Pub Date : 2024-09-10DOI: 10.1103/physreve.110.034309
Raymond Fan, Andreas Hilfinger
Cells sense environmental signals and transmit information intracellularly through changes in the abundance of molecular components. Such molecular abundances can be measured in single cells and exhibit significant heterogeneity in clonal populations even in identical environments. Experimentally observed joint probability distributions can then be used to quantify the covariability and mutual information between molecular abundances along signaling cascades. However, because stationary state abundances along stochastic biochemical reaction cascades are not conditionally independent, their mutual information is not constrained by the data-processing inequality. Here, we report the conditions under which the mutual information between stationary state abundances increases along a cascade of biochemical reactions. This nonmonotonic behavior can be intuitively understood in terms of noise propagation and time-averaging stochastic fluctuations that are short-lived compared to an extrinsic signal. Our results reemphasize that mutual information measurements of stationary state distributions of cellular components may be of limited utility for characterizing cellular signaling processes because they do not measure information transfer.
{"title":"Characterizing the nonmonotonic behavior of mutual information along biochemical reaction cascades","authors":"Raymond Fan, Andreas Hilfinger","doi":"10.1103/physreve.110.034309","DOIUrl":"https://doi.org/10.1103/physreve.110.034309","url":null,"abstract":"Cells sense environmental signals and transmit information intracellularly through changes in the abundance of molecular components. Such molecular abundances can be measured in single cells and exhibit significant heterogeneity in clonal populations even in identical environments. Experimentally observed joint probability distributions can then be used to quantify the covariability and mutual information between molecular abundances along signaling cascades. However, because stationary state abundances along stochastic biochemical reaction cascades are not conditionally independent, their mutual information is not constrained by the data-processing inequality. Here, we report the conditions under which the mutual information between stationary state abundances increases along a cascade of biochemical reactions. This nonmonotonic behavior can be intuitively understood in terms of noise propagation and time-averaging stochastic fluctuations that are short-lived compared to an extrinsic signal. Our results reemphasize that mutual information measurements of stationary state distributions of cellular components may be of limited utility for characterizing cellular signaling processes because they do not measure information transfer.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"11 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201017","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-09DOI: 10.1103/physreve.110.034703
Lidiane Maria de Souza, Junaid Sofi, Erms Pereira
The synthesis of ferroelectric nematic liquid crystals (FNLCs) concludes the long wait for their existence and potential usage in multiple liquid crystal based applications. In FNLCs, electric polarization in the nematic phase significantly decreases the switching time of in-on display pixels. In this article, we report the occurrence of translation symmetry breaking for heat propagation along the director field in the ferroelectric nematic phase. Due to the symmetry of such a phase and close similarity to the bent-core polar liquid crystal phase, a rank-3 tensor describes its scalar order parameter and algebraic deductions. The finite element simulations show the occurrence of the nonsymmetrical thermal conductivity along . The preferential heat transport in FNLCs can allow them to work as an all-thermal monophase non-nanostructured single-material thermal rectifier. We expect that this study will contribute towards the FNLCs application as functional layers and inks.
铁电向列型液晶（FNLC）的合成结束了人们对其存在的漫长等待，以及其在多种液晶应用中的潜在用途。在 FNLC 中，向列相中的电极化可显著缩短导通显示像素的开关时间。在本文中，我们报告了铁电向列相中热量沿导演场 n ̂ 传播时发生平移对称性破坏的情况。由于这种相具有 C∞V 对称性，且与弯芯极性液晶相十分相似，因此用等级-3 张量来描述其标量阶参数和代数推导。有限元模拟显示了沿 n ̂方向的非对称热导率。FNLC 中的优先热传输可使其成为全热单相非纳米结构单一材料热整流器。我们希望这项研究能为 FNLCs 作为功能层和油墨的应用做出贡献。
{"title":"Nonsymmetrical thermal conductivity along the director field in ferroelectric nematic liquid crystals","authors":"Lidiane Maria de Souza, Junaid Sofi, Erms Pereira","doi":"10.1103/physreve.110.034703","DOIUrl":"https://doi.org/10.1103/physreve.110.034703","url":null,"abstract":"The synthesis of ferroelectric nematic liquid crystals (FNLCs) concludes the long wait for their existence and potential usage in multiple liquid crystal based applications. In FNLCs, electric polarization in the nematic phase significantly decreases the switching time of in-on display pixels. In this article, we report the occurrence of translation symmetry breaking for heat propagation along the director field <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mover accent=\"true\"><mi