Projecting social and discursive identities through code-switching on facebook: the case of Greek Cypriots

Two varieties of Greek are spoken on the island of Cyprus: the local dialect, namely the Greek-Cypriot Dialect (GCD), and Standard Modern Greek (SMG). English is also influential, as Cyprus was an English colony until 1960. The dialect is rarely employed for everyday written purposes; however, it is now evident in computer-mediated communication (CMC). As a contribution to the field of code-switching in writing, this study examines how Greek-Cypriot internet users employ GCD, SMG, and English in their Facebook interactions. In particular, we investigate how identities (discursive and social) are performed and indexed through the linguistic choices of Greek-Cypriot internet users. The findings indicate that switches to GCD add a humorous tone and express solidarity and informality. SMG is mostly used for ‘official’ statements, and it is preferred by mature internet users, while English is used with expressions of affect and evaluative comments.

Conditioning and preconditioning of the optimal state estimation problem

Optimal state estimation is a method that requires minimising a weighted, nonlinear, least-squares objective function in order to obtain the best estimate of the current state of a dynamical system. Often the minimisation is non-trivial due to the large scale of the problem, the relative sparsity of the observations and the nonlinearity of the objective function. To simplify the problem the solution is often found via a sequence of linearised objective functions. The condition number of the Hessian of the linearised problem is an important indicator of the convergence rate of the minimisation and the expected accuracy of the solution. In the standard formulation the convergence is slow, indicating an ill-conditioned objective function. A transformation to different variables is often used to ameliorate the conditioning of the Hessian by changing, or preconditioning, the Hessian. There is only sparse information in the literature for describing the causes of ill-conditioning of the optimal state estimation problem and explaining the effect of preconditioning on the condition number. This paper derives descriptive theoretical bounds on the condition number of both the unpreconditioned and preconditioned system in order to better understand the conditioning of the problem. We use these bounds to explain why the standard objective function is often ill-conditioned and why a standard preconditioning reduces the condition number. We also use the bounds on the preconditioned Hessian to understand the main factors that affect the conditioning of the system. We illustrate the results with simple numerical experiments.