DALiuGE: A Graph Execution Framework for Harnessing the Astronomical Data Deluge

The Data Activated Liu Graph Engine - DALiuGE - is an execution framework for processing large astronomical datasets at a scale required by the Square Kilometre Array Phase 1 (SKA1). It includes an interface for expressing complex data reduction pipelines consisting of both data sets and algorithmic components and an implementation run-time to execute such pipelines on distributed resources. By mapping the logical view of a pipeline to its physical realisation, DALiuGE separates the concerns of multiple stakeholders, allowing them to collectively optimise large-scale data processing solutions in a coherent manner. The execution in DALiuGE is data-activated, where each individual data item autonomously triggers the processing on itself. Such decentralisation also makes the execution framework very scalable and flexible, supporting pipeline sizes ranging from less than ten tasks running on a laptop to tens of millions of concurrent tasks on the second fastest supercomputer in the world. DALiuGE has been used in production for reducing interferometry data sets from the Karl E. Jansky Very Large Array and the Mingantu Ultrawide Spectral Radioheliograph; and is being developed as the execution framework prototype for the Science Data Processor (SDP) consortium of the Square Kilometre Array (SKA) telescope. This paper presents a technical overview of DALiuGE and discusses case studies from the CHILES and MUSER projects that use DALiuGE to execute production pipelines. In a companion paper, we provide in-depth analysis of DALiuGE's scalability to very large numbers of tasks on two supercomputing facilities.Comment: 31 pages, 12 figures, currently under review by Astronomy and Computin

Structured Error Recovery for Codeword-Stabilized Quantum Codes

Codeword stabilized (CWS) codes are, in general, non-additive quantum codes that can correct errors by an exhaustive search of different error patterns, similar to the way that we decode classical non-linear codes. For an n-qubit quantum code correcting errors on up to t qubits, this brute-force approach consecutively tests different errors of weight t or less, and employs a separate n-qubit measurement in each test. In this paper, we suggest an error grouping technique that allows to simultaneously test large groups of errors in a single measurement. This structured error recovery technique exponentially reduces the number of measurements by about 3^t times. While it still leaves exponentially many measurements for a generic CWS code, the technique is equivalent to syndrome-based recovery for the special case of additive CWS codes.Comment: 13 pages, 9 eps figure

LoLa: a modular ontology of logics, languages and translations

The Distributed Ontology Language (DOL), currently being standardised within the OntoIOp (Ontology Integration and Interoperability) activity of ISO/TC 37/SC 3, aims at providing a unified framework for (i) ontologies formalised in heterogeneous logics, (ii) modular ontologies, (iii) links between ontologies, and (iv) annotation of ontologies.\ud \ud This paper focuses on the LoLa ontology, which formally describes DOL's vocabulary for logics, ontology languages (and their serialisations), as well as logic translations. Interestingly, to adequately formalise the logical relationships between these notions, LoLa itself needs to be axiomatised heterogeneously---a task for which we choose DOL. Namely, we use the logic RDF for ABox assertions, OWL for basic axiomatisations of various modules concerning logics, languages, and translations, FOL for capturing certain closure rules that are not expressible in OWL (For the sake of tool availability it is still helpful not to map everything to FOL.), and circumscription for minimising the extension of concepts describing default translations

Kerdock Codes Determine Unitary 2-Designs

The non-linear binary Kerdock codes are known to be Gray images of certain extended cyclic codes of length $N = 2^m$ over $\mathbb{Z}_4$. We show that exponentiating these $\mathbb{Z}_4$-valued codewords by $\imath \triangleq \sqrt{-1}$ produces stabilizer states, that are quantum states obtained using only Clifford unitaries. These states are also the common eigenvectors of commuting Hermitian matrices forming maximal commutative subgroups (MCS) of the Pauli group. We use this quantum description to simplify the derivation of the classical weight distribution of Kerdock codes. Next, we organize the stabilizer states to form $N+1$ mutually unbiased bases and prove that automorphisms of the Kerdock code permute their corresponding MCS, thereby forming a subgroup of the Clifford group. When represented as symplectic matrices, this subgroup is isomorphic to the projective special linear group PSL($2,N$). We show that this automorphism group acts transitively on the Pauli matrices, which implies that the ensemble is Pauli mixing and hence forms a unitary $2$-design. The Kerdock design described here was originally discovered by Cleve et al. (arXiv:1501.04592), but the connection to classical codes is new which simplifies its description and translation to circuits significantly. Sampling from the design is straightforward, the translation to circuits uses only Clifford gates, and the process does not require ancillary qubits. Finally, we also develop algorithms for optimizing the synthesis of unitary $2$-designs on encoded qubits, i.e., to construct logical unitary $2$-designs. Software implementations are available at https://github.com/nrenga/symplectic-arxiv18a, which we use to provide empirical gate complexities for up to $16$ qubits.Comment: 16 pages double-column, 4 figures, and some circuits. Accepted to 2019 Intl. Symp. Inf. Theory (ISIT), and PDF of the 5-page ISIT version is included in the arXiv packag

Analysis of Boolean Equation Systems through Structure Graphs

We analyse the problem of solving Boolean equation systems through the use of structure graphs. The latter are obtained through an elegant set of Plotkin-style deduction rules. Our main contribution is that we show that equation systems with bisimilar structure graphs have the same solution. We show that our work conservatively extends earlier work, conducted by Keiren and Willemse, in which dependency graphs were used to analyse a subclass of Boolean equation systems, viz., equation systems in standard recursive form. We illustrate our approach by a small example, demonstrating the effect of simplifying an equation system through minimisation of its structure graph

On the relative proof complexity of deep inference via atomic flows

We consider the proof complexity of the minimal complete fragment, KS, of standard deep inference systems for propositional logic. To examine the size of proofs we employ atomic flows, diagrams that trace structural changes through a proof but ignore logical information. As results we obtain a polynomial simulation of versions of Resolution, along with some extensions. We also show that these systems, as well as bounded-depth Frege systems, cannot polynomially simulate KS, by giving polynomial-size proofs of certain variants of the propositional pigeonhole principle in KS.Comment: 27 pages, 2 figures, full version of conference pape