Differential analysis of matrix convex functions

We analyze matrix convex functions of a fixed order defined on a real interval by differential methods as opposed to the characterization in terms of divided differences given by Kraus. We obtain for each order conditions for matrix convexity which are necessary and locally sufficient, and they allow us to prove the existence of gaps between classes of matrix convex functions of successive orders, and to give explicit examples of the type of functions contained in each of these gaps. The given conditions are shown to be also globally sufficient for matrix convexity of order two. We finally introduce a fractional transformation which connects the set of matrix monotone functions of each order n with the set of matrix convex functions of order n+1

Semantische Modellierung von geomorphologischenObjekten in einem Geoinformationssystem (GIS) unter besonderer Berücksichtigungvon Wänden und steilen Hangbereichen

Die vorliegende Arbeit ist im Graduiertenkolleg "Das Relief - eine strukturierte und veränderliche Grenzfläche" an der Universität Bonn entstanden. Sie befasst sich mit der formalen semantischen Modellierung und geometrischen Repräsentation von Wänden und steilen Hangbereichen aus der Sicht der Geoinformation. Im Fokus stehen die Fragen, wie geomorphologisches Fachwissen auf Grundlage internationaler Standards formalisiert und die im Rasterformat nicht zu fassenden Geometrien dieser z. T. überhängenden Formen repräsentiert werden können. Dabei muss der diskursive Formalisierungsgrad innerhalb der Geomorphologie dem Formalisierungsanspruch der Geoinformation angepasst werden. Wände und steile Hangbereiche stellen ein bedeutendes Naturgefahrenpotential für alpine Gebiete der gesamten Welt dar. Mit Felswänden verbundene Prozesse, wie Felsstürze oder Steinschlag, bedrohen Siedlungen und Tourismus. Die Erforschung dieser Landformen ist Aufgabe der Geomorphologie und nimmt dort wegen ihrer schnell ablaufenden Prozesse eine besondere Stellung ein. Eine auf Rasterdaten basierende Repräsentation ermöglicht allerdings keine ausreichende Analyse dieser Bereiche des Georeliefs, z. T. überhängende Wände sind mit klassischen Luftbildern nicht zu erfassen. Methoden zur terrestrischen Erhebung, etwa mittels Photogrammetrie, sind in der Geomorphologie wenig verbreitet. Auch liegen keine weiterreichenden formalen semantischen Modellierungen der betrachteten Objekte, ihrer funktionalen Beziehungen und anderer, grundlegender Konzepte der Fachwissenschaft vor. Eine geeignete geometrische Repräsentation und eine formale Semantik auf Grundlage internationaler Standards sind aber Voraussetzung für den weltweiten Austausch von Informationen innerhalb der Geomorphologie. Hier wird eine formale semantische Modellierung der grundlegenden Konzepte der Geomorphologie, insbesondere aber von Wänden und steilen Hangbereichen vorgelegt. Dafür wurde das geomorphologische Wissen gesichtet und in die formale Sprache UML überführt, die eine Implementierung des Modells in ein Datenbankmanagementsystem ermöglicht. Als geometrische Repräsentationsform, die einen Austausch von Daten garantiert, wurde der ISO 19107 "Spatial Schema" gewählt. Zur nachhaltigen Speicherung der modellierten Konzepte und geometrischer Repräsentationen kommt das objekt-relationale Datenbankmanagementsystem Oracle Spatial zum Einsatz. Zur Erfassung von z. T. überhängenden Wänden werden die Möglichkeiten der terrestrischen Photogrammetrie unter Verwendung einer handelsüblichen Kamera aufgezeigt. Hierfür wurde eine Möglichkeit geschaffen, die Photos zu orientieren und Neupunkte auf ihnen zu kartieren. Eine semantische Modellierung geomorphologischer Konzepte auf Grundlage internationale Standards ist durchführbar