September 2020 - Categories - categories.org.au

Re: "First" use of 'Category theory' to describe our field
by David Roberts 24 Feb '24

24 Feb '24

Dear Ross, no, that's pretty good! It's mildly surprising that it took ~20 years for the name to 'stick', but maybe less so given that the field grew slowly to start. Thanks, David David Roberts Webpage: https://ncatlab.org/nlab/show/David+Roberts Blog: https://thehighergeometer.wordpress.com On Thu, 11 Jul 2019 at 08:21, Ross Street <ross.street(a)mq.edu.au> wrote: > > Dear David > > From memory, the Pure Mathematics Honours (USyd) course that Max Kelly taught in 1965 > was called ``Category Theory''. It concentrated on different kinds of morphisms > and factorizations in a category, and finished with adjoint functors. > Also John Gray's (UIllinois) 1968-69 graduate course had that name. > > From Eilenberg I heard that each person using categories should have their own category of expertise. > I told this to John Gray who said that was fine; the time had come for that category to be Cat. > > I would suggest that the first category theorists to think of themselves as such were Eilenberg's students at Columbia. > However, Mac Lane was definitely a category theorist. > > This is probably not the verifiable stuff you were seeking. > > Ross > > > On 10 Jul 2019, at 10:01 PM, David Roberts <droberts.65537(a)gmail.com> wrote: > > Hi all, > > the (idle) question is: when did the phrase 'category theory' catch on > for the field? Clearly it didn't leap from either of the heads of > Eilenberg or Mac Lane full-grown, since they used the phrase 'General > theory of natural equivalences'. There are the old 'Reports of the > Midwest Category Seminar' lecture notes (the first in 1967), which > hints that 'category theory' wasn't quite the name in use. > > Even more interesting: who was the first "category theorist", by that name? > > Answers referring to verifiable sources would be best. > > Thoughts? > > David > > > > David Roberts > Webpage: https://ncatlab.org/nlab/show/David+Roberts > Blog: https://thehighergeometer.wordpress.com > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Re: Does essential entail locally connected for hyperconnected geometric morphisms?
by Jens Hemelaer 29 Sep '20

29 Sep '20

CAUTION: The Sender of this email is not from within Dalhousie. Dear Thomas, At the moment, we do not have a counterexample to the statement that pre-cohesive geometric morphisms are locally connected. We think we can construct one of the form PSh(M) --> PSh(N) with M and N monoids, but it will take some more work. All the best, Jens ________________________________ From: Thomas Streicher <streicher(a)mathematik.tu-darmstadt.de> Sent: Monday, September 28, 2020 1:36 PM To: Jens Hemelaer Cc: categories(a)mta.ca; Morgan Rogers Subject: Re: categories: Does essential entail locally connected for hyperconnected geometric morphisms? > Morgan Rogers and I were able to construct a counterexample of the form PSh(M) --> PSh(N) where M and N are monoids. It arises from our joint work-in-progress in which we study exactly these kind of geometric morphisms, in a systematic way. After talking about it with Thomas Streicher, we have now written up the counterexample in more detail. You can find it here: > <https://eur01.safelinks.protection.outlook.com/?url=https%3A%2F%2Farxiv.org…> https://arxiv.org/abs/2009.12241 (3 pages). Dear Jens and Morgan, thanks a lot for your very nice counterexample which I never would have found on my own! Alas, it leaves open Lawvere and Menni's question whether precohesive geometric morphisms are always also locally connected. Does your toolbox also provide a counterexample to this implication. The current one does not do this job since you show the leftmost adjoint does not preserve binary products. (By Lemma 2.7 of Johnstone's 2011 TAC paper preservation of binary products by the leftmost adjoint is equivalent to preservation of exponentials by the inverse image part for hyperconnected and local geometric morphisms.) BTW I think that locally connected, hyperconnected and local is the correct generalization of essential, 2-valued and local from base Set to arbitrary base toposes from the point of view of fibered categories. Best, Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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***SPAM?*** categories: Christian Lair died
by Camell Kachour 29 Sep '20

