Magnon dispersion to four loops in the ABJM and ABJ models

The ABJM model is a superconformal Chern-Simons theory with N=6 supersymmetry which is believed to be integrable in the planar limit. However, there is a coupling dependent function that appears in the magnon dispersion relation and the asymptotic Bethe ansatz that is only known to leading order at strong and weak coupling. We compute this function to four loops in perturbation theory by an explicit Feynman diagram calculation for both the ABJM model and the ABJ extension. We find that all coefficients have maximal transcendentality. We then compute the four-loop wrapping correction for a scalar operator in the 20 of SU(4) and find that it agrees with a recent prediction from the ABJM Y-system of Gromov, Kazakov and Vieira. We also propose a limit of the ABJ model that might be perturbatively integrable at all loop orders but has a short range Hamiltonian.Comment: LaTeX, feynmp, 17 pages; v2: coupling factor in one Feynman diagram corrected: modified result in the ABJ case only, formulations improved, typos fixed, references added; v3: signs of three diagrams corrected, modifying the final resul

Dyonic Giant Magnons in CP^3: Strings and Curves at Finite J

This paper studies giant magnons in AdS_4 x CP^3 using both the string sigma-model and the algebraic curve. We complete the dictionary of solutions by finding the dyonic generalisation of the CP^1 string solution, which matches the `small' giant magnon in the algebraic curve, and by pointing out that the solution recently constructed by the dressing method is the `big' giant magnon. We then use the curve to compute finite-J corrections to all cases, which for the non-dyonic cases always match the AFZ result. For the dyonic RP^3 magnon we recover the S^5 answer, but for the `small' and `big' giant magnons we obtain new corrections.Comment: 22 pages, 3 figures, 2 tables. v2 adds note on breather solution, and minor clarification

Performance Optimizations and Operator Semantics for Streaming Data Flow Programs

Unternehmen sammeln mehr Daten als je zuvor und müssen auf diese Informationen zeitnah reagieren. Relationale Datenbanken eignen sich nicht für die latenzfreie Verarbeitung dieser oft unstrukturierten Daten. Um diesen Anforderungen zu begegnen, haben sich in der Datenbankforschung seit dem Anfang der 2000er Jahre zwei neue Forschungsrichtungen etabliert: skalierbare Verarbeitung unstrukturierter Daten und latenzfreie Datenstromverarbeitung. Skalierbare Verarbeitung unstrukturierter Daten, auch bekannt unter dem Begriff "Big Data"-Verarbeitung, hat in der Industrie schnell Einzug erhalten. Gleichzeitig wurden in der Forschung Systeme zur latenzfreien Datenstromverarbeitung entwickelt, die auf eine verteilte Architektur, Skalierbarkeit und datenparallele Verarbeitung setzen. Obwohl diese Systeme in der Industrie vermehrt zum Einsatz kommen, gibt es immer noch große Herausforderungen im praktischen Einsatz. Diese Dissertation verfolgt zwei Hauptziele: Zuerst wird das Laufzeitverhalten von hochskalierbaren datenparallelen Datenstromverarbeitungssystemen untersucht. Im zweiten Hauptteil wird das "Dual Streaming Model" eingeführt, das eine Semantik zur gleichzeitigen Verarbeitung von Datenströmen und Tabellen beschreibt. Das Ziel unserer Untersuchung ist ein besseres Verständnis über das Laufzeitverhalten dieser Systeme zu erhalten und dieses Wissen zu nutzen um Anfragen automatisch ausreichende Rechenkapazität zuzuweisen. Dazu werden ein Kostenmodell und darauf aufbauende Optimierungsalgorithmen für Datenstromanfragen eingeführt, die Datengruppierung und Datenparallelität einbeziehen. Das vorgestellte Datenstromverarbeitungsmodell beschreibt das Ergebnis eines Operators als kontinuierlichen Strom von Veränderugen auf einer Ergebnistabelle. Dabei behandelt unser Modell die Diskrepanz der physikalischen und logischen Ordnung von Datenelementen inhärent und erreicht damit eine deterministische Semantik und eine minimale Verarbeitungslatenz.Modern companies are able to collect more data and require insights from it faster than ever before. Relational databases do not meet the requirements for processing the often unstructured data sets with reasonable performance. The database research community started to address these trends in the early 2000s. Two new research directions have attracted major interest since: large-scale non-relational data processing as well as low-latency data stream processing. Large-scale non-relational data processing, commonly known as "Big Data" processing, was quickly adopted in the industry. In parallel, low latency data stream processing was mainly driven by the research community developing new systems that embrace a distributed architecture, scalability, and exploits data parallelism. While these systems have gained more and more attention in the industry, there are still major challenges to operate them at large scale. The goal of this dissertation is two-fold: First, to investigate runtime characteristics of large scale data-parallel distributed streaming systems. And second, to propose the "Dual Streaming Model" to express semantics of continuous queries over data streams and tables. Our goal is to improve the understanding of system and query runtime behavior with the aim to provision queries automatically. We introduce a cost model for streaming data flow programs taking into account the two techniques of record batching and data parallelization. Additionally, we introduce optimization algorithms that leverage our model for cost-based query provisioning. The proposed Dual Streaming Model expresses the result of a streaming operator as a stream of successive updates to a result table, inducing a duality between streams and tables. Our model handles the inconsistency of the logical and the physical order of records within a data stream natively, which allows for deterministic semantics as well as low latency query execution

Slumlordism as a Tort

The war against poverty has been fought with rather more vigor than its initiators contemplated. Thus far, however, the major engagements have taken place in the streets of Watts and Chicago, which is not quite what they had in mind. Some, who think it odd that as we pass more laws we get more lawlessness, will perhaps content themselves by observing that the feeding hand is always bitten. Those less easily satisfied have begun to see the need for adopting some legal solutions as far reaching as the problems they are designed to abate; the following article is addressed to them