非线性科学
查看 最近的 文章
显示 2025年07月18日， 星期五 新的列表
- [1] arXiv:2507.11958 (交叉列表自 math.DS) [中文pdf, pdf, html, 其他]
-
标题： 相互作用的宿主与微生物组交换：离散相互作用的元群落理论扩展标题： Interacting Hosts with Microbiome Exchange: An Extension of Metacommunity Theory for Discrete Interactions评论： 55页主题： 动力系统 (math.DS) ; 种群与进化 (q-bio.PE)
微生物组是由环境中相互作用的微生物组成的集合，它们通常显著影响其所占据的环境斑块或宿主。在微生物组模型中，考虑环境内部的局部动态以及不同环境之间的微生物组交换是很重要的。一种将这些及其他跨多个尺度的相互作用纳入考虑的方法是采用元群落理论。元群落模型通常假设在发生局部微生物组动态的环境中，微生物组持续扩散。在这种假设下，每对环境之间的一个参数控制这两个环境之间的扩散率。这种元群落框架非常适合非生物环境斑块，但它无法捕捉到活体宿主微生物组的一个关键方面，即这些宿主通常不会持续相互作用。相反，活体宿主在离散的时间间隔内相互作用。在本文中，我们开发了一个编码这种离散相互作用的建模框架，并使用两个参数分别控制宿主之间的相互作用频率以及每次相互作用时的微生物组交换量。我们在三种参数范围内推导了框架中模型的解析近似，并证明了它们在这些范围内的准确性。我们将这些近似与一个示例模型的数值模拟进行了比较。我们证明，我们的建模框架中的两个参数对于确定微生物组动态都是必要的。动态的关键特征，如宿主间的微生物组收敛，对相互作用频率和强度之间的相互作用非常敏感。
Microbiomes, which are collections of interacting microbes in an environment, often substantially impact the environmental patches or living hosts that they occupy. In microbiome models, it is important to consider both the local dynamics within an environment and exchanges of microbiomes between environments. One way to incorporate these and other interactions across multiple scales is to employ metacommunity theory. Metacommunity models commonly assume continuous microbiome dispersal between the environments in which local microbiome dynamics occur. Under this assumption, a single parameter between each pair of environments controls the dispersal rate between those environments. This metacommunity framework is well-suited to abiotic environmental patches, but it fails to capture an essential aspect of the microbiomes of living hosts, which generally do not interact continuously with each other. Instead, living hosts interact with each other in discrete time intervals. In this paper, we develop a modeling framework that encodes such discrete interactions and uses two parameters to separately control the interaction frequencies between hosts and the amount of microbiome exchange during each interaction. We derive analytical approximations of models in our framework in three parameter regimes and prove that they are accurate in those regimes. We compare these approximations to numerical simulations for an illustrative model. We demonstrate that both parameters in our modeling framework are necessary to determine microbiome dynamics. Key features of the dynamics, such as microbiome convergence across hosts, depend sensitively on the interplay between interaction frequency and strength.
- [2] arXiv:2507.12585 (交叉列表自 physics.soc-ph) [中文pdf, pdf, html, 其他]
-
标题： 社会吸引力对随意群体形成的影响：幂律群体规模和抑制渗流标题： The Impact of Social Attractiveness on Casual Group Formation: Power-Law Group Sizes and Suppressed Percolation主题： 物理与社会 (physics.soc-ph) ; 统计力学 (cond-mat.stat-mech) ; 适应性与自组织系统 (nlin.AO)
非正式群体形成的动态过程长期以来一直是社会科学的研究主题。 虽然早期的随机模型为群体规模分布提供了基础性见解，但它们常常简化了个体行为，并缺乏异质性社会吸引力的机制。 在此，我们重新审视了一个由吸引力驱动的交互模型，这是一个基于代理的框架，其中点状代理在二维场地中随机移动，并表现出不同的社会吸引力，从而导致它们靠近高度有吸引力的名人同伴。 我们将该模型与一个空模型进行比较，其中代理持续移动，这类似于随机几何图。 我们的大量模拟结果显示了显著的结构和动态差异：与空模型不同，吸引力驱动模型的平均度数随着系统大小线性增加，而密度固定，导致更紧凑的群体，并抑制了渗流转变。 至关重要的是，尽管空模型的群体规模分布是指数衰减或双峰的，但吸引力驱动模型稳健地表现出幂律分布，$P(n) \propto n^{-2.5}$，其指数与密度无关。 由于长平衡时间，这些发现是通过计算密集型模拟获得的，为该模型提供了详尽的定量表征，突显了个体吸引力在塑造物理空间中的社会聚集中的关键作用。