29 Sep '20

CAUTION: The Sender of this email is not from within Dalhousie. Dear All, As you may know, Christian Lair passed away last Friday 25th September. This is very sad news. Best regards, Camell. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Re: Seminar talk on Linear Logic
by Harley D. Eades III 28 Sep '20

28 Sep '20

CAUTION: The Sender of this email is not from within Dalhousie. Hi, everyone. There was a link issue with my original post; see below. The link is directing to an old talk. Must be a copy-and-paste error. The following is the correct location: https://the-au-forml-lab.github.io/colloquium_talks/dePaiva.html Thanks Elaine Pimentel for pointing this out to me. Sorry about the confusion. Best, Harley On Mon, Sep 28, 2020 at 8:31 AM Harley D. Eades III <harley.eades(a)gmail.com> wrote: > Hi, everyone. > > On Friday, Oct. 2, 2020 between 1pm and 2pm EDT, Dr. Valeria de Paiva will > be giving a presentation as part of the CS Colloquium Series at Augusta > University. > > Presentation details can be found here: > > https://the-au-forml-lab.github.io/colloquium_talks/dePaiva.html > <https://the-au-forml-lab.github.io/colloquium_talks/Horn.html> > > Valeria's talk will tell us about benchmarking linear logics which should > be fascinating! > > These talks are open to the general public via Zoom. I'll also be living > streaming it on Youtube. So if you are interested in attending the Zoom > meeting please RSVP with me before the talk. Questions will be only taken > from those on Zoom. > > If you care to watch via YouTube, please use the following link: > > https://youtu.be/1HVJLFysmHs > > I hope all of you, your family and friends are doing well! > > Very best, > Harley > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Re: Does essential entail locally connected for hyperconnected geometric morphisms?
by Thomas Streicher 28 Sep '20

28 Sep '20

CAUTION: The Sender of this email is not from within Dalhousie. > Morgan Rogers and I were able to construct a counterexample of the form PSh(M) --> PSh(N) where M and N are monoids. It arises from our joint work-in-progress in which we study exactly these kind of geometric morphisms, in a systematic way. After talking about it with Thomas Streicher, we have now written up the counterexample in more detail. You can find it here: > https://arxiv.org/abs/2009.12241 (3 pages). Dear Jens and Morgan, thanks a lot for your very nice counterexample which I never would have found on my own! Alas, it leaves open Lawvere and Menni's question whether precohesive geometric morphisms are always also locally connected. Does your toolbox also provide a counterexample to this implication. The current one does not do this job since you show the leftmost adjoint does not preserve binary products. (By Lemma 2.7 of Johnstone's 2011 TAC paper preservation of binary products by the leftmost adjoint is equivalent to preservation of exponentials by the inverse image part for hyperconnected and local geometric morphisms.) BTW I think that locally connected, hyperconnected and local is the correct generalization of essential, 2-valued and local from base Set to arbitrary base toposes from the point of view of fibered categories. Best, Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Re: Does essential entail locally connected for hyperconnected geometric morphisms?
by Jens Hemelaer 28 Sep '20

28 Sep '20

CAUTION: The Sender of this email is not from within Dalhousie. Morgan Rogers and I were able to construct a counterexample of the form PSh(M) --> PSh(N) where M and N are monoids. It arises from our joint work-in-progress in which we study exactly these kind of geometric morphisms, in a systematic way. After talking about it with Thomas Streicher, we have now written up the counterexample in more detail. You can find it here: https://arxiv.org/abs/2009.12241 (3 pages). Jens ________________________________ From: <streicher(a)mathematik.tu-darmstadt.de<mailto:streicher@mathematik.tu-darmstadt.de>> Date: Sat, 19 Sep 2020 at 14:28 Subject: categories: Does essential entail locally connected for hyperconnected geometric morphisms? To: <categories(a)mta.ca<mailto:categories@mta.ca>> Consider the functor F from the site for the topos of graphs to the site for the Sierpinski topos such that the object part of F is a bijection. Let f be the geometric morphism whose inverse image part is given by change of base along F. It is the inclusion of graphs with loops only into the category of graphs. Of course, p is essential and one easily sees that it is hyperconnected. One can show that p is not locally connected. However, p is not local since p_* does not preserve coequalizers. My attempts to come up with an example of a hyperconnected local geometric morphism which is is essential but not locally connected have failed so far. But all my instincts tell me that there should be a counterexample! The question came up in discussions with Matias Menni. He told me that one can prove that essential entails locally connected for hyperconnected local geometric morphisms. But his argument uses (ii) => (i) of Lemma 3.2 of Peter Johnstone's paper "Calibrated Toposes" whose proof I, however, find very cryptic. In any case, it would entail a result which I, personally, would find very surprising... I would be grateful for any clarification of this puzzling question. My hope is that someone comes up (with an idea for) a counterexample. But, of course, I also would highly appreciate any argument that such a counterexample cannot exist. Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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ETAPS 2021 2nd joint call for papers
by Tarmo Uustalu 23 Sep '20

