On-Shell Methods for the Two-Loop Dilatation Operator and Finite Remainders

We compute the two-loop minimal form factors of all operators in the SU(2) sector of planar N=4 SYM theory via on-shell unitarity methods. From the UV divergence of this result, we obtain the two-loop dilatation operator in this sector. Furthermore, we calculate the corresponding finite remainder functions. Since the operators break the supersymmetry, the remainder functions do not have the property of uniform transcendentality. However, the leading transcendentality part turns out to be universal and is identical to the corresponding BPS expressions. The remainder functions are shown to satisfy linear relations which can be explained by Ward identities of form factors following from R-symmetry.Comment: 24 pages; v2: typos corrected, some formulations clarified, matches published versio

CDOXplorer: Simulation-based genetic optimization of software deployment and reconfiguration in the cloud

Migrating existing enterprise software to cloud platforms involves the comparison of various cloud deployment options (CDOs). A CDO comprises a combination of a specific cloud environment, deployment architecture, and runtime reconfiguration rules for dynamic resource scaling. Our simulator CDOSim can evaluate CDOs, e.g., regarding response times and costs. However, the design space to be searched for well-suited solutions is very large. In this paper, we approach this optimization problem with the novel genetic algorithm CDOXplorer. It uses techniques of the search-based software engineering field and simulations with CDOSim to assess the fitness of CDOs. An experimental evaluation that employs, among others, the cloud environments Amazon EC2 and Microsoft Windows Azure, shows that CDOXplorer can find solutions that surpass those of other state-of-the-art techniques by up to 60\%. Our experiment code and data and an implementation of CDOXplorer are available as open source software

Research Perspective on Supporting Software Engineering via Physical 3D Models

Building architects, but also civil or mechanical engineers often build from their designs physical3D models for a better presentation, comprehension, and communication among stakeholders. Software engineers usually create visualizations of their software designs as digital objects to be presented on a screen only. 3D software visualization metaphors, such as the software city metaphor, provide a basis for exporting those on-screen software visualizations into physical models. This can be achieved by 3D-printers to transfer the advantages of real, physical, tangible architecture models from traditional engineering disciplines to software engineering. We present a new research perspective of using physical models to support software engineering. Furthermore, we describe four envisioned usage scenarios for physical models which provide a plethora of new research topics. As proof of concept, we investigate the first usage scenario by evaluating the impact of using physical models on program comprehension in teams through a first controlled experiment. Our experiment reveals that the usage of physical models has a diverging influence. However, they improve the team-based program comprehension process for specific tasks by initiating gesture-based interaction. Therefore, the experiment shows that physical models can provide a promising future research direction

Parallel Preconditioners for an Ocean Model in Climate Simulations

In this work, we evaluate different solvers and preconditioners for solving the barotropic system of an ocean model to achieve optimal performance on a high-performance computer. In the field of support theory, we derive upper bounds for the condition number of a system that is preconditioned with a block-Jacobi Steiner graph preconditioner. Furthermore, we analyze the application of a high-level approach for programming preconditioners on FPGAs

Stability and moment estimates for the stochastic singular Φ\Phi-Laplace equation

We study stability, long-time behavior and moment estimates for stochastic evolution equations with additive Wiener noise and with singular drift given by a divergence type quasilinear diffusion operator which may not necessarily exhibit a homogeneous diffusivity. Our results cover the singular $p$-Laplace and, more generally, singular $\Phi$-Laplace equations with zero Dirichlet boundary conditions. We obtain improved moment estimates and quantitative convergence rates of the ergodic semigroup to the unique invariant measure, classified in a systematic way according to the degree of local degeneracy of the potential at the origin. We obtain new concentration results for the invariant measure and establish maximal dissipativity of the associated Kolmogorov operator. In particular, we recover the results for the curve shortening flow in the plane by Es-Sarhir, von Renesse and Stannat, NoDEA 16(9), 2012.Comment: 23 pages, 54 reference

Cache behavior prediction by abstract interpretation

Abstract interpretation is a technique for the static detection of dynamic properties of programs. It is semantics based, that is, it computes approximative properties of the semantics of programs. On this basis, it allows for correctness proofs of analyses. It replaces commonly used ad hoc techniques by systematic, provable ones, and it allows the automatic generation of analyzers from specifications as in the Program Analyzer Generator, PAG. In this paper, abstract interpretation is applied to the problem of predicting the cache behavior of programs. Abstract semantics of machine programs are defined which determine the contents of caches. For interprocedural analysis, existing methods are examined and a new approach that is especially tailored for the cache analysis is presented. This allows for a static classification of the cache behavior of memory references of programs. The calculated information can be used to sharpen worst case execution time estimations. It is possible to analyze instruction, data, and combined instruction/data caches for common (re)placement and write strategies. Experimental results are presented that demonstrate the applicability of the analysis

Two-loop SL(2) form factors and maximal transcendentality

Form factors of composite operators in the SL(2) sector of N=4 SYM theory are studied up to two loops via the on-shell unitarity method. The non-compactness of this subsector implies the novel feature and technical challenge of an unlimited number of loop momenta in the integrand's numerator. At one loop, we derive the full minimal form factor to all orders in the dimensional regularisation parameter. At two loops, we construct the complete integrand for composite operators with an arbitrary number of covariant derivatives, and we obtain the remainder functions as well as the dilatation operator for composite operators with up to three covariant derivatives. The remainder functions reveal curious patterns suggesting a hidden maximal uniform transcendentality for the full form factor. Finally, we speculate about an extension of these patterns to QCD.Comment: 23+13 pages, v2: minor changes, published versio

Windowing Models for Abstractive Summarization of Long Texts

Neural summarization models suffer from the fixed-size input limitation: if text length surpasses the model's maximal number of input tokens, some document content (possibly summary-relevant) gets truncated Independently summarizing windows of maximal input size disallows for information flow between windows and leads to incoherent summaries. We propose windowing models for neural abstractive summarization of (arbitrarily) long texts. We extend the sequence-to-sequence model augmented with pointer generator network by (1) allowing the encoder to slide over different windows of the input document and (2) sharing the decoder and retaining its state across different input windows. We explore two windowing variants: Static Windowing precomputes the number of tokens the decoder should generate from each window (based on training corpus statistics); in Dynamic Windowing the decoder learns to emit a token that signals encoder's shift to the next input window. Empirical results render our models effective in their intended use-case: summarizing long texts with relevant content not bound to the very document beginning