control policy. We formulate the framework for MDPs and extend it to Partially Observable Markov Decision Processes (POMDPs).We acknowledge the support of NSF project CMMI #1663479, titled "From Future Learning to Current Action: Long-Term Sequential Infrastructure Planning under Uncertainty"

Importance measures for inspections in binary networks

Many infrastructure systems can be modeled as networks of components with binary states (intact, damaged). Information about components conditions is crucial for the maintenance process of the system. However, it is often impossible to collect information of all components due to budget constraints. Several metrics have been developed to assess the importance of the components in relation to maintenance actions: an important component is one that should receive high maintenance priority. Instead, in this paper we focus on the priority to be assigned for component inspections and information collection. We investigate metrics based on system level (global) and component level (local) decision making after inspection for networks with different topology, and compare these results with traditional ones. We then discuss the computational challenges of these metrics and provide possible approximation approaches.We acknowledge the support of NSF project CMMI #1653716, titled CAREER: Infrastructure Management under Model Uncertainty: Adaptive Sequential Learning and Decision Making