Computability In Europe Research Articles

Reifying dynamical algebra: Maximal ideals in countable rings, constructively

The existence of a maximal ideal in a general nontrivial commutative ring is tied together with the axiom of choice. Following Berardi, Valentini and thus Krivine but using the relative interpretation of negation (that is, as “implies 0 = 1”) we show, in constructive set theory with minimal logic, how for countable rings one can do without any kind of choice and without the usual decidability assumption that the ring is strongly discrete (membership in finitely generated ideals is decidable). By a functional recursive definition we obtain a maximal ideal in the sense that the quotient ring is a residue field (every noninvertible element is zero), and with strong discreteness even a geometric field (every element is either invertible or else zero). Krull’s lemma for the related notion of prime ideal follows by passing to rings of fractions. By employing a construction variant of set-theoretic forcing due to Joyal and Tierney, we expand our treatment to arbitrary rings and establish a connection with dynamical algebra: We recover the dynamical approach to maximal ideals as a parametrized version of the celebrated double negation translation. This connection allows us to give formal a priori criteria elucidating the scope of the dynamical method. Along the way we do a case study for proofs in algebra with minimal logic, and generalize the construction to arbitrary inconsistency predicates. A partial Agda formalization is available at an accompanying repository.11 See https://github.com/iblech/constructive-maximal-ideals/. This text is a revised and extended version of the conference paper (In Revolutions and Revelations in Computability. 18th Conference on Computability in Europe (2022) Springer). The conference paper only briefly sketched the connection with dynamical algebra; did not compare this connection with other flavors of set-theoretic forcing; and sticked to the case of commutative algebra only, passing on the generalization to inconsistency predicates and well-orders.

Nearly computable real numbers

We call a sequence ( a n ) n of elements of a metric space nearly computably Cauchy if for every increasing computable function r : N → N the sequence ( d ( a r ( n + 1 ) , a r ( n ) ) ) n converges computably to 0. We show that there exists an increasing sequence of rational numbers that is nearly computably Cauchy and unbounded. Then we call a real number α nearly computable if there exists a computable sequence ( a n ) n of rational numbers that converges to α and is nearly computably Cauchy. It is clear that every computable real number is nearly computable, and it follows from a result by Downey and LaForte (Theoretical Computer Science 284 (2002) 539–555) that there exists a nearly computable and left-computable number that is not computable. We observe that the set of nearly computable real numbers is a real closed field and closed under computable real functions with open domain, but not closed under arbitrary computable real functions. Among other things we strengthen results by Hoyrup (Theory of Computing Systems 60 (2017) 396–420) and by Stephan and Wu (In New computational paradigms. First conference on computability in Europe, CiE 2005, Proceedings (2005) 461–469 Springer) by showing that any nearly computable real number that is not computable is weakly 1-generic (and, therefore, hyperimmune and not Martin-Löf random) and strongly Kurtz random (and, therefore, not K-trivial), and we strengthen a result by Downey and LaForte (Theoretical Computer Science 284 (2002) 539–555) by showing that no promptly simple set can be Turing reducible to a nearly computable real number.

Lower bounds on β ( α ) and other properties of α-register machines

This paper extends our paper (In Revolutions and Revelations in Computability. CiE 2022 (2022)) for the conference “Computability in Europe” 2022. After Infinite Time Turing Machines (ITTM) were introduced in Hamkins and Lewis (Journal of Symbolic Logic 65 (2000)), a number of machine models of computability have been generalized to the transfinite. While for some of these models the computational strength has been successfully determined, there are still several white spots on the map of transfinite computability. In this paper, we contribute to the understanding of the computational strength of transfinite machine models by (i) proving lower bounds on the computational strength of α-Infinite Time Register Machines (α-ITRMs) for certain values of α, refuting a conjecture about their strength made in (Annals of Pure and Applied Logic 173 (2022)), (ii) showing that the computational strength of cardinal-recognizing ITRMs is equal to that of ITRMs and (iii) showing that non-solvability of the bounded halting problem, existence of a universal machine and an increase of computational power by allowing machines to recognize cardinals are equivalent for α-ITRMs for all relevant values of α. Finally, we give some results indicating how the picture changes when the use of parameters is dropped or restricted.

