99 research outputs found
Strong wavefront lemma and counting lattice points in sectors
We compute the asymptotics of the number of integral quadratic forms with
prescribed orthogonal decompositions and, more generally, the asymptotics of
the number of lattice points lying in sectors of affine symmetric spaces. A new
key ingredient in this article is the strong wavefront lemma, which shows that
the generalized Cartan decomposition associated to a symmetric space is
uniformly Lipschitz
Laplacians on spheres
Spheres can be written as homogeneous spaces for compact Lie groups in
a small number of ways. In each case, the decomposition of into
irreducible representations of contains interesting information. We recall
these decompositions, and see what they can reveal about the analogous problem
for noncompact real forms of and
Automated stateful protocol verification
This is the final version. Available from the publisher via the link in this record.In protocol verification we observe a wide spectrum from fully automated methods to interactive theorem proving with proof assistants like Isabelle/HOL. In this AFP entry, we present a fully-automated approach for verifying stateful security protocols, i.e., protocols with mutable state that may span several sessions. The approach supports reachability goals like secrecy and authentication. We also include a simple user-friendly transaction-based protocol specification language that is embedded into Isabelle
Mixing Insulin Aspart With Detemir Does Not Affect Glucose Excursion in Children With Type 1 Diabetes
Climate Action In Megacities 3.0
"Climate Action in Megacities 3.0" (CAM 3.0) presents major new insights into the current status, latest trends and future potential for climate action at the city level. Documenting the volume of action being taken by cities, CAM 3.0 marks a new chapter in the C40-Arup research partnership, supported by the City Leadership Initiative at University College London. It provides compelling evidence about cities' commitment to tackling climate change and their critical role in the fight to achieve global emissions reductions
A Principled Approach to Analyze Expressiveness and Accuracy of Graph Neural Networks
Graph neural networks (GNNs) have known an increasing success recently, with many GNN variants achieving state-of-the-art results on node and graph classification tasks. The proposed GNNs, however, often implement complex node and graph embedding schemes, which makes challenging to explain their performance. In this paper, we investigate the link between a GNN's expressiveness, that is, its ability to map different graphs to different representations, and its generalization performance in a graph classification setting. In particular , we propose a principled experimental procedure where we (i) define a practical measure for expressiveness, (ii) introduce an expressiveness-based loss function that we use to train a simple yet practical GNN that is permutation-invariant, (iii) illustrate our procedure on benchmark graph classification problems and on an original real-world application. Our results reveal that expressiveness alone does not guarantee a better performance, and that a powerful GNN should be able to produce graph representations that are well separated with respect to the class of the corresponding graphs
Plancherel formula for Berezin deformation of on Riemannian symmetric space
Consider the space B of complex matrces with norm <1. There
exists a standard one-parameter family of unitary representations of the
pseudounitary group U(p,q) in the space of holomorphic functions on B (i.e.
scalar highest weight representations). Consider the restriction of
to the pseudoorthogonal group O(p,q).
The representation of O(p,q) in on the symmetric space
is a limit of the representations in some
precise sence. Spectrum of a representation is comlicated and it depends
on .
We obtain the complete Plancherel formula for the representations for
all admissible values of the parameter . We also extend this result to
all classical noncompact and compact Riemannian symmetric spaces
Modeling Relational Data with Graph Convolutional Networks
Knowledge graphs enable a wide variety of applications, including question
answering and information retrieval. Despite the great effort invested in their
creation and maintenance, even the largest (e.g., Yago, DBPedia or Wikidata)
remain incomplete. We introduce Relational Graph Convolutional Networks
(R-GCNs) and apply them to two standard knowledge base completion tasks: Link
prediction (recovery of missing facts, i.e. subject-predicate-object triples)
and entity classification (recovery of missing entity attributes). R-GCNs are
related to a recent class of neural networks operating on graphs, and are
developed specifically to deal with the highly multi-relational data
characteristic of realistic knowledge bases. We demonstrate the effectiveness
of R-GCNs as a stand-alone model for entity classification. We further show
that factorization models for link prediction such as DistMult can be
significantly improved by enriching them with an encoder model to accumulate
evidence over multiple inference steps in the relational graph, demonstrating a
large improvement of 29.8% on FB15k-237 over a decoder-only baseline
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