[Last updated: 2024.08.27]

一， 个人介绍

赵金华（Jin-Hua Zhao），理学博士，讲师

研究方向：无序系统的统计物理学(statistical physics of disordered systems)，组合优化问题(combinatorial optimization problems)，图与网络(graphs and networks)

办公室：华南师范大学汕尾校区学院综合楼724室

E-mail: zhaojh@m.scnu.edu.cn

个人主页：http://ds.scnu.edu.cn/a/20221109/116.html

I lead the Complexity and Computation Laboratory (CoCoLab).

个人简历：

2022-现在：华南师范大学数据科学与工程学院，广东汕尾。

2019-2022：华南师范大学量子物质研究院，广东广州。

2017-2018：中国科学院理论物理研究所，北京。

2016-2017：DISAT, Politecnico di Torino, Torino, Italia.

2014-2016：中国科学院理论物理研究所，北京。

2007-2014：中国科学院理论物理研究所，北京。理学博士。

2002-2006：华中科技大学物理系（现物理学院），湖北武汉。理学学士。

二，Research 研究方向

In our CoCoLab, we study the emergent collective behaviors in complex systems and the computationally hard problems on interconnected structures. Our research lies at the intersection of statistical physics, applied mathematics, and computer science, with methods encompassing analytical theory, numerical calculation, and simulation. Specifically, we focus on two lines of research:

(1) Network structure and dynamics

The fascination of complex systems comes from the many facets of macroscopic phenomena born out of a large number of interacting constituent parts yet with a rather simple form of microscopic interactions among constituents. Charactering patterns of macroscopic behaviors of complex systems and further quantitatively establishing relations between interaction structures, dynamics, and function are fundamental problems in complex systems research.

The language of graphs and networks offers a simple paradigm to describe the interaction structure in a complex system, in which a constituent is denoted as a vertex or a node and an interaction as an edge or a link. The interaction structure of a network provides a physical basis for dynamical processes on it, such as failure cascading, information propagation, epidemic spreading, and so on. In our group, we focus on the analytical topics originated from intertwined structure and dynamics on graphs and networks: percolation phenomena on graphs, and its relation with enhancing network robustness.

(1.a) Percolation phenomena on graphs

Complex interconnected systems are exposed to internal noise, external perturbation, and attacks. Percolation theory studies the evolution of macroscopic connectedness of an interconnected system (a lattice, a network, and so on). From the point of view of statistical physics, a percolation phenomenon is probably the simplest example of geometric phase transitions on networks. Percolation theory is also a well-adopted framework to quantify structural robustness of a network, the ability to retain the structural integrity upon perturbation and attacks. In our research, we construct models describing nodal or edge failures in networks, and analytically solve pertinent percolation theory.

See [1,6,10] in Publications for some variants of $K$-core percolation models on networks.

(1.b) Enhancement of network robustness

Building fault-tolerant and robust systems against noises and perturbations is one of major prerequisites to design reliable artificial complex systems. This brings along problems of developing measures to enhance network robustness. In our research, we combine the formal percolation framework and a cost-benefit analysis, an idea from economics, to provide a unified perspective, from which we can evaluate and compare reinforcement measures of different origins in a single framework and further determine the optimal one.

See [12] in Publications for a random node reinforcement scheme on networks.

(2) Combinatorial optimization problems (COPs) on graphs

COPs seek to minimize a function with discrete variables. A typical COP on graphs concerns finding a minimal or maximal set of vertices or edges subjected to some topological constraints. These problems compose a major part of computationally hard problems (such as NP-hard problems) in theoretical computer science, in which a linear solver is impossible in a general case. The computational hardness originates from the rugged landscape of ground-state solutions, in which there are a large number of sub-optimal solutions and those optima are separated by high energy barriers, thus fails exiting local search algorithms. For these problems, heuristic algorithms and physics-inspired methods (simulated annealing) are developed. Generally, we focus on two approaches to optimization problems.

(2.a) Mean-field theory from statistical physics

We adopt methods in spin glass theory (replica trick and cavity method) from statistical physics to study COPs. On the level of ensembles, we try to calculate energy density, entropy density, complexity, and so on, all of which characterize organizational properties and structural transitions in the solution space. On the level of graph instances, we develop algorithms which can beat centrality-based heuristics. In our research, we mainly develop cavity methods, such as belief propagation algorithms, for NP-hard problems, for example covering and matching problems.

See [2,3,4,5,9] in Publications for some algorithmic results on Minimum Vertex Cover (MVC) Problem, Minimum Dominating Set (MDS) Problem, and Feedback Arc Set Problem.

(2.b) Percolation-based analytical theory

For an optimization problem on graphs with local constraints, an optimal local step can be a good start. Iterative local steps reduce a problem till a final residual one. For a graphical optimization, this procedure of iterative removal of constraints intrinsically leads to a percolation model of pruning vertices (variables) and edges (constraints). Solving an extended percolation theory on both its residual and removed subgraphs provides an analytical framework to an approximation of optimization problems. In our research, we adopt this approach on energy densities of several optimization problems.

See [3,4,7,8,11] in Publications for percolation analysis of MDS, MVC, Maximal Matching, and $z$-matching problems.

(3) Probabilistic approaches to stochastic processes in physical problems

Beside the above two main research lines, we are also keen to analytically solvable problems involving random processes from various physical backgrounds, for example, filtration in soft and granular matter.

See [13] in Publications for an analytical work on a generalized Buffon-Laplace Needle Problem.

