Co-occurrence networks formed by bipartite projection are widely studied in many contexts, including politics (bill co-sponsorship), bibliometrics (paper co-authorship), ecology (species co-habitation), and genetics (protein co-expression). It is often useful to focus on the backbone, a binary representation that includes only the most important edges, however many different backbone extraction models exist. In this talk, I will demonstrate the "backbone" package for R, which implements many such models. I will also use it to compare two promising null models: the fixed degree sequence model (FDSM) that imposes hard constraints, and the stochastic degree sequence model (SDSM) that imposes soft constraints, on the bipartite degree sequences. While FDSM is more statistically powerful, SDSM is more efficient and offers a close approximation.

In this talk I will present network-theoretic tools [1-2] to filter information in large-scale datasets and I will show that these are powerful tools to study complex datasets. In particular I will introduce correlation-based information filtering networks and the planar filtered graphs (PMFG) and I will show that applications to financial data-sets can meaningfully identify industrial activities and structural market changes [3-4].

It has been shown that by making use of the 3-clique structure of the PMFG a clustering can be extracted allowing dimensionality reduction that keeps both local information and global hierarchy in a deterministic manner without the use of any prior information [5-6]. However, the algorithm so far proposed to construct the PMFG is numerically costly with O(N3) computational complexity and cannot be applied to large-scale data. There is therefore scope to search for novel algorithms that can provide, in a numerically efficient way, such a reduction to planar filtered graphs. I will introduce a new algorithm, the TMFG (Triangulated Maximally Filtered Graph), that efficiently extracts a planar subgraph which optimizes an objective function. The method is scalable to very large datasets and it can take advantage of parallel and GPUs computing [7]. Filtered graphs are valuable tools for risk management and portfolio optimization too [8-9] and they allow to construct probabilistic sparse modeling for financial systems that can be used for forecasting, stress testing and risk allocation [10].

Filtered graphs can be used not only to extract relevant and significant information but more importantly to extract knowledge from an overwhelming quantity of unstructured and structured data. I will provide a practitioner example by a successful Silicon Valley start-up, Yewno. The key idea underlying Yewno’s products is the concept of the Knowledge Graph, a framework based on filtered graph research, whose goal is to extract signals from evolving corpus of data. The common principle is that a methodology leveraging on developments in Computational linguistics and graph theory is used to build a graph representation of knowledge [11], which can be automatically analysed to discover hidden relations between components in many different complex systems. This Knowledge Graph based framework and inference engine has a wide range of applications, including finance, economics, biotech, law, education, marketing and general research.

[1] T. Aste, T. Di Matteo, S. T. Hyde, Physica A 346 (2005) 20.

[2] T. Aste, Ruggero Gramatica, T. Di Matteo, Physical Review E 86 (2012) 036109.

[3] M. Tumminello, T. Aste, T. Di Matteo, R. N. Mantegna, PNAS 102, n. 30 (2005) 10421.

[4] N. Musmeci, Tomaso Aste, T. Di Matteo, Journal of Network Theory in Finance 1(1) (2015) 1-22.

[5] W.-M. Song, T. Di Matteo, and T. Aste, PLoS ONE 7 (2012) e31929.

[6] N. Musmeci, T. Aste, T. Di Matteo, PLoS ONE 10(3): e0116201 (2015).

[7] Guido Previde Massara, T. Di Matteo, T. Aste, Journal of Complex networks 5 (2), 161 (2016).

[8] F. Pozzi, T. Di Matteo and T. Aste, Scientific Reports 3 (2013) 1665.

[9] N. Musmeci, T. Aste and T. Di Matteo, Scientific Reports 6 (2016) 36320.

[10] Wolfram Barfuss, Guido Previde Massara, T. Di Matteo, T. Aste, Phys.Rev. E 94 (2016) 062306.

[11] Ruggero Gramatica, T. Di Matteo, Stefano Giorgetti, Massimo Barbiani, Dorian Bevec and Tomaso Aste, PLoS One (2014) PLoS ONE 9(1): e84912.

Pair combination repurposing of drugs is a common challenge faced by researchers in the pharmaceutical industry. Network biology and molecular machine learning based drug pair scoring techniques offer computation tools to predict the interaction, polypharmacy side effects and synergy of drugs. In this talk we overview of three things: (a) the theory and unified model of drug pair scoring (b) a relational machine learning model that can solve the pair scoring task (c) the design of large-scale machine learning systems needed to tackle the pair scoring task.

ArXiv links: https://arxiv.org/abs/2111.02916, https://arxiv.org/abs/2110.15087, https://arxiv.org/abs/2202.05240.

ML library: https://github.com/AstraZeneca/chemicalx

A few years back, Smale spaces were shown to exhibit noncommutative Poincaré duality (with Jerry Kaminker and Ian Putnam). The fundamental class was represented as an extension by the compacts. In current work we describe a Fredholm module representation of the fundamental class. The proof uses delicate approximations of the Smale space arising from a refining sequence of (open) Markov partition covers. I hope to explain all these notions in an elementary manner. This is joint work with Dimitris Gerontogiannis and Joachim Zacharias.

Groupoid C*-algebras and twisted groupoid C*-algebras are introduced by Renault in the late ’70. Twisted groupoid C*-algebras have since proved extremely important in the study of structural properties for large classes of C*-algebras. On the other hand, Steinberg algebras are introduced independently by Steinberg and Clark, Farthing, Sims and Tomforde around 2010 which are a purely algebraic analogue of groupoid C*-algebras. Steinberg algebras provide useful insight into the analytic theory of groupoid C*-algebras and give rise to interesting examples of *-algebras. In this talk, I will first recall some relevant background on topological groupoids and twisted groupoid C*-algebras, then I will introduce twisted Steinberg algebras which generalise the Steinberg algebras and provide a purely algebraic analogue of twisted groupoid C*-algebras. If I have enough time, I will further introduce pair of algebras which consist of a Steinberg algebra and an algebra of locally constant functions on the unit space, it is an algebraic analogue of Cartan pairs

We will give a general overview of how one gets groups to act on CAT(0) cube complexes, how compatible such actions are and how this plays out in the setting of Coxeter groups.

We show that ribbon concordance forms a partial ordering on the set of knots, answering a question of Gordon. The proof makes use of representation varieties of the knot groups to S O(N) and relations between them induced by a ribbon concordance.

Gerbes are geometric objects describing the third integer cohomology group of a manifold and the B-field in string theory. Like line bundles, they admit connections and gauge symmetries. In contrast to line bundles, however, there are now isomorphisms between gauge symmetries: the gauge group of a gerbe is a smooth 2-group. Starting from a hands-on example, I will explain gerbes and some of their properties. The main topic of this talk will then be the study of symmetries of gerbes on a manifold with G-action, and how these symmetries assemble into smooth 2-group extensions of G. In the last part, I will survey how this construction can be used to provide a new smooth model for the String group, via a theory of ∞-categorical principal bundles and group extensions.