In electrical impedance tomography, we aim to solve the conductivity within a target body through measurements made on surface of target. This inverse problem is severely ill-posed, especially in real applications with only partial boundary data available. Thus regularization has be introduced. Conventionally promoting smooth features used, however, Mumford--Shah regularizer familiar for image ...

We consider the discrete-time voter model on complete bipartite graphs and study quasi-stationary distribution (QSD) for as size of one partitions tends to infinity while other partition remains fixed. show that QSDs converge weakly a nontrivial limit which features consensus with exception random number dissenting vertices in large partition. Moreover, we explicitly calculate law dissenters it...

We prove a complexity dichotomy theorem for the eight-vertex model. For every setting of the parameters of the model, we prove that computing the partition function is either solvable in polynomial time or #P-hard. The dichotomy criterion is explicit. For tractability, we find some new classes of problems computable in polynomial time. For #P-hardness, we employ Möbius transformations to prove ...