From conformal embeddings to quantum symmetries: an exceptional SU(4) example

We briefly discuss several algebraic tools that are used to describe the quantum symmetries of Boundary Conformal Field Theories on a torus. The starting point is a fusion category, together with an action on another category described by a quantum graph. For known examples, the corresponding modular invariant partition function, which is sometimes associated with a conformal embedding, provides enough information to recover the whole structure. We illustrate these notions with the example of the conformal embedding of SU(4) at level 4 into Spin(15) at level 1, leading to the exceptional quantum graph E4(SU(4)).Comment: 22 pages, 3 color figures. Version 2: We changed the color of figures (ps files) in such a way that they are still understood when converted to gray levels. Version 3: Several references have been adde

From modular invariants to graphs: the modular splitting method

We start with a given modular invariant M of a two dimensional su(n)_k conformal field theory (CFT) and present a general method for solving the Ocneanu modular splitting equation and then determine, in a step-by-step explicit construction, 1) the generalized partition functions corresponding to the introduction of boundary conditions and defect lines; 2) the quantum symmetries of the higher ADE graph G associated to the initial modular invariant M. Notice that one does not suppose here that the graph G is already known, since it appears as a by-product of the calculations. We analyze several su(3)_k exceptional cases at levels 5 and 9.Comment: 28 pages, 7 figures. Version 2: updated references. Typos corrected. su(2) example has been removed to shorten the paper. Dual annular matrices for the rejected exceptional su(3) diagram are determine

Orders and dimensions for sl(2) or sl(3) module categories and Boundary Conformal Field Theories on a torus

After giving a short description, in terms of action of categories, of some of the structures associated with sl(2) and sl(3) boundary conformal field theories on a torus, we provide tables of dimensions describing the semisimple and co-semisimple blocks of the corresponding weak bialgebras (quantum groupoids), tables of quantum dimensions and orders, and tables describing induction - restriction. For reasons of size, the sl(3) tables of induction are only given for theories with self-fusion (existence of a monoidal structure).Comment: 25 pages, 5 tables, 9 figures. Version 2: updated references. Typos corrected. Several proofs added. Examples of ADE and generalized ADE trigonometric identities have been removed to shorten the pape

Root exudation of phloridzin by apple seedlings (Malus x domestica Borkh.) with symptoms of apple replant disease

This study investigates the occurrence of the flavonoid phloridzin (phloretin-2'-O-β-D-glucoside) in root exudates of apple seedlings showing growth reduction related to apple replant disease (ARD). The disease is most likely caused by a complex of soil-borne fungi and bacteria, but the etiology remains to be elucidated. Information on specific exudation processes in the rhizosphere of apple seedlings could contribute to our understanding of the conditions triggering ARD development.To procure ARD symptoms, apple seedlings (Malus x domestica Borkh.) were grown in ARD-conductive soil. Root exudates were collected by submerging the roots in a solution of 0.05 mM CaCl2 for a period of 4 h. The fraction of phenolic root exudates was analyzed using HPLC/DAD (high performance liquid chromatography/diode array detector).Results suggest that (i) phloridzin is a constant root exudate of apple seedlings. It was the most abundant phenol in the collected exudates from replant-diseased as well as healthy seedlings. (ii) Phloridzin exudation, related to root dry matter, was the most intensive at the onset of ARD symptom development and lower during the period when symptoms were most severe or outgrown. (iii) In comparison to healthy seedlings, the phloridzin exudation of apple replantdiseased seedlings was significantly higher only at the onset of ARD symptom development, suggesting a response of the plants to infection.The finding of phloridzin in the root exudates of Malus x domestica Borkh. might have consequences for research on the etiology of ARD. Specialized pathogenic microorganisms could be attracted by this distinct compound. Since it is very characteristic of apple plants, phloridzin might be the compound that ARD-causing microorganisms utilize to recognize their host. For practical applications, phloridzin root exudation could therefore be a parameter in evaluating ARD-susceptibility of different rootstocks

