Meanders and the Temperley-Lieb algebra

The statistics of meanders is studied in connection with the Temperley-Lieb algebra. Each (multi-component) meander corresponds to a pair of reduced elements of the algebra. The assignment of a weight $q$ per connected component of meander translates into a bilinear form on the algebra, with a Gram matrix encoding the fine structure of meander numbers. Here, we calculate the associated Gram determinant as a function of $q$, and make use of the orthogonalization process to derive alternative expressions for meander numbers as sums over correlated random walks.Comment: 85p, uuencoded, uses harvmac (l mode) and epsf, 88 figure

Clinical cardiac electrophysiologic evaluation of the positive inotropic agent, DPI 201-106

DPI 201-106 is a new positive inotropic agent. The cardiac electrophysiology of 16 patients was studied before and during DPI 201-106 administration (loading dose of intravenous DPI 201-106, 1·8 mg kg−1 h−1 administered over 10 min, followed by a maintenance dose of 0·2 mg kg−1 h−1). DPI 201-106 had no effect on the sinus node. The AH interval during fixed-rate atrial pacing became prolonged during DPI 201-106 infusion. There was a significant prolongation of the QT interval [QT (corrected), 417 ± 22 to 502 ± 35 ms, P<0·05; QT (atrial pacing at 600 ms), 374 ±17 to 419 ± 23 ms, P<0·05; QT (ventricular pacing at 600 ms), 409 ± 37 to 449 ± 30 ms, P<0·05]. The ventricular effective refractory period significantly prolonged during DPI 201-106 administration (242 ± 21 to 287 ± 56 ms, P < 0·05), but the supernormal-period duration decreased. The atrial effective refractory period was shortened in four patients and prolonged in one (261 ± 67 to 240 ± 53 ms, NS). The corrected atrial repolarization time (PTac) shortened significantly during DPI 210-106 infusion (479 ± 26 to 445 ± 22 ms at 20 min of the maintenance dose, P<0·05). Atrial fibrillation was initiated in five patients during DPI infusion, but no ventricular arrhythmia was provoked. These findings suggest that DPI 201-106 has novel differential electrophysiological effects on atria and ventricle

Regional differences in mitochondrial DNA methylation in human post-mortem brain tissue

Background: DNA methylation is an important epigenetic mechanism involved in gene regulation, with alterations in DNA methylation in the nuclear genome being linked to numerous complex diseases. Mitochondrial DNA methylation is a phenomenon that is receiving ever-increasing interest, particularly in diseases characterized by mitochondrial dysfunction; however, most studies have been limited to the investigation of specific target regions. Analyses spanning the entire mitochondrial genome have been limited, potentially due to the amount of input DNA required. Further, mitochondrial genetic studies have been previously confounded by nuclear-mitochondrial pseudogenes. Methylated DNA Immunoprecipitation Sequencing is a technique widely used to profile DNA methylation across the nuclear genome; however, reads mapped to mitochondrial DNA are often discarded. Here, we have developed an approach to control for nuclear-mitochondrial pseudogenes within Methylated DNA Immunoprecipitation Sequencing data. We highlight the utility of this approach in identifying differences in mitochondrial DNA methylation across regions of the human brain and pre-mortem blood. Results: We were able to correlate mitochondrial DNA methylation patterns between the cortex, cerebellum and blood. We identified 74 nominally significant differentially methylated regions (p < 0.05) in the mitochondrial genome, between anatomically separate cortical regions and the cerebellum in matched samples (N = 3 matched donors). Further analysis identified eight significant differentially methylated regions between the total cortex and cerebellum after correcting for multiple testing. Using unsupervised hierarchical clustering analysis of the mitochondrial DNA methylome, we were able to identify tissue-specific patterns of mitochondrial DNA methylation between blood, cerebellum and cortex. Conclusions: Our study represents a comprehensive analysis of the mitochondrial methylome using pre-existing Methylated DNA Immunoprecipitation Sequencing data to identify brain region-specific patterns of mitochondrial DNA methylation

Statistical bias in isotope ratios

Dr. Coath is supported in this work by STFC grant ref. ST/F002734/1.This paper presents the mathematics of the systematic bias in the expected value of the ratio of two noise- corrected Poisson-distributed variables, such as ion counting measurements. Such bias can lead to the reporting of incorrect ratios and, in some cases, systematic correlations with other measurements which can impact the scientific interpretation. We describe a novel method of treating such measurements which results in a negligible, exponentially small bias. We also re-examine the conventional approach deriving an exact expression for the bias including the noise correction explicitly.PostprintPeer reviewe

Classification of one-dimensional quasilattices into mutual local-derivability classes

One-dimensional quasilattices are classified into mutual local-derivability (MLD) classes on the basis of geometrical and number-theoretical considerations. Most quasilattices are ternary, and there exist an infinite number of MLD classes. Every MLD class has a finite number of quasilattices with inflation symmetries. We can choose one of them as the representative of the MLD class, and other members are given as decorations of the representative. Several MLD classes of particular importance are listed. The symmetry-preserving decorations rules are investigated extensively.Comment: 42 pages, latex, 5 eps figures, Published in JPS

A transfer matrix approach to the enumeration of plane meanders

A closed plane meander of order $n$ is a closed self-avoiding curve intersecting an infinite line $2n$ times. Meanders are considered distinct up to any smooth deformation leaving the line fixed. We have developed an improved algorithm, based on transfer matrix methods, for the enumeration of plane meanders. While the algorithm has exponential complexity, its rate of growth is much smaller than that of previous algorithms. The algorithm is easily modified to enumerate various systems of closed meanders, semi-meanders, open meanders and many other geometries.Comment: 13 pages, 9 eps figures, to appear in J. Phys.