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Matthias Volk

Publications and source records attributed to Matthias Volk.

29 records · Page 2Linked to original sources
arXiv2019

Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder

We reproduce the two-loop seven-point remainder function in planar, maximally supersymmetric Yang-Mills theory by direct integration of conformally-regulated chiral integrands. The remainder function is obtained as part of the two-loop logarithm of the MHV amplitude, the regularized form of which we compute directly in this scheme. We compare the scheme-dependent anomalous dimensions and related quantities in the conformal regulator with those found for the Higgs regulator.

hep-th↗
arXiv2019

A Quantum Framework for AdS/dCFT through Fuzzy Spherical Harmonics on $S^4$

We consider a non-supersymmetric domain-wall version of $\mathcal{N} = 4$ SYM theory where five out of the six scalar fields have non-zero classical values on one side of a wall of codimension one. The classical fields have commutators which constitute an irreducible representation of the Lie algebra $\mathfrak{so}(5)$ leading to a highly non-trivial mixing between color and flavor components of the quantum fields. Making use of fuzzy spherical harmonics on $S^4$, we explicitly solve the mixing problem and derive not only the spectrum of excitations at the quantum level but also the propagators of the original fields needed for perturbative quantum computations. As an application, we derive the one-loop one-point function of a chiral primary and find complete agreement with a supergravity prediction of the same quantity in a double-scaling limit which involves a limit of large instanton number in the dual D3-D7 probe-brane setup.

hep-th↗
arXiv2019

Rooting Out Letters: Octagonal Symbol Alphabets and Algebraic Number Theory

It is widely expected that NMHV amplitudes in planar, maximally supersymmetric Yang-Mills theory require symbol letters that are not rationally expressible in terms of momentum-twistor (or cluster) variables starting at two loops for eight particles. Recent advances in loop integration technology have made this an `experimentally testable' hypothesis: compute the amplitude at some kinematic point, and see if algebraic symbol letters arise. We demonstrate the feasibility of such a test by directly integrating the most difficult of the two-loop topologies required. This integral, together with its rotated image, suffices to determine the simplest NMHV component amplitude: the unique component finite at this order. Although each of these integrals involve algebraic symbol alphabets, the combination contributing to this amplitude is---surprisingly---rational. We describe the steps involved in this analysis, which requires several novel tricks of loop integration and also a considerable degree of algebraic number theory. We find dramatic and unusual simplifications, in which the two symbols initially expressed as almost ten million terms in over two thousand letters combine in a form that can be written in five thousand terms and twenty-five letters.

hep-th↗
arXiv2019

Safety Analysis for Vehicle Guidance Systems with Dynamic Fault Trees

This paper considers the design-phase safety analysis of vehicle guidance systems. The proposed approach constructs dynamic fault trees (DFTs) to model a variety of safety concepts and E/E architectures for drive automation. The fault trees can be used to evaluate various quantitative measures by means of model checking. The approach is accompanied by a large-scale evaluation: The resulting DFTs with up to 300 elements constitute larger-than-before DFTs, yet the concepts and architectures can be evaluated in a matter of minutes.

cs.SE↗
arXiv2019

A Quantum Check of Non-Supersymmetric AdS/dCFT

Via a challenging field-theory computation, we confirm a supergravity prediction for the non-supersymmetric D3-D7 probe-brane system with probe geometry AdS_4 x S^2 x S^2, stabilized by fluxes. Supergravity predicts, in a certain double-scaling limit, the value of the one-point functions of chiral primaries of the dual defect version of N=4 SYM theory, where the fluxes translate into SO(3) x SO(3)-symmetric, Lie-algebra-valued vacuum expectation values for all six scalar fields. Using a generalization of the technique based on fuzzy spherical harmonics developed for the related D3-D5 probe-brane system, we diagonalize the resulting mass matrix of the field theory. Subsequently, we calculate the planar one-loop correction to the vacuum expectation values of the scalars in dimensional reduction and find that it is UV finite and non-vanishing. We then proceed to calculating the one-loop correction to the planar one-point function of any single-trace scalar operator and explicitly evaluate this correction for a 1/2-BPS operator of length L at two leading orders in the double-scaling limit, finding exact agreement with the supergravity prediction.

hep-th↗
arXiv2018

One Net Fits All: A unifying semantics of Dynamic Fault Trees using GSPNs

Dynamic Fault Trees (DFTs) are a prominent model in reliability engineering. They are strictly more expressive than static fault trees, but this comes at a price: their interpretation is non-trivial and leaves quite some freedom. This paper presents a GSPN semantics for DFTs. This semantics is rather simple and compositional. The key feature is that this GSPN semantics unifies all existing DFT semantics from the literature. All semantic variants can be obtained by choosing appropriate priorities and treatment of non-determinism.

cs.SE↗
arXiv2017

A storm is Coming: A Modern Probabilistic Model Checker

We launch the new probabilistic model checker storm. It features the analysis of discrete- and continuous-time variants of both Markov chains and MDPs. It supports the PRISM and JANI modeling languages, probabilistic programs, dynamic fault trees and generalized stochastic Petri nets. It has a modular set-up in which solvers and symbolic engines can easily be exchanged. It offers a Python API for rapid prototyping by encapsulating storm's fast and scalable algorithms. Experiments on a variety of benchmarks show its competitive performance.

cs.SE↗
arXiv2016

Advancing Dynamic Fault Tree Analysis

This paper presents a new state space generation approach for dynamic fault trees (DFTs) together with a technique to synthesise failures rates in DFTs. Our state space generation technique aggressively exploits the DFT structure --- detecting symmetries, spurious non-determinism, and don't cares. Benchmarks show a gain of more than two orders of magnitude in terms of state space generation and analysis time. Our approach supports DFTs with symbolic failure rates and is complemented by parameter synthesis. This enables determining the maximal tolerable failure rate of a system component while ensuring that the mean time of failure stays below a threshold.

cs.SE↗
arXiv2014

Accelerating Parametric Probabilistic Verification

We present a novel method for computing reachability probabilities of parametric discrete-time Markov chains whose transition probabilities are fractions of polynomials over a set of parameters. Our algorithm is based on two key ingredients: a graph decomposition into strongly connected subgraphs combined with a novel factorization strategy for polynomials. Experimental evaluations show that these approaches can lead to a speed-up of up to several orders of magnitude in comparison to existing approaches

cs.SE↗
arXiv2012

The COMICS Tool - Computing Minimal Counterexamples for Discrete-time Markov Chains

This report presents the tool COMICS, which performs model checking and generates counterexamples for DTMCs. For an input DTMC, COMICS computes an abstract system that carries the model checking information and uses this result to compute a critical subsystem, which induces a counterexample. This abstract subsystem can be refined and concretized hierarchically. The tool comes with a command-line version as well as a graphical user interface that allows the user to interactively influence the refinement process of the counterexample.

cs.SE↗