Validation of a new approach for distinguishing anesthetized from awake state in patients using directed transfer function applied to raw EEG

We test whether a measure based on the directed transfer function (DTF) calculated from short segments of electroencephalography (EEG) time-series can be used to monitor the state of the patients also during sevoflurane anesthesia as it can for patients undergoing propofol anesthesia. We collected and analyzed 25-channel EEG from 7 patients (3 females, ages 41–56 years) undergoing surgical anesthesia with sevoflurane, and quantified the sensor space directed connectivity for every 1-s epoch using DTF. The resulting connectivity parameters were compared to corresponding parameters from our previous study (n = 8, patients anesthetized with propofol and remifentanil, but otherwise using a similar protocol). Statistical comparisons between and within studies were done using permutation statistics, a data driven algorithm based on the DTF-parameters was employed to classify the epochs as coming from awake or anesthetized state. According to results of the permutation tests, DTF-parameter topographies were significantly different between the awake and anesthesia state at the group level. However, the topographies were not significantly different when comparing results computed from sevoflurane and propofol data, neither in the awake nor in anesthetized state. Optimizing the algorithm for simultaneously having high sensitivity and specificity in classification yielded an accuracy of 95.1% (SE = 0.96%), with sensitivity of 98.4% (SE = 0.80%) and specificity of 94.8% (SE = 0.10%). These findings indicate that the DTF changes in a similar manner when humans undergo general anesthesia caused by two distinct anesthetic agents with different molecular mechanisms of action.

The Deletion-Insertion model applied to the genome rearrangement problem

Permutations are frequently used in solving the genome rearrangement problem, whose goal is finding the shortest sequence of mutations transforming one genome into another. We introduce the Deletion-Insertion model (DI) to model small-scale mutations in species with linear chromosomes, such as humans. Applying one restriction to this model, we obtain the transposition model for genome rearrangement, which was shown to be NP-hard in [4]. We use combinatorial reasoning and permutation statistics to develop a polynomial-time algorithm to approximate the minimum number of transpositions required in the transposition model and to analyze the sharpness of several bounds on transpositions between genomes.

Hopping from Chebyshev Polynomials to Permutation Statistics

We prove various formulas which express exponential generating functions counting permutations by the peak number, valley number, double ascent number, and double descent number statistics in terms of the exponential generating function for Chebyshev polynomials, as well as cyclic analogues of these formulas for derangements. We give several applications of these results, including formulas for the (-1)-evaluation of some of these distributions. Our proofs are combinatorial and involve the use of monomino-domino tilings, the modified Foata-Strehl action (a.k.a. valley-hopping), and a cyclic analogue of this action due to Sun and Wang.

Shuffle-Compatible Permutation Statistics II: The Exterior Peak Set

This paper is a continuation of the work "Shuffle-compatible permutation statistics" by Gessel and Zhuang (but can be read independently from the latter). We study the shuffle-compatibility of permutation statistics — a concept introduced by Gessel and Zhuang, although various instances of it have appeared throughout the literature before. We prove that (as Gessel and Zhuang have conjectured) the exterior peak set statistic (Epk) is shuffle-compatible. We furthermore introduce the concept of an "LR-shuffle-compatible" statistic, which is stronger than shuffle-compatibility. We prove that Epk and a few other statistics are LR-shuffle-compatible. Furthermore, we connect these concepts with the quasisymmetric functions, in particular the dendriform structure on them.