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We show the existence of additive kinematic formulas for general flag area measures, which generalizes a recent result by Wannerer. Building on previous work by the second named author, we introduce an algebraic framework to compute these formulas explicitly. This is carried out in detail in the case of the incomplete flag manifold consisting of all (p+1)-planes containing a unit vector.
We show how nonlocal boundary conditions of Robin type can be encoded in the pointwise expression of the fractional operator. Notably, the fractional Laplacian of functions satisfying homogeneous nonlocal Neumann conditions can be expressed as a regional operator with a kernel having logarithmic behaviour at the boundary.
We provide a Hopf boundary lemma for the regional fractional Laplacian (−Δ)sΩ, with Ω ⊂ RN a bounded open set. More precisely, given u a pointwise or weak super-solution of the equation (−Δ)s u = c(x)u in Ω, we show that the ratio u(x)∕(dist(x, 𝜕Ω))2s−1 is strictly Ω positive as x approaches the boundary 𝜕Ω of Ω. We also prove a strong maximum principle for distributional super-solutions.
We show explicit formulas for the evaluation of (possibly higher-order) fractional Laplacians (-△)ˢ of some functions supported on ellipsoids. In particular, we derive the explicit expression of the torsion function and give examples of s-harmonic functions. As an application, we infer that the weak maximum principle fails in eccentric ellipsoids for s ∈ (1; √3 + 3/2) in any dimension n ≥ 2. We build a counterexample in terms of the torsion function times a polynomial of degree 2. Using point inversion transformations, it follows that a variety of bounded and unbounded domains do not satisfy positivity preserving properties either and we give some examples.
The annotation of texts and other material in the field of digital humanities and Natural Language Processing (NLP) is a common task of research projects. At the same time, the annotation of corpora is certainly the most time- and cost-intensive component in research projects and often requires a high level of expertise according to the research interest. However, for the annotation of texts, a wide range of tools is available, both for automatic and manual annotation. Since the automatic pre-processing methods are not error-free and there is an increasing demand for the generation of training data, also with regard to machine learning, suitable annotation tools are required. This paper defines criteria of flexibility and efficiency of complex annotations for the assessment of existing annotation tools. To extend this list of tools, the paper describes TextAnnotator, a browser-based, multi-annotation system, which has been developed to perform platform-independent multimodal annotations and annotate complex textual structures. The paper illustrates the current state of development of TextAnnotator and demonstrates its ability to evaluate annotation quality (inter-annotator agreement) at runtime. In addition, it will be shown how annotations of different users can be performed simultaneously and collaboratively on the same document from different platforms using UIMA as the basis for annotation.
In particle collider experiments, elementary particle interactions with large momentum transfer produce quarks and gluons (known as partons) whose evolution is governed by the strong force, as described by the theory of quantum chromodynamics (QCD)1. These partons subsequently emit further partons in a process that can be described as a parton shower2, which culminates in the formation of detectable hadrons. Studying the pattern of the parton shower is one of the key experimental tools for testing QCD. This pattern is expected to depend on the mass of the initiating parton, through a phenomenon known as the dead-cone effect, which predicts a suppression of the gluon spectrum emitted by a heavy quark of mass mQ and energy E, within a cone of angular size mQ/E around the emitter3. Previously, a direct observation of the dead-cone effect in QCD had not been possible, owing to the challenge of reconstructing the cascading quarks and gluons from the experimentally accessible hadrons. We report the direct observation of the QCD dead cone by using new iterative declustering techniques4,5 to reconstruct the parton shower of charm quarks. This result confirms a fundamental feature of QCD. Furthermore, the measurement of a dead-cone angle constitutes a direct experimental observation of the non-zero mass of the charm quark, which is a fundamental constant in the standard model of particle physics.
Polarization of Λ and ¯Λ hyperons along the beam direction in Pb-Pb collisions at √sNN=5.02 TeV
(2022)
The polarization of the Λ and ¯Λ hyperons along the beam (z) direction, Pz, has been measured in Pb-Pb collisions at √sNN=5.02 TeV recorded with ALICE at the Large Hadron Collider (LHC). The main contribution to Pz comes from elliptic flow-induced vorticity and can be characterized by the second Fourier sine coefficient Pz,s2=⟨Pzsin(2φ−2Ψ2)⟩, where φ is thhyperon azimuthal emission angle and Ψ2 is the elliptic flow plane angle. We report the measurement of Pz,s2 for different collision centralities and in the 30%–50% centrality interval as a function of the hyperon transverse momentum and rapidity. The Pz,s2 is positive similarly as measured by the STAR Collaboration in Au-Au collisions at √sNN=200 GeV, with somewhat smaller amplitude in the semicentral collisions. This is the first experimental evidence of a nonzero hyperon Pz in Pb-Pb collisions at the LHC. The comparison of the measured Pz,s2 with the hydrodynamic model calculations shows sensitivity to the competing contributions from thermal and the recently found shear-induced vorticity, as well as to whether the polarization is acquired at the quark-gluon plasma or the hadronic phase.
We show that throughout the satisfiable phase the normalized number of satisfying assignments of a random 2-SAT formula converges in probability to an expression predicted by the cavity method from statistical physics. The proof is based on showing that the Belief Propagation algorithm renders the correct marginal probability that a variable is set to “true” under a uniformly random satisfying assignment.
Der Inhalt dieser Arbeit ist die Entwicklung und Evaluation einer mobilen Webanwendung für die Annotation von Texten. Dem Benutzer ist es durch diese Webanwendung, im folgenden auch MobileAnnotator genannt, möglich Wörter und Textausschnitte zu kategorisieren oder auch mit Wissensquellen, zum Beispiel Wikipedia, zu verknüpfen. Der MobileAnnotator ist dabei für mobile Endgeräte ausgelegt und insbesondere für Smartphones optimiert worden.
Für die Funktionalität verwendet der MobileAnnotator die Architektur des bereits existierenden und etablierten TextAnnotators. Dieser stellt bereits eine Vielzahl von Annotations Werkzeugen bereit, von denen zwei auf den MobileAnnotator übertragen wurden. Da der TextAnnotator vollständig für einen Desktopbetrieb ausgelegt wurde, ist es jedoch nicht möglich diese Werkzeuge ohne Anpassungen für ein mobiles Gerät umzubauen. Der MobileAnnotator beschränkt sich somit auf ein Mindestmaß an Funktionen dieser Werkzeuge um sie dem Benutzer in geeigneter Art und Weise verfügbar zu machen.
Für die Evaluation der Benutzerfreundlichkeit des MobileAnnotator und dessen Werkzeuge wurde anschließend eine Studie durchgeführt. Den Probanten war es innerhalb der Studie möglich Aussagen über die Bedienbarkeit des MobileAnnotators zu treffen und einen Vergleich zwischen dem Mobile- und TextAnnotator zu ziehen.