130,518 research outputs found
A Convenient Category of Domains
We motivate and define a category of "topological domains",
whose objects are certain topological spaces, generalising
the usual -continuous dcppos of domain theory.
Our category supports all the standard constructions of domain theory,
including the solution of recursive domain equations. It also
supports the construction of free algebras for (in)equational
theories, provides a model of parametric polymorphism,
and can be used as the basis for a theory of computability.
This answers a question of Gordon Plotkin, who asked
whether it was possible to construct a category of domains
combining such properties
Towards a Convenient Category of Topological Domains
We propose a category of topological spaces that promises to be convenient for the purposes of domain theory as a mathematical theory for modelling computation. Our notion of convenience presupposes the usual properties of domain theory, e.g. modelling the basic type constructors, fixed points, recursive types, etc. In addition, we seek to model parametric polymorphism, and also to provide a flexible toolkit for modelling computational effects as free algebras for algebraic theories. Our convenient category is obtained as an application of recent work on the remarkable closure conditions of the category of quotients of countably-based topological spaces. Its convenience is a consequence of a connection with realizability models
Stable left and right Bousfield localisations
We study left and right Bousfield localisations of stable model categories
which preserve stability. This follows the lead of the two key examples:
localisations of spectra with respect to a homology theory and A-torsion
modules over a ring R with A a perfect R-algebra. We exploit stability to see
that the resulting model structures are technically far better behaved than the
general case. We can give explicit sets of generating cofibrations, show that
these localisations preserve properness and give a complete characterisation of
when they preserve monoidal structures. We apply these results to obtain
convenient assumptions under which a stable model category is spectral. We then
use Morita theory to gain an insight into the nature of right localisation and
its homotopy category. We finish with a correspondence between left and right
localisation.Comment: 30 page
A Graph-structured Dataset for Wikipedia Research
Wikipedia is a rich and invaluable source of information. Its central place
on the Web makes it a particularly interesting object of study for scientists.
Researchers from different domains used various complex datasets related to
Wikipedia to study language, social behavior, knowledge organization, and
network theory. While being a scientific treasure, the large size of the
dataset hinders pre-processing and may be a challenging obstacle for potential
new studies. This issue is particularly acute in scientific domains where
researchers may not be technically and data processing savvy. On one hand, the
size of Wikipedia dumps is large. It makes the parsing and extraction of
relevant information cumbersome. On the other hand, the API is straightforward
to use but restricted to a relatively small number of requests. The middle
ground is at the mesoscopic scale when researchers need a subset of Wikipedia
ranging from thousands to hundreds of thousands of pages but there exists no
efficient solution at this scale.
In this work, we propose an efficient data structure to make requests and
access subnetworks of Wikipedia pages and categories. We provide convenient
tools for accessing and filtering viewership statistics or "pagecounts" of
Wikipedia web pages. The dataset organization leverages principles of graph
databases that allows rapid and intuitive access to subgraphs of Wikipedia
articles and categories. The dataset and deployment guidelines are available on
the LTS2 website \url{https://lts2.epfl.ch/Datasets/Wikipedia/}
On the Model of Computation of Place/Transition Petri Nets
In the last few years, the semantics of Petri nets has been investigated in several different ways. Apart from the classical "token game", one can model the behaviour of Petri nets via non-sequential processes, via unfolding constructions, which provide formal relationships between nets and domains, and via algebraic models, which view Petri nets as essentially algebraic theories whose models are monoidal categories. In this paper we show that these three points of view can be reconciled. More precisely, we introduce the new notion of decorated processes of Petri nets and we show that they induce on nets the same semantics as that of unfolding. In addition, we prove that the decorated processes of a net N can be axiomatized as the arrows of a symmetric monoidal category which, therefore, provides the aforesaid unification
- …