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.

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We present the probabilistic model checker Storm. Storm supports the analysis of discrete- and continuous-time variants of both Markov chains and Markov decision processes. Storm has three major distinguishing features. It supports multiple input languages for Markov models, including the Jani and Prism modeling languages, dynamic fault trees, generalized stochastic Petri nets, and the probabilistic guarded command language. It has a modular setup in which solvers and symbolic engines can easily be exchanged. Its Python API allows for rapid prototyping by encapsulating Storm’s fast and scalable algorithms. This paper reports on the main features of Storm and explains how to effectively use them. A description is provided of the main distinguishing functionalities of Storm. Finally, an empirical evaluation of different configurations of Storm on the QComp 2019 benchmark set is presented.

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. PreliminariesDefinition 1 (Discrete-time Markov chain). A discrete-time Markov chain (DTMC) is a tuple D = (S, I, P ) with a non-empty finite set S of states, an initial

It has recently been demonstrated that Feynman integrals relevant to a wide range of perturbative quantum field theories involve periods of Calabi-Yau manifolds of arbitrarily large dimension. While the number of Calabi-Yau manifolds of dimension three or higher is considerable (if not infinite), those relevant to most known examples come from a very simple class: degree-2k hypersurfaces in k-dimensional weighted projective space WP 1,...,1,k . In this work, we describe some of the basic properties of these spaces and identify additional examples of Feynman integrals that give rise to hypersurfaces of this type. Details of these examples at three loops and of illustrations of open questions at four loops are included as ancillary files to this work.

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 × S 2 × 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) × 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.

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.