The dynamics of casual group formation has long been a subject of interest in social sciences. While early stochastic models offered foundational insights into group size distributions, they often simplified individual behaviors and lacked mechanisms for heterogeneous social appeal. Here, we re-examine the attractiveness-driven interaction model, an agent-based framework where point-like agents move randomly in a 2D arena and exhibit varied social appeal, leading them to pause near highly attractive celebrity peers. We compare this model to a null model where the agents are continuously in movement, which resembles a Random Geometric Graph. Our extensive simulations reveal significant structural and dynamic differences: unlike the null model, the attractiveness-driven model's average degree increases linearly with system size for fixed density, resulting in more compact groups and the suppression of a percolation transition. Crucially, while the null model's group size distribution is either exponentially decaying or bimodal, the attractiveness-driven model robustly exhibits a power-law distribution, $P(n) \propto n^{-2.5}$, with an exponent independent of density. These findings, obtained through computationally intensive simulations due to long equilibration times, offer a thorough quantitative characterization of this model, highlighting the critical role of individual attractiveness in shaping social aggregation in physical space.
- [3] arXiv:2507.12636 (交叉列表自 cond-mat.mes-hall) [中文pdf, pdf, html, 其他]
-
标题： 极化子流体中的自旋弛豫：量子流体力学方法标题： Spin relaxation in a polariton fluid: quantum hydrodynamic approach评论： 12页 + 15页的补充材料主题： 中尺度与纳米尺度物理 (cond-mat.mes-hall) ; 模式形成与孤子 (nlin.PS) ; 量子物理 (quant-ph)
腔极化子是在强耦合 regime 中出现在量子微腔中的基本激发，表现出量子集体行为的明显特征。 独特自旋结构和强非线性响应的结合为直接实验观察各种非平凡的光学偏振现象提供了可能性。 自旋弛豫过程在此至关重要。 然而，目前尚缺乏对其协同描述的数学形式。 在本文中，基于两组分液体的量子流体动力学方法，我们推导出了一组相应的方程，其中能量和自旋弛豫项自然出现。 我们详细分析了这些项如何影响外部磁场中自旋极化子液滴的动力学以及均匀极化子凝聚体的基本激发的色散。 尽管我们专注于腔极化子的情况，但我们的方法可以应用于其他自旋玻色凝聚体的情况，其中自旋弛豫过程起着重要作用。
Cavity polaritons, the elementary excitations appearing in quantum microcavities in the strong-coupling regime, reveal clear signatures of quantum collective behavior. The combination of unique spin structure and strong nonlinear response opens the possibility of direct experimental observation of a plethora of nontrivial optical polarization phenomena. Spin relaxation processes are of crucial importance here. However, a mathematical formalism for their coherent description is still absent. In the present paper, based on the quantum hydrodynamics approach for a two-component liquid, we derive the set of the corresponding equations where both energy and spin relaxation terms appear naturally. We analyze in detail how these terms affect the dynamics of spinor polariton droplets in the external magnetic field and the dispersion of elementary excitations of a uniform polariton condensate. Although we focus on the case of cavity polaritons, our approach can be applied to other cases of spinor bosonic condensates, where the processes of spin relaxation play a major role.
