Auswahl der wissenschaftlichen Literatur zum Thema „String-nets“

AbstractIn Schweigert and Yang (Methods Appl Symmetry Integr Geom, 2021) it was shown how string-net spaces for the Cardy bulk algebra in the Drinfeld center $${\mathsf {Z}}({\mathsf {C}})$$ Z ( C ) of a modular tensor category $${\mathsf {C}}$$ C give rise to a consistent set of correlators. We extend their results to include open-closed world sheets and allow for more general field algebras, which come in the form of $$({\mathsf {C}}|{\mathsf {Z}}({\mathsf {C}}))$$ ( C | Z ( C ) ) -Cardy algebras. To be more precise, we show that a set of fundamental string-nets with input data from a $$({\mathsf {C}}|{\mathsf {Z}}({\mathsf {C}}))$$ ( C | Z ( C ) ) -Cardy algebra gives rise to a solution of the sewing constraints formulated in Kong et al. (Adv Math 262:604–681, 2014) and that any set of fundamental string-nets solving the sewing constraints determine a $$({\mathsf {C}}|{\mathsf {Z}}({\mathsf {C}}))$$ ( C | Z ( C ) ) -Cardy algebra up to isomorphism. Hence we give an alternative proof of the results in Kong et al. (2014) in terms of string-nets.

Macropods have been captured by a variety of techniques: hand nets, trap yards, baited traps, cannon nets, drugged baits, syringe darts and stunning. These techniques differ in selectivity, in the likelihood of physical trauma or capture myopathy, and in the number of personnel required. Each technique is also limited to particular habitats or environmental conditions. A new draw-string trap was developed to capture kangaroos moving under fences, using a tunnel of soft netting attached to a steel weldmesh floor and suspended from a weldmesh frame. Draw-string closures at each end of the netting allowed selective and safe capture of kangaroos by two operators.

ABSTRACT In the surface waters of sulfidic springs near Regensburg, Bavaria, Germany, the SM1 euryarchaeon, together with filamentous bacteria, forms the recently described unique string-of-pearls community. In addition to naturally occurring string-of-pearls communities, the growth of these communities was also observed on polyethylene nets provided as an artificial attachment material in the streamlets of springs. In order to learn more about the distribution and origin of the SM1 euryarchaeon and its possible occurrence in the subsurface, polyethylene nets were incubated as deeply as possible in different spring holes. After a short residence time, slime-like, milky drops, almost completely composed of SM1 euryarchaeon, were attached to the nets, indicating that this organism grows independent of a partner in deeper earth layers. A newly designed in situ biofilm trapping system allowed the quantitative harvesting of organisms exhibiting this newly discovered lifestyle of the SM1 euryarchaeon for detailed biological studies. The discovery of naturally occurring archaeal biofilms extends our knowledge of the biology and ecological significance of archaea in their environments.

Abstract Sickle cell disease (SCD) is an inherited hemoglobin disorder caused by a single base change (A-T) in the beta-globin gene of hemoglobin with ensuing recurring inflammation that results in progressive end-organ damage and early mortality. Production of neutrophil extracellular traps (NETs) have been shown to be a key component of this inflammatory process in SCD pathophysiology. We sought to determine the relevance of NETosis versus a different type of programmed cell death (apoptosis) in SCD. We used an indirect assay using healthy neutrophils exposed to paired plasma samples (n=16) from SCD patients in steady-state and crisis for 30 min to 7 hrs, and a direct approach of observing neutrophils (3 healthy and 3 SCD) themselves up to 4 hrs. Features of NETosis (histone citrullination, nuclear decondensation, string nets) and apoptosis (piknotic nuclei, c-Parp, membrane damage) were assessed by imaging flow cytometry and fluorescence microscopy. Additionally, plasma titers for 20 inflammatory analytes were determined for the 16 paired SCD samples and 4 healthy controls. High circulating IL-6 levels at crisis found in 9/16 of the paired samples correlated with an increased number of NETs at crisis compared to steady-state. NETs were also observed directly in SCD neutrophils at steady state but not consistently. When NETs or histone citrullination were absent or low, c-Parp was typically detected. Additionally, membrane damage was observed in neutrophils from all SCD donors. The data suggest that the SCD environment disrupts neutrophil homeostasis and activate multiple cell death programs. SCD NETosis appears to be heterogeneous, its contribution to the disease pathophysiology remains to be determined.

