The infinitesimal characters of discrete series for real spherical spaces

Let $Z=G/H$ be the homogeneous space of a real reductive group and a unimodular real spherical subgroup, and consider the regular representation of $G$ on $L^2(Z)$. It is shown that all representations of the discrete series, that is, the irreducible subrepresentations of $L^2(Z)$, have infinitesimal characters which are real and belong to a lattice. Moreover, let $K$ be a maximal compact subgroup of $G$. Then each irreducible representation of $K$ occurs in a finite set of such discrete series representations only. Similar results are obtained for the twisted discrete series, that is, the discrete components of the space of square integrable sections of a line bundle, given by a unitary character on an abelian extension of $H$.Comment: To appear in GAF

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

Ellipticity and discrete series

We explain by elementary means why the existence of a discrete series representation of a real reductive group $G$ implies the existence of a compact Cartan subgroup of $G$. The presented approach has the potential to generalize to real spherical spaces

Joint Verification and Reranking for Open Fact Checking Over Tables

Structured information is an important knowledge source for automatic verification of factual claims. Nevertheless, the majority of existing research into this task has focused on textual data, and the few recent inquiries into structured data have been for the closed-domain setting where appropriate evidence for each claim is assumed to have already been retrieved. In this paper, we investigate verification over structured data in the open-domain setting, introducing a joint reranking-and-verification model which fuses evidence documents in the verification component. Our open-domain model achieves performance comparable to the closed-domain state-of-the-art on the TabFact dataset, and demonstrates performance gains from the inclusion of multiple tables as well as a significant improvement over a heuristic retrieval baseline

Competence of graph convolutional network in anti-money laundering in Bitcoin Blockchain

Graph networks are extensively used as an essential framework to analyse the interconnections between transactions and capture illicit behaviour in Bitcoin blockchain. Due to the complexity of Bitcoin transaction graph, the prediction of illicit transactions has become a challenging problem to unveil illicit services over the network. Graph Convolutional Network, a graph neural network based spectral approach, has recently emerged and gained much attention regarding graph-structured data. Previous research has highlighted the degraded performance of the latter approach to predict illicit transactions using, a Bitcoin transaction graph, so-called Elliptic data derived from Bitcoin blockchain. Motivated by the previous work, we seek to explore graph convolutions in a novel way. For this purpose, we present a novel approach that is modelled using the existing Graph Convolutional Network intertwined with linear layers. Concisely, we concatenate node embeddings obtained from graph convolutional layers with a single hidden layer derived from the linear transformation of the node feature matrix and followed by Multi-layer Perceptron. Our approach is evaluated using Elliptic data, wherein efficient accuracy is yielded. The proposed approach outperforms the original work of same data set

Facilitating the analysis of COVID-19 literature through a knowledge graph

At the end of 2019, Chinese authorities alerted the World Health Organization (WHO) of the outbreak of a new strain of the coronavirus, called SARS-CoV-2, which struck humanity by an unprecedented disaster a few months later. In response to this pandemic, a publicly available dataset was released on Kaggle which contained information of over 63,000 papers. In order to facilitate the analysis of this large mass of literature, we have created a knowledge graph based on this dataset. Within this knowledge graph, all information of the original dataset is linked together, which makes it easier to search for relevant information. The knowledge graph is also enriched with additional links to appropriate, already existing external resources. In this paper, we elaborate on the different steps performed to construct such a knowledge graph from structured documents. Moreover, we discuss, on a conceptual level, several possible applications and analyses that can be built on top of this knowledge graph. As such, we aim to provide a resource that allows people to more easily build applications that give more insights into the COVID-19 pandemic

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

On the algebraic K-theory of the complex K-theory spectrum

Let p>3 be a prime, let ku be the connective complex K-theory spectrum, and let K(ku) be the algebraic K-theory spectrum of ku. We study the p-primary homotopy type of the spectrum K(ku) by computing its mod (p,v_1) homotopy groups. We show that up to a finite summand, these groups form a finitely generated free module over a polynomial algebra F_p[b], where b is a class of degree 2p+2 defined as a higher Bott element.Comment: Revised and expanded version, 42 pages