- [4] arXiv:2507.12858 (交叉列表自 q-bio.NC) [中文pdf, pdf, html, 其他]
-
标题： 通过循环神经网络中的互信息优化出现功能分化结构标题： Emergence of Functionally Differentiated Structures via Mutual Information Optimization in Recurrent Neural Networks主题： 神经与认知 (q-bio.NC) ; 适应性与自组织系统 (nlin.AO)
大脑中的功能分化随着不同区域的专业化而出现，这对于理解大脑作为一个复杂系统的行为至关重要。 先前的研究使用具有特定约束的人工神经网络对这一过程进行了建模。 在此，我们提出了一种新方法，通过互信息神经估计最小化神经子群之间的互信息，从而在循环神经网络中诱导功能分化。 我们将该方法应用于一个2位工作记忆任务和一个涉及Lorenz和Rössler时间序列的混沌信号分离任务。 对网络性能、相关模式和权重矩阵的分析表明，互信息最小化在实现高任务性能的同时，也表现出清晰的功能模块性和适度的结构模块性。 重要的是，我们的结果表明，通过相关结构测量的功能分化比由突触权重定义的结构模块性更早出现。 这表明功能专业化先于并可能驱动发育中的神经网络内的结构重组。 我们的发现为信息论原则如何在人工和生物大脑发育过程中支配专门功能和模块化结构的出现提供了新的见解。
Functional differentiation in the brain emerges as distinct regions specialize and is key to understanding brain function as a complex system. Previous research has modeled this process using artificial neural networks with specific constraints. Here, we propose a novel approach that induces functional differentiation in recurrent neural networks by minimizing mutual information between neural subgroups via mutual information neural estimation. We apply our method to a 2-bit working memory task and a chaotic signal separation task involving Lorenz and R\"ossler time series. Analysis of network performance, correlation patterns, and weight matrices reveals that mutual information minimization yields high task performance alongside clear functional modularity and moderate structural modularity. Importantly, our results show that functional differentiation, which is measured through correlation structures, emerges earlier than structural modularity defined by synaptic weights. This suggests that functional specialization precedes and probably drives structural reorganization within developing neural networks. Our findings provide new insights into how information-theoretic principles may govern the emergence of specialized functions and modular structures during artificial and biological brain development.
- [5] arXiv:2507.12887 (交叉列表自 quant-ph) [中文pdf, pdf, html, 其他]
-
标题： 无监督技术检测量子混沌标题： Unsupervised Techniques to Detect Quantum Chaos评论： 17页期刊参考： 低温物理 50 (2024)主题： 量子物理 (quant-ph) ; 混沌动力学 (nlin.CD)
传统的量子混沌光谱探测需要量子哈密顿量的本征值，有时还需要本征向量。 这涉及计算成本高昂的对角化过程。 我们测试一种无监督神经网络是否可以直接从哈密顿量矩阵中检测量子混沌。 我们使用一个具有潜在随机图结构和随机耦合常数的单体哈密顿量，其中有一个参数决定了图的随机性。 光谱分析显示，增加潜在图中的随机性会导致从可积光谱统计到混沌光谱的转变。 我们表明，可以通过无监督神经网络，或者更具体地说，通过自组织映射，直接将哈密顿量矩阵输入神经网络来检测这种转变，而无需任何对角化过程。
Conventional spectral probes of quantum chaos require eigenvalues, and sometimes, eigenvectors of the quantum Hamiltonian. This involves computationally expensive diagonalization procedures. We test whether an unsupervised neural network can detect quantum chaos directly from the Hamiltonian matrix. We use a single-body Hamiltonian with an underlying random graph structure and random coupling constants, with a parameter that determines the randomness of the graph. The spectral analysis shows that increasing the amount of randomness in the underlying graph results in a transition from integrable spectral statistics to chaotic ones. We show that the same transition can be detected via unsupervised neural networks, or more specifically, Self-Organizing Maps by feeding the Hamiltonian matrix directly into the neural network, without any diagonalization procedure.
- [6] arXiv:2507.12940 (交叉列表自 physics.comp-ph) [中文pdf, pdf, html, 其他]
-
标题： 均衡化超自旋机标题： Equalized Hyperspin Machine评论： 19页，10图主题： 计算物理 (physics.comp-ph) ; 混沌动力学 (nlin.CD) ; 光学 (physics.optics)
可靠地模拟自旋模型对于解决传统计算设备难以处理的复杂优化问题至关重要。 最近引入的超自旋机器，这是一个由线性和非线性耦合的参数振荡器组成的网络，提供了一个通用的经典矢量自旋模型的多功能模拟器，在任意维度中找到模拟自旋哈密顿量的最小值，并实现新颖的退火算法。 在超自旋机器中，振荡器随时间演化以最小化一个成本函数，为了使系统能够可靠地模拟目标自旋模型，该成本函数必须类似于所需的自旋哈密顿量。 如果超自旋振幅在稳态时相等，则满足这一条件。 目前，尚不存在一种机制来强制振幅相等。 在此，我们弥补了这一差距，并介绍了一种方法，在稳态中使振幅相等的情况下模拟超自旋机器。 我们采用了一个额外的振荡器网络（称为均衡器），通过反对称非线性耦合连接到超自旋机器，并均衡超自旋振幅。 我们通过大规模数值模拟，最多达到$10000$个超自旋，展示了这种均衡后的超自旋机器的性能。 与没有均衡的超自旋机器相比，我们发现均衡后的超自旋机器（i）能达到数量级更低的自旋能量，且（ii）其性能对系统参数的敏感性显著降低。 均衡后的超自旋机器提供了一个具有竞争力的自旋哈密顿量最小化器，并为将振幅均衡与复杂的退火协议相结合以进一步提升自旋机器的性能打开了可能性。
