Flexibility Properties in Complex Analysis and Affine Algebraic Geometry

In the last decades affine algebraic varieties and Stein manifolds with big (infinite-dimensional) automorphism groups have been intensively studied. Several notions expressing that the automorphisms group is big have been proposed. All of them imply that the manifold in question is an Oka–Forstnerič manifold. This important notion has also recently merged from the intensive studies around the homotopy principle in Complex Analysis. This homotopy principle, which goes back to the 1930s, has had an enormous impact on the development of the area of Several Complex Variables and the number of its applications is constantly growing. In this overview chapter we present three classes of properties: (1) density property, (2) flexibility, and (3) Oka–Forstnerič. For each class we give the relevant definitions, its most significant features and explain the known implications between all these properties. Many difficult mathematical problems could be solved by applying the developed theory, we indicate some of the most spectacular ones.

Applied Graph Theory in Computer Vision and Pattern Recognition

This book will serve as a foundation for a variety of useful applications of graph theory to computer vision, pattern recognition, and related areas. It covers a representative set of novel graph-theoretic methods for complex computer vision and pattern recognition tasks. The first part of the book presents the application of graph theory to low-level processing of digital images such as a new method for partitioning a given image into a hierarchy of homogeneous areas using graph pyramids, or a study of the relationship between graph theory and digital topology. Part II presents graph-theoretic learning algorithms for high-level computer vision and pattern recognition applications, including a survey of graph based methodologies for pattern recognition and computer vision, a presentation of a series of computationally efficient algorithms for testing graph isomorphism and related graph matching tasks in pattern recognition and a new graph distance measure to be used for solving graph matching problems. Finally, Part III provides detailed descriptions of several applications of graph-based methods to real-world pattern recognition tasks. It includes a critical review of the main graph-based and structural methods for fingerprint classification, a new method to visualize time series of graphs, and potential applications in computer network monitoring and abnormal event detection.

Applications of random set theory in econometrics

In recent years, the econometrics literature has shown a growing interest in the study of partially identified models, in which the object of economic and statistical interest is a set rather than a point. The characterization of this set and the development of consistent estimators and inference procedures for it with desirable properties are the main goals of partial identification analysis. This review introduces the fundamental tools of the theory of random sets, which brings together elements of topology, convex geometry, and probability theory to develop a coherent mathematical framework to analyze random elements whose realizations are sets. It then elucidates how these tools have been fruitfully applied in econometrics to reach the goals of partial identification analysis.

Development of a method for fast and automatic radiocarbon measurement of aerosol samples by online coupling of an elemental analyzer with a MICADAS AMS

A fast and automatic method for radiocarbon analysis of aerosol samples is presented. This type of analysis requires high number of sample measurements of low carbon masses, but accepts precisions lower than for carbon dating analysis. The method is based on online Trapping CO2 and coupling an elemental analyzer with a MICADAS AMS by means of a gas interface. It gives similar results to a previously validated reference method for the same set of samples. This method is fast and automatic and typically provides uncertainties of 1.5–5% for representative aerosol samples. It proves to be robust and reliable and allows for overnight and unattended measurements. A constant and cross contamination correction is included, which indicates a constant contamination of 1.4 ± 0.2 μg C with 70 ± 7 pMC and a cross contamination of (0.2 ± 0.1)% from the previous sample. A Real-time online coupling version of the method was also investigated. It shows promising results for standard materials with slightly higher uncertainties than the Trapping online approach.

Influence of topology on the scale setting

Recently a new method to set the scale in lattice gauge theories, based on the gradient flow generated by the Wilson action, has been proposed, and the systematic errors of the new scales t0 and w0 have been investigated by various groups. The Wilson flow provides also an interesting alternative smoothing procedure particularly useful for the measurement of the topological charge as a pure gluonic observable. We show the viability of this method for N=1 supersymmetric Yang-Mills theory by analysing the configurations produced by the DESY-Muenster Collaboration. The relation between the scale and the topological charge has been investigated showing a strong correlation. We have found that the scale has a linear dependence on the topological charge, the slope of which increases decreasing the volume and the gluino mass. Moreover we have investigated this dependence as a function of the reference parameter used to define the scale: the tuning of this parameter turns out to be fundamental for a more reliable scale setting. Similar conclusions hold for the Sommer parameter r0.

Characterization of the Axial Jet Separator with a CO2/Helium Mixture: Toward GC-AMS Hyphenation

Development of interfaces for sample introduction from high pressures is important for real-time online hyphenation of chromatographic and other separation devices with mass spectrometry (MS) or accelerator mass spectrometry (AMS). Momentum separators can reduce unwanted low-density gases and introduce the analyte into the vacuum. In this work, the axial jet separator, a new momentum interface, is characterized by theory and empirical optimization. The mathematical model describes the different axial penetration of the components of a jetgas mixture and explains the empirical results for injections of CO2 in helium into MS and AMS instruments. We show that the performance of the new interface is sensitive to the nozzle size, showing good qualitative agreement with the mathematical model. Smaller nozzle sizes are more preferable due to their higher inflow capacity. The CO2 transmission efficiency of the interface into a MS instrument is ~14% (CO2/helium separation factor of 2.7). The interface receives and delivers flows of ~17.5 mL/min and ~0.9 mL/min, respectively. For the interfaced AMS instrument, the ionization and overall efficiencies are 0.7-3% and 0.1-0.4%, respectively, for CO2 amounts of 4-0.6 µg C, which is only slightly lower compared to conventional systems using intermediate trapping. The ionization efficiency depends on to the carbon mass flow in the injected pulse and is suppressed at high CO2 flows. Relative to a conventional jet separator, the transmission efficiency of the axial jet separator is lower, but its performance is less sensitive to misalignments.

The algebraic density property for affine toric varieties

In this paper we generalize the algebraic density property to not necessarily smooth affine varieties relative to some closed subvariety containing the singular locus. This property implies the remarkable approximation results for holomorphic automorphisms of the Andersén–Lempert theory. We show that an affine toric variety X satisfies this algebraic density property relative to a closed T-invariant subvariety Y if and only if X∖Y≠TX∖Y≠T. For toric surfaces we are able to classify those which possess a strong version of the algebraic density property (relative to the singular locus). The main ingredient in this classification is our proof of an equivariant version of Brunella's famous classification of complete algebraic vector fields in the affine plane.