We present novel Markov-type and Nikolskii-type inequalities for multivariate polynomials associated with arbitrary downward closed multi-index sets in any dimension. Moreover, we show how the constant of these inequalities changes, when the polynomial is expanded in series of tensorized Legendre or Chebyshev or Gegenbauer or Jacobi orthogonal polynomials indexed by a downward closed multi-inde...

Various problems in AI and multiagent systems can be tackled by finding the “most desirable” elements of a set given some binary relation. Examples can be found in areas as diverse as voting theory, game theory, and argumentation theory. Some particularly attractive solution sets are defined in terms of a covering relation—a transitive subrelation of the original relation. We consider three dif...

The paper considers several issues related to efficient use of tree automata in formal verification. First, a new efficient algorithm for inclusion checking on non-deterministic tree automata is proposed. The algorithm traverses the automaton downward, utilising antichains and simulations to optimise its run. Results of a set of experiments are provided, showing that such an approach often very...

Twelve consecutive cases are reviewed of unilateral hypotropia due to various causes. In most of them the presenting complaint was of ipsilateral blepharoptosis. Some patients had undergone previous ineffective surgery. The surgical techniques employed and the results obtained are discussed, with emphasis on the necessity to test for inferior rectus restriction. Some interesting sensory results...

In this paper, we study the downward routing for network control/actuation in large-scale and heterogeneous wireless sensor networks (WSNs) and Internet of Things (IoT). We propose the Opportunistic Source Routing (OSR), a scalable and reliable downward routing protocol for WSNs/IoT. OSR introduces opportunistic routing into traditional source routing based on the parent set of a node’s upward ...

Data mapping is a procedure for transforming seismic or acoustic data collected with one set of source/receiver locations and wavespeed model, to data equivalent to that collected in a diierent source/receiver connguration and wavespeed model. A major application of this general process is downward continuation of the waveeeld, or wave-equation datuming. Unlike many previous implementations of ...

We study several geometric set cover and set packing problems involving configurations of points and geometric objects in Euclidean space. We show that it is APX-hard to compute a minimum cover of a set of points in the plane by a family of axis-aligned fat rectangles, even when each rectangle is an ǫ-perturbed copy of a single unit square. We extend this result to several other classes of obje...