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Local Koopman spectral problem is studied to resolve all dynamics for a nonlinear system. The proposed spectral problem is compatible with the linear spectral theory for various linear systems, and several properties of local Koopman…
Network flows over time are a fascinating generalization of classical (static) network flows, introducing an element of time. They naturally model problems where travel and transmission are not instantaneous and flow may vary over time. Not…
Graph theory constitutes a widely used and established field providing powerful tools for the characterization of complex networks. The intricate topology of networks can also be investigated by means of the collective dynamics observed in…
Dynamic mode decomposition (DMD) is a data-driven technique used for capturing the dynamics of complex systems. DMD has been connected to spectral analysis of the Koopman operator, and essentially extracts spatial-temporal modes of the…
Temporal graphs are graphs where the presence or properties of their vertices and edges change over time. When time is discrete, a temporal graph can be defined as a sequence of static graphs over a discrete time span, called lifetime, or…
In the pursuit of autonomous learning systems, the foundational assumption of stationarity, the premise that data distributions and model behaviors remain constant, is fundamentally untenable. Historically, the research community has…
Interactions among units in complex systems occur in a specific sequential order thus affecting the flow of information, the propagation of diseases, and general dynamical processes. We investigate the Laplacian spectrum of temporal…
Graphs are widely used for modeling various types of interactions, such as email communications and online discussions. Many of such real-world graphs are temporal, and specifically, they grow over time with new nodes and edges. Counting…
Spatial networks have recently attracted great interest in various fields of research. While the traditional network-theoretic viewpoint is commonly restricted to their topological characteristics (often disregarding existing spatial…
Networks have become indispensable and ubiquitous structures in many fields to model the interactions among different entities, such as friendship in social networks or protein interactions in biological graphs. A major challenge is to…
Dynamic networks have intrinsic structural, computational, and multidisciplinary advantages. Link prediction estimates the next relationship in dynamic networks. However, in the current link prediction approaches, only bipartite or…
Complex systems often have features that can be modeled by advanced mathematical tools [1]. Of special interests are the features of complex systems that have a network structure as such systems are important for modeling technological and…
Recent advances in data collection and storage have allowed both researchers and industry alike to collect data in real time. Much of this data comes in the form of 'events', or timestamped interactions, such as email and social media…
The interplay between topology and dynamics in complex networks is a fundamental but widely unexplored problem. Here, we study this phenomenon on a prototype model in which the network is shaped by a dynamical variable. We couple the…
This paper describes a method for learning low-dimensional approximations of nonlinear dynamical systems, based on neural-network approximations of the underlying Koopman operator. Extended Dynamic Mode Decomposition (EDMD) provides a…
Time-dependent flow fields are typically generated by a computational fluid dynamics (CFD) method, which is an extremely time-consuming process. However, the latent relationship between the flow fields is governed by the Navier-Stokes…
We present an approach to construct approximate Koopman-type decompositions for dynamical systems depending on static or time-varying parameters. Our method simultaneously constructs an invariant subspace and a parametric family of…
Logistics and transportation networks require a large amount of resources to realize necessary connections between locations and minimizing these resources is a vital aspect of planning research. Since such networks have dynamic connections…
Temporal dynamics, characterised by time-varying degree heterogeneity and homophily effects, are often exhibited in many real-world networks. As observed in an MIT Social Evolution study, the in-degree and out-degree of the nodes show…
Dynamic networks, a.k.a. graph streams, consist of a set of vertices and a collection of timestamped interaction events (i.e., temporal edges) between vertices. Temporal motifs are defined as classes of (small) isomorphic induced subgraphs…