Parallel Longest Common SubSequence Analysis In Chapel

One of the most critical problems in the field of string algorithms is the longest common subsequence problem (LCS). The problem is NP-hard for an arbitrary number of strings but can be solved in polynomial time for a fixed number of strings. In this paper, we select a typical parallel LCS algorithm and integrate it into our large-scale string analysis algorithm library to support different types of large string analysis. Specifically, we take advantage of the high-level parallel language, Chapel, to integrate Lu and Liu's parallel LCS algorithm into Arkouda, an open-source framework. Through Arkouda, data scientists can easily handle large string analytics on the back-end high-performance computing resources from the front-end Python interface. The Chapel-enabled parallel LCS algorithm can identify the longest common subsequences of two strings, and experimental results are given to show how the number of parallel resources and the length of input strings can affect the algorithm's performance.Comment: The 27th Annual IEEE High Performance Extreme Computing Conference (HPEC), Virtual, September 25-29, 202

Design and characterization of all-cryogenic low phase-noise sapphire K-band oscillator for sattelite communication

An all-cryogenic oscillator consisting of a frequency-tunable sapphire resonator, a high-temperature superconducting filter and a pseudomorphic high electron-mobility transistor amplifier was designed for the K-band frequency range and investigated. Due to the high quality factor of the resonator above 1000 000 and the low amplifier phase noise of approximately -133 dBc/Hz at a frequency offset of 1kHz from the carrier, we have achieved oscillator phase-noise values superior to quartz-stabilized oscillators at the same carrier frequency for offset frequencies higher than 100 Hz. In addition to, low phase noise, our prototype oscillator possesses mechanical and electrical frequency tunability. We have implemented a two-step electrical tuning arrangement consisting of a varactor phase shifter integrated within the amplifier circuit (fine tuning by 5'kHz) and a dielectric plunger moved by a piezomechanical transducer inside the resonator housing (course tuning by 50 kHz). This tuning range is sufficient for phase locking and for electronic compensation of temperature drifts occurring during operation of the device employing a miniaturized closed-cycle Stirling-type cryocooler

AMST: Alignment to Median Smoothed Template for Focused Ion Beam Scanning Electron Microscopy Image Stacks

Alignment of stacks of serial images generated by focused ion Beam Scanning electron Microscopy (FIB-SEM) is generally performed using translations only, either through slice-by-slice alignments with SIFT or alignment by template matching. However, limitations of these methods are two-fold: the introduction of a bias along the dataset in the z-direction which seriously alters the morphology of observed organelles and a missing compensation for pixel size variations inherent to the image acquisition itself. These pixel size variations result in local misalignments and jumps of a few nanometers in the image data that can compromise downstream image analysis. We introduce a novel approach which enables affine transformations to overcome local misalignments while avoiding the danger of introducing a scaling, rotation or shearing trend along the dataset. Our method first computes a template dataset with an alignment method restricted to translations only. This pre-aligned dataset is then smoothed selectively along the z-axis with a median filter, creating a template to which the raw data is aligned using affine transformations. Our method was applied to FIB-SEM datasets and showed clear improvement of the alignment along the z-axis resulting in a significantly more accurate automatic boundary segmentation using a convolutional neural network

Walking speed and spatiotemporal step mean measures are reliable during feedback-controlled treadmill walking; however, spatiotemporal step variability is not reliable

The purpose of the study was to compare the effects of a feedback-controlled treadmill (FeedbackTM) to a traditional fixed-speed treadmill (FixedTM) on spatiotemporal gait means, variability, and dynamics. The study also examined inter-session reliability when using the FeedbackTM. Ten young adults walked on the FeedbackTM for a 5-minute familiarization followed by a 16-minute experimental trial. They returned within one week and completed a 5-minute familiarization followed by a 16-minute experimental trial each for FeedbackTM and FixedTM conditions. Mean walking speed and step time, length, width, and speed means and coefficient of variation were calculated from all experimental conditions. Step time, length, width, and speed gait dynamics were analyzed using detrended fluctuation analysis. Mean differences between experimental trials were determined using ANOVAs and reliability between FeedbackTM sessions was determined by intraclass correlation coefficient. No difference was found in mean walking speed nor spatiotemporal variables, with the exception of step width, between the experimental trials. All mean spatiotemporal variables demonstrated good to excellent reliability between sessions, while coefficient of variation was not reliable. Gait dynamics of step time, length, width, and speed were significantly more persistent during the FeedbackTM condition compared to FixedTM, especially step speed. However, gait dynamics demonstrated fair to poor reliability between FeedbackTM sessions. When walking on the FeedbackTM, users maintain a consistent set point, yet the gait dynamics around the mean are different when compared to walking on a FixedTM. In addition, spatiotemporal gait dynamics and variability may not be consistent across separate days when using the FeedbackTM