C6

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 classical theorem of Molloy and Johansson states that if a graph is triangle free and has maximum degree at most $\Delta$, then it has chromatic number at most $\frac{\Delta}{\log \Delta}$. This was extended to graphs with few edges in their neighbourhoods by Alon-Krivelevich and Sudakov, and to list chromatic number by Vu. I will give a full and self-contained proof of these results that relies only on induction and the first moment method.

MSO can be used not only to accept/reject words, but also to transform words into other words, e.g. the doubling function w $\mapsto$ ww. The traditional model for this is called MSO transductions; the idea is that each position of the output word is interpreted in some position of the input word, and MSO is used to define the order on output positions and their labels. I will explain that an extension, where output positions are interpreted using $k$-tuples of input positions, is (a) is also well behaved; and (b) this is surprising.

We will consider line defects in d-dimensional CFTs. The ambient CFT places nontrivial constraints on renormalization group flows on such line defects. We will see that the flow on line defects is consequently irreversible and furthermore a canonical decreasing entropy function exists. This construction generalizes the g theorem to line defects in arbitrary dimensions. We will demonstrate this generalization in some concrete examples, including a flow between Wilson loops in 4 dimensions, and an O(3) bosonic theory coupled to an impurity in the large spin representation of the bulk global symmetry.

The stabilization of thermo-mechanical systems is a classical problem in thermodynamics and well

understood in a context of gases. The objective of this talk is to indicate the role of null-Lagrangians and

certain transport/stretching identities in stabilizing thermomechanical systems associated with general

thermoelastic free energies. This allows to prove various convergence results among thermomechan-

ical theories, and suggests a variational scheme for the approximation of the equations of adiabatic

thermoelasticity.

We will talk about our recent results on the uniqueness of regular reflection solutions for the potential flow equation in a natural class of self-similar solutions. The approach is based on a nonlinear version of method of continuity. An important property of solutions for the proof of uniqueness is the convexity of the free boundary.

There was major progress on perfect graphs in the early 2000's: Chudnovsky, Robertson, Thomas and I proved the ``strong perfect graph theorem'' that a graph is perfect if and only if it has no odd hole or odd antihole; and Chudnovsky, Cornuejols, Liu, Vuscovic and I found a polynomial-time algorithm to test whether a graph has an odd hole or odd antihole, and thereby test if it is perfect. (A ``hole'' is an induced cycle of length at least four, and an ``antihole'' is a hole in the complement graph.)

What we couldn't do then was test whether a graph has an odd hole, and this has stayed open for the last fifteen years, despite some intensive effort. I am happy to report that in fact it can be done in poly-time (in time O(|G|^{12}) at the last count), and in this talk we explain how.

Joint work with Maria Chudnovsky, Alex Scott, and Sophie Spirkl.