Dimension rigidity in conformal structures

Let $\Lambda$ be the limit set of a conformal dynamical system, i.e. a Kleinian group acting on either finite- or infinite-dimensional real Hilbert space, a conformal iterated function system, or a rational function. We give an easily expressible sufficient condition, requiring that the limit set is not too much bigger than the radial limit set, for the following dichotomy: $\Lambda$ is either a real-analytic manifold or a fractal in the sense of Mandelbrot (i.e. its Hausdorff dimension is strictly greater than its topological dimension). Our primary focus is on the infinite-dimensional case. An important component of the strategy of our proof comes from the rectifiability techniques of Mayer and Urba\'nski ('03), who obtained a dimension rigidity result for conformal iterated function systems (including those with infinite alphabets). In order to handle the infinite dimensional case, both for Kleinian groups and for iterated function systems, we introduce the notion of pseudorectifiability, a variant of rectifiability, and develop a theory around this notion similar to the theory of rectifiable sets. Our approach also extends existing results in the finite-dimensional case, where it unifies the realms of Kleinian groups, conformal iterated function systems, and rational functions. For Kleinian groups, we improve on the rigidity result of Kapovich ('09) by substantially weakening its hypothesis of geometrical finiteness. Moreover, our proof, based on rectifiability, is entirely different than that of Kapovich, which depends on homological algebra. Another advantage of our approach is that it allows us to use the "demension" of \v{S}tan$'$ko ('69) as a substitute for topological dimension. For example, we prove that any dynamically defined version of Antoine's necklace must have Hausdorff dimension strictly greater than 1 (i.e. the demension of Antoine's necklace)

A look under the hood: design and development of the first smartweb system demonstrator

Experience shows that decisions in the early phases of the development of a multimodal system prevail throughout the life-cycle of a project. The distributed architecture and the requirement for robust multimodal interaction in our project SmartWeb resulted in an approach that uses and extends W3C standards like EMMA and RDFS. These standards for the interface structure and content allowed us to integrate available tools and techniques. However, the requirements in our system called for various extensions, e. g., to introduce result feedback tags for an extended version of EMMA. The interconnection framework depends on a commercial telephone voice dialog system platform for the dialog-centric components while the information access processes are linked using web service technology. Also in the area of this underlying infrastructure, enhancements and extensions were necessary. The first demonstration system is operable now and will be presented at the Football Worl

Interoperable Data Analytics Reference Architectures Empowering Digital-Twin-Aided Manufacturing

The use of mature, reliable, and validated solutions can save significant time and cost when introducing new technologies to companies. Reference Architectures represent such best-practice techniques and have the potential to increase the speed and reliability of the development process in many application domains. One area where Reference Architectures are increasingly utilized is cloud-based systems. Exploiting the high-performance computing capability offered by clouds, while keeping sovereignty and governance of proprietary information assets can be challenging. This paper explores how Reference Architectures can be applied to overcome this challenge when developing cloud-based applications. The presented approach was developed within the DIGITbrain European project, which aims at supporting small and medium-sized enterprises (SMEs) and mid-caps in realizing smart business models called Manufacturing as a Service, via the efficient utilization of Digital Twins. In this paper, an overview of Reference Architecture concepts, as well as their classification, specialization, and particular application possibilities are presented. Various data management and potentially spatially detached data processing configurations are discussed, with special attention to machine learning techniques, which are of high interest within various sectors, including manufacturing. A framework that enables the deployment and orchestration of such overall data analytics Reference Architectures in clouds resources is also presented, followed by a demonstrative application example where the applicability of the introduced techniques and solutions are showcased in practice

Ressourceneffizienz durch Industrie 4.0: Potenziale für KMU des verarbeitenden Gewerbes

Die digitale Transformation in der industriellen Produktion bietet erhebliche Potenziale zur Steigerung von Material- und Energieeffizienz in Unternehmen. Gleichzeitig benötigen die eingesetzten Technologien der Digitalisierung auch selbst Ressourcen: Bei der Produktion von IKT-Komponenten werden Materialien, darunter auch kritische Rohstoffe, verwendet. Weiterhin kann die digitale Transformation zu einem höheren Energieverbrauch führen. Diesem Spannungsfeld aus Chancen und Herausforderungen widmet sich die Studie „Ressourceneffizienz durch Industrie 4.0 – Potenziale für KMU des verarbeitenden Gewerbes“

Rapid effects of aggressive interactions on aromatase activity and oestradiol in discrete brain regions of wild male white-crowned sparrows

Testosterone (T) is critical for the activation of aggressive behaviours. In many vertebrate species, circulating T levels rapidly increase after aggressive encounters during the early or mid- breeding season. During the late breeding season, circulating T concentrations did not change in wild male white-crowned sparrows after an aggressive encounter, and in these animals, changes in local neural metabolism of T might be more important than changes in systemic T levels. Local neural aromatization of T into 17β-œstradiol (E(2)) often mediates the actions of T, and we hypothesized that in the late breeding season, brain aromatase is rapidly modulated after aggressive interactions, leading to changes in local concentrations of E(2). Here, wild male white-crowned sparrows in the late breeding season were exposed to simulated territorial intrusion (STI) (song playback and live decoy) or control (CON) for 30 min. STI significantly increased aggressive behaviours. Using Palkovits punch technique, 13 brain regions were collected. There was high aromatase activity in several nuclei, but enzymatic activity in the CON and STI groups did not differ in any region. E(2) concentrations were much higher in the brain than the plasma. STI did not affect circulating levels of E(2) but rapidly reduced E(2) concentrations in the hippocampus, ventromedial nucleus of the hypothalamus, and bed nucleus of the stria terminalis. Surprisingly, there were no correlations between aromatase activity and E(2) concentrations in the brain, nor were aromatase activity or brain E(2) correlated with aggressive behaviour or plasma hormone levels. This is one of the first studies to measure E(2) in microdissected brain regions, and the first study to do so in free-ranging animals. These data demonstrate that social interactions have rapid effects on local E(2) concentrations in specific brain regions