The three-dimensional organization of the genome exhibits rich, scale-dependent structure, as revealed by both chromosome contact maps (e.g., Hi-C maps) and chromatin density measured by microscopy. Recent studies have reported multifractal scaling in these data. Yet, the origin of this scaling behavior remains unclear: existing efforts describe it through postulated models. Here, we show that the multifractal structure of Hi-C maps is a direct consequence of the power-law contact probability $P(s)$, which is itself an empirical observable measured from Hi-C maps. Starting from $P(s)$ with a single exponent $γ$, we analytically derive the mass exponent $τ(q)$, which characterizes how the $q$-th moment of contact density scales with box size $l$ used to coarse-grain the genomic coordinate. This multifractal behavior reflects the geometric competition between intra- and inter-segment contacts. We find that the slope of $τ(q)$ at large $q$ is given by $2 -γ$ when $γ<1$, and by $1$ when $γ\geq 1$. We further show that this behavior is robust to noise and consistent across diverse organisms, indicating that it is a universal feature of chromatin organization. We extend our analysis into double-exponent $P(s)$, and show the $l$ dependence in multifractal behavior. Taken together, these results provide a physical explanation for multifractal scaling and establish a direct link between the multifractality in Hi-C maps and polymer contact statistics, with the large-$q$ slope of $τ(q)$ mapping onto a known polymer contact exponent.
Inhomogeneous sandpile model: Crossover from multifractal scaling to finite size scaling
本文研究了一个非均匀沙堆模型，其中定义了两种不同的倾倒规则。对于任何站点，仅应用一个规则，对应于Bak、Tang和Wiesenfeld模型{[} P. Bak，C. Tang和K. Wiesenfeld，Phys. Rev. Lett. \textbf{59}，381（1987）{]}或Manna两态沙堆模型{[} S. S. Manna，J. Phys. A \textbf{24}，L363（1991）{]}.引入参数$c$，其描述随机部署的站点的密度，并且其中应用随机Manna规则。结果表明，雪崩面积指数$τ_{a}$、雪崩尺寸指数$τ_{s}$和容量分形维数$D_{s}$依赖于密度$c$.发现Bak，Tang，and Wiesenfeld模型的多重分形标度（$c=0$）与有限尺寸标度之间存在交叉，临界密度$c$在区间$0<c<0.01$内.这些结果表明，局部动力学规则是重要的，可以改变模型的整体性质。
Generalized multifractality at the spin quantum Hall transition: Percolation mapping and pure-scaling observables
本文推广了二维无序超导体自旋量子霍尔跃迁临界本征态的广义多重分形分析[J. F. Karcher等人，Annals of Physics，435，168584（2021）]。一个映射到经典渗流的广义多重分形可观的一组特定的。这样，相应的指数的准确的分析结果得到。此外，正的纯标度本征函数观测量的一般结构，这允许一个非常有效的数值确定标度指数。特别是，所有指数对应的多项式纯缩放可观的顺序$q=5$的数字。对于导出的渗流映射的观测量，分析和数值结果是完全一致的。分析和数值结果清楚地表明，广义抛物线（即，与二次Casimir算子的本征值成比例）对于广义多重分形指数的谱不成立。这排除了Wess-Zumino-Novikov-Witten模型，以及更一般的，任何具有局部共形不变性的理论，作为自旋量子霍尔跃迁的定点理论的候选者。在这项工作中开发的可观察的建设铺平了道路，调查广义多重分形在安德森本地化的临界点的各种对称类。
Disentangling intermittent flow structure contributions to anomalous scaling and multifractality in turbulence
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（塔塔基础研究所国际理论科学中心）；Department of Mechanical Engineering, Indian Institute of Technology, Kanpur（坎普尔印度理工学院机械工程系）
Multifractal scaling of flux penetration in the Iron-based Superconductor Ba(Fe$_{0.93}$Co$_{0.07}$)$_{2}$As$_2$
用磁光成像和Bitter装饰方法研究了最佳掺杂的铁基超导体Ba（Fe $_{1-x}$ Co $_{x}$）$_{2}$ As $_2$（$x = 0.07 \pm 0.005$）中磁通前沿的穿透。粗糙化和增长的磁通量前沿的高阶分析揭示了异常的标度特性，指示非高斯相关的无序势。高阶空间关联函数揭示了粗糙化的多重分形行为，同时发现了通常的Kardar-Parisi-Zhang生长指数，这两个指数都与温度无关。的缩放行为是明显不同的，从其他模式的磁通量渗透，如介导的雪崩，这表明多尺度是一个强大的工具粗糙界面的表征。我们提出了一个基于二维渗流和团簇聚集的非均匀无序超导体的涡旋穿透方案。
Resolving Spurious Multifractality in Discrete Systems: A Finite-Size Scaling Protocol for MFDFA in the 2D Ising Model
Comisión Nacional de Energía Atómica (CNEA)（国家原子能委员会）；Universidad Tecnológica Nacional, Facultad Regional Haedo（国家技术大学哈埃多区域学院）；Instituto Sábato. Universidad Nacional de San Martín（萨巴托研究所，圣马丁国立大学）；Department of Mathematical Sciences, UTEP（UTEP数学科学系）
Ecole Polytechnique（巴黎综合理工学院）；Institut Jean Le Rond d’Alembert, UMR CNRS 7190, Sorbonne Université（索邦大学让·勒朗·达朗贝尔研究所）；Chair of EconophysiX & Complex Systems, Ecole Polytechnique（巴黎综合理工学院经济物理学与复杂系统讲席）；Capital Fund Management（资本基金管理公司）；Académie des Sciences（法兰西科学院）
