Diagram spaces, diagram spectra, and spectra of units

This article compares the infinite loop spaces associated to symmetric spectra, orthogonal spectra, and EKMM S-modules. Each of these categories of structured spectra has a corresponding category of structured spaces that receives the infinite loop space functor \Omega^\infty. We prove that these models for spaces are Quillen equivalent and that the infinite loop space functors \Omega^\infty agree. This comparison is then used to show that two different constructions of the spectrum of units gl_1 R of a commutative ring spectrum R agree.Comment: 62 pages. The definition of the functor \mathbb{Q} is changed. Sections 8, 9, 17 and 18 contain revisions and/or new materia

A Survey on Automated Fact-Checking

Fact-checking has become increasingly important due to the speed with which both information and misinformation can spread in the modern media ecosystem. Therefore, researchers have been exploring how factchecking can be automated, using techniques based on natural language processing, machine learning, knowledge representation, and databases to automatically predict the veracity of claims. In this paper, we survey automated fact-checking stemming from natural language processing, and discuss its connections to related tasks and disciplines. In this process, we present an overview of existing datasets and models, aiming to unify the various definitions given and identify common concepts. Finally, we highlight challenges for future research

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

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

Laplacians on spheres

Spheres can be written as homogeneous spaces $G/H$ for compact Lie groups in a small number of ways. In each case, the decomposition of $L^2(G/H)$ into irreducible representations of $G$ contains interesting information. We recall these decompositions, and see what they can reveal about the analogous problem for noncompact real forms of $G$ and $H$

Performing Security Proofs of Stateful Protocols

This is the author accepted manuscript. The final version is available from IEEE via the DOI in this recordIn protocol verification we observe a wide spectrum from fully automated methods to interactive theorem proving with proof assistants like Isabelle/HOL. The latter provide overwhelmingly high assurance of the correctness, which automated methods often cannot: due to their complexity, bugs in such automated verification tools are likely and thus the risk of erroneously verifying a flawed protocol is non-negligible. There are a few works that try to combine advantages from both ends of the spectrum: a high degree of automation and assurance. We present here a first step towards achieving this for a more challenging class of protocols, namely those that work with a mutable long-term state. To our knowledge this is the first approach that achieves fully automated verification of stateful protocols in an LCF-style theorem prover. The approach also includes a simple user-friendly transaction-based protocol specification language embedded into Isabelle, and can also leverage a number of existing results such as soundness of a typed model.Danish Council for Independent ResearchEuropean Union Horizon 202

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

The Asymptotic distribution of circles in the orbits of Kleinian groups

Let P be a locally finite circle packing in the plane invariant under a non-elementary Kleinian group Gamma and with finitely many Gamma-orbits. When Gamma is geometrically finite, we construct an explicit Borel measure on the plane which describes the asymptotic distribution of small circles in P, assuming that either the critical exponent of Gamma is strictly bigger than 1 or P does not contain an infinite bouquet of tangent circles glued at a parabolic fixed point of Gamma. Our construction also works for P invariant under a geometrically infinite group Gamma, provided Gamma admits a finite Bowen-Margulis-Sullivan measure and the Gamma-skinning size of P is finite. Some concrete circle packings to which our result applies include Apollonian circle packings, Sierpinski curves, Schottky dances, etc.Comment: 31 pages, 8 figures. Final version. To appear in Inventiones Mat

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