23 Sep '20

CAUTION: The Sender of this email is not from within Dalhousie. ****************************************************************** JOINT CALL FOR PAPERS 24th European Joint Conferences on Theory and Practice of Software ETAPS 2021 Luxembourg, Luxembourg, 27 March-1 April 2021 http://www.etaps.org/2021 ****************************************************************** We are closely monitoring the development of the COVID-19 pandemic. If it is not viable to hold ETAPS 2021 as a physical conference, we will run it virtually on the same dates. We will decide in January 2021 at the latest. If ETAPS 2021 can go ahead as a physical conference, accepted authors may still present remotely. -- ABOUT ETAPS -- ETAPS is the primary European forum for academic and industrial researchers working on topics relating to software science. ETAPS, established in 1998, is a confederation of four annual conferences, accompanied by satellite workshops. ETAPS 2021 is the twenty-fourth event in the series. -- MAIN CONFERENCES (29 March-1 April) -- * ESOP: European Symposium on Programming (PC chair: Nobuko Yoshida, Imperial College London, UK) * FASE: Fundamental Approaches to Software Engineering (PC chairs: Esther Guerra, Univ. Autónoma de Madrid, Spain, and Mariëlle Stoelinga, Univ. Twente, The Netherlands) * FoSSaCS: Foundations of Software Science and Computation Structures (PC chairs: Stefan Kiefer, Univ. of Oxford, UK, and Christine Tasson, IRIF, Univ. Paris Diderot, France) * TACAS: Tools and Algorithms for the Construction and Analysis of Systems (PC chairs: Jan Friso Groote, Techn. Univ. Eindhoven, The Netherlands, and Kim G. Larsen, Aalborg Univ., Denmark) TACAS '21 will host the 10th Competition on Software Verification (SV-COMP). -- INVITED SPEAKERS -- The invited speakers and tutorialists planned for ETAPS 2020 have been reinvited: * Unifying speakers: Lars Birkedal (Aarhus Universitet, Denmark) a further speaker to be reconfirmed * ESOP invited speaker: Isil Dillig (University of Texas at Austin, USA) * FASE invited speaker: Willem Visser (Stellenbosch University, South Africa) * Tutorial speakers: Erika Ábrahám (RWTH Aachen University, Germany) Madhusudan Parthasararathy (University of Illinois at Urbana-Champaign, USA) -- IMPORTANT DATES * Papers due: 15 October 2020 23:59 AoE (=GMT-12) * Rebuttal (ESOP, FoSSaCS and, for selected papers, TACAS): 7 December 00:01 AoE - 9 December 23:59 AoE * Notification: 23 December 2020 * Camera-ready versions due: 22 January 2021 -- SUBMISSION INSTRUCTIONS -- The four main conferences of ETAPS 2021 solicit contributions of the following types. All page limits are given **excluding bibliography**. * ESOP: regular research papers of max 25 pp * FASE: regular research papers and empirical evaluation papers of max 18 pp, tool demonstration papers of max 6 pp + mandatory appendix of max 6 pp, * FoSSaCS: regular research papers of max 18 pp * TACAS: regular research papers, case study papers and regular tool papers of max 16 pp, tool demonstration papers of max 6 pp For definitions of the different paper types and specific instructions, where they are present, see the webpages of the individual conferences. All accepted papers will appear in the conference proceedings and have presentations during the conference. A condition of submission is that, if the submission is accepted, one of the authors attends the conference to give the presentation. **Remote attendance and presentation will be possible if ETAPS 2021 goes ahead as a physical conference.** Submitted papers must be in English presenting original research. They must be unpublished and not submitted for publication elsewhere. In particular, simultaneous submission of the same contribution to multiple ETAPS conferences is forbidden. Submissions must follow the formatting guidelines of Springer's LNCS and be submitted electronically in pdf through the Easychair author interface of the respective conference. Submissions not adhering to the specified format and length may be rejected immediately. FASE will use double-blind reviewing. Authors are asked to omit their names and institutions; refer to own prior work in the third person; not to include acknowledgements that might identify them. Regular tool paper and tool demonstration paper submissions to TACAS must be accompanied by an artifact. The artifact will be evaluated and the outcome will be taken into account in the acceptance decision of the paper. ESOP and FoSSaCS will use an author rebuttal phase. TACAS will have rebuttal for selected papers. -- PUBLICATION The proceedings will be published in the Advanced Research in Computing and Software Science (ARCoSS) subline of Springer's LNCS series. The proceedings volumes will appear in gold open access, so the published versions of all papers will be available for everyone to download from the publisher's website freely, from the date of online publication, perpetually. The copyright of the papers will remain with the authors. -- SATELLITE EVENTS (27-28 March) -- A number of satellite workshops will take place before the main conferences. -- CITY AND HOST INSTITUTION -- Luxembourg is the capital of the small European nation of the same name. Built amid deep gorges cut by the Alzette and Pétrusse rivers, it is famed for its ruins of medieval fortifications. The vast Bock Casemates tunnel network encompasses a dungeon, prison and the Archaeological Crypt, considered the city's birthplace. Along ramparts above, the Chemin de la Corniche promenade offers dramatic viewpoints. ETAPS 2021 is organised by the Interdisciplinary Centre for Security, Reliability and Trust (SnT), Université du Luxembourg. -- ORGANIZERS -- General chair: Peter Y. A. Ryan (SnT & Université du Luxembourg) Workshops chair: Joaquin Garcia-Alfaro (Telecom SudParis, France) Organization chair: Peter Roenne (SnT Luxembourg) Event manager: Magali Martin (SnT Luxembourg) -- FURTHER INFORMATION -- Please do not hesitate to contact the organizers at etaps2021 at uni.lu . [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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addendum to my question from today
by Thomas Streicher 18 Sep '20

