A random quantum circuit is a minimally structured model to study entanglement dynamics of many-body systems. We consider one-dimensional with noisy Haar-random unitary gates using density matrix operator and tensor contraction methods. It shown that the evolution circuits properly characterized by logarithmic negativity. By performing exact numerical calculations, we find that, as physical err...

Certain operator algebras A on a Hilbert space have the property that every densely defined linear transformation commuting with A is closable. Such algebras are said to have the closability property. They are important in the study of the transitive algebra problem. More precisely, if A is a two-transitive algebra with the closability property, then A is dense in the algebra of all bounded ope...

The traditional Kalman filter can be viewed as a recursive stochastic algorithm that approximates an unknown function via a linear combination of prespecified basis functions given a sequence of noisy samples. In this paper, we generalize the algorithm to one that approximates the fixed point of an operator that is known to be a Euclidean norm contraction. Instead of noisy samples of the desire...

We devise and analyze vertex-based, Péclet-robust, lowest-order schemes for advection-diffusion equations that support polyhedral meshes. The schemes are formulated using Compatible Discrete Operators (CDO), namely primal and dual discrete differential operators, a discrete contraction operator for advection, and a discrete Hodge operator for diffusion. Moreover, discrete boundary operators are...

Let ε > 0. We prove that there exists an operator Tε : `2 → `2such that for any polynomial P we have ‖P (Tε)‖ ≤ (1 +ε)‖P‖∞, but Tε isnot similar to a contraction, i.e. there does not exist an invertible operatorS : `2 → `2 such that‖S−1TεS‖ ≤ 1. This answers negatively a question at-tributed to Halmos after his well-known 1970 paper (“Ten problems in Hilbertspace”). ...

and to be power bounded (notation: T ∈ (PW)) if (1) holds for every polynomial of the special form p(ζ) = ζ where n is a positive integer. If T ∈ (PB) [resp., T ∈ (PW)], then there is a smallest number M ≥ 1 which satisfies (1) [resp., (1) restricted]. This number will be called the polynomial bound [resp., the power bound] of T and will be denoted by Mpb(T ) [resp., Mpw(T )]. (If T / ∈ (PB) [r...

Discrete exterior calculus (DEC) offers a coordinate-free discretization of exterior calculus especially suited for computations on curved spaces. We present an extended version of DEC on surface meshes formed by general polygons that bypasses the construction of any dual mesh and the need for combinatorial subdivisions. At its core, our approach introduces a polygonal wedge product that is com...

We present a framework for investigating merging operators for belief sets. This framework is a generalisation of our earlier work concerning consistency-based belief revision and contraction. Two distinct merging operators are identified: in the first approach, belief sources are consistently combined so that the result of merging K1 and K2 is a maximal consistent (if possible) set of formulas...

Ontology evolution is an important problem in the Semantic Web research. Recently, Alchourrón, Gärdenfors and Markinson’s (AGM) theory on belief change has been applied to deal with this problem. However, most of current work only focuses on the feasibility of the application of AGM postulates on contraction to description logics (DLs), a family of ontology languages. So the explicit constructi...

Judicious use of interval arithmetic, combined with careful pen and paper estimates, leads to effective strategies for computer assisted analysis of nonlinear operator equations. The method of radii polynomials is an efficient tool for bounding the smallest and largest neighborhoods on which a Newton-like operator associated with a nonlinear equation is a contraction mapping. The method has bee...