Nerode et al. [ 131 showed that a correct concurrent program can be viewed as a winning strategy in a suitably defined two player game played between the Programmer and the Computer in which the program specification is defined by the rules of the game together with the winning condition. This gives rise to the question as to whether there are useful algorithms to extract (provably) winning str...

Let T be a (possibly nonlinear) continuous operator on Hilbert space H. If, for some starting vector x , the orbit sequence {T k x, k = 0, 1, . . .} converges, then the limit z is a fixed point of T ; that is, T z = z. An operator N on a Hilbert space H is nonexpansive (ne) if, for each x and y in H, ‖Nx − Ny‖ ‖x − y‖. Even when N has fixed points the orbit sequence {Nk x} need not converge; co...

In this paper we discuss a relation between Learning Theory and Regularization of linear ill-posed inverse problems. It is well known that Tikhonov regularization can be profitably used in the context of supervised learning, where it usually goes under the name of regularized least-squares algorithm. Moreover the gradient descent algorithm was studied recently, which is an analog of Landweber r...

Vector valued data appearing in concrete applications often possess sparse expansions with respect to a preassigned frame for each vector component individually. Additionally, different components may also exhibit common sparsity patterns. Recently, there were introduced sparsity measures that take into account such joint sparsity patterns, promoting coupling of non-vanishing components. These ...

Quantities of interest appearing in concrete applications often possess sparse expansions with respect to a preassigned frame. Recently, there were introduced sparsity measures which are typically constructed on the basis of weighted l1 norms of frame coefficients. One can model the reconstruction of a sparse vector from noisy linear measurements as the minimization of the functional defined by...

A highly optimized simulated annealing (SA) algorithm is applied to reconstruct permittivity images of real two-phase gasoil flows through a cylindrical vessel using electrical capacitance tomography (ECT). ECT yields low-accuracy images but is robust, inexpensive and much faster than many other tomography processes. This non-intrusive method essentially measures nonconductive system distributi...

For a two-variable formula ψ(X,Y ) of Monadic Logic of Order (MLO) the Church Synthesis Problem concerns the existence and construction of an operator Y = F (X) such that ψ(X,F (X)) is universally valid over Nat . Büchi and Landweber proved that the Church synthesis problem is decidable; moreover, they showed that if there is an operator F that solves the Church Synthesis Problem, then it can a...

This paper considers an inverse initial value problem of diffusion equation with local and nonlocal operators. For this ill-posed problem, we give prove a result conditional stability. Meanwhile, Landweber iterative regularization method is used to overcome the ill-posedness, based on stability, convergence estimates Hölder type for are derived under a-priori a-posteriori choice rules regulariz...