18 Sep '20

CAUTION: The Sender of this email is not from within Dalhousie. I should have added that the question I asked today is very related to the one raised by Lawvere and Menni at the end of section 10 of their TAC 30 paper from 2015. In my eyes the relation is as follows. Even if not all essential hyperconnected local gm's are locally connected there still remains the question whether the implication holds under the additional assumption that the inverse image part of the gm p : EE-->SS preserves (ordinary) exponentials. Of course, locally connected amounts to p^* preserving dependent function spaces (the Pi_u for u in SS. So the question is whether for the purpose at stake it suffices that p^* preserves ordinary (non-dependent) function spaces. Thomas S. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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Does essential entail locally connected for hyperconnected geometric morphisms?
by streicher＠mathematik.tu-darmstadt.de 18 Sep '20

18 Sep '20

CAUTION: The Sender of this email is not from within Dalhousie. Consider the functor F from the site for the topos of graphs to the site for the Sierpinski topos such that the object part of F is a bijection. Let f be the geometric morphism whose inverse image part is given by change of base along F. It is the inclusion of graphs with loops only into the category of graphs. Of course, p is essential and one easily sees that it is hyperconnected. One can show that p is not locally connected. However, p is not local since p_* does not preserve coequalizers. My attempts to come up with an example of a hyperconnected local geometric morphism which is is essential but not locally connected have failed so far. But all my instincts tell me that there should be a counterexample! The question came up in discussions with Matias Menni. He told me that one can prove that essential entails locally connected for hyperconnected local geometric morphisms. But his argument uses (ii) => (i) of Lemma 3.2 of Peter Johnstone's paper "Calibrated Toposes" whose proof I, however, find very cryptic. In any case, it would entail a result which I, personally, would find very surprising... I would be grateful for any clarification of this puzzling question. My hope is that someone comes up (with an idea for) a counterexample. But, of course, I also would highly appreciate any argument that such a counterexample cannot exist. Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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[Call for Participation] ICLP 2020 - The 36th International Conference on Logic Programming
by Laura Pandolfo 18 Sep '20