三， Publications 科研成果

A timely updated list can be found at:

 --arXiv: https://url.scnu.edu.cn/record/view/index.html?key=98a7fc27c06d1ebfa15fcede4b801b57

 --Google Scholar: https://scholar.google.com/citations?hl=zh-CN&user=il6Tyg8AAAAJ

[*: co-first author; #: corresponding author]

13, Yan-Jie Min*, De-Quan Zhu*, and Jin-Hua Zhao#, Buffon-Laplace Needle Problem as a geometric probabilistic approach to filtration process, arXiv:2402.06670[math.HO] (30 pages)

https://url.scnu.edu.cn/record/view/index.html?key=c51de50535cbd4729af0bab1e658f2f6

12, Rui Ma, Yanqing Hu, and Jin-Hua Zhao#, Random node reinforcement and $K$-core structure of complex networks, Chaos, Solitons and Fractals 173, 113706 (2023) (11 pages)

https://url.scnu.edu.cn/record/view/index.html?key=b75c7fe44d892841e79149e15eb0b58c

11, Jin-Hua Zhao#, A local algorithm and its percolation analysis of bipartite $z$-matching problem, Journal of Statistical Mechanics (2023) 053401 (25 pages)

https://url.scnu.edu.cn/record/view/index.html?key=14650792f34686bfd36be824f125863c

10, Jiarong Xie*, Xiangrong Wang*, Ling Feng, Jin-Hua Zhao, Wenyuan Liu, Yamir Moreno, and Yanqing Hu#, Indirect influence in social networks as an induced percolation phenomenon, Proceedings of National Academy of Sciences of USA 119, e210015119 (2022) (10+33 pages)

https://url.scnu.edu.cn/record/view/index.html?key=7ee74caaccde0126f7bfc6bd1e8665bb

9, Chun-Yan Zhao#, Yan-Rong Fu and Jin-Hua Zhao#, A residual-based message passing algorithm for constraint satisfaction problems, Communications in Theoretical Physics, 74, 035601 (2022) (10 pages)

https://url.scnu.edu.cn/record/view/index.html?key=3b0466c227fa58a5a70502d841dd6554

8, Jin-Hua Zhao# and Hai-Jun Zhou, Two faces of greedy leaf removal procedure on graphs, Journal of Statistical Mechanics (2019) 083401 (29 pages)

https://url.scnu.edu.cn/record/view/index.html?key=9717a8d477c8d6220dd56a39068f6448

7, Jin-Hua Zhao# and Hai-Jun Zhou, Controllability and maximum matchings of complex networks, Physical Review E 99, 012319 (2019) (10 pages)

https://url.scnu.edu.cn/record/view/index.html?key=4e232d41d44e5220f75ad29f86d71bc2

6, Jin-Hua Zhao#, Generalized $k$-core pruning process on directed networks, Journal of Statistical Mechanics (2017) 063407 (26 pages)

https://url.scnu.edu.cn/record/view/index.html?key=402e45b9a2546bfa1a1c3c2974962a7d

5, Jin-Hua Zhao and Hai-Jun Zhou#, Feedback arcs and node hierarchy in directed networks, Chinese Physics B 26, 078901 (2017) (15 pages)

https://url.scnu.edu.cn/record/view/index.html?key=7a7db1a1293acb05442cfb47c1ca786c

4, Yusupjan Habibulla, Jin-Hua Zhao, and Hai-Jun Zhou#, The Directed Dominating Set Problem: Generalized Leaf Removal and Belief Propagation, Lecture Notes in Computer Science 9130, 78-88 (2015) (11 pages)

https://url.scnu.edu.cn/record/view/index.html?key=657e5805b0088a1972c1d2e2f663f1bb

3, Jin-Hua Zhao, Yusupjan Habibulla and Hai-Jun Zhou#, Statistical Mechanics of the Minimum Dominating Set Problem, Journal of Statistical Physics 159, 1154-1174 (2015) (21 pages)

https://url.scnu.edu.cn/record/view/index.html?key=8bbd398e0a5210931df4a134d56b71bf

2, Jin-Hua Zhao and Hai-Jun Zhou#, Statistical physics of hard combinatorial optimization: Vertex cover problem, Chinese Physics B 23, 078901 (2014) (7 pages)

https://url.scnu.edu.cn/record/view/index.html?key=5b9198ba08c6f6b76bea096079e1abd7

1, Jin-Hua Zhao, Hai-Jun Zhou#, and Yang-Yu Liu, Inducing effect on the percolation transition in complex networks, Nature Communications 4, 2412(2013) (6+49 pages)

https://url.scnu.edu.cn/record/view/index.html?key=d4e4f97688e9d6d301b1bc587bc34851

四, Grants 科研项目

1, 广东省自然科学基金-面上项目，广东省基础与应用基础研究基金，“图上组合优化问题的统计物理研究：渗流理论和自旋玻璃理论”，项目编号：No.2022A1515011765，研究期限：2022.01-2024.12。项目负责人。

五、Teaching 教学

2024-2025学年第一学期：《数据结构》、《数据结构实验》。

2023-2024学年第二学期：《面向对象程序设计（C++语言）》。

2023-2024学年第一学期：《数据结构》、《数据结构实验》。

2022-2023学年第二学期：《面向对象程序设计（C++语言）》。

2022-2023学年第一学期：《数据结构》、《数据结构实验》。

2020-2021学年第二学期：《计算物理基础》。

2019-2020学年第一学期：《量子统计》。

六，Group members (current and former) 课题组成员

闵严洁Yan-Jie Min（2023.01-）

朱德权De-Quan Zhu（2023.01-）

马瑞Rui Ma (2020.09-2023.07)[co-advised with 王倩 from IQM-SCNU]

七、Join us

有意向加入课题组的同学可联系PI。基本要求：对编程、算法、数学感兴趣。