The parameterized model-checking problem for a class of first-order sentences (queries) asks to decide whether a given sentence from the class holds true in a given relational structure (database); the parameter is the length of the sentence. In 1995 Vardi observed a polynomial time algorithm deciding the model-checking problem for queries with a bounded number of variables. We study its parame...

The nonlinear Schrödinger equation with a third-order dispersive term is considered. Infinite families of embedded solitons, parameterized by the propagation velocity, are found through a gauge transformation. By applying this transformation, an embedded soliton can acquire any velocity above a certain threshold value. It is also shown that these families of embedded solitons are linearly stabl...

We show that the model-checking problem for successorinvariant first-order logic is fixed-parameter tractable on graphs with excluded topological subgraphs when parameterised by both the size of the input formula and the size of the exluded topological subgraph. Furthermore, we show that model-checking for order-invariant first-order logic is tractable on coloured posets of bounded width, param...

We study the complexity of model checking formulas in first-order logic parameterized by the number of distinct variables in the formula. This problem, which is not known to be fixedparameter tractable, resisted to be properly classified in the context of parameterized complexity. We show that it is complete for a newly-defined complexity class that we propose as an analog of the classical clas...

In physical design and optimization for VLSI/ULSI, parameterized model order reduction can be used to handle large design objectives. In this paper we propose an efficient yet accurate parameterized model order reduction method EMPIRE for physical design with multiple parameters. It is the first practical algorithm using implicit moment matching to handle high order moments of very large number...