18 Sep '20

CAUTION: The Sender of this email is not from within Dalhousie. ============================================== *ICLP 2020 - The 36th International Conference on Logic Programming* *September 18 - September 25, 2020* University of Calabria, Rende, Italy https://iclp2020.unical.it <https://iclp2020.unical.it/> ============================================== Since the first conference held in Marseille in 1982, the *International Conference on Logic Programming (ICLP)* has been the premier international event for presenting research in logic programming. ****CONFERENCE ONLINE**** The conference general chairs together with the program chairs and the ALP Executive, have decided to hold ICLP2020 as a fully virtual conference on the original week (September 18-25, 2020). ****REGISTRATION**** (https://iclp2020.unical.it/registration) Registration is REQUIRED and covers the Main conference together with all associated events, i.e., Workshops, Doctoral Consortium, and Autumn School, whereas the Italian Conference in Computational Logic (CILC) is a co-located event and, therefore, not included in the ICLP registration. ****PROGRAM**** (https://iclp2020.unical.it/program) The ICLP 2020 main conference and all the workshops will be held in a virtual manner. The conference format is a mix of pre-recorded and asynchronous talks, and live engagement such as Q&A sessions. Full details of the main conference program can be seen here: https://iclp2020.unical.it/program <https://iclp2020.unical.it/program> ****INVITED SPEAKERS**** (https://iclp2020.unical.it/invited-speakers) We are happy to announce that invited speakers' events will be freely accessible to all via live streaming at the following Facebook page: https://fb.me/iclp2020conference. *Sep 20th, 2020 - _Francesca Rossi_ (T.J. Watson IBM Research Lab, USA)* Talk Title: "When Is It Morally Acceptable to Break the Rules? A Preference-Based Approach" - This is the "EurAI talk" *Sep 21th, 2020 - _Esra Erdem_ (Sabanci University, Turke)* Talk Title: "Applications of Answer Set Programming where Theory meets Practice" *Sep 22th, 2020 - _Joao Marquez-Silva_ (ANITI, University of Toulouse, France)* Talk Title: "Formal Reasoning Methods for Explainability in Machine Learning" *Sep 23th, 2020 - _Luc De Raedt_ (KU Leuven, Belgium)* Talk Title: "From Probabilistic Logics to Neuro-Symbolic Artificial Intelligence" *Sep 24th, 2020 - _Marina De Vos_ (University of Bath, UK)* Talk Title: "Norms, Policy and Laws: Modelling, Compliance and Violation" - This is the "Woman in LP Talk" /*All the invited talks will be held from 2:30 PM – 3:30 PM (CEST)/ ****ORGANIZATION**** *General Chairs:* *Sergio Greco, University of Calabria, Italy *Nicola Leone, University of Calabria, Italy *Program Chairs:* *Francesco Ricca, University of Calabria, Italy *Alessandra Russo, Imperial College London, UK *Organizing Chairs:* *Marco Calautti, University of Calabria, Italy *Carmine Dodaro, University of Calabria, Italy *Track Chairs:* *Alexander Artikis, University of Piraeus & NCSR Demokritos, Greece (Applications Track) *Angelika Kimmig, Cardiff University, UK (Applications Track) *Gerhard Friedrich, Universität Klagenfurt, Austria (Research Challenges Track) *Fabrizio Riguzzi, Università di Ferrara, Italy (Research Challenges Track) *Paul Fodor, Stony Brook University, USA (Sister and Journal Track) *Marco Maratea, University of Genova, Italy (Sister and Journal Track) *Francesca Alessandra Lisi, University of Bari Aldo Moro, Italy (Women in Logic Programming) *Alessandra Mileo, INSIGHT Centre for Data Analytics, Dublin City University, Irland (Women in Logic Programming) *Workshop Chair:* *Martin Gebser, Universität Klagenfurt, Austria *Publicity Chair:* *Laura Pandolfo, University of Sassari, Italy *Program Committee:* Mario