{"@context":"https:\/\/schema.org\/","@type":"PublicationVolume","@id":"#volume620","volumeNumber":6341,"name":"Dagstuhl Seminar Proceedings, Volume 6341","dateCreated":"2007-02-26","datePublished":"2007-02-26","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"Periodical","@id":"#series119","name":"Dagstuhl Seminar Proceedings","issn":"1862-4405","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume620"},"hasPart":[{"@type":"ScholarlyArticle","@id":"#article1559","name":"06341 Abstracts Collection \u2013 Computational Structures for Modelling Space, Time and Causality","abstract":"From 20.08.06 to 25.08.06, the Dagstuhl Seminar 06341 ``Computational Structures for Modelling Space, Time and Causality'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl.\r\nDuring the seminar, several participants presented their current\r\nresearch, and ongoing work and open problems were discussed. Abstracts of\r\nthe presentations given during the seminar as well as abstracts of\r\nseminar results and ideas are put together in this paper. The first section\r\ndescribes the seminar topics and goals in general.\r\nLinks to extended abstracts or full papers are provided, if available.","keywords":["Borel hierarchy","causets","Chu spaces","computations in higher types","computable analysis","constructive topology","differential calculus","digital topology","dihomotopy","domain theory","domain representation","formal topology","higher dimensional automata","mereo\\-topology","partial metrics"],"author":[{"@type":"Person","name":"Kopperman, Ralph","givenName":"Ralph","familyName":"Kopperman"},{"@type":"Person","name":"Panangaden, Prakash","givenName":"Prakash","familyName":"Panangaden"},{"@type":"Person","name":"Smyth, Michael B.","givenName":"Michael B.","familyName":"Smyth"},{"@type":"Person","name":"Spreen, Dieter","givenName":"Dieter","familyName":"Spreen"}],"position":1,"pageStart":1,"pageEnd":23,"dateCreated":"2007-02-26","datePublished":"2007-02-26","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Kopperman, Ralph","givenName":"Ralph","familyName":"Kopperman"},{"@type":"Person","name":"Panangaden, Prakash","givenName":"Prakash","familyName":"Panangaden"},{"@type":"Person","name":"Smyth, Michael B.","givenName":"Michael B.","familyName":"Smyth"},{"@type":"Person","name":"Spreen, Dieter","givenName":"Dieter","familyName":"Spreen"}],"copyrightYear":"2007","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06341.1","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume620"},{"@type":"ScholarlyArticle","@id":"#article1560","name":"A convenient category of domains","abstract":"We motivate and define a category of \"topological domains\",\r\nwhose objects are certain topological spaces, generalising\r\nthe usual $omega$-continuous dcppos of domain theory.\r\nOur category supports all the standard constructions of domain theory,\r\nincluding the solution of recursive domain equations. It also\r\nsupports the construction of free algebras for (in)equational\r\ntheories, provides a model of parametric polymorphism,\r\nand can be used as the basis for a theory of computability.\r\nThis answers a question of Gordon Plotkin, who asked\r\nwhether it was possible to construct a category of domains \r\ncombining such properties.","keywords":["Domain theory","topology of datatypes"],"author":[{"@type":"Person","name":"Battenfeld, Ingo","givenName":"Ingo","familyName":"Battenfeld"},{"@type":"Person","name":"Schr\u00f6der, Matthias","givenName":"Matthias","familyName":"Schr\u00f6der"},{"@type":"Person","name":"Simpson, Alex","givenName":"Alex","familyName":"Simpson"}],"position":2,"pageStart":1,"pageEnd":0,"dateCreated":"2007-02-26","datePublished":"2007-02-26","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Battenfeld, Ingo","givenName":"Ingo","familyName":"Battenfeld"},{"@type":"Person","name":"Schr\u00f6der, Matthias","givenName":"Matthias","familyName":"Schr\u00f6der"},{"@type":"Person","name":"Simpson, Alex","givenName":"Alex","familyName":"Simpson"}],"copyrightYear":"2007","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06341.2","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume620"},{"@type":"ScholarlyArticle","@id":"#article1561","name":"Closure and Causality","abstract":"We present a model of causality which is defined by the intersection of two\r\ndistinct closure systems, ${cal I}$ and ${cal T}$. Next we present \r\nempirical evidence to demonstrate that this model has practical validity by\r\nexamining computer trace data to reveal causal dependencies between\r\nindividual code modules. From over 498,000 events in the transaction \r\nmanager of an open source system we tease out 66 apparent causal\r\ndependencies. Finally, we explore how to mathematically model the\r\ntransformation of a causal topology resulting from unforlding events.","keywords":["Closure","causality","antimatroid","temporal","software engineering"],"author":{"@type":"Person","name":"Pfaltz, John L.","givenName":"John L.","familyName":"Pfaltz"},"position":3,"pageStart":1,"pageEnd":13,"dateCreated":"2007-02-26","datePublished":"2007-02-26","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Pfaltz, John L.","givenName":"John L.","familyName":"Pfaltz"},"copyrightYear":"2007","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06341.3","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume620"},{"@type":"ScholarlyArticle","@id":"#article1562","name":"Elementary Differential Calculus on Discrete, Continuous and Hybrid Spaces","abstract":"We unify a variety of continuous and discrete types of change of state phenomena using a \r\nscheme whose instances are differential calculi on structures that embrace both topological \r\nspaces and graphs as well as hybrid ramifications of such structures. These calculi include the \r\nelementary differential calculus on real and complex vector spaces.