On the Existence of Breathers Solutions in non-linear Klein-Gordon equations with periodic coefficients

Motiviert durch die Existenz sog. Breather-Lösungen in der Sine-Gordon Gleichung betrachten wir die kubisch-nicht-nichtlineare Klein-Gordon Gleichung und setzen uns zum Ziel räumlich periodische Koeffizienten zu finden, mit denen Breather-Lösungen, räumlich lokalisierte, zeitlich periodiche Lösungen nachgewiesen werden können. Dazu benutzen wir Floquettheorie, Invariante Mannigfaltigkeitstheorie und Störungstheorie für DGLn um die Existenz einer Breather-Lösungen nachzuweisen

Architecture representations for quantum convolutional neural networks

The Quantum Convolutional Neural Network (QCNN) is a quantum circuit model inspired by the architecture of Convolutional Neural Networks (CNNs). The success of CNNs is largely due to its ability to learn high level features from raw data rather than requiring manual feature design. Neural Architecture Search (NAS) continues this trend by learning network architecture, alleviating the need for its manual construction and have been able to generate state of the art models automatically. Search space design is a crucial step in NAS and there is currently no formal framework through which it can be achieved for QCNNs. In this work we provide such a framework by utilizing techniques from NAS to create an architectural representation for QCNNs that facilitate search space design and automatic model generation. This is done by specifying primitive operations, such as convolutions and pooling, in such a way that they can be dynamically stacked on top of each other to form different architectures. This way, QCNN search spaces can be created by controlling the sequence and hyperparameters of stacked primitives, allowing the capture of different design motifs. We show this by generating QCNNs that belong to a popular family of parametric quantum circuits, those resembling reverse binary trees. We then benchmark this family of models on a music genre classification dataset, GTZAN. Showing that alternating architecture impact model performance more than other modelling components such as choice of unitary ansatz and data encoding, resulting in a way to improve model performance without increasing its complexity. Finally we provide an open source python package that enable dynamic QCNN creation by system or hand, based off the work presented in this paper, facilitating search space design.Comment: 18 pages, 9 figure

Allergen-specific immunotherapy of Hymenoptera venom allergy:also a matter of diagnosis

Stings of hymenoptera can induce IgE-mediated hypersensitivity reactions in venom-allergic patients, ranging from local up to severe systemic reactions and even fatal anaphylaxis. Allergic patients' quality of life can be mainly improved by altering their immune response to tolerate the venoms by injecting increasing venom doses over years. This venom-specific immunotherapy is highly effective and well tolerated. However, component-resolved information about the venoms has increased in the last years. This knowledge is not only able to improve diagnostics as basis for an accurate therapy, but was additionally used to create tools which enable the analysis of therapeutic venom extracts on a molecular level. Therefore, during the last decade the detailed knowledge of the allergen composition of hymenoptera venoms has substantially improved diagnosis and therapy of venom allergy. This review focuses on state of the art diagnostic and therapeutic options as well as on novel directions trying to improve therapy

Quantum-inspired algorithm for direct multi-class classification

Over the last few decades, quantum machine learning has emerged as a groundbreaking discipline. Harnessing the peculiarities of quantum computation for machine learning tasks offers promising advantages. Quantum-inspired machine learning has revealed how relevant benefits for machine learning problems can be obtained using the quantum information theory even without employing quantum computers. In the recent past, experiments have demonstrated how to design an algorithm for binary classification inspired by the method of quantum state discrimination, which exhibits high performance with respect to several standard classifiers. However, a generalization of this quantuminspired binary classifier to a multi-class scenario remains nontrivial. Typically, a simple solution in machine learning decomposes multi-class classification into a combinatorial number of binary classifications, with a concomitant increase in computational resources. In this study, we introduce a quantum-inspired classifier that avoids this problem. Inspired by quantum state discrimination, our classifier performs multi-class classification directly without using binary classifiers. We first compared the performance of the quantum-inspired multi-class classifier with eleven standard classifiers. The comparison revealed an excellent performance of the quantum-inspired classifier. Comparing these results with those obtained using the decomposition in binary classifiers shows that our method improves the accuracy and reduces the time complexity. Therefore, the quantum-inspired machine learning algorithm proposed in this work is an effective and efficient framework for multi-class classification. Finally, although these advantages can be attained without employing any quantum component in the hardware, we discuss how it is possible to implement the model in quantum hardware