Alviano, University of Calabria, Italy Nicos Angelopoulos, Wellcome Sanger Institute, UK Marcello Balduccini, Saint Joseph's University, USA Mutsunori Banbara, Nagoya University, Japan Chitta Baral, Arizona State University, USA Roman Barták, Charles University, Czech Republic Christoph Benzmüller, University of Luxembourg, Luxembourg Alex Brik, Google, USA François Bry, Ludwig Maximilian University of Munich, Germany Pedro Cabalar, University of Corunna, Spain Francesco Calimeri, University of Calabria, Italy Manuel Carro, Technical University of Madrid (UPM) and IMDEA Software Institute, Spain Angelos Charalambidis, University of Athens, Greece Michael Codish, Ben-Gurion University of the Negev, Israel Stefania Costantini, University of Aquila, Italy Marc Denecker, Katholieke Universiteit Leuven, Belgium Martín Diéguez, University of Pau, France Carmine Dodaro, University of Calabria, Italy Agostino Dovier, University of Udine, Italy Thomas Eiter, Vienna University of Technology, Austria Wolfgang Faber, Alpen-Adria-Universität Klagenfurt, Austria Thom Fruehwirth, University of Ulm, Germany Marco Gavanelli, University of Ferrara, Italy Martin Gebser, Alpen-Adria-Universität Klagenfurt, Austria Michael Gelfond, Texas Tech University, USA Laura Giordano, Università del Piemonte Orientale, Italy Gopal Gupta, University of Texas at Austin, USA Michael Hanus, CAU Kiel, Germany Manuel V. Hermenegildo, IMDEA Software Institute and Universidad Politécnica de Madrid, Spain Katsumi Inoue, National Institute of Informatics, Japan Tomi Janhunen, Tampere University, Finland Jianmin Ji, University of Science and Technology of China, China Nikos Katzouris, NCSR Demokritos, Greece Michael Kifer, Stony Brook University, USA Zeynep Kiziltan, University of Bologna, Italy Ekaterina Komendantskaya, Heriot-Watt University, UK Evelina Lamma, Universita di Ferrara, Italy Michael Leuschel, University of Dusseldorf, Germany Vladimir Lifschitz, The University of Texas at Austin, USA Francesca Alessandra Lisi, Università degli Studi di Bari "Aldo Moro", Italy Yanhong A. Liu, Stony Brook University, USA Marco Maratea, University of Genova, Italy Viviana Mascardi, University of Genova, Italy Yunsong Meng, General Motors, USA Emilia Oikarinen, University of Helsinki, Finland Magdalena Ortiz, Vienna University of Technology, Austria Simona Perri, University of Calabria, Italy Enrico Pontelli, New Mexico State University, USA Ricardo Rocha, University of Porto, Portugal Fariba Sadri, Imperial College London, UK Chiaki Sakama, Wakayama University, Japan Torsten Schaub, University of Potsdam, Germany Konstantin Schekotihin, Alpen-Adria-Universität Klagenfurt, Austria Tom Schrijvers, Katholieke Universiteit Leuven, Belgium Guillermo R. Simari, Universidad del Sur in Bahia Blanca, Argentina Tran Cao Son, New Mexico State University, USA Mohan Sridharan, University of Birmingham, UK Theresa Swift, NOVALINKS, Universidade Nova de Lisboa, Portugal Paul Tarau, University of North Texas, Denton, USA Hans Tompits, Vienna University of Technology, Austria Francesca Toni, Imperial College London, UK Irina Trubitsyna, University of Calabria, DIMES Mirek Truszczynski, University of Kentucky, US German Vidal, Universitat Politecnica de Valencia, Spain Alicia Villanueva, Universitat Politècnica de València, Spain David Warren, SUNY Stony Brook, USA Jan Wielemaker, Vrije Universiteit Amsterdam, Netherlands Stefan Woltran, Vienna University of Technology, Austria Jia-Huai You, University of Alberta, Canada Shiqi Zhang, SUNY Binghamton, USA Neng-Fa Zhou, CUNY Brooklyn College and Graduate Center, USA -- -- *Dona il 5x1000* all'Università degli Studi di Sassaricodice fiscale: 00196350904 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

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