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Resilient ecological systems will be better able to maintain their structure and function in the emerging Anthropocene. Estimating the resilience of different systems will therefore provide valuable insight for conservation decision-makers,…
Stability guarantees are crucial when ensuring a fully autonomous robot does not take undesirable or potentially harmful actions. Unfortunately, global stability guarantees are hard to provide in dynamical systems learned from data,…
Chemical systems are interpreted through the species they contain and the reactions they may undergo, i.e., their chemical reaction network (CRN). In spite of their central importance to chemistry, the structure of CRNs continues to be…
This work concerns the development of deep networks that are certifiably robust to adversarial attacks. Joint robust classification-detection was recently introduced as a certified defense mechanism, where adversarial examples are either…
Compositionally complex alloys hold the promise of simultaneously attaining superior combinations of properties, such as corrosion resistance, light-weighting, and strength. Achieving this goal is a challenge due in part to a large number…
Cells and microorganisms employ dynamic shape changes to enable steering and avoidance for efficient spatial exploration and collective organization. In contrast, active colloids, their synthetic counterparts, currently lack similar…
Considering the control problem for nonlinear uncertain systems, the tolerable range of uncertain control input gain is a fundamental issue. The paper presents the necessary and sufficient condition for the well-performed closed-loop system…
Analysis of large continuous-time stochastic systems is a computationally intensive task. In this work we focus on population models arising from chemical reaction networks (CRNs), which play a fundamental role in analysis and design of…
e discuss the relevance of the Stillinger and Weber approach to the glass transition investigating the non-equilibrium behavior of models with non-trivial dynamics, but with simple equilibrium properties. We consider a family of 1D…
The erratic nature of chaotic behavior is thought to erode the stability of periodic behavior, including topological oscillations. However, we discover that in the presence of chaos, non-trivial topology not only endures but also provides…
Anomaly detection in industrial systems is crucial for preventing equipment failures, ensuring risk identification, and maintaining overall system efficiency. Traditional monitoring methods often rely on fixed thresholds and empirical…
This paper introduces robust differential dynamic logic (a fragment of differential dynamic logic) to specify and reason about robust hybrid systems. Practically meaningful syntactic restrictions naturally ensure that definable properties…
Recurrent neural policies are widely used in partially observable control and meta-RL tasks. Their abilities to maintain internal memory and adapt quickly to unseen scenarios have offered them unparalleled performance when compared to…
In this paper, we derive two sufficient conditions to diagnose the persistence of two classes of delayed complex balanced chemical reaction network systems equipped with mass-action kinetics. One class is identified by $\dim…
Most complex systems are nonlinear, relying on emergent behavior from interacting subsystems, often characterized by oscillatory dynamics. Collective oscillatory behavior is essential for the proper functioning of many real world systems.…
A natural condition on the structure of the underlying chemical reaction network, namely weak reversibility, is shown to guarantee the existence of an equilibrium (steady state) in each positive stoichiometric compatibility class for the…
We consider kinetic systems and prove their stability working in weighted spaces in which the systems are symmetric. We prove stability for various explicit and implicit semi-discrete and fully discrete schemes. The applications include…
Recurrent neural networks (RNNs) are a popular choice for modeling sequential data. Modern RNN architectures assume constant time-intervals between observations. However, in many datasets (e.g. medical records) observation times are…
A comparative study of the dynamics of inherent structures at low temperatures is performed on different models of glass formers: a three dimensional Lennard-Jones binary mixture (LJBM), facilitated spin models (either symmetrically…
A range of defense methods have been proposed to improve the robustness of neural networks on adversarial examples, among which provable defense methods have been demonstrated to be effective to train neural networks that are certifiably…