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Methods for efficiently controlling dynamics propagated on networks are usually based on identifying the most influential nodes. Knowledge of these nodes can be used for the targeted control of dynamics such as epidemics, or for modifying…
Network analysis defines a number of centrality measures to identify the most central nodes in a network. Fast computation of those measures is a major challenge in algorithmic network analysis. Aside from closeness and betweenness, Katz…
End-to-end learning of dynamical systems with black-box models, such as neural ordinary differential equations (ODEs), provides a flexible framework for learning dynamics from data without prescribing a mathematical model for the dynamics.…
Centrality is an important notion in network analysis and is used to measure the degree to which network structure contributes to the importance of a node in a network. While many different centrality measures exist, most of them apply to…
We develop efficient and effective strategies for the update of Katz centralities after node and edge removal in simple graphs. We provide explicit formulas for the ``loss of walks" a network suffers when nodes/edges are removed, and use…
In complex networks, each node has some unique characteristics that define the importance of the node based on the given application-specific context. These characteristics can be identified using various centrality metrics defined in the…
Realizations of stochastic process are often observed temporal data or functional data. There are growing interests in classification of dynamic or functional data. The basic feature of functional data is that the functional data have…
Identifying important nodes in complex networks is a fundamental problem in network analysis. Although a plethora of measures has been proposed to identify important nodes in static (i.e., time-invariant) networks, there is a lack of tools…
The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…
Predicting the behaviors of pedestrian crowds is of critical importance for a variety of real-world problems. Data driven modeling, which aims to learn the mathematical models from observed data, is a promising tool to construct models that…
Continuous normalizing flows (CNFs) and diffusion models (DMs) generate high-quality data from a noise distribution. However, their sampling process demands multiple iterations to solve an ordinary differential equation (ODE) with high…
Under a smart grid paradigm, there has been an increase in sensor installations to enhance situational awareness. The measurements from these sensors can be leveraged for real-time monitoring, control, and protection. However, these…
We propose a novel framework, Continuous_Time Attention, which infuses partial differential equations (PDEs) into the Transformer's attention mechanism to address the challenges of extremely long input sequences. Instead of relying solely…
Deep sequence models have achieved notable success in time-series analysis, such as interpolation and forecasting. Recent advances move beyond discrete-time architectures like Recurrent Neural Networks (RNNs) toward continuous-time…
There has been an increasing interest in modeling continuous-time dynamics of temporal graph data. Previous methods encode time-evolving relational information into a low-dimensional representation by specifying discrete layers of neural…
We present a network-based modal analysis technique that identifies key dynamical paths along which perturbations amplify over a time-varying base flow. This analysis is built upon the Katz centrality, which reveals the flow structures that…
We analyze a recently proposed temporal centrality measure applied to an empirical network based on person-to-person contacts in an emergency department of a busy urban hospital. We show that temporal centrality identifies a distinct set of…
In complex networks, centrality metrics quantify the connectivity of nodes and identify the most important ones in the transmission of signals. In many real world networks, especially in transportation systems, links are dynamic, i.e. their…
Causal inference in continuous-time sequential decision problems is challenged by hidden confounders. We show that, in latent state-space models with time-varying interventions, observability of the latent dynamics from observed data is…
Ordinary differential equations (ODEs) can provide mechanistic models of temporally local changes of processes, where parameters are often informed by external knowledge. While ODEs are popular in systems modeling, they are less established…