255 research outputs found
Dihomotopy classes of dipaths in the geometric realization of a cubical set: from discrete to continuous and back again
Get PDFThe geometric models of concurrency - Dijkstra's PV-models and V. Pratt's Higher Dimensional Automata - rely on a translation of discrete or algebraic information to geometry. In both these cases, the translation is the geometric realisation of a semi cubical complex, which is then a locally partially ordered space, an lpo space. The aim is to use the algebraic topology machinery, suitably adapted to the fact that there is a preferred time direction. Then the results - for instance dihomotopy classes of dipaths, which model the number of inequivalent computations should be used on the discrete model and give the corresponding discrete objects. We prove that this is in fact the case for the models considered: Each dipath is dihomotopic to a combinatorial dipath and if two combinatorial dipaths are dihomotopic, then they are combinatorially equivalent. Moreover, the notions of dihomotopy (LF., E. Goubault, M. Raussen) and d-homotopy (M. Grandis) are proven to be equivalent for these models - hence the Van Kampen theorem is available for dihomotopy. Finally we give an idea of how many spaces have a local po-structure given by cubes. The answer is, that any cubicalized space has such a structure after at most one subdivision. In particular, all triangulable spaces have a cubical local po-structure.The geometric models of concurrency - Dijkstra's PV-models and V. Pratt's Higher Dimensional Automata - rely on a translation of discrete or algebraic information to geometry. In both these cases, the translation is the geometric realisation of a semi cubical complex, which is then a locally partially ordered space, an lpo space. The aim is to use the algebraic topology machinery, suitably adapted to the fact that there is a preferred time direction. Then the results - for instance dihomotopy classes of dipaths, which model the number of inequivalent computations should be used on the discrete model and give the corresponding discrete objects. We prove that this is in fact the case for the models considered: Each dipath is dihomotopic to a combinatorial dipath and if two combinatorial dipaths are dihomotopic, then they are combinatorially equivalent. Moreover, the notions of dihomotopy (LF., E. Goubault, M. Raussen) and d-homotopy (M. Grandis) are proven to be equivalent for these models - hence the Van Kampen theorem is available for dihomotopy. Finally we give an idea of how many spaces have a local po-structure given by cubes. The answer is, that any cubicalized space has such a structure after at most one subdivision. In particular, all triangulable spaces have a cubical local po-structure
Applications of Combinatorial Topology to Computer Science (Dagstuhl Seminar 12121)
No full textThis report documents the program of Dagstuhl Seminar 12121 "Applications of Combinatorial Topology to Computer Science". The seminar brought together researchers working on applications of combinatorial topology to various fields of computer science. The goal was to foster communication across these fields by providing researchers in each field the opportunity to explain their research programs to the others. The fields covered included distributed computing, persistent homology, semantics of concurrency, and sensor networks
Dipaths and dihomotopies in a cubical complex
No full textIn the geometric realization of a cubical complex without degeneracies, a -set, dipaths and dihomotopies may not be combinatorial, i.e., not geometric realizations of combinatorial dipaths and equivalences. When we want to use geometric/topological tools to classify dipaths on the 1-skeleton, combinatorial dipaths, up to dihomotopy, and in particular up to combinatorial dihomotopy, we need that all dipahts are in fact dihomotopic to a combinatorial dipath. And moreover that two combinatorial dipaths which are dihomotopic are then combinatorially dihomotopic. We prove that any dipath from a vertex to a vertex is dihomotopic to a combinatorial dipath, in a non-selfintersecting -set. And that two combinatorial dipaths which are dihomotopic threough a non-combinatorial dihomogopy are in fact combinatorially dihomotopic, in a geometric -set. Moreover, we prove that in a geometric -set, the d-homotopy introdced in [M. Grandis (2003)] coincides with the dihomotopy in [L. Fajstrup, E. Goubault, M. Raussen (1999)]. Udgivelsesdato: AUGIn the geometric realization of a cubical complex without degeneracies, a -set, dipaths and dihomotopies may not be combinatorial, i.e., not geometric realizations of combinatorial dipaths and equivalences. When we want to use geometric/topological tools to classify dipaths on the 1-skeleton, combinatorial dipaths, up to dihomotopy, and in particular up to combinatorial dihomotopy, we need that all dipahts are in fact dihomotopic to a combinatorial dipath. And moreover that two combinatorial dipaths which are dihomotopic are then combinatorially dihomotopic. We prove that any dipath from a vertex to a vertex is dihomotopic to a combinatorial dipath, in a non-selfintersecting -set. And that two combinatorial dipaths which are dihomotopic threough a non-combinatorial dihomogopy are in fact combinatorially dihomotopic, in a geometric -set. Moreover, we prove that in a geometric -set, the d-homotopy introdced in [M. Grandis (2003)] coincides with the dihomotopy in [L. Fajstrup, E. Goubault, M. Raussen (1999)]
On directed coverings
