Classifications of Computable Structures

Let K be a family of structures, closed under isomorphism, in a fixed computable language. We consider effective lists of structures from K such that every structure in K is isomorphic to exactly one structure on the list. Such a list is called a computable classification of K, up to isomorphism. Using the technique of Friedberg enumeration, we show that there is a computable classification of the family of computable algebraic fields, and that with a 0\u27-oracle, we can obtain similar classifications of the families of computable equivalence structures and of computable finite-branching trees. However, there is no computable classification of the latter, nor of the family of computable torsion-free abelian groups of rank 1, even though these families are both closely allied with computable algebraic fields

Klimawandel und Risikomanagement im norddeutschen Küstenschutz: eine Diskursanalyse

'Im Umgang mit den lokalen Konsequenzen des Klimawandels durch einen erhöhten Meeresspiegel spielt das politisch-administrative System eine zentrale Rolle. Der folgende Beitrag basiert auf Ergebnissen einer Diskursanalyse des politisch-administrativen Küstenschutzsystems an der deutschen Nordseeküste und untersucht den Bedarf langfristiger Vorsorgemaßnahmen. Als Teil des interdisziplinären Forschungsverbundes KRIM analysieren die Forscher sowohl natürliche wie soziale Adaptionsmöglichkeiten auf Extremereignisse (formuliert als lokale Klimaszenarien für das Jahr 2050). Besonderes Augenmerk gilt dabei dem methodischen Zugang. So werden unterschiedliche Aspekte der politisch-administrativen Risikobewertung (die Möglichkeit des Deichversagens, die Rolle der Klimaforschung für den Küstenschutz sowie die Bedeutung diskursiver und institutioneller Grenzziehungen) mit Blick auf die methodische Ausrichtung der Diskursanalyse untersucht. Ein zentrales Ergebnis dabei ist, dass die gegenwärtigen Unsicherheiten der Klima(wirkungs)forschung im Rahmen von Sicherheitsdiskursen interpretiert und absorbiert werden, welche sowohl auf lokalem Erfahrungswissen wie auf historisch gewachsenen administrativen Küstenschutzkompetenzen gründen.' (Autorenreferat)'Dealing with the local consequences of climate change and an accelerated sea-level rise, the political-administrative system plays a central role. The following article focuses on results of a discourse analysis of the political-administrative coastal protection system at the German North Sea coast and assesses the demands for long-term precautionary action. As part of the interdisciplinary research project KRIM we analyse both natural and social adaption options to extreme incidents (formulated as climate scenarios for the year 2050). Along with a summary of the discourse analysis, special attention is given to our methodological approach. Different aspects of the political-administrative risk assessment (the possibility of dike failure, the role of climate change research for coastal protection, the importance of discursive and institutional boundary work) are brought up and wrapped to the methodological issues of our discourse analysis. The core thesis here is that the uncertainties of climate impact research get interpreted and absorbed within safety-discourses that draw on local know-how as well as on historical growing competences in coastal protection.' (author's abstract

Block-Spin Approach to Electron Correlations

We consider an expansion of the ground state wavefunction of quantum lattice many-body systems in a basis whose states are tensor products of block-spin wavefunctions. We demonstrate by applying the method to the antiferromagnetic spin-1/2 chain that by selecting the most important many-body states the technique affords a severe truncation of the Hilbert space while maintaining high accuracy.Comment: 17 pages, 3 Postscript figure

Exact Groundstates for Antiferromagnetic Spin-One Chains with Nearest and Next-Nearest Neighbour Interactions

We have found the exact ground state for a large class of antiferromagnetic spin-one chains with nearest and next-nearest neighbour interactions. The ground state is characterized as a matrix product of local site states and has the properties characteristic of the Haldane scenario.Comment: 8 pages, to appear in Z. Phys. B, preprint Cologne-94-474

chroGPS, a global chromatin positioning system for the functional analysis and visualization of the epigenome

