The Critical Exponent is Computable for Automatic Sequences

The critical exponent of an infinite word is defined to be the supremum of the exponent of each of its factors. For k-automatic sequences, we show that this critical exponent is always either a rational number or infinite, and its value is computable. Our results also apply to variants of the critical exponent, such as the initial critical exponent of Berthe, Holton, and Zamboni and the Diophantine exponent of Adamczewski and Bugeaud. Our work generalizes or recovers previous results of Krieger and others, and is applicable to other situations; e.g., the computation of the optimal recurrence constant for a linearly recurrent k-automatic sequence.Comment: In Proceedings WORDS 2011, arXiv:1108.341

Renormalization and blow up for charge one equivariant critical wave maps

We prove the existence of equivariant finite time blow up solutions for the wave map problem from 2+1 dimensions into the 2-sphere. These solutions are the sum of a dynamically rescaled ground-state harmonic map plus a radiation term. The local energy of the latter tends to zero as time approaches blow up time. This is accomplished by first "renormalizing" the rescaled ground state harmonic map profile by solving an elliptic equation, followed by a perturbative analysis

Final data reduction and analysis of the AS and E OSO-4 grazing incidence X-ray telescope experiment

Final data analysis of grazing incidence of solar X ray telescope experiment of OSO- 4 satellit

Generalized full sparse tiling of loop chains

2013 Fall.Includes bibliographical references.Computer and computational scientists are tackling increasingly large and complex problems and are seeking ways of improving the performance of their codes. The key issue faced is how to reach an effective balance between parallelism and locality. In trying to reach this balance, a problem commonly encountered is that of ascertaining the data dependences. Approaches that rely on automatic extraction of data dependences are frequently stymied by complications such as interprocedural and alias analysis. Placing the dependence analysis burden upon the programmer creates a significant barrier to adoption. In this work, we present a new programming abstraction, the loop chain, that specifies a series of loops and the data they access. Given this abstraction, a compiler, inspector, or runtime optimizer can avoid the computationally expensive process of formally determining data dependences, yet still determine beneficial and legal data and iteration reorderings. One optimization method that has been previously applied to irregular scientific codes is full sparse tiling. Full sparse tiling has been used to improve the performance of a handful of scientific codes, but in each case the technique had to be applied from scratch by an expert after careful manual analysis of the possible data dependence patterns. The full sparse tiling approach was extended and generalized as part of this work to apply to any code represented by the loop chain abstraction. Using only the abstraction, the generalized algorithm can produce a new data and iteration ordering as well as a parallel execution schedule. Insight into tuning a generalized full sparse tiled application was gained through a study of the different factors influencing tile count. This work lays the foundation for an efficient autotuning approach to optimizing tile count

Dynamic stem cell heterogeneity.

Recent lineage-tracing studies based on inducible genetic labelling have emphasized a crucial role for stochasticity in the maintenance and regeneration of cycling adult tissues. These studies have revealed that stem cells are frequently lost through differentiation and that this is compensated for by the duplication of neighbours, leading to the consolidation of clonal diversity. Through the combination of long-term lineage-tracing assays with short-term in vivo live imaging, the cellular basis of this stochastic stem cell loss and replacement has begun to be resolved. With a focus on mammalian spermatogenesis, intestinal maintenance and the hair cycle, we review the role of dynamic heterogeneity in the regulation of adult stem cell populations.B.D.S. acknowledges the financial support of the Wellcome Trust [098357/Z/12/Z] as well as core grants from the Wellcome Trust [092096] and Cancer Research UK [C6946/A14492].This is the author accepted manuscript. The final version is available via The Company of Biologists at http://dev.biologists.org/content/142/8/1396.abstract

Continuing data analysis of the AS/E grazing incidence X-ray telescope experiment on the OSO-4 satellite

The work to correct and extend the calculation of the theoretical solar X-ray spectrum produced during earlier OSO-4 data analysis is reported along with the work to formulate models of active regions, and compare these models with the experimental values. An atlas of solar X-ray photographs is included, and solar X-ray observations are correlated with the solar wind