Approximating Kolmogorov complexity

It is well known that the Kolmogorov complexity function (the minimal length of a program producing a given string, when an optimal programming language is used) is not computable and, moreover, does not have computable lower bounds. In this paper we investigate a more general question: can this function be approximated? By approximation we mean two things: firstly, some (small) difference between the values of the complexity function and its approximation is allowed; secondly, at some (rare) points the values of the approximating function may be arbitrary. For some values of the parameters such approximation is trivial (e.g., the length function is an approximation with error d except for a O ( 2 − d ) fraction of inputs). However, if we require a significantly better approximation, the approximation problem becomes hard, and we prove it in several settings. Firstly, we show that a finite table that provides good approximations for Kolmogorov complexities of n-bit strings, necessarily has high complexity. Secondly, we show that there is no good computable approximation for Kolmogorov complexity of all strings. In particular, Kolmogorov complexity function is neither generically nor coarsely computable, as well as its approximations, and the time-bounded Kolmogorov complexity (for any computable time bound) deviates significantly from the unbounded complexity function. We also prove hardness of Kolmogorov complexity approximation in another setting: the mass problem whose solutions are good approximations for Kolmogorov complexity function is above the halting problem in the Medvedev lattice. Finally, we mention some proof-theoretic counterparts of these results. A preliminary version of this paper was presented at CiE 2019 conference (In Computing with Foresight and Industry – 15th Conference on Computability in Europe, CiE 2019, Durham, UK, July 15–19, 2019, Proceedings (2019) 230–239 Springer).

Lessons learned from urgent computing in Europe: Tackling the COVID-19 pandemic

PRACE (Partnership for Advanced Computing in Europe), an international not-for-profit association that brings together the five largest European supercomputing centers and involves 26 European countries, has allocated more than half a billion core hours to computer simulations to fight the COVID-19 pandemic. Alongside experiments, these simulations are a pillar of research to assess the risks of different scenarios and investigate mitigation strategies. While the world deals with the subsequent waves of the pandemic, we present a reflection on the use of urgent supercomputing for global societal challenges and crisis management.

Virgo and Gravitational-Wave Computing in Europe

Advanced Virgo is an interferometer for the detection of gravitational waves at the European Gravitational Observatory in Italy. Along with the two Advanced LIGO interferometers in the US, Advanced Virgo is being used to collect data from astrophysical sources such as compact binary coalescences and is currently running the third observational period, collecting gravitational wave event candidates at a rate of more than once per week. Data from the interferometer are processed by running search pipelines for several expected signals, from coalescing compact binaries to continuous waves and burst events. Furthermore, detector characterisation studies are run. Some of the processing needs to be done with low latency, to be able to provide triggers for other observatories and make multi-messenger observations possible. Deep searches are run offline on external computing centres. Thus, data needs also to be reliably and promptly distributed from the EGO site to computer centres in Europe and the US for further analysis and archival storage. Two of the defining characteristics of Virgo computing are the heterogeneity of the activities and the need to interoperate with LIGO. A very wide array of analysis pipelines differing in scientific target, implementation details and running environment assumptions have to be allowed to run ubiquitously and uniformly on dedicated resources and, in perspective, on heterogeneous infrastructures. The current status, possible strategies and outlook of Virgo computing are discussed.

Integrating LHCb workflows on HPC resources: status and strategies

High Performance Computing (HPC) supercomputers are expected to play an increasingly important role in HEP computing in the coming years. While HPC resources are not necessarily the optimal fit for HEP workflows, computing time at HPC centers on an opportunistic basis has already been available to the LHC experiments for some time, and it is also possible that part of the pledged computing resources will be offered as CPU time allocations at HPC centers in the future. The integration of the experiment workflows to make the most efficient use of HPC resources is therefore essential. This paper describes the work that has been necessary to integrate LHCb workflows at a specific HPC site, the Marconi-A2 system at CINECA in Italy, where LHCb benefited from a joint PRACE (Partnership for Advanced Computing in Europe) allocation with the other Large Hadron Collider (LHC) experiments. This has required addressing two types of challenges: on the software application workloads, for optimising their performance on a many-core hardware architecture that differs significantly from those traditionally used in WLCG (Worldwide LHC Computing Grid), by reducing memory footprint using a multi-process approach; and in the distributed computing area, for submitting these workloads using more than one logical processor per job, which had never been done yet in LHCb.

13TH COMPUTABILITY IN EUROPE CONFERENCE (CIE 2017) UNVEILING DYNAMICS AND COMPLEXITY CO-SPONSORED BY THE ASSOCIATION FOR SYMBOLIC LOGIC Turku, Finland June 12–16, 2017

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The LinkSCEEM FP7 Infrastructure Project: Linking Scientific Computing in Europe and the Eastern Mediterranean

Linking Scientific Computing in Europe and the Eastern Mediterranean (LinkSCEEM) was an FP7 infrastructure project that established a high-performance computing ecosystem in the Eastern Mediterranean region by interlinking and coordinating regional compute resources to form an integrated e-Infrastructure. The overarching objective of LinkSCEEM was to enable scientific research in the region by engaging and supporting research communities, with an initial emphasis in the fields of climate research, digital cultural heritage, and synchrotron radiation applications.

