The distribution of cycles in breakpoint graphs of signed permutations

Breakpoint graphs are ubiquitous structures in the field of genome rearrangements. Their cycle decomposition has proved useful in computing and bounding many measures of (dis)similarity between genomes, and studying the distribution of those cycles is therefore critical to gaining insight on the distributions of the genomic distances that rely on it. We extend here the work initiated by Doignon and Labarre, who enumerated unsigned permutations whose breakpoint graph contains $k$ cycles, to signed permutations, and prove explicit formulas for computing the expected value and the variance of the corresponding distributions, both in the unsigned case and in the signed case. We also compare these distributions to those of several well-studied distances, emphasising the cases where approximations obtained in this way stand out. Finally, we show how our results can be used to derive simpler proofs of other previously known results

Adaptive, locally-linear models of complex dynamics

The dynamics of complex systems generally include high-dimensional, non-stationary and non-linear behavior, all of which pose fundamental challenges to quantitative understanding. To address these difficulties we detail a new approach based on local linear models within windows determined adaptively from the data. While the dynamics within each window are simple, consisting of exponential decay, growth and oscillations, the collection of local parameters across all windows provides a principled characterization of the full time series. To explore the resulting model space, we develop a novel likelihood-based hierarchical clustering and we examine the eigenvalues of the linear dynamics. We demonstrate our analysis with the Lorenz system undergoing stable spiral dynamics and in the standard chaotic regime. Applied to the posture dynamics of the nematode $C. elegans$ our approach identifies fine-grained behavioral states and model dynamics which fluctuate close to an instability boundary, and we detail a bifurcation in a transition from forward to backward crawling. Finally, we analyze whole-brain imaging in $C. elegans$ and show that the stability of global brain states changes with oxygen concentration.Comment: 25 pages, 16 figure

Relative Auditory Distance Discrimination With Virtual Nearby Sound Sources

In this paper a psychophysical experiment targeted at exploring relative distance discrimination thresholds with binaurally rendered virtual sound sources in the near field is described. Pairs of virtual sources are spatialized around 6 different spatial locations (2 directions 7 3 reference distances) through a set of generic far-field Head-Related Transfer Functions (HRTFs) coupled with a near-field correction model proposed in the literature, known as DVF (Distance Variation Function). Individual discrimination thresholds for each spatial location and for each of the two orders of presentation of stimuli (approaching or receding) are calculated on 20 subjects through an adaptive procedure. Results show that thresholds are higher than those reported in the literature for real sound sources, and that approaching and receding stimuli behave differently. In particular, when the virtual source is close (< 25 cm) thresholds for the approaching condition are significantly lower compared to thresholds for the receding condition, while the opposite behaviour appears for greater distances (~ 1 m). We hypothesize such an asymmetric bias to be due to variations in the absolute stimulus level

The Extended Edit Distance Metric

Similarity search is an important problem in information retrieval. This similarity is based on a distance. Symbolic representation of time series has attracted many researchers recently, since it reduces the dimensionality of these high dimensional data objects. We propose a new distance metric that is applied to symbolic data objects and we test it on time series data bases in a classification task. We compare it to other distances that are well known in the literature for symbolic data objects. We also prove, mathematically, that our distance is metric.Comment: Technical repor