Get PDFIn [1], we study coverings in the setting of directed topology. Unfortunately, there is a condition missing in the definition of a directed covering. Some of the results in [1] require this extra condition and in fact it was claimed to follow from the original definition. It is the purpose of this note to give the right definition and point out how this affects the statements in that paper. Moreover, we give an example of a dicovering in the sense of [1], which does not satisfy the extra condition. Fortunately, with the extra condition, the subsequent results are now correct.[1] L. Fajstrup, Dicovering spaces, Homology Homotopy Appl. 5 (2003), no. 2, 1-17.</p
Classification of dicoverings
Get PDFThe dicoverings of a "well pointed" d-space are classified as quotients of the universal dicovering space under congruence relations. We prove that the subcategory of d-spaces generated by the subcategory of directed cubes is equal to the category generated by the interval and the directed interval. Similarly, the category of topological spaces generated by simplices may be generated by the interval.The dicoverings of a "well pointed" d-space are classified as quotients of the universal dicovering space under congruence relations. We prove that the subcategory of d-spaces generated by the subcategory of directed cubes is equal to the category generated by the interval and the directed interval. Similarly, the category of topological spaces generated by simplices may be generated by the interval
KONSTRUKSI LISBETH SALANDER DALAM NOVEL THE GIRL WITH DRAGON TATTOO KARYA STIEG LARSSON
No full textABSTRAK
Tulisan ini mendeskripsikan konstruksi yang dibuat pengarang atas tokoh utama perempuan, Lisbeth Salander, dalam novel karya Stieg Larsson, The Girl with the Dragon Tattoo. Tulisan ini bertujuan untuk mengetahui keberpihakan pengarang atas tokohnya perempuannya mengingat pengarang novel sendiri adalah seorang lelaki. Untuk meneliti hal di atas, Penulis menggunakan Analisis Wacana Feminis dengan menggunakan metode analisis Sara Mills. Hasil analisis menunjukkan bahwa pengarang memberikan keleluasaan pada Lisbeth Salander untuk menceritakan dirinya sendiri dan ketika dia diceritakan oleh tokoh lain, maka telah dibingkai dengan narasi-narasi positif. Di sisi lain, semua tokoh lelaki memosisikan Lisbeth pun dengan posisi sebagai rekan setara, kecuali satu tokoh yang memosisikannya sebagai subordinat. Hal di atas menunjukkan, meski pengarang seorang lelaki, ia berpihak pada Lisbeth.
ABSTRACT
This paper aim to describe about the author‟s construction of Lisbeth Salander, the main female character of Stieg Larsson,‟ The Girl with the Dragon Tattoo.‟ This paper made to know about the alignments of the author to her. This study uses Feminist Discourse Analysis with Sara Mills‟s method. The analysis shows that the author gives Lisbeth Salander much discretion to tell about herself and when she is told by any other man character, she is given some positif frame of narations. In the other side, all the man characters puts her as equal partner, except one antagonist man character who puts her as subordinat. The things make this novel, even as it is written by a man, has tended to Lisbeth
Cubical local partial orders on cubically subdivided spaces - Existence and construction
No full textThe geometric models of higher dimensional automata (HDA) and Dijkstra's PV-model are cubically subdivided topological spaces with a local partial order. If a cubicalization of a topological space is free of immersed cubic Möbius bands, then there are consistent choices of direction in all cubes, such that any n-cube in the cubic subdivision is dihomeomorphic to [0,1]^n with the induced partial order from R^n. After subdivision once, any cubicalized space has a cubical local partial order. In particular, all triangularized spaces have a cubical local partial order. This implies in particular that the underlying geometry of an HDA may be quite complicated. Udgivelsesdato: NOV 12The geometric models of higher dimensional automata (HDA) and Dijkstra's PV-model are cubically subdivided topological spaces with a local partial order. If a cubicalization of a topological space is free of immersed cubic Möbius bands, then there are consistent choices of direction in all cubes, such that any n-cube in the cubic subdivision is dihomeomorphic to [0,1]^n with the induced partial order from R^n. After subdivision once, any cubicalized space has a cubical local partial order. In particular, all triangularized spaces have a cubical local partial order. This implies in particular that the underlying geometry of an HDA may be quite complicated
Cut-off Theorems for the PV-model
Get PDFWe prove cut-off results for deadlocks and serializability of a -thread
run in parallel with itself: For a thread which accesses a set
of resources, each with a maximal capacity
, the PV-program , where copies of
are run in parallel, is deadlock free for all if and only if is
deadlock free where . This is a sharp
bound: For all and finite there
is a thread using these resources such that has a deadlock, but
does not for . Moreover, we prove a more general theorem: There are no
deadlocks in if and only if there are no deadlocks in
for any subset . For , is serializable for all if and only
if is serializable. For general capacities, we define a local obstruction
to serializability. There is no local obstruction to serializability in
for all if and only if there is no local obstruction to serializability in
for . The obstructions may be
found using a deadlock algorithm in . These serializability results
also have a generalization: If there are no local obstructions to
serializability in any of the -dimensional sub programs,
, then is serializable
- …