L'ordre topologique est un ordre quantique particulier qui apparaît dans les systèmes quantiques gappés et fortement interactifs, et qui ne peut pas être décrit par un paramètre d'ordre local et une brisure spontanée de symétrie. En deux dimensions et à température nulle, cet ordre est caractérisé par une dégénérescence de l'état fondamental dépendant de la topologie de la variété, de l'intrication à longue portée et la présence de quasi-particules avec des nombres quantiques et des statistiques d'échange fractionnaires (également appelées anyons). Cette thèse étudie l'ordre topologique à température finie au moyen de deux modèles jouets exactement solubles : le modèle de string-net (réseau de cordes) de Levin et Wen et le modèle du double quantique de Kitaev. L'accent principal est mis sur le modèle de string-net, qui réalise tous les ordres topologiques doublés achiraux, c'est-à-dire tous les ordres topologiques décrits par un centre de Drinfeld. Ce modèle prend comme entrée une catégorie de fusion unitaire et produit le centre de Drinfeld correspondant en sortie. Dans un premier temps, nous dérivons une formule pour les dégénérescences spectrales du modèle, qui dépendent à la fois de la topologie et de l'ordre topologique considéré. En particulier, les dégénérescences dépendent non seulement du centre de Drinfeld mais aussi de la catégorie d'entrée. Ensuite, nous calculons la fonction de partition, à partir de laquelle nous obtenons l'entropie, la chaleur spécifique, et montrons qu'il n'y a pas de transition de phase à température finie. Nous identifions un ensemble particulier d'objets du centre de Drinfeld, appelés fluxons purs, qui dominent le comportement de la fonction de partition dans la limite thermodynamique, et étudions leurs propriétés. Nous obtenons également les moyennes thermiques des opérateurs de cordes fermées et étudions l'information mutuelle. Enfin, nous appliquons notre approche aux modèles du double quantique, où nous dérivons également une formule générale pour les dégénérescences spectrales, la fonction de partition et l'entropie d'intrication, permettant une étude plus générale et détaillée des propriétés à température finie par rapport aux études précédentes
Topological order is a special kind of quantum order which appears in strongly interacting gappedquantum systems and does not admit a description by a local order parameter and spontaneous symmetry breaking. In two dimensions and at zero temperature, it is instead characterized by a ground-state degeneracy dependent on the manifold topology, long-range entanglement, and the presence of quasiparticles with fractional quantum numbers and exchange statistics (also called anyons). This thesis investigates topological order at finite temperature by means of two exactly-solvable toy models: the string-net model of Levin and Wen and the Kitaev quantum double model. The main focus is on the string-net model, which realizes all achiral doubled topological orders, i.e., all topological orders described by Drinfeld centers. This model takes a unitary fusion category as aninput, and produces the corresponding Drinfeld center as an output. First, we derive a formula forthe spectral degeneracies that depend on both the topology, and the topological order considered. In particular, the degeneracies depend not only on the Drinfeld center but also on theinput category. Next, we compute the partition function, from which we obtain the entropy, specific heat, and show that there is no finite-temperature phase transition. We identify a particular set of objects of the Drinfeld center, called pure fluxons, which drive the partition function in the thermodynamic limit, and study their properties. We also obtain the thermal averages of closed string operators, and study the mutual information. Finally, we carry over our approach to the quantum double models, where we also derive a general formula for the spectral degeneracies, partition function and entanglement entropy, allowing for a more general and detailed study of finite-temperature properties compared to previous studies

Abstract Aperiodic metamaterials represent a class of structural systems that are composed of different building blocks (cells), instead of a self-repeating chain of the same unit cells. Optimizing aperiodic cellular structural systems thus presents high-dimensional design problems, that become intractable to solve using purely high-fidelity structural analysis coupled with optimization. Specialized analytical modeling along with metamodel based optimization can provide a more tractable alternative to designing such aperiodic metamaterials. To explore this concept, this paper presents an initial design automation framework applied to a case study representative of a simple 1D metamaterial system. The case under consideration is a drill string, where vibration suppression is of utmost importance. The drill string comprises a set of nonuniform rings attached to the outer surface of a longitudinal rod. As such, the resultant system can now be perceived as an aperiodic 1D metamaterial with each ring/gap representing a cell. Despite being a 1D system, the simultaneous consideration of multiple degrees of freedom (associated with torsional, axial, and lateral motions) poses significant computational challenges. To deal with these challenges, a transfer matrix method (TMM) is employed to analytically determine the frequency response of the drill string. However, due to the minute scale cost of the TMM method, the optimization remains computationally burdensome. This latter challenge is addressed by training a suite of neural networks on a set of TMM samples, with each network providing the response w.r.t. a specific frequency. Optimization is then performed to minimize mass subject to constraints on the gap between consecutive resonance peaks in one case, and minimizing this gap in the second case. Crucial improvements are accomplished over the initial baselines in both cases. Further novel contributions occur through the development of an inverse modeling approach that can learn optimal inverse designs with minimum mass and a desirable non-resonant frequency range, which partially mimics band gap behavior in perfectly periodic dispersive structures. To this end, we introduce the use of an emerging modeling formalism called in-vertible neural nets. Our study indicates that the inverse model is able to generate constraint satisfying designs with slightly higher mass.

ABSTRACT: U-Net is used by seismologists for picking phases of seismic waveforms. Applying U-net to process laboratory acoustic emission (AE) signals is useful for lab-scale experiments. In this paper, we document experiments on training two different U-Nets with a dataset containing 6532 manual pickings. This is to prepare for optimizing (or challenging) the maximum phase picking accuracy in the next step. Two label options (i.e., manual picking versus AIC auto-picking), two mask options, and two loss function options are considered in the training experiments. We observe the accuracy of the U-Nets, the shape of the output probability string, and the training and validation loss curves. The training time for U-Net-Two is shorter than that of U-Net-One. The binary-cross-entropy loss function is, as expected, proper for the initial stage of training. Applying the alternative option of the loss function may be useful for fine-tuning the model. We find that the length of the non-zero probability points in the label should be adjusted according to the frequency of the waveform. Shifting the signals and labels simultaneously will not affect the training. In the future this "shifting treatment" will be used for data augmentation. 1. INTRODUCTION While originally developed for biomedical imaging segmentation [1], U-Net is useful for many other tasks that require classification at the data-point-scale. In recent years, the application of U-Net for picking different phases of seismic waveforms has received broad attention [2]. Such a technique for processing seismic waveforms has immediate application to laboratory AE signal processing. However, training a U-Net for processing laboratory AE signals faces many challenges. First, environmental noise in laboratory AE signals can be catalog based, so the usefulness of conducting transfer learning using a well-trained U-Net is limited. Second, the training of a U-Net demands a large amount of manually labeled P-wave arrivals. Previously successful training of a U-Net for seismic waveform processing utilized an extensive data pool consisting of over 700,000 manually labelled P and S arrival times picked from over 30 years of earthquake recordings provided by the Northern California Earthquake Data Center [2].