2,781 research outputs found
CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters
The rise of graph-structured data such as social networks, regulatory
networks, citation graphs, and functional brain networks, in combination with
resounding success of deep learning in various applications, has brought the
interest in generalizing deep learning models to non-Euclidean domains. In this
paper, we introduce a new spectral domain convolutional architecture for deep
learning on graphs. The core ingredient of our model is a new class of
parametric rational complex functions (Cayley polynomials) allowing to
efficiently compute spectral filters on graphs that specialize on frequency
bands of interest. Our model generates rich spectral filters that are localized
in space, scales linearly with the size of the input data for
sparsely-connected graphs, and can handle different constructions of Laplacian
operators. Extensive experimental results show the superior performance of our
approach, in comparison to other spectral domain convolutional architectures,
on spectral image classification, community detection, vertex classification
and matrix completion tasks
Type Inference for the receptive distributed Pi-calculus
In this paper we study the type inference problem for an extended version of the type system of d_1^r very closed to the one of Hennessy and Riely's d. These are distributed Pi-calculus involving explicit notions of locations and migration where the location space is flat and communication is local. Moreover, location names are typed and we use an explicit subtyping relation over location types that enable us to define a notion of principal typing. We provide an inference type algorithm computing a principal type for all typable term
04241 Abstracts Collection -- Graph Transformations and Process Algebras for Modeling Distributed and Mobile Systems
Recently there has been a lot of research, combining concepts of process algebra with those of the theory of graph grammars and graph transformation systems. Both can be viewed as general frameworks in which one can specify and reason about concurrent and distributed systems. There are many areas where both theories overlap and this reaches much further than just using graphs to give a graphic representation to processes.
Processes in a communication network can be seen in two different ways: as terms in an algebraic theory, emphasizing their behaviour and their interaction with the environment, and as nodes (or edges) in a graph, emphasizing their topology and their connectedness. Especially topology, mobility and dynamic reconfigurations at
runtime can be modelled in a very intuitive way using graph transformation. On the other hand the definition and proof of behavioural equivalences is often easier in the process algebra setting.
Also standard techniques of algebraic semantics for universal constructions, refinement and compositionality can take better advantage of the process algebra representation. An important example where the combined theory is more convenient than both alternatives is for defining the concurrent (noninterleaving), abstract semantics of distributed systems. Here graph transformations lack abstraction and process algebras lack expressiveness.
Another important example is the work on bigraphical reactive systems with the aim of deriving a labelled transitions system from an unlabelled reactive system such that the resulting bisimilarity is a congruence. Here, graphs seem to be a convenient framework, in which this theory can be stated and developed.
So, although it is the central aim of both frameworks to model and reason about concurrent systems, the semantics of processes can have a very different flavour in these theories. Research in this area aims at combining the advantages of both frameworks and translating concepts of one theory into the other. The Dagsuthl Seminar, which took place from 06.06. to 11.06.2004, was aimed at bringing together researchers of the two communities in order to share their ideas and develop new concepts. These proceedings4 of the do not only contain abstracts of the talks given at the seminar, but also summaries of topics of central interest. We would like to thank all participants of the seminar for coming and sharing their ideas and everybody who has contributed to the proceedings
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Probabilistic concurrent game semantics
This thesis presents a variety of models for probabilistic programming languages in the framework of concurrent games.
Our starting point is the model of concurrent games with symmetry of Castellan, Clairambault and Winskel. We show that they form a symmetric monoidal closed bicategory, and that this can be turned into a cartesian closed bicategory using a linear exponential pseudo-comonad inspired by linear logic.
Then, we enrich this with probability, relying heavily on Winskel's model of probabilistic concurrent strategies. We see that the bicategorical structure is not perturbed by the addition of probability. We apply this model to two probabilistic languages: a probabilistic untyped λ-calculus, and Probabilistic PCF. For the former, we relate the semantics to the probabilistic Nakajima trees of Leventis, thus obtaining a characterisation of observational equivalence for programs in terms of strategies. For the latter, we show a definability result in the spirit of the game semantics tradition. This solves an open problem, as it is notoriously difficult to model Probabilistic PCF with sequential game semantics.
Finally, we introduce a model for measurable game semantics, in which games and strategies come equipped with measure-theoretic structure allowing for an accurate description of computation with continuous data types. The objective of this model is to support computation with arbitrary probability measures on the reals. In the last part of this thesis we see how this can be done by equipping strategies with parametrised families of probability measures (also known as stochastic kernels), and we construct a bicategory of measurable concurrent games and probabilistic measurable strategies
Compositional Reasoning for Explicit Resource Management in Channel-Based Concurrency
We define a pi-calculus variant with a costed semantics where channels are
treated as resources that must explicitly be allocated before they are used and
can be deallocated when no longer required. We use a substructural type system
tracking permission transfer to construct coinductive proof techniques for
comparing behaviour and resource usage efficiency of concurrent processes. We
establish full abstraction results between our coinductive definitions and a
contextual behavioural preorder describing a notion of process efficiency
w.r.t. its management of resources. We also justify these definitions and
respective proof techniques through numerous examples and a case study
comparing two concurrent implementations of an extensible buffer.Comment: 51 pages, 7 figure
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