Related papers: Reciprocal relationship between detectability and …
When employing non-linear methods to characterise complex systems, it is important to determine to what extent they are capturing genuine non-linear phenomena that could not be assessed by simpler spectral methods. Specifically, we are…
The existence of observables that are incompatible or not jointly measurable is a characteristic feature of quantum mechanics, which lies at the root of a number of nonclassical phenomena, such as uncertainty relations, wave--particle dual…
We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error…
The existence of incompatibility is one of the most fundamental features of quantum theory, and can be found at the core of many of the theory's distinguishing features, such as Bell inequality violations and the no-broadcasting theorem. A…
A fundamental task in statistical learning is quantifying the joint dependence or association between two continuous random variables. We introduce a novel, fully non-parametric measure that assesses the degree of association between…
Selection of the preferred classical set of states in the process of decoherence -- so important for cosmological considerations -- is discussed with an emphasis on the role of information loss and entropy. {\it Persistence of correlations}…
A common assumption in causal inference from observational data is that there is no hidden confounding. Yet it is, in general, impossible to verify this assumption from a single dataset. Under the assumption of independent causal mechanisms…
This paper continues the study of local detectability and observability requirements on components of distributed observers networks to ensure detectability properties of the network. First, we present a sketch of an elementary proof of the…
When studying non-Hermitian electronic systems, an obvious question is how various non-Hermitian effects affect measurable quantities like the conductance. Here, we show that uniformly dissipative circuits can exhibit nonreciprocal…
This paper introduce the notion of output contraction that expands the contraction notion to the time-varying nonlinear systems with output. It pertains to the systems' property that any pair of outputs from the system converge to each…
Under the introduction of any interface in its trajectory, an optical beam experiences polarization-dependent deflections in the longitudinal and transverse directions with respect to the plane of incidence. The physics of such optical beam…
Non-commutative versions of Arveson's curvature invariant and Euler characteristic for a commuting $n$-tuple of operators are introduced. The non-commutative curvature invariant is sensitive enough to determine if an $n$-tuple is free. In…
A high-gain extended observer is designed for a class of nonlinear uncertain systems. This observer has the ability of estimating system uncertainty, and it can be used to estimate the derivatives of signal up to order n. The controller…
In this work, we establish a connection between nonlinear electronic spectroscopy and the protocol for the non-disturbance condition, the non-fullfilment of which is a witness of nonclassicality and can be related to the presence of…
The universality of quantum theory has been questioned ever since it was proposed. Key to this long-unsolved question is to test whether a given physical system has non-classical features. Here we connect recently proposed witnesses of…
We derive new Heisenberg-type uncertainty relations for both joint measurability and the error-disturbance tradeoff for arbitrary observables of finite-dimensional systems. The relations are formulated in terms of a directly operational…
For arbitrary linear time-invariant systems, the existence of a strong functional observer is investigated. Such observer determines, from the available measurement on the plant, an estimate of a function of the state and the input. This…
This work develops a new direct adaptive control framework that extends the certainty equivalence principle to general nonlinear systems with unmatched model uncertainties. The approach adjusts the rate of adaptation online to eliminate the…
The predictability of a sequence is defined as the asymptotic performance of the best performing predictor in a given class. The value of the predictability of a sequence will in general depend on the choice of this predictor class. The…
Nonuniformity is a central concept in computational complexity with powerful connections to circuit complexity and randomness. Nonuniform reductions have been used to study the isomorphism conjecture for NP and completeness for larger…