Enumerating Tarski fixed points on lattices of binary relations

We study the problem of enumerating Tarski fixed points, focusing on the relational lattices of equivalences, quasiorders and binary relations. We present a polynomial space enumeration algorithm for Tarski fixed points on these lattices and other lattices of polynomial height. It achieves polynomial delay when enumerating fixed points of increasing isotone maps on all three lattices, as well as decreasing isotone maps on the lattice of binary relations. In those cases in which the enumeration algorithm does not guarantee polynomial delay on the three relational lattices on the other hand, we prove exponential lower bounds for deciding the existence of three fixed points when the isotone map is given as an oracle, and that it is NP-hard to find three or more Tarski fixed points. More generally, we show that any deterministic or bounded-error randomized algorithm must perform a number of queries asymptotically at least as large as the lattice width to decide the existence of three fixed points when the isotone map is given as an oracle. Finally, we demonstrate that our findings yield a polynomial delay and space algorithm for listing bisimulations and instances of some related models of behavioral or role equivalence

How SMEs can participate in the potentials of Big Data within Industry 4.0

Through digital interconnection along the value chain, the concept of Industry 4.0 aims to generate data transparency that results in the generation of Big Data. To approach the expected potentials, several barriers exist in the context of Small and Medium-Sized Enterprises (SMEs). On the one hand, large enterprises are much better prepared to profit from the value of big data in comparison to SMEs, which are often suppliers in global value chains and do not have contact to end customers. Further, the data generation within SMEs is often too small and unstandardized in order to generate sufficient input for Big Data. On the other hand, large enterprises require their suppliers, often SMEs, to share their data so that Big Data can be generated in the first place. This paper builds on a literature review on extant research in the field of Industry 4.0, Big Data, and SMEs, and describes insights from an industrial case study. Condensing the findings of literature review and case study, the paper shows approaches how SMEs can be integrated within the concept of Industry 4.0, providing benefits for both, SMEs, and their often larger customers. Thereupon, implications for future research and managerial practice are derived

Massive Conformal Symmetry and Integrability for Feynman Integrals

In the context of planar holography, integrability plays an important role for solving certain massless quantum field theories such as N=4 SYM theory. In this letter we show that integrability also features in the building blocks of massive quantum field theories. At one-loop order we prove that all massive n-gon Feynman integrals in generic spacetime dimensions are invariant under a massive Yangian symmetry. At two loops similar statements can be proven for graphs built from two n-gons. At generic loop order we conjecture that all graphs cut from regular tilings of the plane with massive propagators on the boundary are invariant. We support this conjecture by a number of numerical tests for higher loops and legs. The observed Yangian extends the bosonic part of the massive dual conformal symmetry that was found a decade ago on the Coulomb branch of N=4 SYM theory. By translating the Yangian level-one generators from dual to original momentum space, we introduce a massive generalization of momentum space conformal symmetry. Even for non-dual conformal integrals this novel symmetry persists. The Yangian can thus be understood as the closure of massive dual conformal symmetry and this new massive momentum space conformal symmetry, which suggests an interpretation via AdS/CFT. As an application of our findings, we bootstrap the hypergeometric building blocks for examples of massive Feynman integrals.Comment: 6 pages, v2: typos corrected, clarifications added, v3: minor improvements/corrections, title adapted to journal titl

Quaternionic spherical harmonics and a sharp multiplier theorem on quaternionic spheres

A sharp $L^p$ spectral multiplier theorem of Mihlin--H\"ormander type is proved for a distinguished sub-Laplacian on quaternionic spheres. This is the first such result on compact sub-Riemannian manifolds where the horizontal space has corank greater than one. The proof hinges on the analysis of the quaternionic spherical harmonic decomposition, of which we present an elementary derivation

A Fragment of Dependence Logic Capturing Polynomial Time

In this paper we study the expressive power of Horn-formulae in dependence logic and show that they can express NP-complete problems. Therefore we define an even smaller fragment D-Horn* and show that over finite successor structures it captures the complexity class P of all sets decidable in polynomial time. Furthermore we study the question which of our results can ge generalized to the case of open formulae of D-Horn* and so-called downwards monotone polynomial time properties of teams

Potentials for AI-Based Data-Driven Business Models in Industry 4.0

Whereas the topics of artificial intelligence (AI) and business model innovation have attracted significant attention in academic research, publications at the intersection of both topics are rather sparse. In response, this paper attempts to interconnect the topics conceptually. In particular, it focuses on AI-driven business models in the context of Industry 4.0, highlighting examples and applications in the industrial context. In industry, first applications of AI applications have been known since several decades, such as in pattern recognition by cameras for failure detection. While applications in process or quality optimization have been improved since then, the clear connection to business models is not always clear. Therefore, this paper attempts to differentiate between examples of AI-driven business models that monetize, e.g., process optimization, or data-driven approaches of entire industrial platforms. In doing so, the present paper presents an overview of categories for AI-driven business model innovation across several industrial examples. As a result, future research can adopt and advance this overview to catego