Invariance of the Null Distribution of the Multiple Coherence

In this paper we investigate the invariance of the null distribution of the multiple coherence (MC) to the statistics of the examined signals. We show that when the MC is computed between a group of signals x_i[n], i=1,...,K and a signal y[n], the null distribution of the MC is independent of the distribution of x_i[n] and y[n] if at a given frequency the joint distribution of the spectra of the segments of x_i[n] and y[n] is rotationally symmetric with respect to the rotation of the spectra of the segments of x_i[n] or y[n]. The significance of this result lies in the improvement of the multiple coherence analysis. Hitherto, the null distribution of the MC was known only for signals with the multivariate Gaussian distribution; therefore, an MC estimate could be evaluated for its statistical significance only in this limited case. With the results presented in this paper, it will be possible to evaluate the statistical significance of MC estimates for much wider class of signals

Simple singularities of multigerms of curves

We classify stably simple reducible curve singularities in complex spaces of any dimension. This extends the same classification of of irreducible curve singularities obtained by V.I.Arnold. The proof is essentially based on the method of complete transversals by J.W.Bruce et al.Comment: 18 page

Broadband Spectrum Survey Measurements for Cognitive Radio Applications

It is well known that the existing spectrum licensing system results in a gross under-utilization of the frequency spectrum. Spectrum background measurements – spectrum surveys – provide useful data for spectrum regulation, planning or finding frequency niches for spectrum sharing. Dynamic spectrum sharing as a main goal of cognitive radio (CR) is the modern option on how to optimize usage of the frequency spectrum. A spectrum survey measurement system is introduced with results obtained from a variety of markedly different scenarios allowing us, unlike other studies, to focus on wideband and fast spectrum scans. The sensitivity of the receiver is no worse than -113 dBm in the whole band. The utilization of the frequency spectrum is analyzed to prove its under-utilization and to show spectrum sharing opportunities. This was shown to be true in the frequency band higher than 2.5 GHz. A comparison with other spectrum survey campaigns is provided

The Effect of Mutators on Adaptability in Time-Varying Fitness Landscapes

This Letter studies the quasispecies dynamics of a population capable of genetic repair evolving on a time-dependent fitness landscape. We develop a model that considers an asexual population of single-stranded, conservatively replicating genomes, whose only source of genetic variation is due to copying errors during replication. We consider a time-dependent, single-fitness-peak landscape where the master sequence changes by a single point mutation every time $\tau$. We are able to analytically solve for the evolutionary dynamics of the population in the point-mutation limit. In particular, our model provides an analytical expression for the fraction of mutators in the dynamic fitness landscape that agrees well with results from stochastic simulations.Comment: 4 pages, 3 figure