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The problem of quickest detection of dynamic events in networks is studied. At some unknown time, an event occurs, and a number of nodes in the network are affected by the event, in that they undergo a change in the statistics of their…
A fundamental premise of statistical physics is that the particles in a physical system are interchangeable, and hence the state of each specific component is representative of the system as a whole. This assumption breaks down for complex…
This paper addresses problems on the structural design of control systems taking explicitly into consideration the possible application to large-scale systems. We provide an efficient and unified framework to solve the following major…
Network-structured data becomes ubiquitous in daily life and is growing at a rapid pace. It presents great challenges to feature engineering due to the high non-linearity and sparsity of the data. The local and global structure of the…
Partial Differential Equations are infinite dimensional encoded representations of physical processes. However, imbibing multiple observation data towards a coupled representation presents significant challenges. We present a fully…
This paper deals with identifiability of undirected dynamical networks with single-integrator node dynamics. We assume that the graph structure of such networks is known, and aim to find graph-theoretic conditions under which the state…
This paper considers transfer functions in consensus systems where agents have identical SISO dynamics of arbitrary order. The interconnecting structure is a directed graph. The transfer functions for various inputs and outputs are…
Community structure is pervasive in various real-world networks, portraying the strong local clustering of nodes. Unveiling the community structure of a network is deemed to a crucial step towards understanding the dynamics on the network.…
Knowledge about existence, strength, and dominant direction of causal influences is of paramount importance for understanding complex systems. With limited amounts of realistic data, however, current methods for investigating causal links…
The fully dynamic transitive closure problem asks to maintain reachability information in a directed graph between arbitrary pairs of vertices, while the graph undergoes a sequence of edge insertions and deletions. The problem has been…
Data-driven methods for the identification of the governing equations of dynamical systems or the computation of reduced surrogate models play an increasingly important role in many application areas such as physics, chemistry, biology, and…
Electronic structure calculations are routinely carried out within the framework of density-functional theory, often with great success. For electrons in reduced dimensions, however, there is still a need for better approximations to the…
Previous work on undirected small-world networks established the paradigm that locally structured networks tend to have high density of short loops. On the other hand, many realistic networks are directed. Here we investigate the local…
Visualizing high dimensional data by projecting them into two or three dimensional space is one of the most effective ways to intuitively understand the data's underlying characteristics, for example their class neighborhood structure.…
Density-functional theory is a formally exact description of a many-body quantum system in terms of its density; in practice, however, approximations to the universal density functional are required. In this work, a model based on deep…
In the scope of discrete finite-state models of interacting components, we present a novel algorithm for identifying sets of local states of components whose activity is necessary for the reachability of a given local state. If all the…
Dynamical models underpin our ability to understand and predict the behavior of natural systems. Whether dynamical models are developed from first-principles derivations or from observational data, they are predicated on our choice of state…
We present an algorithm to compute stabilizing minimum dwell times for discrete-time switched linear systems without the explicit knowledge of state-space models of their subsystems. Given a set of finite traces of state trajectories of the…
Units of complex systems -- such as neurons in the brain or individuals in societies -- must communicate efficiently to function properly: e.g., allowing electrochemical signals to travel quickly among functionally connected neuronal areas…
Whilst the partial differential equations that govern the dynamics of our world have been studied in great depth for centuries, solving them for complex, high-dimensional conditions and domains still presents an incredibly large…