Floatation Analysis. Part I

Real Analysis: Part I

SPATIAL DATA ANALYSIS Part I

In the Bodmin Tors example above, notice from Figure 14a (p.20) that the clustering structure is actually quite different from that of the Redwood Seedling example in 12a (p.12). Rather than small isolate clumps, there appear to be two large groups of points in the northwest and southwest, separated by a large empty region. Moreover, the points within each group are actually quite uniform with ...

Delta-Complete Reachability Analysis (Part I)

We give a new framework for safety verification of nonlinear hybrid systems, based on deltadecidability of first-order logic formulas over the real numbers. We use expressive logic formulas (which can contain nonlinear ODEs with no analytic solutions) to encode bounded model checking and invariant-based reasoning. Based on the encoding, we solve bounded reachability and invariant validation pro...

Forward Analysis for WSTS, Part I: Completions

Well-structured transition systems provide the right foundation to compute a finite basis of the set of predecessors of the upward closure of a state. The dual problem, to compute a finite representation of the set of successors of the downward closure of a state, is harder: Until now, the theoretical framework for manipulating downward-closed sets was missing. We answer this problem, using ins...

Multi-Resolution Fourier Analysis Part I: Fundamentals

In the first paper of this series, we propose a multi-resolution theory of Fourier spectral estimates of finite duration signals. It is shown that multi-resolution capability, achieved without further observation, is obtained by constructing multi-resolution signals from the only observed finite duration signal. Achieved resolutions meet bounds of the uncertainty principle (Heisenberg inequalit...