211 research outputs found

    Boundary triples and Weyl functions for Dirac operators with singular interactions

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    In this article we develop a systematic approach to treat Dirac operators Aη,τ,λA_{\eta, \tau, \lambda} with singular electrostatic, Lorentz scalar, and anomalous magnetic interactions of strengths η,τ,λ∈R\eta, \tau, \lambda \in \mathbb{R}, respectively, supported on points in R\mathbb{R}, curves in R2\mathbb{R}^2, and surfaces in R3\mathbb{R}^3 that is based on boundary triples and their associated Weyl functions. First, we discuss the one-dimensional case which also serves as a motivation for the multidimensional setting. Afterwards, in the two and three-dimensional situation we construct quasi, generalized, and ordinary boundary triples and their Weyl functions, and provide a detailed characterization of the associated Sobolev spaces, trace theorems, and the mapping properties of integral operators which play an important role in the analysis of Aη,τ,λA_{\eta, \tau, \lambda}. We make a substantial step towards more rough interaction supports Σ\Sigma and consider general compact Lipschitz hypersurfaces. We derive conditions for the interaction strengths such that the operators Aη,τ,λA_{\eta, \tau, \lambda} are self-adjoint, obtain a Krein-type resolvent formula, and characterize the essential and discrete spectrum. These conditions include purely Lorentz scalar and purely non-critical anomalous magnetic interactions as well as the confinement case, the latter having an important application in the mathematical description of graphene. Using a certain ordinary boundary triple, we show the self-adjointness of Aη,τ,λA_{\eta, \tau, \lambda} for arbitrary combinations of the interaction strengths (including critical ones) under the condition that Σ\Sigma is C∞C^{\infty}-smooth and derive its spectral properties. In particular, in the critical case, a loss of Sobolev regularity in the operator domain and a possible additional point of the essential spectrum are observed.Comment: 56 pages; to appear in Reviews in Mathematical Physic

    Obtaining Robust Control and Navigation Policies for Multi-Robot Navigation via Deep Reinforcement Learning

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    Multi-robot navigation is a challenging task in which multiple robots must be coordinated simultaneously within dynamic environments. We apply deep reinforcement learning (DRL) to learn a decentralized end-to-end policy which maps raw sensor data to the command velocities of the agent. In order to enable the policy to generalize, the training is performed in different environments and scenarios. The learned policy is tested and evaluated in common multi-robot scenarios like switching a place, an intersection and a bottleneck situation. This policy allows the agent to recover from dead ends and to navigate through complex environments.Comment: 13 page

    Accuracy evaluation of a Low-Cost Differential Global Positioning System for mobile robotics

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    Differential GPS, commonly referred as DGPS, is a well-known and very accurate localization system for many outdoor applications in particular for mobile outdoor robotics. The most common drawback of DGPS systems are the high costs for both base station and receivers. In this paper, we present a setup that uses third-party open-source software and a Ublox ZED-F9P chip to build a ROS-enabled low-cost DGPS setup that is ready to use in a few hours. The main goal of this paper is to analyze and evaluate the repetitive and absolute accuracy of the system. The first measurement also examines the differences between a SAPOS base station and a locally installed one consisting of low-cost components. During the evaluation process of the absolute accuracy, a moving mobile robot is used on the receiver side. It is tracked through a highly accurate VICON motion capture system.Comment: Submitted to IEEE Sensors 202

    A general framework for consistent estimation of charge transport properties via random walks in random environments

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    A general framework is proposed for the study of the charge transport properties of materials via random walks in random environments (RWRE). The material of interest is modeled by a random environment, and the charge carrier is modeled by a random walker. The framework combines a model for the fast generation of random environments that realistically mimic materials morphology with an algorithm for efficient estimation of key properties of the resulting random walk. The model of the environment makes use of tools from spatial statistics and the theory of random geometric graphs. More precisely, the disordered medium is represented by a random spatial graph with directed edge weights, where the edge weights represent the transition rates of a Markov jump process (MJP) modeling the motion of the random walker. This MJP is a multiscale stochastic process. In the long term, it explores all vertices of the random graph model. In the short term, however, it becomes trapped in small subsets of the state space and makes many transitions in these small regions. This behavior makes efficient estimation of velocity by Monte Carlo simulations a challenging task. Therefore, we use aggregate Monte Carlo (AMC), introduced in [T. Brereton et al., Methodol. Comput. Appl. Probab., 16 (2014), pp. 465-484], for estimating the velocity of a random walker as it passes through a realization of the random environment. In this paper, we prove the strong consistency of the AMC velocity estimator and use this result to conduct a detailed case study, in which we describe the motion of holes in an amorphous mesophase of an organic semiconductor, dicyanovinyl-substituted oligothiophene (DCV4T). In particular, we analyze the effect of system size (i.e., number of molecules) on the velocity of single charge carriers

