We generalise some well-known graph parameters to operator systems by considering their underlying quantum channels. In particular, we introduce the quantum complexity as the dimension of the smallest co-domain Hilbert space a quantum channel requires to realise a given operator system as its non-commutative confusability graph. We describe quantum complexity as a generalised minimum semidefini...

We investigate the eigenvalues of the semi-circulant preconditioned matrix for the finite difference scheme corresponding to the second-order elliptic operator with the variable coefficients given by Lvu := −∆u + a(x, y)ux + b(x, y)uy + d(x, y)u, where a and b are continuously differentiable functions and d is a positive bounded function. The semi-circulant preconditioning operator Lcu is const...

The problems which are NP-complete in nature are always attracting the computer scientists to develop some heuristic algorithms, generating optimal solution in time-space efficient manner compared to the existing ones. Coloring of the vertices of a graph with minimum number of colours belongs to the same category, where the algorithm designers are trying to propose some new algorithms for bette...

We consider a Schrödinger operator HD A with a non-vanishing radial magnetic field B = dA and Dirichlet boundary conditions on the unit disk. We assume growth conditions on B near the boundary which guarantee in particular the compactness of the resolvent of this operator. Under some assumptions on an additional radial potential V the operator HD A − V has a discrete negative spectrum and we ob...

We address the problem of teleoperating a mobile robot using shared autonomy: an on-board controller performs obstacle avoidance while the operator uses the manipulandum of a haptic probe to designate the desired speed and rate of turn. Sensors on the robot are used to measure obstacle range information. We describe a strategy to convert such range information into forces, which are reflected t...

Operator-probability adaptation in a genetic-algorithm/ heuristic hybrid for minimum cost routing and wavelength allocation of multi-wavelength all-optical transport networks is described. The hybrid algorithm uses an object-oriented representation of networks, and incorporates four operators: path mutation, single-point crossover, reroute and shift-out. The adaptation algorithm is based on tha...

This paper sets out to study the spectral minimum for operator belonging to the family of random Schrödinger operators of the form Hλ,ω = −∆+Wper + λVω, where we suppose that Vω is of Anderson type and the single site is assumed to be with an indefinite sign. Under some assumptions we prove that there exists λ0 > 0 such that for any λ ∈ [0, λ0], the minimum of the spectrum of Hλ,ω is obtained b...

We construct entanglement witnesses using fundamental quantum operators of spin models which contain two-particle interactions and have a certain symmetry. By choosing the Hamiltonian as such an operator, our method can be used for detecting entanglement by energy measurement. We apply this method to the Heisenberg model in a cubic lattice with a magnetic field, the XY model and other familiar ...

Based on the graphic theory and improved genetic algorithm, an improved genetic algorithm to search the minimum spanning trees is given. The algorithm uses binary code to represent the problem of minimum spanning trees. It designs the corresponding fitness function, operator and few controlling strategies to improve its speed and evolutionary efficiency. Only one solution can be gotten with run...

We investigate minimum energy paths of the quasi-linear problem with the p-Laplacian operator and a double-well potential. We adapt the String method of E., Ren, and Vanden-Eijnden (J. Chem. Phys., vol. 126 2007) to locate saddle-type solutions. In one-dimension, the String method is shown to find a minimum energy path that can align along one-dimensional “ridges” of saddle-continua. We then ap...