und weist weitreichende Vorteile auf. Diese sind neben einer differenzierten Betrachtungsmöglichkeit vor allem die Repräsentation von 3D-Geometrien. Weiter können auf Klassenkonzepte basierende semantische Modellierungen in DBMS überführt und die modellierten Phänomene damit informationstechnisch verarbeitet werden. Methoden der terrestrischen Photogrammetrie ermöglichen es, mit der hier entwickelten Software "GeoSamt" die besonderen Stellen des Reliefs aufzuklären.Semantic modelling of geomorphological objects within a geoinformation system (GIS) with emphasis on walls and steep slopes This thesis was written within the research training Group “Landform - a structured and variable boundary layer”. It occupies itself with formal semantic modelling and geometric representation of walls and steep slopes for financial geoinformational purposes. The main focus is on the questions of how to formalise specific knowledge of geomorphology on the basis of international standards and how to represent the geometries of partially overhanging forms, which cannot be captured in raster format, with concepts of geoinformation. Therefore, the semantic gap between geomorphology and geoinformation has to be considered. Walls and steep slopes are a major threat in alpine regions all over the world. Processes associated with rockwalls, such as rockfall, threaten settlements and the tourist infrastructure. It is the task of geomorphology to investigate these landforms. Because of their special processes and their significance within the concept of the sediment cascade, the investigation of these landforms is of special interest. A representation based on raster data does not, however, render a sufficient analysis of these parts of the georeliefs possible, as partially overhanging walls cannot be captured from above. Methods of terrestrial data capture, e.g. photogrammetry, are scarcely used in geomorphology. Moreover, far-reaching formal semantic modelling of the objects in question, their functional relations and other basic concepts of geomorphology do not yet exist. However, a suitable geometric representation and formal semantics based on international standards are prerequisites for the analysis of objects, their genesis and their interaction in a GIS. They are therefore vital for interdisciplinary investigation of land surfaces and the interchange of information. The present work introduces a formal semantic model of basic geomorphological concepts, focussed on walls and steep slopes. For this task, the specific existing geomorphological knowledge was screened and transferred into UML, which enabled an implementation of the model in a database management system. The ISO 19107 „Spatial Schema” was chosen as a geometric form of representation that guarantees an easy data exchange. The object-relational database management system Oracle Spatial was used for the persistent storage of the modelled semantic concepts and the geometric representation. In order to capture partly overhanging walls, the facilities of terrestrial photogrammetry were documented, using a consumer camera. For this the possibility to orientate the photos and to map new points was created. Semantic modelling of geomorphological concepts based on international standards is feasible and offers a number of advantages. Apart from rendering a differentiated investigation possible, these are especially the representations of 3D geometries. Furthermore, semantic modelling based on class concepts can be transferred into the DBMS and thus the modelled phenomena can be processed. Methods of terrestrial photogrammetry combined with the software „GeoSamt“ - which was developed for this work - allow a thorough investigation of the specific parts of the relief