Algorithms for computing the double cut and join distance on both gene order and intergenic sizes

BackgroundCombinatorial works on genome rearrangements have so far ignored the influence of intergene sizes, i.e. the number of nucleotides between consecutive genes, although it was recently shown decisive for the accuracy of inference methods (Biller et al. in Genome Biol Evol 8:1427–39, 2016; Biller et al. in Beckmann A, Bienvenu L, Jonoska N, editors. Proceedings of Pursuit of the Universal-12th conference on computability in Europe, CiE 2016, Lecture notes in computer science, vol 9709, Paris, France, June 27–July 1, 2016. Berlin: Springer, p. 35–44, 2016). In this line, we define a new genome rearrangement model called wDCJ, a generalization of the well-known double cut and join (or DCJ) operation that modifies both the gene order and the intergene size distribution of a genome.ResultsWe first provide a generic formula for the wDCJ distance between two genomes, and show that computing this distance is strongly NP-complete. We then propose an approximation algorithm of ratio 4/3, and two exact ones: a fixed-parameter tractable (FPT) algorithm and an integer linear programming (ILP) formulation.ConclusionsWe provide theoretical and empirical bounds on the expected growth of the parameter at the center of our FPT and ILP algorithms, assuming a probabilistic model of evolution under wDCJ, which shows that both these algorithms should run reasonably fast in practice.

Climate SPHINX: evaluating the impact of resolution and stochastic physics parameterisations in the EC-Earth global climate model

Abstract. The Climate SPHINX (Stochastic Physics HIgh resolutioN eXperiments) project is a comprehensive set of ensemble simulations aimed at evaluating the sensitivity of present and future climate to model resolution and stochastic parameterisation. The EC-Earth Earth system model is used to explore the impact of stochastic physics in a large ensemble of 30-year climate integrations at five different atmospheric horizontal resolutions (from 125 up to 16 km). The project includes more than 120 simulations in both a historical scenario (1979–2008) and a climate change projection (2039–2068), together with coupled transient runs (1850–2100). A total of 20.4 million core hours have been used, made available from a single year grant from PRACE (the Partnership for Advanced Computing in Europe), and close to 1.5 PB of output data have been produced on SuperMUC IBM Petascale System at the Leibniz Supercomputing Centre (LRZ) in Garching, Germany. About 140 TB of post-processed data are stored on the CINECA supercomputing centre archives and are freely accessible to the community thanks to an EUDAT data pilot project. This paper presents the technical and scientific set-up of the experiments, including the details on the forcing used for the simulations performed, defining the SPHINX v1.0 protocol. In addition, an overview of preliminary results is given. An improvement in the simulation of Euro-Atlantic atmospheric blocking following resolution increase is observed. It is also shown that including stochastic parameterisation in the low-resolution runs helps to improve some aspects of the tropical climate – specifically the Madden–Julian Oscillation and the tropical rainfall variability. These findings show the importance of representing the impact of small-scale processes on the large-scale climate variability either explicitly (with high-resolution simulations) or stochastically (in low-resolution simulations).

Preface

This special issue of Mathematical Structures in Computer Science is dedicated to the memory of Barry Cooper (October 9, 1943–October 26, 2015). Barry's life in research had a huge impact on the development of the world of computability. Aside from his enormous achievements in classical computability theory, he contributed immensely to the promotion of interdisciplinary developments related to computability, in particular, by founding the Association for Computability in Europe (CiE) and its annual, highly successful conference series.

Using Science Gateways for Bridging the Differences between Research Infrastructures

Researchers can perform large-scale analyses on diverse computing and data infrastructures such as NGIs (National Grid Infrastructures), XSEDE (Extreme Science and Engineering Discovery Environment) and PRACE (Partnership for Advanced Computing in Europe). Some are national like NGIs and XSEDE, some are international like PRACE and all of them require a more or less restrictive application process to get access to resources. Science gateways integrating diverse infrastructures provide the possibility to re-use methods independent of such underlying infrastructures and thus potentially deliver the technical prerequisite for creating reproducible science. To achieve this goal, science gateways have to be integrated seamlessly with security mechanisms and job, data as well as workflow management of the targeted resources. This paper gives an overview on general findings for porting science gateways as well as the challenges faced for porting the German MoSGrid science gateway (Molecular Simulation Grid) to exploit XSEDE and PRACE infrastructures.