PennyLane: Automatic differentiation of hybrid quantum-classical computations

PennyLane is a Python 3 software framework for optimization and machine learning of quantum and hybrid quantum-classical computations. The library provides a unified architecture for near-term quantum computing devices, supporting both qubit and continuous-variable paradigms. PennyLane's core feature is the ability to compute gradients of variational quantum circuits in a way that is compatible with classical techniques such as backpropagation. PennyLane thus extends the automatic differentiation algorithms common in optimization and machine learning to include quantum and hybrid computations. A plugin system makes the framework compatible with any gate-based quantum simulator or hardware. We provide plugins for Strawberry Fields, Rigetti Forest, Qiskit, Cirq, and ProjectQ, allowing PennyLane optimizations to be run on publicly accessible quantum devices provided by Rigetti and IBM Q. On the classical front, PennyLane interfaces with accelerated machine learning libraries such as TensorFlow, PyTorch, and autograd. PennyLane can be used for the optimization of variational quantum eigensolvers, quantum approximate optimization, quantum machine learning models, and many other applications.Comment: Code available at https://github.com/XanaduAI/pennylane/ . Significant contributions to the code (new features, new plugins, etc.) will be recognized by the opportunity to be a co-author on this pape

Linking metabolites in eight bioactive forage species to their in vitro methane reduction potential across several cultivars and harvests

An in vitro Hohenheim gas test was conducted to analyze the fermentation end-products from 17 cultivars of eight polyphenol containing forage species. The polyphenol composition and proanthocyanidin (PA) structural features of all the cultivars were analyzed with UPLC-MS/MS in leaves of vegetative or generative plants. The samples were incubated with and without polyethylene glycol (PEG, a tannin-binding agent) to separate the tannin-effect on methane (CH4, ml/200 mg DM) production from that of forage quality. Sulla and big trefoil, two particularly PA rich species, were found to have the highest CH4 reduction potential of up to 47% when compared to the samples without PEG. However, concomitant reduction in gas production (GP, ml/200 mg DM) of up to 44% was also observed. An increase in both GP and CH4 production under PEG treatments, confirms the role of tannins in CH4 reduction. Moreover, PA structural features and concentration were found to be an important source of variation for CH4 production from PA containing species. Despite having low polyphenol concentrations, chicory and plantain were found to reduce CH4 production without reducing GP. Additionally, interspecies variability was found to be higher than intraspecies variability, and these results were consistent across growth stages, indicating the findings' representativeness

Assessing the Potential of Diverse Forage Mixtures to Reduce Enteric Methane Emissions In Vitro

Methane emissions from ruminants are a major contributor to agricultural greenhouse gas emissions. Thus, eight different forage species were combined in binary mixtures with Lolium perenne in increasing proportions, in vitro, to determine their methane reduction potential in ruminants. Species were sampled in two consecutive years where possible. The aims were: a) to determine if mixtures with specific forages, particularly those rich in plant specialized metabolites (PSM), can reduce methane emissions compared to ryegrass monocultures, b) to identify whether there is a linear-dose effect relationship in methane emissions from the legume or herb addition, and c) whether these effects are maintained across sampling years. Results showed that all dicot species studied, including the non-tannin-containing species, reduced methane production. The tannin-rich species, Sanguisorba minor and Lotus pedunculatus, showed the greatest methane reduction potential of up to 33%. Due to concomitant reductions in the forage digestibility, Cichorium intybus yielded the lowest methane emissions per digestible forage unit. Contrary to total gas production, methane production was less predictable, with a tendency for the lowest methane production being obtained with a 67.5% share of the legume or herb partner species. Thus, linear increments in the partner species share did not result in linear changes in methane concentration. The methane reduction potential differed across sampling years, but the species ranking in methane concentration was stable