arXiv subjects

Daniel A. Eisenberg

Publications and source records attributed to Daniel A. Eisenberg.

6 recordsLinked to original sources

arXiv2026

Towards a Theory of Quantitative Vulnerability Analysis for Engineering Systems

Since the 1980s, risk analysis for engineering systems has been defined based on a tuple of scenarios, $\mathcal{S}$, likelihoods, $L$, and consequences, $C$, where $Risk = (\mathcal{S},L,C)$. We argue that equating this triplet with risk alone is insufficient and potentially misleading. Instead, we define this tuple as a vulnerability space $\mathcal{V} = (\mathcal{S},L,C)$, which becomes risk only when one makes specific interpretations of likelihood and consequence. Here, an interpretation has mathematical meaning, and defines a map that assigns data elements about system vulnerability to a perspective. Formally, we define a vulnerability perspective as a specific choice of interpretations of likelihood and consequence data that allows vulnerability analysis measures to be defined and analyzed. We argue that risk is only one of four common perspectives on $\mathcal{V}$ and demonstrate mathematically why each perspective should remain a distinct concept. First, we show how interpretation of $C$ as a set-valued function produces reliability measures, not risk measures. Then, we show how interpretation of $L$ via possibility theory will produce adversarial and safety measures distinct from risk. This new theoretical framework clarifies the conceptual, mathematical, and practical differences between risk, reliability, adversarial, and safety perspectives---four common engineering system analyses often conflated in the literature. A consequence of our theory is that no single perspective will reveal all vulnerabilities of an engineering system, suggesting decision-making via risk analysis may incur unavoidable and underappreciated tradeoffs from other vulnerability perspectives.

eess.SY↗

arXiv2026

Markov Decision Process Approximation Methods for Water Distribution Network Inspection and Maintenance: A Case Study of the U.S. Virgin Islands

We develop a repair-oriented inspection and maintenance decision framework for water distribution networks. This work is motivated by utilities operating in data-sparse environments, such as in remote locations like the U.S. Virgin Islands, where data collection about network state and underground pipeline outages is limited to above-ground and easy to access information (e.g., water tank levels and pump operations). We formulate the problem as a discounted Markov decision process and integrate it with high-fidelity hydraulic simulation. The model captures latent system dynamics without requiring pipe-level sensing. The results reveal state-dependent optimal policies and heterogeneous failure characteristics across pipes, including rare but high-impact behaviors. We further show that certain observable system states uniquely correspond to specific pipe failures, enabling a form of virtual sensing. These findings demonstrate that system-level dynamics can support inspection planning and maintenance decisions under uncertainty in resource-constrained settings.

cs.CE↗

arXiv2023

A Tri-Level Optimization Model for Interdependent Infrastructure Network Resilience Against Compound Hazard Events

Resilient operation of interdependent infrastructures against compound hazard events is essential for maintaining societal well-being. To address consequence assessment challenges in this problem space, we propose a novel tri-level optimization model applied to a proof-of-concept case study with fuel distribution and transportation networks -- encompassing one realistic network; one fictitious, yet realistic network; as well as networks drawn from three synthetic distributions. Mathematically, our approach takes the form of a defender-attacker-defender (DAD) model -- a multi-agent tri-level optimization, comprised of a defender, attacker, and an operator acting in sequence. Here, our notional operator may choose proxy actions to operate an interdependent system comprised of fuel terminals and gas stations (functioning as supplies) and a transportation network with traffic flow (functioning as demand) to minimize unmet demand at gas stations. A notional attacker aims to hypothetically disrupt normal operations by reducing supply at the supply terminals, and the notional defender aims to identify best proxy defense policy options which include hardening supply terminals or allowing alternative distribution methods such as trucking reserve supplies. We solve our DAD formulation at a metropolitan scale and present practical defense policy insights against hypothetical compound hazards. We demonstrate the generalizability of our framework by presenting results for a realistic network; a fictitious, yet realistic network; as well as for three networks drawn from synthetic distributions. Additionally, we demonstrate the scalability of the framework by investigating runtime performance as a function of the network size. Steps for future research are also discussed.

eess.SY↗

arXiv2022

Finding shortest and nearly shortest path nodes in large substantially incomplete networks

Dynamic processes on networks, be it information transfer in the Internet, contagious spreading in a social network, or neural signaling, take place along shortest or nearly shortest paths. Unfortunately, our maps of most large networks are substantially incomplete due to either the highly dynamic nature of networks, or high cost of network measurements, or both, rendering traditional path finding methods inefficient. We find that shortest paths in large real networks, such as the network of protein-protein interactions (PPI) and the Internet at the autonomous system (AS) level, are not random but are organized according to latent-geometric rules. If nodes of these networks are mapped to points in latent hyperbolic spaces, shortest paths in them align along geodesic curves connecting endpoint nodes. We find that this alignment is sufficiently strong to allow for the identification of shortest path nodes even in the case of substantially incomplete networks. We demonstrate the utility of latent-geometric path-finding in problems of cellular pathway reconstruction and communication security.

physics.soc-ph↗

arXiv2018

Stability of a Giant Connected Component in a Complex Network

We analyze the stability of the network's giant connected component under impact of adverse events, which we model through the link percolation. Specifically, we quantify the extent to which the largest connected component of a network consists of the same nodes, regardless of the specific set of deactivated links. Our results are intuitive in the case of single-layered systems: the presence of large degree nodes in a single-layered network ensures both its robustness and stability. In contrast, we find that interdependent networks that are robust to adverse events have unstable connected components. Our results bring novel insights to the design of resilient network topologies and the reinforcement of existing networked systems.

physics.soc-ph↗

arXiv2017

The "weak" interdependence of infrastructure systems produces mixed percolation transitions in multilayer networks

In this work, we propose an interdependent, multilayer network model and percolation process that matches infrastructures better than previous models by allowing some nodes to survive when their interdependent neighbors fail. We consider a node-to-link failure propagation mechanism and establish "weak" interdependence across layers via a tolerance parameter $α$ which quantifies the likelihood that a node survives when one of its interdependent neighbors fails. We measure the robustness of any individual layer by the final size of its giant component. Analytical and numerical results show that weak interdependence produces a striking phenomenon: layers at different positions within the multilayer system experience distinct percolation transitions. Especially, layers with high super degree values percolate in an abrupt manner, while those with low super degree values exhibit both continuous and abrupt transitions. This novel phenomenon we call \emph{mixed percolation transitions} has significant implications for network robustness. Previous results that do not consider cascade tolerance and layer super degree may be under- or over-estimating the vulnerability of real systems. Moreover, since $α$ represents a generic measure of various risk management strategies used to buffer infrastructure assets from cascades, our model reveals how nodal protection activities influence failure dynamics in interdependent, multilayer systems.

nlin.AO↗