Offshore Wind Energy Climate Projection Using UPSCALE Climate Data under the RCP8.5 Emission Scenario.

In previous work, the authors demonstrated how data from climate simulations can be utilized to estimate regional wind power densities. In particular, it was shown that the quality of wind power densities, estimated from the UPSCALE global dataset in offshore regions of Mexico, compared well with regional high resolution studies. Additionally, a link between surface temperature and moist air density in the estimates was presented. UPSCALE is an acronym for UK on PRACE (the Partnership for Advanced Computing in Europe)—weather-resolving Simulations of Climate for globAL Environmental risk. The UPSCALE experiment was performed in 2012 by NCAS (National Centre for Atmospheric Science)-Climate, at the University of Reading and the UK Met Office Hadley Centre. The study included a 25.6-year, five-member ensemble simulation of the HadGEM3 global atmosphere, at 25km resolution for present climate conditions. The initial conditions for the ensemble runs were taken from consecutive days of a test configuration. In the present paper, the emphasis is placed on the single climate run for a potential future climate scenario in the UPSCALE experiment dataset, using the Representation Concentrations Pathways (RCP) 8.5 climate change scenario. Firstly, some tests were performed to ensure that the results using only one instantiation of the current climate dataset are as robust as possible within the constraints of the available data. In order to achieve this, an artificial time series over a longer sampling period was created. Then, it was shown that these longer time series provided almost the same results than the short ones, thus leading to the argument that the short time series is sufficient to capture the climate. Finally, with the confidence that one instantiation is sufficient, the future climate dataset was analysed to provide, for the first time, a projection of future changes in wind power resources using the UPSCALE dataset. It is hoped that this, in turn, will provide some guidance for wind power developers and policy makers to prepare and adapt for climate change impacts on wind energy production. Although offshore locations around Mexico were used as a case study, the dataset is global and hence the methodology presented can be readily applied at any desired location.

On the parallel computation thesis

We develop a generic programming language for parallel algorithms, one that works for all data structures and control structures. We show that any parallel algorithm satisfying intuitively-appealing postulates can be modeled by a collection of cells, each of which is an abstract state machine, augmented with the ability to spawn new cells. The cells all run the same algorithm and communicate via a shared global memory. Using a formal definition of what makes such an algorithm effective, we prove the validity of the Parallel Computation Thesis, according to which all reasonable parallel models of computation have roughly equivalent running times. La filosofia e scritta in questo grandissimo libro che continuamente ci sta aperto innanzi a gli occhi (io dico l’universo) ma non si puo intender se prima non s’ impara a intender la lingua e conoscere i caratteri ne’ quali e scritto. Egli e scritto in lingua matematica e i caratteri sono triangoli, cerchi, ed altre figure geometriche senza i quali mezi e impossibile a intenderne umanamente parola; senza questi e un aggirarsi vanamente per un oscuro laberinto. —Galileo Galilei (Il Saggiatore) This work was carried out in partial fulfillment of the requirements for the Ph.D. degree [22] of the second author. The first author’s research benefitted from a fellowship at the Paris Institute for Advanced Studies (France), with the financial support of the French state, managed by the French National Research Agency’s “Investissements d’avenir” program (ANR11-LABX-0027-01 Labex RFIEA+). A portion of this article was presented in a talk entitled, “Generic Parallel Algorithms,” at Computability in Europe (CiE) 2014 [16]. “Philosophy is written in this grand book, the universe, which stands continually open

Barry Cooper (1943–2015): The engine of Computability in Europe

Barry Cooper (1943–2015): The engine of Computability in Europe

Special and thematic issues then and now: Appendix 1

Special and thematic issues have always been at the heart of the Journal. As humanists, we are experts in the art of classification, and it is no wonder that the record of one of the first conferences on the use of computers for the humanities grouped together the published papers in seven thematic chapters. Computers for the Humanities? (Pierson, 1965)—notice the meaningful question mark in the title—published papers on the interaction of computers with the printed word, the use of computers in the study of literature, history, and the arts, as well as on social studies. The Association for Literary and Linguistic Computing (ALLC) was founded in 1973 by Joan M. Smith and Roy Wisbey, following the second successful international symposium on Literary and Linguistic Computing in Edinburgh in 1972. The first symposium took place at Cambridge in 1970 ‘to promote the exchange of ideas and to provide a means of communication for those engaged in natural language processing’ (Smith, 1973, p. 28). These ‘means of communication’ were the ALLC Bulletin , which started to appear in 1973, and the peer-reviewed ALLC Journal, which was first published in 1980. Both publications merged into the journal Literary and Linguistic Computing (LLC), the predecessor to Digital Scholarship in the Humanities (DSH), from 1986 onwards. However, the most important goal of the newly founded association was to facilitate personal contacts between researchers by way of seminars, regional meetings, and national or international colloquia (Wisbey, 1973). In 1974, the ALLC started a series of biannual conferences on literary and linguistic computing in Europe in the even years, alternating with the biannual series of the International Conference on Computers in the Humanities (ICCH) in the USA and Canada in the odd years.1 In this respect, the timing of the ALLC Journal was no … dshjournal{at}edwardz.be