Enhanced LoD concepts for virtual 3D city models

Virtual 3D city models contain digital three dimensional representations of city objects like buildings, streets or technical infrastructure. Because size and complexity of these models continuously grow, a Level of Detail (LoD) concept effectively supporting the partitioning of a complete model into alternative models of different complexity and providing metadata, addressing informational content, complexity and quality of each alternative model is indispensable. After a short overview on various LoD concepts, this paper discusses the existing LoD concept of the CityGML standard for 3D city models and identifies a number of deficits. Based on this analysis, an alternative concept is developed and illustrated with several examples. It differentiates between first, a Geometric Level of Detail (GLoD) and a Semantic Level of Detail (SLoD), and second between the interior building and ist exterior shell. Finally, a possible implementation of the new concept is demonstrated by means of an UML model

THE INFLUENCE OF LEVELS OF DETAIL (LOD0-2) AND BUFFER SIZES ON PARAMETER EFFECTIVENESS FOR FINE DUST DISTRIBUTION MODELLING

Building models represented in CityGML Level of Detail 0 to 2 were used to calculate urban morphological parameters to test their effectiveness of correlation with measured total number concentration of fine dust in Berlin. Land use regression modelling as an alternative to physical based models explains the distribution of urban fine and ultrafine particles applying a multi linear regression model. Descriptive parameters are identified by high correlations with measured fine dust values. Here, different height information and geometry representations from LoD0-LoD2 were used to calculate six parameters associated with the ventilation and advection capacity of an urban environment (‘averaged heights of buildings’, ‘height-width ratio’, ‘porosity’, ‘frontal area index’, and ‘building surfaces’ for wall surfaces and for wall and roof surfaces). Parameters were correlated with measurements of the total number concentration of fine dust in the city of Berlin. Initial results show ambivalent correlations for both, different buffer sizes and implementation of the parameters with building representations in different levels of detail

Stochastic Process Associated with Traveling Wave Solutions of the Sine-Gordon Equation

Stochastic processes associated with traveling wave solutions of the sine-Gordon equation are presented. The structure of the forward Kolmogorov equation as a conservation law is essential in the construction and so is the traveling wave structure. The derived stochastic processes are analyzed numerically. An interpretation of the behaviors of the stochastic processes is given in terms of the equation of motion.Comment: 12 pages, 9 figures; corrected typo

SLE for theoretical physicists

This article provides an introduction to Schramm(stochastic)-Loewner evolution (SLE) and to its connection with conformal field theory, from the point of view of its application to two-dimensional critical behaviour. The emphasis is on the conceptual ideas rather than rigorous proofs.Comment: 43 pages, to appear in Annals of Physics; v.2: published version with minor correction

Operator monotones, the reduction criterion and the relative entropy

We introduce the theory of operator monotone functions and employ it to derive a new inequality relating the quantum relative entropy and the quantum conditional entropy. We present applications of this new inequality and in particular we prove a new lower bound on the relative entropy of entanglement and other properties of entanglement measures.Comment: Final version accepted for publication, added references in reference [1] and [13

Growth processes related to the dispersionless Lax equations

This paper is a short review of the connection between certain types of growth processes and the integrable systems theory, written from the viewpoint of the latter. Starting from the dispersionless Lax equations for the 2D Toda hierarchy, we interpret them as evolution equations for conformal maps in the plane. This provides a unified approach to evolution of smooth domains (such as Laplacian growth) and growth of slits. We show that the L\"owner differential equation for a parametric family of conformal maps of slit domains arises as a consistency condition for reductions of the dispersionless Toda hierarchy. It is also demonstrated how the both types of growth processes can be simulated by the large $N$ limit of the Dyson gas picture for the model of normal random matrices.Comment: 16 pages, 2 figures, typos corrected, references adde

Spectral inequalities for Kubo-Ando operator means

Eigenvalue and singular value inequalities, involving Kubo-Ando operator connections or means, are established. Previous results from Lemos and Soares in 2018 are generalized or complemented, some log-majorizations are included. As a consequence, a refinement of an independent result by Ando and by Visick in 1995 on the eigenvalues of the Hadamard product is derived. Some singular value inequalities by Zou in 2017 are further extended.FCT - Fundação para a Ciência e a Tecnologiapublishe

Proposal for a new LoD and multi-representation concept for CityGML

The Open Geospatial Consortium (OGC) CityGML standard offers a Level of Detail (LoD) concept that enables the representation of CityGML features from a very detailed to a less detailed description. Due to a rising application variety, the current LoD concept seems to be too inflexible. Here, we present a multi representation concept (MRC) that enables a user-defined definition of LoDs. Because CityGML is an international standard, official profiles of the MRC are proposed. However, encoding of the defined profiles reveals many problems including mapping the conceptual model to the normative encoding, missing technologies and so on. Therefore, we propose to use the MRC as a meta model for the further definition of an LoD concept for CityGML 3.0