Related papers: Zero-class admissibility of observation operators

The paper is devoted to the problem of global exact controllability for a wide class of neutral and mixed time-delay systems. We consider an equivalent operator model in Hilbert space and formulate steering conditions of controllable states…

The principle of relativity is extended to accommodate finite-mass observers with quantum properties by introducing two operational requirements: (i) equivalence of observers at the level of transition amplitudes, and (ii) the impossibility…

We consider the observability problem for non-autonomous evolution systems (i.e., the operators governing the system depend on time). We introduce an averaged Hautus condition and prove that for skew-adjoint operators it characterizes exact…

Optimized, necessary and sufficient conditions for the identification of the Schmidt number will be derived in terms of general Hermitian operators. These conditions apply to arbitrary mixed quantum states. The optimization procedure…

We consider the difference $f(-\Delta +V)-f(-\Delta)$ of functions of Schr\"odinger operators in $L^2(\mathbb R^d)$ and provide conditions under which this difference is trace class. We are particularly interested in non-smooth functions…

Class-agnostic object counting aims to count object instances of an arbitrary class at test time. It is challenging but also enables many potential applications. Current methods require human-annotated exemplars as inputs which are often…

Critical observability is a property of cyber-physical systems to detect whether the current state belongs to a set of critical states. In safety-critical applications, critical states model operations that may be unsafe or of a particular…

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…

This paper concerns open-world classification, where the classifier not only needs to classify test examples into seen classes that have appeared in training but also reject examples from unseen or novel classes that have not appeared in…

We introduce and tackle the problem of zero-shot object detection (ZSD), which aims to detect object classes which are not observed during training. We work with a challenging set of object classes, not restricting ourselves to similar…

In this paper we introduce two new generalized variational inequalities, and we give some existence results of the solutions for these variational inequalities involving operators belonging to a recently introduced class of operators. We…

We put into evidence graphs with adjacency operator whose singular subspace is prescribed by the kernel of an auxiliary operator. In particular, for a family of graphs called admissible, the singular continuous spectrum is absent and there…

We propose two interrelated advances in the theory of adjointable operators on Hilbert C*-modules. First, we give a set of equivalent, verifiable conditions characterizing positivity of general $n\times n$ block operator matrices acting on…

We prove the following characterization of the weak expectation property for operator systems in terms of Wittstock's matricial Riesz separation property: an operator system $S$ satisfies the weak expectation property if and only if…

For commuting linear operators $P_0,P_1,..., P_\ell$ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition $P=P_0P_1... P_\ell$ in terms of the component…

This paper is a continuation of our paper [Med. J. Math 19, Article number: 31 (2022)] in which we extended the notion of generalized Drazin-Riesz invertible operators to closed operators. We establish here, results relating the notion of…

The sensitivity of image classifiers to small perturbations in the input is often viewed as a defect of their construction. We demonstrate that this sensitivity is a fundamental property of classifiers. For any arbitrary classifier over the…

We study the necessary and sufficient conditions on Abelianizable first class constraints. The necessary condition is derived from topological considerations on the structure of gauge group. The sufficient condition is obtained by applying…

We consider a second order self-adjoint operator in a domain which can be bounded or unbounded. The boundary is partitioned into two parts with Dirichlet boundary condition on one of them, and Neumann condition on the other. We assume that…

We generalize our results of \cite{AP2} and \cite{AP3} to the case of maximal dissipative operators. We obtain sharp conditions on a function analytic in the upper half-plane to be operator Lipschitz. We also show that a H\"older function…