Construction of Parseval wavelets from redundant filter systems

We consider wavelets in L^2(R^d) which have generalized multiresolutions. This means that the initial resolution subspace V_0 in L^2(R^d) is not singly generated. As a result, the representation of the integer lattice Z^d restricted to V_0 has a nontrivial multiplicity function. We show how the corresponding analysis and synthesis for these wavelets can be understood in terms of unitary-matrix-valued functions on a torus acting on a certain vector bundle. Specifically, we show how the wavelet functions on R^d can be constructed directly from the generalized wavelet filters.Comment: 34 pages, AMS-LaTeX ("amsproc" document class) v2 changes minor typos in Sections 1 and 4, v3 adds a number of references on GMRA theory and wavelet multiplicity analysis; v4 adds material on pages 2, 3, 5 and 10, and two more reference

Handling Qualities Assessment of a Pilot Cueing System for Autorotation Maneuvers

This paper details the design and limited flight testing of a preliminary system for visual pilot cueing during autorotation maneuvers. The cueing system is based on a fully-autonomous, multi-phase autorotation control law that has been shown to successfully achieve autonomous autorotation landing in unmanned helicopters. To transition this control law to manned systems, it is employed within a cockpit display to drive visual markers which indicate desired collective pitch and longitudinal cyclic positions throughout the entire maneuver, from autorotation entry to touchdown. A series of simulator flight experiments performed at University of Liverpool’s HELIFLIGHT-R simulator are documented, in which pilots attempt autorotation with and without the pilot cueing system in both good and degraded visual environments. Performance of the pilot cueing system is evaluated based on both subjective pilot feedback and objective measurements of landing survivability metrics, demonstrating suitable preliminary performance of the system

Language processing within the human medial temporal lobe

Although the hippocampal formation is essential for verbal memory, it is not fully understood how it contributes to language comprehension. We recorded event-related potentials (ERPs) directly from two substructures of the medial temporal lobe (MTL), the rhinal cortex and the hippocampus proper, while epilepsy patients listened to sentences that either were correct or contained semantic or syntactic violations. Semantic violations elicited a large negative ERP response peaking at approximately 400 ms in the rhinal cortex. In contrast, syntactically incorrect sentences elicited a negative deflection of 500-800 ms in the hippocampus proper. The results suggest that functionally distinct aspects of integration in language comprehension are supported by different MTL structures: the rhinal cortex is involved in semantic integration, whereas the hippocampus proper subserves processes of syntactic integration. An analysis of phase synchronization within the gamma band between rhinal and hippocampal recording sites showed that both of the above-mentioned ERP components were preceded by an increase of phase synchronization. In contrast to these short phasic increases of phase synchronization in both violation conditions, correct sentences were associated with a long-lasting synchronization in a late time window, possibly reflecting the integration of semantic and syntactic information as required for normal comprehension

Aspects of noncommutative Lorentzian geometry for globally hyperbolic spacetimes

Connes' functional formula of the Riemannian distance is generalized to the Lorentzian case using the so-called Lorentzian distance, the d'Alembert operator and the causal functions of a globally hyperbolic spacetime. As a step of the presented machinery, a proof of the almost-everywhere smoothness of the Lorentzian distance considered as a function of one of the two arguments is given. Afterwards, using a $C^*$-algebra approach, the spacetime causal structure and the Lorentzian distance are generalized into noncommutative structures giving rise to a Lorentzian version of part of Connes' noncommutative geometry. The generalized noncommutative spacetime consists of a direct set of Hilbert spaces and a related class of $C^*$-algebras of operators. In each algebra a convex cone made of self-adjoint elements is selected which generalizes the class of causal functions. The generalized events, called {\em loci}, are realized as the elements of the inductive limit of the spaces of the algebraic states on the $C^*$-algebras. A partial-ordering relation between pairs of loci generalizes the causal order relation in spacetime. A generalized Lorentz distance of loci is defined by means of a class of densely-defined operators which play the r\^ole of a Lorentzian metric. Specializing back the formalism to the usual globally hyperbolic spacetime, it is found that compactly-supported probability measures give rise to a non-pointwise extension of the concept of events.Comment: 43 pages, structure of the paper changed and presentation strongly improved, references added, minor typos corrected, title changed, accepted for publication in Reviews in Mathematical Physic