Development of tools to jointly visualize the genome and the epigenome remains a challenge. chroGPS is a computational approach that addresses this question. chroGPS uses multidimensional scaling techniques to represent similarity between epigenetic factors, or between genetic elements on the basis of their epigenetic state, in 2D/3D reference maps. We emphasize biological interpretability, statistical robustness, integration of genetic and epigenetic data from heterogeneous sources, and computational feasibility. Although chroGPS is a general methodology to create reference maps and study the epigenetic state of any class of genetic element or genomic region, we focus on two specific kinds of maps: chroGPSfactors, which visualizes functional similarities between epigenetic factors, and chroGPSgenes, which describes the epigenetic state of genes and integrates gene expression and other functional data. We use data from the modENCODE project on the genomic distribution of a large collection of epigenetic factors in Drosophila, a model system extensively used to study genome organization and function. Our results show that the maps allow straightforward visualization of relationships between factors and elements, capturing relevant information about their functional properties that helps to interpret epigenetic information in a functional context and derive testable hypotheses

Optimal topological simplification of discrete functions on surfaces

We solve the problem of minimizing the number of critical points among all functions on a surface within a prescribed distance {\delta} from a given input function. The result is achieved by establishing a connection between discrete Morse theory and persistent homology. Our method completely removes homological noise with persistence less than 2{\delta}, constructively proving the tightness of a lower bound on the number of critical points given by the stability theorem of persistent homology in dimension two for any input function. We also show that an optimal solution can be computed in linear time after persistence pairs have been computed.Comment: 27 pages, 8 figure

Mathematical Explanations and Mathematical Applications

One of the key questions in the philosophy of mathematics is the role and status of mathematical applications in the natural sciences. The importance of mathematics for science is indisputable, but philosophers have disagreed on what the relation between mathematical theories and scientific theories are. This chapter presents these topics through a distinction between mathematical applications and mathematical explanations. Particularly important is the question whether mathematical applications are ever indispensable. If so, it has often been argued, such applications should count as proper mathematical explanations. Following Quine, many philosophers have also contended that if there are indispensable mathematical applications in the natural sciences, then the mathematical objects posited in those applications have an independent existence like the scientific objects. Thus the question of mathematical explanations and applications has an important relevance for the ontology of mathematics.Peer reviewe

My Journey...Through a Bone Marrow/Stem Cell Transplant

This is an activity book for you to use during your bone marrow/stem cell transplant. This book has pictures to color, games, puzzles, activities, and information. In the back of the book are blank calendar and journal pages to write on. SHARE THIS BOOK

Decoherence-protected quantum gates for a hybrid solid-state spin register

Protecting the dynamics of coupled quantum systems from decoherence by the environment is a key challenge for solid-state quantum information processing. An idle qubit can be efficiently insulated from the outside world via dynamical decoupling, as has recently been demonstrated for individual solid-state qubits. However, protection of qubit coherence during a multi-qubit gate poses a non-trivial problem: in general the decoupling disrupts the inter-qubit dynamics, and hence conflicts with gate operation. This problem is particularly salient for hybrid systems, wherein different types of qubits evolve and decohere at vastly different rates. Here we present the integration of dynamical decoupling into quantum gates for a paradigmatic hybrid system, the electron-nuclear spin register. Our design harnesses the internal resonance in the coupled-spin system to resolve the conflict between gate operation and decoupling. We experimentally demonstrate these gates on a two-qubit register in diamond operating at room temperature. Quantum tomography reveals that the qubits involved in the gate operation are protected as accurately as idle qubits. We further illustrate the power of our design by executing Grover's quantum search algorithm, achieving fidelities above 90% even though the execution time exceeds the electron spin dephasing time by two orders of magnitude. Our results directly enable decoherence-protected interface gates between different types of promising solid-state qubits. Ultimately, quantum gates with integrated decoupling may enable reaching the accuracy threshold for fault-tolerant quantum information processing with solid-state devices.Comment: This is original submitted version of the paper. The revised and finalized version is in print, and is subjected to the embargo and other editorial restrictions of the Nature journa