The mini-course explores the way time flows in dynamic social networks. We will use subjective clocks to open a window to the human soul. The course will cover the second part of my book Analyzing Narratives in Social Networks (https://link.springer.com/book/10.1007/978-3-030-68299-6).

In the first lecture, we will cover chapters 11, 12, and 13. In the second lecture, we will cover chapters 14, 15, and 16.

Chapter 11 studies the perception of time in narrative. We model the narrative of a reader's experience of time as an evolving social network. This chapter takes the function analysis approach, which uses functions as the principal mathematical object. Therefore, the evolving social network is a function of time.

Chapter 12 introduces the notion of subjective and objective clocks. We model subjective time in narrative, and introduce a the subjective clock to allow machines to measure subjective time. We define clocks as an increasing monotonic function. This definition deviates from the traditional definition of clocks as oscillators. The advantage of the monotonic definition is that it is inclusive of both psychological/subjective clocks and objective clocks.

Chapter 13 explains how to compare clocks. Following the stochastic process definition of Martingales, the basic idea is to remove all Euclidean symmetries (such as translation and rotation) from the two clocks. This is equivalent to removing the linear part of those clocks. We introduce the $M$ diagram, which allows for representation of the two clocks as a function of each other after cancelling the Euclidean symmetry. We compare clocks by finding the point at which clocks begin to deviate from one another.

Chapter 14 uses the relationships between clocks to identify critical events in the evolution of a social network. We use the drift between the weighted clock and the event clock to identify critical events in weighted social networks. Chapter 14 defines the law of two clocks, which we can implement in narrative processing.

Chapter 15 provides techniques to transform evolving social networks into a real function. This helps us simplify the analysis of social networks. We use these techniques in narrative processing.

Chapter 16 defines higher orders of social networks and gives some explanation of evolving social network surfaces. We related social network surfaces to sub-stories within a larger overarching narrative.

n this talk, we shall introduce a calculus for a presentation of compact, orientable, connected 3-manifolds with boundary in terms of diagrams embedded in S^3 in a form akin to the standard surgery presentation of closed, orientable, connected 3-manifolds. The motivation to introduce such a presentation of manifolds is to give a completely combinatorial description of the category 3Cob, whose arrows are 3-dimensional cobordisms, which is an ongoing project. We hope this could support further investigations of faithfulness of 3-dimensional Topological Quantum Field Theories.

This is a joint work with Bojana Femić, Vladimir Grujić and Zoran Petrić.

Direct Access is the operation of returning, given an index j, the j-th answer of a conjunctive query Q on a given database for some given order on the answers set of Q. While this problem is #P-hard in general (wrt combined complexity), many conjunctive queries are structured enough so that for some lexicographical ordering of their answers, one can have a direct access to the answer of Q that takes polylogarithmic time in the size of the database after polynomial time precomputation. Previous work have precisely characterized the tractable classes and given fine grained lower bounds on the time needed for precomputation depending on the structure of the query. We give a generalization of these tractability results to the case of signed conjunctive queries, that is, conjunctive queries that may contain negative atoms. Our technique is based on solving the ranked access for a class of circuits that can represent relational data. Our result then follows from the fact that the tractable (signed) conjunctive queries can be transformed into polynomial size circuit. We recover the known tractable classes from the literature in the case of positive conjunctive queries using this technique and also discover new island of tractability for signed conjunctive queries. In particular, our result generalizes to the Ranked Access Problem the known tractabilities of counting the number of answers to beta-acyclic negative queries and of deciding whether a negative query with bounded nested-width has an answer. This is join work with Oliver Irwin and appeared at ICDT 2024:

- ArXiv version: https://arxiv.org/abs/2310.15800 - Published version: https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2024.13

In decentralized finance (DeFi), malicious adversaries were able to steal over 2 billions dollars in crypto assets over the past two years. One very common strategy malicious adversaries use is to borrow large assets through flash loans to launch their exploits against vulnerable DeFi smart contracts deployed on the Blockchain. Flash loans are loans that are only valid within a blockchain transaction and must be repaid with fees by the end of that transaction. Unlike normal loans, flash loans allow borrowers to borrow large assets without upfront collateral deposits.

In this talk, I will first present a work on automated synthesis of adversarial transactions that exploit DeFi smart contracts using flash loans. To bypass the complexity of a DeFi protocol and needs for source code analysis, we propose a new technique to approximate the DeFi protocol functional behaviors using numerical methods (polynomial linear regression and nearest-neighbor interpolation). We then construct an optimization query using the approximated functions of the DeFi protocol to find an adversarial attack that is constituted of a sequence of functions invocations with optimal parameters that provides the maximum profit. To improve the accuracy of the approximation, we propose a novel counterexample driven approximation refinement technique.

I will then present a followup work studying a category of DeFi attacks known as oracle manipulation attacks and the effectiveness of the current mechanisms used to protect against those attacks. I will show that those mechanisms are inadequate to ensure DeFi smart contracts safety when confronted with significant oracle deviations. I will then present a new framework to identify parameters that allow to secure DeFi smart contracts against oracle manipulation attacks. In the framework, we first perform symbolic analysis on the given contract and construct a summary model of constraints. We then leverage an SMT solver to identify parameters values that allow to secure smart contracts against oracle deviations.

The talk is based on two ICSE 2024 papers that are joint works with Zhiyang Chen, Xun Deng, Andreas Veneris, and Fan Long (University of Toronto) and Cyrus Minwalla and Han Du (Bank of Canada).

Littlewood's conjecture is a famous and long-standing open problem which states that, for every $(\alpha,\beta) \in \mathbb{R}^2$, $n\|n\alpha\|\|n\beta\|$ can be arbitrarily small for some integer $n$. This problem is closely related to the action of diagonal matrices on $\mathrm{SL}(3,\mathbb{R})/\mathrm{SL}(3,\mathbb{Z})$, and a groundbreaking result was shown by Einsiedler, Katok and Lindenstrauss from the measure rigidity for this action, saying that Littlewood's conjecture is true except on a set of Hausdorff dimension zero. In this talk, I will explain about a new quantitative result on Littlewood's conjecture which gives, for every $(\alpha,\beta) \in \mathbb{R}^2$ except on sets of small Hausdorff dimension, an estimate of the number of integers $n$ which make $n\|n\alpha\|\|n\beta\|$ small. The keys for the proof are the measure rigidity and further studies on behavior of empirical measures for the diagonal action.

Since artificial intelligence is nowadays also increasingly applied in safety-critical applications such as autonomous driving and human robot collaboration, there is an urgent need for approaches that can efficiently verify that the corresponding neural networks are safe. In general, verification tasks involving neural networks can be classified into the two groups open-loop verification and closed-loop verification. For open-loop verification one aims to prove certain properties of a standalone neural network, while for closed-loop verification the neural network acts as a controller for a dynamic system. This presentation demonstrates a novel verification technique that is based on a polynomial abstraction of the input-output-relation of the single neurons, which proves to be beneficial for both open- as well as closed-loop neural network verification.