arXiv subjects

Yifan Jia

Publications and source records attributed to Yifan Jia.

24 records · Page 2Linked to original sources

arXiv2024

A Comprehensive Review of Community Detection in Graphs

The study of complex networks has significantly advanced our understanding of community structures which serves as a crucial feature of real-world graphs. Detecting communities in graphs is a challenging problem with applications in sociology, biology, and computer science. Despite the efforts of an interdisciplinary community of scientists, a satisfactory solution to this problem has not yet been achieved. This review article delves into the topic of community detection in graphs, which serves as a thorough exposition of various community detection methods from perspectives of modularity-based method, spectral clustering, probabilistic modelling, and deep learning. Along with the methods, a new community detection method designed by us is also presented. Additionally, the performance of these methods on the datasets with and without ground truth is compared. In conclusion, this comprehensive review provides a deep understanding of community detection in graphs.

cs.SI↗

arXiv2024

A generic quantum Wielandt's inequality

Quantum Wielandt's inequality gives an optimal upper bound on the minimal length $k$ such that length-$k$ products of elements in a generating system span $M_n(\mathbb{C})$. It is conjectured that $k$ should be of order $\mathcal{O}(n^2)$ in general. In this paper, we give an overview of how the question has been studied in the literature so far and its relation to a classical question in linear algebra, namely the length of the algebra $M_n(\mathbb{C})$. We provide a generic version of quantum Wielandt's inequality, which gives the optimal length with probability one. More specifically, we prove based on [KS16] that $k$ generically is of order $Θ(\log n)$, as opposed to the general case, in which the best bound to date is $\mathcal O(n^2 \log n)$. Our result implies a new bound on the primitivity index of a random quantum channel. Furthermore, we shed new light on a long-standing open problem for Projected Entangled Pair State, by concluding that almost any translation-invariant PEPS (in particular, Matrix Product State) with periodic boundary conditions on a grid with side length of order $Ω( \log n )$ is the unique ground state of a local Hamiltonian. We observe similar characteristics for matrix Lie algebras and provide numerical results for random Lie-generating systems.

quant-ph↗

arXiv2023

Hay from the haystack: explicit examples of exponential quantum circuit complexity

The vast majority of quantum states and unitaries have circuit complexity exponential in the number of qubits. In a similar vein, most of them also have exponential minimum description length, which makes it difficult to pinpoint examples of exponential complexity. In this work, we construct examples of constant description length but exponential circuit complexity. We provide infinite families such that each element requires an exponential number of two-qubit gates to be generated exactly from a product and where the same is true for the approximate generation of the vast majority of elements in the family. The results are based on sets of large transcendence degree and discussed for tensor networks, diagonal unitaries, and maximally coherent states.

quant-ph↗

arXiv2021

Adversarial Attacks and Mitigation for Anomaly Detectors of Cyber-Physical Systems

The threats faced by cyber-physical systems (CPSs) in critical infrastructure have motivated research into a multitude of attack detection mechanisms, including anomaly detectors based on neural network models. The effectiveness of anomaly detectors can be assessed by subjecting them to test suites of attacks, but less consideration has been given to adversarial attackers that craft noise specifically designed to deceive them. While successfully applied in domains such as images and audio, adversarial attacks are much harder to implement in CPSs due to the presence of other built-in defence mechanisms such as rule checkers(or invariant checkers). In this work, we present an adversarial attack that simultaneously evades the anomaly detectors and rule checkers of a CPS. Inspired by existing gradient-based approaches, our adversarial attack crafts noise over the sensor and actuator values, then uses a genetic algorithm to optimise the latter, ensuring that the neural network and the rule checking system are both deceived.We implemented our approach for two real-world critical infrastructure testbeds, successfully reducing the classification accuracy of their detectors by over 50% on average, while simultaneously avoiding detection by rule checkers. Finally, we explore whether these attacks can be mitigated by training the detectors on adversarial samples.

cs.CR↗

arXiv2021

Comment on "Generators of matrix algebras in dimension 2 and 3"

Theorem 7 in Ref. [Linear Algebra Appl., 430, 1-6, (2009)] states sufficient conditions to determine whether a pair generates the algebra of 3x3 matrices over an algebraically closed field of characteristic zero. In that case, an explicit basis for the full algebra is provided, which is composed of words of small length on such pair. However, we show that this theorem is wrong since it is based on the validity of an identity which is not true in general.

math.RA↗

arXiv2018

Toward `verifying' a Water Treatment System

Modeling and verifying real-world cyber-physical systems is challenging, which is especially so for complex systems where manually modeling is infeasible. In this work, we report our experience on combining model learning and abstraction refinement to analyze a challenging system, i.e., a real-world Secure Water Treatment system (SWaT). Given a set of safety requirements, the objective is to either show that the system is safe with a high probability (so that a system shutdown is rarely triggered due to safety violation) or not. As the system is too complicated to be manually modeled, we apply latest automatic model learning techniques to construct a set of Markov chains through abstraction and refinement, based on two long system execution logs (one for training and the other for testing). For each probabilistic safety property, we either report it does not hold with a certain level of probabilistic confidence, or report that it holds by showing the evidence in the form of an abstract Markov chain. The Markov chains can subsequently be implemented as runtime monitors in SWaT.

cs.AI↗