Quantinar: a blockchain p2p ecosystem for honest scientific research

Living in the Information Age, the power of data and correct statistical analysis has never been more prevalent. Academics, practitioners and many other professionals nowadays require an accurate application of quantitative methods. Though many branches are subject to a crisis of integrity, which is shown in improper use of statistical models, $p$-hacking, HARKing or failure to replicate results. We propose the use of a peer-to-peer education network, Quantinar, to spread quantitative analysis knowledge embedded with code in the form of Quantlets. The integration of blockchain technology makes Quantinar a decentralised autonomous organisation (DAO) that ensures fully transparent and reproducible scientific research

Asynchronous Approximation of a Single Component of the Solution to a Linear System

We present a distributed asynchronous algorithm for approximating a single component of the solution to a system of linear equations $Ax = b$, where $A$ is a positive definite real matrix, and $b \in \mathbb{R}^n$. This is equivalent to solving for $x_i$ in $x = Gx + z$ for some $G$ and $z$ such that the spectral radius of $G$ is less than 1. Our algorithm relies on the Neumann series characterization of the component $x_i$, and is based on residual updates. We analyze our algorithm within the context of a cloud computation model, in which the computation is split into small update tasks performed by small processors with shared access to a distributed file system. We prove a robust asymptotic convergence result when the spectral radius $\rho(|G|) < 1$, regardless of the precise order and frequency in which the update tasks are performed. We provide convergence rate bounds which depend on the order of update tasks performed, analyzing both deterministic update rules via counting weighted random walks, as well as probabilistic update rules via concentration bounds. The probabilistic analysis requires analyzing the product of random matrices which are drawn from distributions that are time and path dependent. We specifically consider the setting where $n$ is large, yet $G$ is sparse, e.g., each row has at most $d$ nonzero entries. This is motivated by applications in which $G$ is derived from the edge structure of an underlying graph. Our results prove that if the local neighborhood of the graph does not grow too quickly as a function of $n$, our algorithm can provide significant reduction in computation cost as opposed to any algorithm which computes the global solution vector $x$. Our algorithm obtains an $\epsilon \|x\|_2$ additive approximation for $x_i$ in constant time with respect to the size of the matrix when the maximum row sparsity $d = O(1)$ and $1/(1-\|G\|_2) = O(1)$

Cybersecurity Games: Mathematical Approaches for Cyber Attack and Defense Modeling

Cyber-attacks targeting individuals and enterprises have become a predominant part of the computer/information age. Such attacks are becoming more sophisticated and prevalent on a day-to-day basis. The exponential growth of cyber plays and cyber players necessitate the inauguration of new methods and research for better understanding the cyber kill chain, particularly with the rise of advanced and novel malware and the extraordinary growth in the population of Internet residents, especially connected Internet of Things (IoT) devices. Mathematical modeling could be used to represent real-world cyber-attack situations. Such models play a beneficial role when it comes to the secure design and evaluation of systems/infrastructures by providing a better understanding of the threat itself and the attacker\u27s conduct during the lifetime of a cyber attack. Therefore, the main goal of this dissertation is to construct a proper theoretical framework to be able to model and thus evaluate the defensive strategies/technologies\u27 effectiveness from a security standpoint. To this end, we first present a Markov-based general framework to model the interactions between the two famous players of (network) security games, i.e., a system defender and an attacker taking actions to reach its attack objective(s) in the game. We mainly focus on the most significant and tangible aspects of sophisticated cyber attacks: (1) the amount of time it takes for the adversary to accomplish its mission and (2) the success probabilities of fulfilling the attack objective(s) by translating attacker-defender interactions into well-defined games and providing rigorous cryptographic security guarantees for a system given both players\u27 tactics and strategies. We study various attack-defense scenarios, including Moving Target Defense (MTD) strategies, multi-stage attacks, and Advanced Persistent Threats (APT). We provide general theorems about how the probability of a successful adversary defeating a defender’s strategy is related to the amount of time (or any measure of cost) spent by the adversary in such scenarios. We also introduce the notion of learning in cybersecurity games and describe a general game of consequences meaning that each player\u27s chances of making a progressive move in the game depend on its previous actions. Finally, we walk through a malware propagation and botnet construction game in which we investigate the importance of defense systems\u27 learning rates to fight against the self-propagating class of malware such as worms and bots. We introduce a new propagation modeling and containment strategy called the learning-based model and study the containment criterion for the propagation of the malware based on theoretical and simulation analysis

Structural Results and Applications for Perturbed Markov Chains

Each day, most of us interact with a myriad of networks: we search for information on the web, connect with friends on social media platforms, and power our homes using the electrical grid. Many of these interactions have improved our lives, but some have caused new societal issues - social media facilitating the rise of fake news, for example. The goal of this thesis is to advance our understanding of these systems, in hopes improving beneficial interactions with networks while reducing the harm of detrimental ones. Our primary contributions are threefold. First, we devise new algorithms for estimating Personalized PageRank (PPR), a measure of similarity between the nodes in a network used in applications like web search and recommendation systems. In contrast to most existing PPR estimators, our algorithms exploit local graph structure to reduce estimation complexity. We show the analysis of such algorithms is tractable for certain random graph models, and that the key insights obtained from these models hold empirically for real graphs. Our second contribution is to apply ideas from the PPR literature to two other problems. First, we show that PPR estimators can be adapted to the policy evaluation problem in reinforcement learning. More specifically, we devise policy evaluation algorithms inspired by existing PPR estimators that leverage certain side information to reduce the sample complexity of existing methods. Second, we use analytical ideas from the PPR literature to show that convergence behavior and robustness are intimately related for a certain class of Markov chains. Finally, we study social learning over networks as a model for the spread of fake news. For this model, we characterize the learning outcome in terms of a novel measure of the “density” of users spreading fake news. Using this characterization, we also devise optimal strategies for seeding fake news spreaders so as to disrupt learning. These strategies empirically outperform intuitive heuristics on real social networks (despite not being provably optimal for such graphs) and thus provide new insights regarding vulnerabilities in social learning. While the topics studied in this thesis are diverse, a unifying mathematical theme is that of perturbed Markov chains. This includes perturbations that yield useful interpretations in various applications, that provide algorithmic and analytical advantages, and that disrupt some underlying system or process. Throughout the thesis, the perturbed Markov chain theme guides our analysis and suggests more general methodologies.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/155213/1/dvial_1.pd