\r\n\r\nOne class of spaces that has been increasingly receiving attention in recent years is the class of \r\nconvergence spaces [cf. Heckmann, R., TCS v.305, (159--186)(2003)]. The class of convergence spaces together with the continuous functions among convergence spaces forms a Cartesian-closed category CONV that contains as full subcategories both the category TOP of \r\ntopological spaces and an embedding of the category DIGRAPH of reflexive directed graphs. \r\n(More can importantly be said about these embeddings.) These properties of CONV serve to assure that we can construct continuous products of continuous functions, and that there is \r\nalways at least one convergence structure available in function spaces with respect to which \r\nthe operations of function application and composition are continuous. The containment of TOP and DIGRAPH in CONV allows to combine arbitrary topological spaces with discrete \r\nstructures (as represented by digraphs) to obtain hybrid structures, which generally are not topological spaces.\r\n\r\nWe give a differential calculus scheme in CONV that addresses three issues in particular. \r\n\r\n1. For convergence spaces $X$ and $Y$ and function $f: X longrightarrow Y$, the scheme gives necessary and sufficient conditions for a candidate differential $df: X longrightarrow Y$ \r\nto be a (not necessarily \"the\", depending on the spaces involved) differential of $f$ at $x_0$. \r\n\r\n2. The chain rule holds and the differential relation between functions distributes over Cartesian products: e.g. if $Df$, $Dg$ and $Dh$ are, respectively, differentials of $f$ at \r\n$(g(x_0),h(x_0))$ and $g$ and $h$ at $x_0$, then $Df circ (Dg times Dh)$ is a differential of $f circ (g times h)$ at $x_0$.\r\n\r\n3. When specialized to real and complex vector spaces, the scheme is in agreement with ordinary elementary differential calculus on these spaces.\r\n\r\nMoreover, with two additional constraints having to do with self-differentiation of differentials and translation invariance (for example, a linear operator on, say, $C^2$, is its own differential everywhere) there is a (unique) maximum differential calculus in CONV.","keywords":["Hybrid space","convergence space","differential","calculus","chain rule","hybrid dynamical system","discrete structure","topological space"],"author":{"@type":"Person","name":"Blair, Howard","givenName":"Howard","familyName":"Blair"},"position":4,"pageStart":1,"pageEnd":2,"dateCreated":"2007-02-26","datePublished":"2007-02-26","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Blair, Howard","givenName":"Howard","familyName":"Blair"},"copyrightYear":"2007","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06341.4","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume620"},{"@type":"ScholarlyArticle","@id":"#article1563","name":"Enriched categories and models for spaces of dipaths","abstract":"Partially ordered sets, causets, partially ordered spaces and their local counterparts are now often used to model systems in computer science and theoretical physics. The order models `time' which is often not globally given. In this setting directed paths are important objects of study as they correspond to an evolving state or particle traversing the system. Many physical problems rely on the analysis of models of the path space of space-time manifold. Many problems in concurrent systems use `spaces' of paths in a system. Here we review some ideas from algebraic topology that suggest how to model the dipath space of a pospace by a simplicially enriched category.","keywords":"Enriched category","author":{"@type":"Person","name":"Porter, Timothy","givenName":"Timothy","familyName":"Porter"},"position":5,"pageStart":1,"pageEnd":0,"dateCreated":"2007-02-26","datePublished":"2007-02-26","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Porter, Timothy","givenName":"Timothy","familyName":"Porter"},"copyrightYear":"2007","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06341.5","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume620"},{"@type":"ScholarlyArticle","@id":"#article1564","name":"Instant topological relationships hidden in the reality","abstract":"In most applications of general topology, topology usually is not the first, \r\nprimary structure, but the information which finally leads to the construction of\r\nthe certain, for some purpose required topology, is filtered by more or less \r\nthick filter of the other mathematical structures. This fact has two main \r\nconsequences:\r\n\r\n(1) Most important applied constructions may be done in the primary \r\nstructure, bypassing the topology.\r\n\r\n(2) Some topologically important information from the reality may be lost \r\n(filtered out by the other, front-end mathematical structures).\r\n\r\nThus some natural and direct connection between topology and the reality \r\ncould be useful. In this contribution we will discuss a pointless topological \r\nstructure which directly reflects relationship between various locations which \r\nare glued together by possible presence of a physical object or a virtual \r\n``observer\".","keywords":["Pointless topology","reality"],"author":{"@type":"Person","name":"Kov\u00e1r, Martin Maria","givenName":"Martin Maria","familyName":"Kov\u00e1r"},"position":6,"pageStart":1,"pageEnd":2,"dateCreated":"2007-02-26","datePublished":"2007-02-26","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Kov\u00e1r, Martin Maria","givenName":"Martin Maria","familyName":"Kov\u00e1r"},"copyrightYear":"2007","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.06341.6","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume620"}]}