The reliable simulation of spin models is of critical importance to tackle complex optimization problems that are intractable on conventional computing machines. The recently introduced hyperspin machine, which is a network of linearly and nonlinearly coupled parametric oscillators, provides a versatile simulator of general classical vector spin models in arbitrary dimension, finding the minimum of the simulated spin Hamiltonian and implementing novel annealing algorithms. In the hyperspin machine, oscillators evolve in time minimizing a cost function that must resemble the desired spin Hamiltonian in order for the system to reliably simulate the target spin model. This condition is met if the hyperspin amplitudes are equal in the steady state. Currently, no mechanism to enforce equal amplitudes exists. Here, we bridge this gap and introduce a method to simulate the hyperspin machine with equalized amplitudes in the steady state. We employ an additional network of oscillators (named equalizers) that connect to the hyperspin machine via an antisymmetric nonlinear coupling and equalize the hyperspin amplitudes. We demonstrate the performance of such an equalized hyperspin machine by large-scale numerical simulations up to $10000$ hyperspins. Compared to the hyperspin machine without equalization, we find that the equalized hyperspin machine (i) Reaches orders of magnitude lower spin energy, and (ii) Its performance is significantly less sensitive to the system parameters. The equalized hyperspin machine offers a competitive spin Hamiltonian minimizer and opens the possibility to combine amplitude equalization with complex annealing protocols to further boost the performance of spin machines.
- [7] arXiv:2507.13104 (交叉列表自 math-ph) [中文pdf, pdf, html, 其他]
-
标题： 从冻结中得到的椭圆长程自旋链的模族标题： Modular families of elliptic long-range spin chains from freezing评论： v1:23+5页，1图主题： 数学物理 (math-ph) ; 高能物理 - 理论 (hep-th) ; 量子代数 (math.QA) ; 精确可解与可积系统 (nlin.SI)
我们考虑通过“冻结”具有自旋的可积量子多体系统来构建具有q-变形长程相互作用的量子可积自旋链。 输入是一个自旋-Ruijsenaars系统以及其无自旋经典Ruijsenaars-Schneider系统的平衡配置。 对于一个特定的平衡选择，得到的长程自旋链具有实数谱并允许短程极限，从而提供从最近邻到长程相互作用自旋的可积插值。 我们关注椭圆情况。 我们首先定义模群在无自旋椭圆Ruijsenaars-Schneider系统上的作用，以表明对于固定的椭圆参数，它有一整个模族的经典平衡配置。 这些通常具有常数但非零动量。 然后我们使用变形量子化的框架，在任何经典平衡下冻结椭圆自旋-Ruijsenaars系统，同时保持量子可积性。 正如我们在之前的工作中所展示的，结果包括Heisenberg、Inozemtsev和Haldane-Shastry链及其xxz类似q-变形（面型），或Fukui-Kawakami的反对周期Haldane-Shastry链、Sechin-Zotov的椭圆推广，以及Matushko-Zotov的完全各向异性q-变形（顶点型）。
We consider the construction of quantum-integrable spin chains with q-deformed long-range interactions by `freezing' integrable quantum many-body systems with spins. The input is a spin-Ruijsenaars system along with an equilibrium configuration of the underlying spinless classical Ruijsenaars-Schneider system. For a distinguished choice of equilibrium, the resulting long-range spin chain has a real spectrum and admits a short-range limit, providing an integrable interpolation from nearest-neighbour to long-range interacting spins. We focus on the elliptic case. We first define an action of the modular group on the spinless elliptic Ruijsenaars-Schneider system to show that, for a fixed elliptic parameter, it has a whole modular family of classical equilibrium configurations. These typically have constant but nonzero momenta. Then we use the setting of deformation quantisation to provide a uniform framework for freezing elliptic spin-Ruijsenaars systems at any classical equilibrium whilst preserving quantum integrability. As we showed in previous work, the results include the Heisenberg, Inozemtsev and Haldane-Shastry chains along with their xxz-like q-deformations (face-type), or the antiperiodic Haldane-Shastry chain of Fukui-Kawakami, its elliptic generalisation of Sechin-Zotov, and their completely anisotropic q-deformations due to Matushko-Zotov (vertex type).