Virtuelle Mikroskopie: Erste Anwendungen

Zusammenfassung: Die rasante Entwicklung der Computertechnologie ermöglicht es seit kurzem, ganze histologische Präparate einzuscannen. Die digitalisierten Präparate können über den Webbrowser von beliebig vielen Pathologen oder Studierenden gleichzeitig und ortsunabhängig am Computerbildschirm mikroskopiert werden. Für die Benutzung des virtuellen Mikroskops wird lediglich ein Computerarbeitsplatz mit einer schnellen Internetanbindung benötigt. Damit steht die virtuelle Mikroskopie einem sehr breiten Nutzerkreis offen. Ein virtuelles Mikroskopsystem besteht aus 3Komponenten: Akquisition, Server und Client. Die Entwicklung entsprechender Systeme durch Universitäten und kommerzielle Anbieter ist weltweit in vollem Gang. Vorgestellt wird ein neu entwickeltes virtuelles Mikroskopsystem mit dem Namen vMic, das virtuelle Präparate von sehr hoher Bildqualität liefert. Erste erfolgreiche Anwendungen in Form von Online-Schnittseminaren und einem Histologiepraktikum für Zahnmediziner sind frei im Internet einsehbar (http://www.vmic.unibas.ch). Kommerziell erhältliche und einfach zu bedienende ultraschnelle Präparatscanner und die rasch voranschreitende technische Entwicklung eröffnen der virtuellen Mikroskopie zahlreiche Einsatzmöglichkeiten in Lehre, Forschung und Dienstleistung. Dank zusätzlicher Funktionen ist es gut möglich, dass reale Mikroskope in einigen Jahren durch Computerarbeitsplätze ersetzt werde

New and extended parameterization of the thermodynamic model AIOMFAC: calculation of activity coefficients for organic-inorganic mixtures containing carboxyl, hydroxyl, carbonyl, ether, ester, alkenyl, alkyl, and aromatic functional groups

We present a new and considerably extended parameterization of the thermodynamic activity coefficient model AIOMFAC (Aerosol Inorganic-Organic Mixtures Functional groups Activity Coefficients) at room temperature. AIOMFAC combines a Pitzer-like electrolyte solution model with a UNIFAC-based group-contribution approach and explicitly accounts for interactions between organic functional groups and inorganic ions. Such interactions constitute the salt-effect, may cause liquid-liquid phase separation, and affect the gas-particle partitioning of aerosols. The previous AIOMFAC version was parameterized for alkyl and hydroxyl functional groups of alcohols and polyols. With the goal to describe a wide variety of organic compounds found in atmospheric aerosols, we extend here the parameterization of AIOMFAC to include the functional groups carboxyl, hydroxyl, ketone, aldehyde, ether, ester, alkenyl, alkyl, aromatic carbon-alcohol, and aromatic hydrocarbon. Thermodynamic equilibrium data of organic-inorganic systems from the literature are critically assessed and complemented with new measurements to establish a comprehensive database. The database is used to determine simultaneously the AIOMFAC parameters describing interactions of organic functional groups with the ions H^+, Li^+, Na^+, K^+, NH_(4)^+, Mg^(2+), Ca^(2+), Cl^−, Br^−, NO_(3)^−, HSO_(4)^−, and SO_(4)^(2−). Detailed descriptions of different types of thermodynamic data, such as vapor-liquid, solid-liquid, and liquid-liquid equilibria, and their use for the model parameterization are provided. Issues regarding deficiencies of the database, types and uncertainties of experimental data, and limitations of the model, are discussed. The challenging parameter optimization problem is solved with a novel combination of powerful global minimization algorithms. A number of exemplary calculations for systems containing atmospherically relevant aerosol components are shown. Amongst others, we discuss aqueous mixtures of ammonium sulfate with dicarboxylic acids and with levoglucosan. Overall, the new parameterization of AIOMFAC agrees well with a large number of experimental datasets. However, due to various reasons, for certain mixtures important deviations can occur. The new parameterization makes AIOMFAC a versatile thermodynamic tool. It enables the calculation of activity coefficients of thousands of different organic compounds in organic-inorganic mixtures of numerous components. Models based on AIOMFAC can be used to compute deliquescence relative humidities, liquid-liquid phase separations, and gas-particle partitioning of multicomponent mixtures of relevance for atmospheric chemistry or in other scientific fields