Tropical Cyclones in the UPSCALE Ensemble of High-Resolution Global Climate Models*

Abstract The U.K. on Partnership for Advanced Computing in Europe (PRACE) Weather-Resolving Simulations of Climate for Global Environmental Risk (UPSCALE) project, using PRACE resources, constructed and ran an ensemble of atmosphere-only global climate model simulations, using the Met Office Unified Model Global Atmosphere 3 (GA3) configuration. Each simulation is 27 years in length for both the present climate and an end-of-century future climate, at resolutions of N96 (130 km), N216 (60 km), and N512 (25 km), in order to study the impact of model resolution on high-impact climate features such as tropical cyclones. Increased model resolution is found to improve the simulated frequency of explicitly tracked tropical cyclones, and correlations of interannual variability in the North Atlantic and northwestern Pacific lie between 0.6 and 0.75. Improvements in the deficit of genesis in the eastern North Atlantic as resolution increases appear to be related to the representation of African easterly waves and the African easterly jet. However, the intensity of the modeled tropical cyclones as measured by 10-m wind speed remains weak, and there is no indication of convergence over this range of resolutions. In the future climate ensemble, there is a reduction of 50% in the frequency of Southern Hemisphere tropical cyclones, whereas in the Northern Hemisphere there is a reduction in the North Atlantic and a shift in the Pacific with peak intensities becoming more common in the central Pacific. There is also a change in tropical cyclone intensities, with the future climate having fewer weak storms and proportionally more strong storms.

High-resolution global climate modelling: the UPSCALE project, a large-simulation campaign

Abstract. The UPSCALE (UK on PRACE: weather-resolving Simulations of Climate for globAL Environmental risk) project constructed and ran an ensemble of HadGEM3 (Hadley Centre Global Environment Model 3) atmosphere-only global climate simulations over the period 1985–2011, at resolutions of N512 (25 km), N216 (60 km) and N96 (130 km) as used in current global weather forecasting, seasonal prediction and climate modelling respectively. Alongside these present climate simulations a parallel ensemble looking at extremes of future climate was run, using a time-slice methodology to consider conditions at the end of this century. These simulations were primarily performed using a 144 million core hour, single year grant of computing time from PRACE (the Partnership for Advanced Computing in Europe) in 2012, with additional resources supplied by the Natural Environment Research Council (NERC) and the Met Office. Almost 400 terabytes of simulation data were generated on the HERMIT supercomputer at the High Performance Computing Center Stuttgart (HLRS), and transferred to the JASMIN super-data cluster provided by the Science and Technology Facilities Council Centre for Data Archival (STFC CEDA) for analysis and storage. In this paper we describe the implementation of the project, present the technical challenges in terms of optimisation, data output, transfer and storage that such a project involves and include details of the model configuration and the composition of the UPSCALE data set. This data set is available for scientific analysis to allow assessment of the value of model resolution in both present and potential future climate conditions.

Advancements of the UltraScan scientific gateway for open standards‐based cyberinfrastructures

SUMMARYThe UltraScan data analysis application is a software package that is able to take advantage of computational resources in order to support the interpretation of analytical ultracentrifugation experiments. Since 2006, the UltraScan scientific gateway has been used with Web browsers in TeraGrid by scientists studying the solution properties of biological and synthetic molecules. UltraScan supports its users with a scientific gateway in order to leverage the power of supercomputing. In this contribution, we will focus on several advancements of the UltraScan scientific gateway architecture with a standardized job management while retaining its lightweight design and end user interaction experience. This paper also presents insights into a production deployment of UltraScan in Europe. The approach is based on open standards with respect to job management and submissions to the Extreme Science and Engineering Discovery Environment in the USA and to similar infrastructures in Europe such as the European Grid Infrastructure or the Partnership for Advanced Computing in Europe (PRACE). Our implementation takes advantage of the Apache Airavata framework for scientific gateways that lays the foundation for easy integration into several other scientific gateways. Copyright © 2014 John Wiley & Sons, Ltd.