- [8] arXiv:2507.13310 (交叉列表自 physics.soc-ph) [中文pdf, pdf, html, 其他]
-
标题： 在线参与对线下抗议的溢出效应建模：网络上的随机动力学和平均场近似标题： Modelling the spillover from online engagement to offline protest: stochastic dynamics and mean-field approximations on networks评论： 44页，33图主题： 物理与社会 (physics.soc-ph) ; 社会与信息网络 (cs.SI) ; 动力系统 (math.DS) ; 适应性与自组织系统 (nlin.AO) ; 种群与进化 (q-bio.PE)
社交媒体正在改变线下生活的各个方面，从日常决策如用餐选择到冲突的发展进程。 在本研究中，我们提出了一种耦合建模框架，包含一个在线社交网络层，以分析特定主题上的参与如何溢出到线下抗议活动。 我们开发了一个随机模型，并推导了几种不同复杂度的平均场模型。 这些模型使我们能够估计繁殖数并预测活动激增可能发生的时间。 一个关键因素是在线和线下领域之间的传播率；为了出现线下爆发，这一比率必须处于一个临界范围内，既不太低也不太高。 此外，利用合成网络，我们研究了网络结构如何影响这些近似值的准确性。 我们的研究结果表明，低密度网络需要更复杂的近似，而简单的模型可以有效地表示高密度网络。 然而，在两个现实世界的网络上进行测试时，增加复杂度并未提高准确性。
Social media is transforming various aspects of offline life, from everyday decisions such as dining choices to the progression of conflicts. In this study, we propose a coupled modelling framework with an online social network layer to analyse how engagement on a specific topic spills over into offline protest activities. We develop a stochastic model and derive several mean-field models of varying complexity. These models allow us to estimate the reproductive number and anticipate when surges in activity are likely to occur. A key factor is the transmission rate between the online and offline domains; for offline outbursts to emerge, this rate must fall within a critical range, neither too low nor too high. Additionally, using synthetic networks, we examine how network structure influences the accuracy of these approximations. Our findings indicate that low-density networks need more complex approximations, whereas simpler models can effectively represent higher-density networks. When tested on two real-world networks, however, increased complexity did not enhance accuracy.
交叉提交 (展示 8 之 8 条目 )
- [9] arXiv:2505.04874 (替换) [中文pdf, pdf, html, 其他]
-
标题： Mackey-Glass方程中随机共振与随机混沌的共存标题： Coexistence of stochastic resonance and stochastic chaos in Mackey-Glass equations评论： 4页，4图 + 补充材料（4页，6图）主题： 混沌动力学 (nlin.CD)
我们研究了在噪声存在下的Mackey-Glass方程的动力学行为。 在弱非线性区域，观察到基于确定性吸引子的两个准稳态之间的切换动力学，即随机共振（SR）。 在强非线性区域，我们新发现了具有多个正李雅普诺夫指数的混沌随机共振。 与在弱非线性区域观察到的SR不同，共振点先于最大李雅普诺夫指数的零交叉点出现，导致SR和随机混沌共存。 还基于原点处不稳定螺旋的线性模态分析，提供了弱非线性和强非线性区域中共振周期的精确理论估计。
We investigated the dynamics of the Mackey-Glass equation in the presence of noise. In the weak nonlinearity region, stochastic resonance (SR) is observed as switching dynamics between two quasi-stationary states based on deterministic attractors. In the strong nonlinearity region, we newly discover chaotic SR with multiple positive Lyapunov exponents. Unlike the SR observed in the weak nonlinearity region, the resonance point precedes the zero-crossing point of the largest Lyapunov exponent, resulting in the coexistence of SR and stochastic chaos. A precise theoretical estimation of resonant periods in the weak and strong nonlinearity regions is also provided based on a linear mode analysis of the unstable spiral at the origin.