Polymer and Fock representations for a Scalar field

In loop quantum gravity, matter fields can have support only on the `polymer-like' excitations of quantum geometry, and their algebras of observables and Hilbert spaces of states can not refer to a classical, background geometry. Therefore, to adequately handle the matter sector, one has to address two issues already at the kinematic level. First, one has to construct the appropriate background independent operator algebras and Hilbert spaces. Second, to make contact with low energy physics, one has to relate this `polymer description' of matter fields to the standard Fock description in Minkowski space. While this task has been completed for gauge fields, important gaps remained in the treatment of scalar fields. The purpose of this letter is to fill these gaps.Comment: 13 pages, no figure

General Framework for phase synchronization through localized sets

We present an approach which enables to identify phase synchronization in coupled chaotic oscillators without having to explicitly measure the phase. We show that if one defines a typical event in one oscillator and then observes another one whenever this event occurs, these observations give rise to a localized set. Our result provides a general and easy way to identify PS, which can also be used to oscillators that possess multiple time scales. We illustrate our approach in networks of chemically coupled neurons. We show that clusters of phase synchronous neurons may emerge before the onset of phase synchronization in the whole network, producing a suitable environment for information exchanging. Furthermore, we show the relation between the localized sets and the amount of information that coupled chaotic oscillator can exchange

Konzept zur Ermittlung und Beurteilung der Kohlenstoffspeicher urbaner Böden am Beispiel Berlins

Städte sind Hotspots anthropogener CO2-Emissionen. Sie besitzen daher eine besondere Verantwortung für die Umsetzung von Maßnahmen und Strategien zur Vermeidung von Treibhausgasemissionen. Ein systematisches Management der C-Speicher der Berliner Stadtnatur (Boden und Vegetation) fehlt bisher – trotz großen Potenzials. Übergeordnetes Ziel des Projektes ist es, den städtischen Klimaschutz über den Schutz und die Entwicklung der C-Speicher von Böden und grüner Infrastruktur (Vegetation) und damit die Aufnahme und Fixierung von atmosphärischem CO2 zu stärken. Das Forschungsprojekt NatKoS („natürliche Kohlenstoffspeicher“) erarbeitet von 2016–2019 eine belastbare Daten- und Bewertungsgrundlage für die Corg-Speicher der Böden und der Vegetation in Berlin. Die Heterogenität und Eigenheiten der urbanen Böden und die damit verbundenen Schwierigkeiten sind eine besondere Herausforderung bei der Konzipierung der Datenerhebung und Bodenbewertung. Das Konzept soll eine Differenzierung nach städtischen Nutzungsformen, ausgewählten Bodeneigenschaften sowie der Schutzwürdigkeit der Böden ermöglichen. Historische Analysen der Flächennutzung unterstützen zudem die Entwicklungsprognosen für die Corg-Speicher bei städtebaulichen Projekten oder sonstigen Flächennutzungsplanungen. Die Forschungsergebnisse besitzen daher eine große Planungsrelevanz für die Stadtentwicklung mit dem Ziel „klimaneutrales Berlin 2050“

Non-transitive maps in phase synchronization

Concepts from the Ergodic Theory are used to describe the existence of non-transitive maps in attractors of phase synchronous chaotic systems. It is shown that for a class of phase-coherent systems, e.g. the sinusoidally forced Chua's circuit and two coupled R{\"o}ssler oscillators, phase synchronization implies that such maps exist. These ideas are also extended to other coupled chaotic systems. In addition, a phase for a chaotic attractor is defined from the tangent vector of the flow. Finally, it is discussed how these maps can be used to real time detection of phase synchronization in experimental systems

Recoil Correction to Hydrogen Energy Levels: A Revision

Recent calculations of the order (Z\alpha)^4(m/M)Ry pure recoil correction to hydrogen energy levels are critically revised. The origins of errors made in the previous works are elucidated. In the framework of a successive approach, we obtain the new result for the correction to S levels. It amounts to -16.4 kHz in the ground state and -1.9 kHz in the 2S state.Comment: 15 pages, Latex, no figure