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Quantum coherence, the physical property underlying fundamental phenomena such as multi-particle interference and entanglement, has emerged as a valuable resource upon which exotic modern technologies are founded. In general, the most…
As attribution-based explanation methods are increasingly used to establish model trustworthiness in high-stakes situations, it is critical to ensure that these explanations are stable, e.g., robust to infinitesimal perturbations to an…
The key observation about quantum reality is that it often appears as if, at some moment, the probability of a quantum event becomes a definite outcome for us. A careful analysis suggests, however, that what we perceive as a definite state…
We introduce an approach which allows a detailed structural and quantitative analysis of multipartite entanglement. The sets of states with different structures are convex and nested. Hence, they can be distinguished from each other using…
Simultaneous estimation of multiple parameters in quantum metrological models is complicated by factors relating to the (i) existence of a single probe state allowing for optimal sensitivity for all parameters of interest, (ii) existence of…
Distinguishing whether a system supports alternate low-energy (locally stable) states -- stable (true vacuum) versus metastable (false vacuum) -- by direct observation can be difficult when the lifetime of the state is very long but…
A useful sampling-reconstruction model should be stable with respect to different kind of small perturbations, regardless whether they result from jitter, measurement errors, or simply from a small change in the model assumptions. In this…
The coherence of an individual quantum state can be meaningfully discussed only when referring to a preferred basis. This arbitrariness can however be lifted when considering sets of quantum states. Here we introduce the concept of set…
Often in Software Engineering, a modeling formalism has to support scenarios of inconsistency in which several requirements either reinforce or contradict each other. Paraconsistent transition systems are proposed in this paper as one such…
The quasi steady-state (QSS) model tries to reach a good compromise between accuracy and efficiency in long-term stability analysis. However, the QSS model is unable to provide correct approximations and stability assessment for the…
The quantum fluctuations of a physical property can be observed in the measurement statistics of any measurement that is at least partially sensitive to that physical property. Quantum theory indicates that the effective distribution of…
Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…
Employing model predictive control to systems with unbounded, stochastic disturbances poses the challenge of guaranteeing safety, i.e., repeated feasibility and stability of the closed-loop system. Especially, there are no strict repeated…
In this paper, we consider stochastic master equations describing the evolution of quantum spin-1/2 systems interacting with electromagnetic fields undergoing continuous-time measurements. We suppose that the initial states and the exact…
Multistability is a phenomenon prevalent in many natural systems. In climate, for example, it allows the possibility of irreversible consequences on planetary scale as a result of climate change. Indeed, a climate ``tipping element'' is a…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
Stability is among the most important concepts in dynamical systems. Local stability is well-studied, whereas determining how "globally stable" a nonlinear system is very challenging. Over the last few decades, many different ideas have…
Large Language Models are built on the so-called distributional semantic approach to linguistic meaning that has the distributional hypothesis at its core. The distributional hypothesis involves a holistic conception of word meaning: the…
An input-output approach to stability analysis is explored for networked systems with uncertain link dynamics. The main result consists of a collection of integral quadratic constraints, which together imply robust stability of the…
In this paper, a theoretical foundation for the Quasi Steady-State (QSS) model in power system long-term stability analysis is developed. Sufficient conditions under which the QSS model gives accurate approximations of the long-term…