- [10] arXiv:2406.09074 (替换) [中文pdf, pdf, html, 其他]
-
标题： 光子-磁振子晶体的非线性视角下的纠缠特性标题： Entanglement properties of photon-magnon crystal from nonlinear perspectiveM. Wanic, C. Jasiukiewicz, Z. Toklikishvili, V. Jandieri, M. Trybus, E. Jartych, S. K. Mishra, L. Chotorlishvili评论： 本文已接受发表于《Physica D：非线性现象》主题： 中尺度与纳米尺度物理 (cond-mat.mes-hall) ; 混沌动力学 (nlin.CD)
量化两个连续玻色模之间的纠缠，例如自旋波和光子，并不容易。 通过量子朗之万方程计算的对数负性会受到热噪声的影响。 然而，这种方法需要进一步的近似。 一般非线性系统的相空间包含拓扑不同的区域，稳态可能对应于不同类型的固定点，如鞍点、稳定或不稳定螺旋点以及节点。 在本工作中，我们提出了一种新的方法。 即，我们推导出了完整的非线性方程组，其中包括自旋波和光子数算符及相位的方程。 我们表明，不仅数算符，相位对于探索固定点的特性以及自旋波-光子纠缠也很重要。 我们表明，非线性微分方程的定性理论方法也适用于光子-自旋波纠缠问题。 我们的主要发现是，纠缠在鞍点区域内不成立。 另一方面，纠缠的最大值对应于稳定节点和稳定螺旋区域之间的边界附近区域。 我们的方法非常普遍。 然而，我们针对一个特定系统进行了计算：基于钇铁石榴石（YIG）薄膜的光子-自旋波晶体，该薄膜上钻有周期性的空气孔。 我们的兴趣集中在特定波长和频率的自旋波，这些自旋波对应于自旋波凝聚态。 这些自旋波与相同频率的光子强烈耦合。 我们详细讨论了源于磁电耦合和有效Dzyaloshinskii-Moriya相互作用的自旋波和光子之间的相互作用。 我们表明，这种相互作用负责系统中稳健的光子-自旋波纠缠。
Quantifying the entanglement between two continuous bosonic modes, such as magnons and photons, is not trivial. The logarithmic negativity, calculated through the quantum Langevin equations is subjected to thermal noise. However this method requires further approximation. The phase space of a generic nonlinear system contains topologically different regions, and the steady state may correspond to the different types of fixed points, such as Saddle Points, Stable or unstable Spirals, and Nodes. In the present work, we propose a new procedure. Namely, we derived the complete set of nonlinear equations, which includes equations for the magnon and photon number operators and phases. We show that not only number operators but also phases are important for exploring the character of the fixed point, and magnon-photon entanglement. We showed that methods of the qualitative theory of nonlinear differential equations are also relevant for photon-magnon entanglement problems. Our main finding is that entanglement is not defined in the Saddle Point region. On the other hand, the maximum of the entanglement corresponds to the region near the border between the Stable node and Stable spiral regions. Our approach is quite general. However, we did calculations for a particular system: photon-magnon crystal based on the yttrium iron garnet (YIG) film with the periodic air holes drilled in the film. Our interest focuses on magnons with a particular wavelength and frequency corresponding to the magnon condensate. Those magnons couple strongly with the photons of similar frequency. We discuss in detail the interaction between magnons and photons originating from the magneto-electric coupling and the effective Dzyaloshinskii-Moriya interaction. We show that this interaction is responsible for the robust photon-magnon entanglement in the system.
- [11] arXiv:2501.05365 (替换) [中文pdf, pdf, html, 其他]
-
标题： 非稳态尾部在动力学流行病模型中的控制标题： Control of Overpopulated Tails in Kinetic Epidemic Models主题： 优化与控制 (math.OC) ; 适应性与自组织系统 (nlin.AO) ; 物理与社会 (physics.soc-ph) ; 种群与进化 (q-bio.PE)
我们为数学流行病学中的受控分 compartmental 模型引入基于模型的转移率，重点研究控制策略对描述接触形成动力学的相互作用多智能体系统的影响。 在动能控制问题的框架下，我们比较两种典型的控制协议：一种是直接影响动力学的加性控制，另一种是针对智能体之间相互作用强度的控制。 对于 SIR 分 compartmental 化，推导出出现的受控宏观模型，以说明其对流行病进展和接触相互作用动力学的影响。 数值结果表明，这种方法在引导动力学和控制流行病趋势方面的有效性，即使在接触分布表现出过度填充尾部的情况下也是如此。
We introduce model-based transition rates for controlled compartmental models in mathematical epidemiology, with a focus on the effects of control strategies applied to interacting multi-agent systems describing contact formation dynamics. In the framework of kinetic control problems, we compare two prototypical control protocols: one additive control directly influencing the dynamics and another targeting the interaction strength between agents. The emerging controlled macroscopic models are derived for an SIR compartmentalization to illustrate their impact on epidemic progression and contact interaction dynamics. Numerical results show the effectiveness of this approach in steering the dynamics and controlling epidemic trends, even in scenarios where contact distributions exhibit an overpopulated tail.
