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Adaptive radar systems will be required to operate in different frequency bands with spectrum requirements that will likely change both in time and with geographic region. A new algorithm is presented that allows direct optimisation of an amplifier's load reflection coefficient to find a Pareto optimum between the power-added efficiency (PAE) and adjacentchannel power ratio. Comparisons of simulation and measurement results are presented. The new algorithm's results compare well with traditionally acquired data and show consistency between the optimum values for PAE that are obtained from different starting points. Measurement comparison is performed with the previous optimisation algorithm reported by the authors, and results show that up to a 50% reduction in the number of measured experimental queries can be obtained. This translates into a significant time savings in reconfiguring a radar transmitter power amplifier.

We introduce weighted versions of the classicalČech and Vietoris-Rips complexes. We show that a version of the Vietoris-Rips Lemma holds for these weighted complexes and that they enjoy appropriate stability properties. We also give some preliminary applications of these weighted complexes.2010 Mathematics Subject Classification. 55N35 (primary), 55U99 68U10 (secondary).

Dream reports collected after rapid eye movement sleep (REM) awakenings are, on average, longer, more vivid, bizarre, emotional and story-like compared to those collected after non-REM. However, a comparison of the word-to-word structural organization of dream reports is lacking, and traditional measures that distinguish REM and non-REM dreaming may be confounded by report length. This problem is amenable to the analysis of dream reports as non-semantic directed word graphs, which provide a structural assessment of oral reports, while controlling for individual differences in verbosity. Against this background, the present study had two main aims: Firstly, to investigate differences in graph structure between REM and non-REM dream reports, and secondly, to evaluate how non-semantic directed word graph analysis compares to the widely used measure of report length in dream analysis. To do this, we analyzed a set of 133 dream reports obtained from 20 participants in controlled laboratory awakenings from REM and N2 sleep. We found that: (1) graphs from REM sleep possess a larger connectedness compared to those from N2; (2) measures of graph structure can predict ratings of dream complexity, where increases in connectedness and decreases in randomness are observed in relation to increasing dream report complexity; and (3) measures of the Largest Connected Component of a graph can improve a model containing report length in predicting sleep stage and dream report complexity. These results indicate that dream reports sampled after REM awakening have on average a larger connectedness compared to those sampled after N2 (i.e. words recur with a longer range), a difference which appears to be related to underlying differences in dream complexity. Altogether, graph analysis represents a promising method for dream research, due to its automated nature and potential to complement report length in dream analysis.

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