The paper deals with difference schemes for the heat-conduction equation with nonlocal boundary conditions containing two real parameters, α and γ. Such schemes have been investigated for some special parameter values, but the general case was not considered previously. The eigenvalue problem arises as a result of variable division and is solved here explicitly. The so-called reality domains we...

We study the problem k-Set Splitting in fixed parameter complexity. We show that the problem can be solved in time O∗(2.6494k), improving on the best currently known running time of O∗(8k). This is done by showing that a non-trivial instance must have a small minimal Set Cover, and using this to reduce the problem to a series of small instances of Max Sat. We also give a linear kernel containin...

This paper is dedicated to bounded error identification with complex valued non-linear models. Complex intervals are characterized by using polar forms and a new inclusion function is given for the addition of sectors. The latter is expressed as an optimization problem solved analytically. The new complex interval arithmetic is used with actual data and a complex valued non-linear model for the...

We present an algorithm that constructively produces a solution to the k-dominating set problem for planar graphs in time O(c √ n), where c = 36 √ 34. To obtain this result, we show that the treewidth of a planar graph with domination number γ(G) is O( √ γ(G)), and that such a tree decomposition can be found in O( √ γ(G)n) time. The same technique can be used to show that the k-face cover probl...

This article considers inverse problems of shape recovery from noisy boundary data, where the forward problem involves the inversion of elliptic PDEs. The piecewise constant solution, a scaling and translation of a characteristic function, is described in terms of a smoother level set function. A fast and simple dynamic regularization method has been recently proposed that has a robust stopping...

We consider stability analysis and state feedback synthesis for Linear Parameter Varying (LPV) systems. LPV systems are de"ned as linear systems whose dynamics depend on exogenous time-varying parameters. Stability analysis of LPV systems involves testing the stability of a family of possible parameter trajectories. Similarly, stabilization and optimal control of LPV systems involves constructi...

We resolve positively a long standing open question regarding the fixed-parameter tractability of the parameterized Directed Feedback Vertex Set problem. In particular, we propose an algorithm which solves this problem in O(8k! ∗ poly(n)).

In model identification, calibration or sensitivity analysis, the model-parameter values may be required to yield model-output values that satisfy specified constraints, for given initial conditions and forcing. Inequality constraints on scalar functions of the model outputs (henceforth called output bounds) confine the parameters to their feasible set. Output bounds are fundamental to regional...