- [12] arXiv:2502.02386 (替换) [中文pdf, pdf, html, 其他]
-
标题： 通过超边复制的超图链接预测标题： Hypergraph Link Prediction via Hyperedge Copying主题： 社会与信息网络 (cs.SI) ; 适应性与自组织系统 (nlin.AO) ; 数据分析、统计与概率 (physics.data-an) ; 物理与社会 (physics.soc-ph)
我们提出了一种时间演化的超图生成模型，其中超边通过复制之前的超边而形成。 我们的模型能够再现许多经验超图中的几种典型事实，可以从数据中学习，并在完整的超图上定义似然，而不是基于自我的或其他子超图。 分析我们的模型，我们得出了节点度、边大小和边交集大小分布的描述，这些分布是根据模型参数得出的。 我们还展示了经验超图的一些特征，这些特征是或不是被我们的模型成功捕捉的。 我们提供了一个可扩展的随机期望最大化算法，可以将我们的模型拟合到包含数百万个节点和边的超图数据集上。 最后，我们在超图链接预测任务上评估了我们的模型，发现仅使用11个参数的模型实例就可以与大型神经网络达到具有竞争力的预测性能。
We propose a generative model of temporally-evolving hypergraphs in which hyperedges form via noisy copying of previous hyperedges. Our proposed model reproduces several stylized facts from many empirical hypergraphs, is learnable from data, and defines a likelihood over a complete hypergraph rather than ego-based or other sub-hypergraphs. Analyzing our model, we derive descriptions of node degree, edge size, and edge intersection size distributions in terms of the model parameters. We also show several features of empirical hypergraphs which are and are not successfully captured by our model. We provide a scalable stochastic expectation maximization algorithm with which we can fit our model to hypergraph data sets with millions of nodes and edges. Finally, we assess our model on a hypergraph link prediction task, finding that an instantiation of our model with just 11 parameters can achieve competitive predictive performance with large neural networks.
- [13] arXiv:2506.20572 (替换) [中文pdf, pdf, html, 其他]
-
标题： 一种生物物理方法用于通信系统的网络设计标题： A biophysical approach to the design of networks of communication systems评论： 7页主题： 物理与社会 (physics.soc-ph) ; 适应性与自组织系统 (nlin.AO)
受原生动物\textit{多核黏菌}生长动力学的启发，我们采用了一种形式化方法，用于描述在通道网络上的适应性、不可压缩的哈根-泊肃叶流动，以识别欧几里得空间中连接不同节点的图。这些图相对于其长度来说要么是次优的，要么是最优的。有时，我们会推导出与史特林树拓扑等价的图树结构。这种方法可以用于辅助决策通信网络的设计，例如光纤网、高速公路或铁路网络。作为该方法实用性的展示，我们明确地将这一框架应用于葡萄牙铁路网络。
Inspired by the growth dynamics of the protist \textit{Physarum polycephalum}, we employ a formalism that describes adaptive, incompressible Hagen-Poiseuille flows on channel networks to identify graphs connecting different nodes within Euclidean space. These graphs are either suboptimal or optimal with respect to their length. Occasionally, we derive graph tree configurations that are topologically equivalent to Steiner trees. This methodology can be utilised to assist in making decisions regarding the design of communication networks, such as fibre webs, motorways, or railway networks. As a demonstration of the practicality of this approach, we explicitly apply this framework to the Portuguese railway network.
