Related papers: Omega-Regular Robustness
Based on the generalized Routh-Hurwitz criterion, we propose a sufficient and necessary criterion for testing the stability of fractional-order linear systems with order {\alpha}{\in}[1,2), called the fractional-order Routh-Hurwitz…
Motivated by biochemical reaction networks, a generalization of the classical secant condition for the stability analysis of cyclic interconnected commensurate fractional-order systems is provided. The main result presents a sufficient…
The fundamental property of strongly monotone systems, and strongly cooperative systems in particular, is the limit set dichotomy due to Hirsch: if x(0) < y(0), then either omega(x) < omega(y), or omega(x) = omega(y) and both sets consist…
Explainable Recommender Systems is an important field of study which provides reasons behind the suggested recommendations. Explanations with recommender systems are useful for developers while debugging anomalies within the system and for…
We show that, from a topological point of view, considering the Borel and the Wadge hierarchies, 1-counter B\"uchi automata have the same accepting power than Turing machines equipped with a B\"uchi acceptance condition. In particular, for…
Multilingual language models achieve strong aggregate performance yet often behave unpredictably across languages, scripts, and cultures. We argue that mechanistic explanations for such models should satisfy a \emph{causal} standard: claims…
There has been a long-standing and at times fractious debate whether complex and large systems can be stable. In ecology, the so-called `diversity-stability debate' arose because mathematical analyses of ecosystem stability were either…
System requirements related to concepts like information flow, knowledge, and robustness cannot be judged in terms of individual system executions, but rather require an analysis of the relationship between multiple executions. Such…
Why are large, complex ecosystems stable? Both theory and simulations of current models predict the onset of instability with growing size and complexity, so for decades it has been conjectured that ecosystems must have some unidentified…
With the rapid growth of information, recommender systems have become integral for providing personalized suggestions and overcoming information overload. However, their practical deployment often encounters ``dirty'' data, where noise or…
Continuous phase estimation is known to be superior in accuracy as compared to static estimation. The estimation process is, however, desired to be made robust to uncertainties in the underlying parameters. Here, homodyne phase estimation…
Individuals use models to guide decisions, but many models are wrong. This paper studies which misspecified models are likely to persist when individuals also entertain alternative models. Consider an agent who uses her model to learn the…
In this work, it has been indicated that the key features requisite for preserving causality and stability of the popularly existing relativistic hydrodynamic theories, can be translated into each other. It has been shown here, that a…
In this paper, we present a novel framework for quantifying a lower bound on resilience in continuous-time (non)linear systems subject to external disturbances while ensuring satisfaction of signal temporal logic specifications. Unlike…
We investigate certain structural properties of random interdependent networks. We start by studying a property known as $r$-robustness, which is a strong indicator of the ability of a network to tolerate structural perturbations and…
Recent natural language processing (NLP) techniques have accomplished high performance on benchmark datasets, primarily due to the significant improvement in the performance of deep learning. The advances in the research community have led…
We continue here [She88] but we do not rely on it. The motivation was a conjecture of Galvin stating that 2^{omega} >= omega_2 + omega_2-> [omega_1]^{n}_{h(n)} is consistent for a suitable h: omega-> omega. In section 5 we disprove this and…
Despite their empirical success, neural networks remain vulnerable to small, adversarial perturbations. A longstanding hypothesis suggests that flat minima, regions of low curvature in the loss landscape, offer increased robustness. While…
We establish new results on the possible growth rates for the sequence (f_n) counting the number of orbits of a given oligomorphic group on unordered sets of size n. Macpherson showed that for primitive actions, the growth is at least…
We consider a random network of nonlinear maps exhibiting a wide range of local dynamics, with the links having normally distributed interaction strengths. The stability of such a system is examined in terms of the asymptotic fraction of…