    Synergy of cations in high entropy oxide lithium ion battery anode

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    High entropy oxides (HEOs) with chemically disordered multi-cation structure attract intensive interest as negative electrode materials for battery applications. The outstanding electrochemical performance has been attributed to the high-entropy stabilization and the so-called ‘cocktail effect’. However, the configurational entropy of the HEO, which is thermodynamically only metastable at room-temperature, is insufficient to drive the structural reversibility during conversion-type battery reaction, and the ‘cocktail effect’ has not been explained thus far. This work unveils the multi-cations synergy of the HEO Mg0.2_{0.2}Co0.2_{0.2}Ni0.2_{0.2}Cu0.2_{0.2}Zn0.2_{0.2}O at atomic and nanoscale during electrochemical reaction and explains the ‘cocktail effect’. The more electronegative elements form an electrochemically inert 3-dimensional metallic nano-network enabling electron transport. The electrochemical inactive cation stabilizes an oxide nanophase, which is semi-coherent with the metallic phase and accommodates Li+^+ ions. This self-assembled nanostructure enables stable cycling of micron-sized particles, which bypasses the need for nanoscale pre-modification required for conventional metal oxides in battery applications. This demonstrates elemental diversity is the key for optimizing multi-cation electrode materials

    Deep learning-based classification of blue light cystoscopy imaging during transurethral resection of bladder tumors

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    Bladder cancer is one of the top 10 frequently occurring cancers and leads to most cancer deaths worldwide. Recently, blue light (BL) cystoscopy-based photodynamic diagnosis was introduced as a unique technology to enhance the detection of bladder cancer, particularly for the detection of flat and small lesions. Here, we aim to demonstrate a BL image-based artificial intelligence (AI) diagnostic platform using 216 BL images, that were acquired in four different urological departments and pathologically identified with respect to cancer malignancy, invasiveness, and grading. Thereafter, four pre-trained convolution neural networks were utilized to predict image malignancy, invasiveness, and grading. The results indicated that the classification sensitivity and specificity of malignant lesions are 95.77% and 87.84%, while the mean sensitivity and mean specificity of tumor invasiveness are 88% and 96.56%, respectively. This small multicenter clinical study clearly shows the potential of AI based classification of BL images allowing for better treatment decisions and potentially higher detection rates

    Clinical and Cost-Effectiveness of PSYCHOnlineTHERAPY: Study Protocol of a Multicenter Blended Outpatient Psychotherapy Cluster Randomized Controlled Trial for Patients With Depressive and Anxiety Disorders

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    Introduction: Internet- and mobile-based interventions (IMIs) and their integration into routine psychotherapy (i.e., blended therapy) can offer a means of complementing psychotherapy in a flexible and resource optimized way. Objective: The present study will evaluate the non-inferiority, cost-effectiveness, and safety of two versions of integrated blended psychotherapy for depression and anxiety compared to standard cognitive behavioral therapy (CBT). Methods: A three-armed multicenter cluster-randomized controlled non-inferiority trial will be conducted comparing two implementations of blended psychotherapy (PSYCHOnlineTHERAPYfix/flex) compared to CBT. Seventy-five outpatient psychotherapists with a CBT-license will be randomized in a 1:1:1 ratio. Each of them is asked to include 12 patients on average with depressive or anxiety disorders resulting in a total sample size of N = 900. All patients receive up to a maximum of 16 psychotherapy sessions, either as routine CBT or alternating with Online self-help sessions (fix: 8/8; flex: 0–16). Assessments will be conducted at patient study inclusion (pre-treatment) and 6, 12, 18, and 24 weeks and 12 months post-inclusion. The primary outcome is depression and anxiety severity at 18 weeks post-inclusion (post-treatment) using the Patient Health Questionnaire Anxiety and Depression Scale. Secondary outcomes are depression and anxiety remission, treatment response, health-related quality of life, patient satisfaction, working alliance, psychotherapy adherence, and patient safety. Additionally, several potential moderators and mediators including patient characteristics and attitudes toward the interventions will be examined, complemented by ecological day-to-day digital behavior variables via passive smartphone sensing as part of an integrated smart-sensing sub-study. Data-analysis will be performed on an intention-to-treat basis with additional per-protocol analyses. In addition, cost-effectiveness and cost-utility analyses will be conducted from a societal and a public health care perspective. Additionally, qualitative interviews on acceptance, feasibility, and optimization potential will be conducted and analyzed. Discussion: PSYCHOnlineTHERAPY will provide evidence on blended psychotherapy in one of the largest ever conducted psychotherapy trials. If shown to be non-inferior and cost-effective, PSYCHOnlineTHERAPY has the potential to innovate psychotherapy in the near future by extending the ways of conducting psychotherapy. The rigorous health care services approach will facilitate a timely implementation of blended psychotherapy into standard care

    Similarities in element  content between comet 67P/Churyumov–Gerasimenko coma dust and selected meteorite samples

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    We have analysed the element composition and the context of particles collected within the coma of 67P/Churyumov–Gerasimenko with Rosetta’s COmetary Secondary Ion Mass Analyzer (COSIMA). A comparison has been made between on board cometary samples and four meteorite samples measured in the laboratory with the COSIMA reference model. Focusing on the rock-forming elements, we have found similarities with chondrite meteorites for some ion count ratios. The composition of 67P/Churyumov–Gerasimenko particles measured by COSIMA shows an enrichment in volatile elements compared to that of the investigated Renazzo (CR2) carbonaceous meteorite sample.</p
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