- [14] arXiv:2506.21918 (替换) [中文pdf, pdf, html, 其他]
-
标题： 基于共振计算的异常波浪无模型预测标题： Model-free Forecasting of Rogue Waves using Reservoir Computing评论： 25页 14图。定稿版本期刊参考： CNSNS，第152卷，第一部分，2026年1月，109087主题： 计算工程、金融与科学 (cs.CE) ; 模式形成与孤子 (nlin.PS)
最近的研究表明，储备计算能够模拟各种混沌动力系统，但其在哈密顿系统中的应用仍相对未被探索。 本文研究了储备计算在从非线性薛定谔方程中捕捉异常波动力学的有效性，这是一个具有调制不稳定的挑战性哈密顿系统。 无模型的方法从五个不稳定模式的呼吸子模拟中学习。 一个适当调整的并行回声状态网络可以预测来自两个不同测试数据集的动力学。 第一组是训练数据的延续，而第二组涉及高阶呼吸子。 对一步预测能力的调查显示出测试数据与模型之间显著的一致性。 此外，我们展示了训练后的储备可以在面对未见过的动力学时，相对长时间地预测异常波的传播。 最后，我们介绍了一种显著提高储备计算在自主模式下预测性能的方法，增强了其长期预测能力。 这些结果推进了储备计算在时空哈密顿系统中的应用，并强调了在设计训练数据时相空间覆盖的重要性。
Recent research has demonstrated Reservoir Computing's capability to model various chaotic dynamical systems, yet its application to Hamiltonian systems remains relatively unexplored. This paper investigates the effectiveness of Reservoir Computing in capturing rogue wave dynamics from the nonlinear Schr\"{o}dinger equation, a challenging Hamiltonian system with modulation instability. The model-free approach learns from breather simulations with five unstable modes. A properly tuned parallel Echo State Network can predict dynamics from two distinct testing datasets. The first set is a continuation of the training data, whereas the second set involves a higher-order breather. An investigation of the one-step prediction capability shows remarkable agreement between the testing data and the models. Furthermore, we show that the trained reservoir can predict the propagation of rogue waves over a relatively long prediction horizon, despite facing unseen dynamics. Finally, we introduce a method to significantly improve the Reservoir Computing prediction in autonomous mode, enhancing its long-term forecasting ability. These results advance the application of Reservoir Computing to spatio-temporal Hamiltonian systems and highlight the critical importance of phase space coverage in the design of training data.
- [15] arXiv:2507.10863 (替换) [中文pdf, pdf, 其他]
-
标题： 非平衡双温度$(T_x, T_y)$诺斯-霍弗细胞模型中的混沌标题： Chaos in a Nonequilibrium Two-Temperature $(T_x, T_y)$ Nosé-Hoover Cell Model主题： 统计力学 (cond-mat.stat-mech) ; 混沌动力学 (nlin.CD)
我们重新研究了一个嵌入在二维周期性2x2单元中的双温Nosé-Hoover游动粒子，该单元在$(x,y) = (\pm 1, \pm 1)$处有四个光滑的排斥角落，以探索各向异性恒温器下的混沌。 该模型在x和y方向上使用单独的恒温器，从而实现对平衡的受控偏离。 通过积分完整的六维运动方程并计算完整的李雅普诺夫谱，我们确认了混沌，并以高数值精度量化了相空间收缩。 总收缩率被解释为熵产生，随着恒温器各向异性非线性增长，并遵循超二次幂律，$\Lambda\propto -\delta^{2.44}$，与线性响应理论不符。 近似的 Kaplan-Yorke维数揭示了一个分形吸引子，随着$|T_x - T_y|$的增加而集中。 动量统计显示在强驱动下表现出显著的非高斯行为。 尽管该模型具有耗散性，但仍保持严格的时间可逆性，提供了一个教学丰富的微观可逆性与宏观熵产生共存的实例。
We revisit a two-temperature Nos\'e-Hoover wanderer particle embedded in a two-dimensional periodic 2x2 cell with four smooth repulsive corners at $(x,y) = (\pm 1, \pm 1)$ to explore chaos with anisotropic thermostatting. The model employs separate thermostats in the x and y directions, enabling controlled deviations from equilibrium. By integrating the full six-dimensional equations of motion and computing the complete Lyapunov spectrum, we confirm chaos and quantify phase-space contraction with high numerical precision. The total contraction rate, interpreted as entropy production, grows nonlinearly with the thermostat anisotropy and follows a superquadratic power law, $\Lambda\propto -\delta^{2.44}$, deviating from linear-response theory. The approximate Kaplan-Yorke dimension reveals a fractal attractor that concentrates as $|T_x - T_y|$ increases. Momentum statistics show significant non-Gaussian behavior under strong driving. Despite its dissipative nature, the model remains strictly time-reversible, offering a pedagogically rich example of microscopic reversibility coexisting with macroscopic entropy production.