mathvariant=\"bold-italic\">n</mi><mo>̂</mo></mover></mrow></math> in the ferroelectric nematic phase. Due to the <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>C</mi><mrow><mi>∞</mi><mi>V</mi></mrow></msub></math> symmetry of such a phase and close similarity to the bent-core polar liquid crystal phase, a rank-3 tensor describes its scalar order parameter and algebraic deductions. The finite element simulations show the occurrence of the nonsymmetrical thermal conductivity along <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mover accent=\"true\"><mi mathvariant=\"bold-italic\">n</mi><mo>̂</mo></mover></mrow></math>. The preferential heat transport in FNLCs can allow them to work as an all-thermal monophase non-nanostructured single-material thermal rectifier. We expect that this study will contribute towards the FNLCs application as functional layers and inks.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"728 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-09DOI: 10.1103/physreve.110.034308
Renzo Zagarra, Karina Laneri, Alejandro B. Kolton
We numerically investigate the geometry and transport properties of infection fronts within the spatial SIR model in two dimensions. The model incorporates short-range correlated quenched random transmission rates. Our findings reveal that the critical average transmission rate for the steady-state propagation of the infection is overestimated by the naive mean-field homogenization. Furthermore, we observe that the velocity, profile, and harmfulness of the fronts, given a specific average transmission, are sensitive to the details of randomness. In particular, we find that the harmfulness of the front is larger the more uniform the transmission rate is, suggesting potential optimization in vaccination strategies under constraints like fixed average-transmission rates or limited vaccine resources. The large-scale geometry of the advancing fronts presents nevertheless robust universal features and, for a statistically isotropic and short-range correlated disorder, we get a roughness exponent and a dynamical exponent , which are roughly compatible with the one-dimensional Kardar-Parisi-Zhang (KPZ) universality class. We find that the KPZ term and the disorder-induced effective noise are present and have a kinematic origin.
我们在二维空间 SIR 模型中对感染前沿的几何形状和传输特性进行了数值研究。该模型包含短程相关淬火随机传播率。我们的研究结果表明，感染稳态传播的临界平均传播率被天真的平均场均质化所高估。此外，我们还发现，在特定的平均传播率下，前沿的速度、轮廓和有害程度对随机性的细节非常敏感。特别是，我们发现传播率越均匀，前沿的危害性就越大，这表明在固定的平均传播率或有限的疫苗资源等约束条件下，疫苗接种策略有可能得到优化。对于统计上各向同性和短程相关的无序状态，我们得到了粗糙度指数α≈0.42±0.10和动态指数z≈1.6±0.10，这与一维卡达尔-帕里什-张（KPZ）普遍性类基本一致。我们发现 KPZ 项和无序诱导的有效噪声是存在的，并且具有运动学起源。
{"title":"Infection fronts in randomly varying transmission-rate media","authors":"Renzo Zagarra, Karina Laneri, Alejandro B. Kolton","doi":"10.1103/physreve.110.034308","DOIUrl":"https://doi.org/10.1103/physreve.110.034308","url":null,"abstract":"We numerically investigate the geometry and transport properties of infection fronts within the spatial SIR model in two dimensions. The model incorporates short-range correlated quenched random transmission rates. Our findings reveal that the critical average transmission rate for the steady-state propagation of the infection is overestimated by the naive mean-field homogenization. Furthermore, we observe that the velocity, profile, and harmfulness of the fronts, given a specific average transmission, are sensitive to the details of randomness. In particular, we find that the harmfulness of the front is larger the more uniform the transmission rate is, suggesting potential optimization in vaccination strategies under constraints like fixed average-transmission rates or limited vaccine resources. The large-scale geometry of the advancing fronts presents nevertheless robust universal features and, for a statistically isotropic and short-range correlated disorder, we get a roughness exponent <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>α</mi><mo>≈</mo><mn>0.42</mn><mo>±</mo><mn>0.10</mn></mrow></math> and a dynamical exponent <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>z</mi><mo>≈</mo><mn>1.6</mn><mo>±</mo><mn>0.10</mn></mrow></math>, which are roughly compatible with the one-dimensional Kardar-Parisi-Zhang (KPZ) universality class. We find that the KPZ term and the disorder-induced effective noise are present and have a kinematic origin.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"31 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-09DOI: 10.1103/physreve.110.034204
R. Arun, M. Sathish Aravindh, A. Venkatesan, M. Lakshmanan
Recent studies on reservoir computing essentially involve a high-dimensional dynamical system as the reservoir, which transforms and stores the input as a higher-dimensional state for temporal and nontemporal data processing. We demonstrate here a method to predict temporal and nontemporal tasks by constructing virtual nodes as constituting a reservoir in reservoir computing using a nonlinear map, namely, the logistic map, and a simple finite trigonometric series. We predict three nonlinear systems, namely, Lorenz, Rössler, and Hindmarsh-Rose, for temporal tasks and a seventh-order polynomial for nontemporal tasks with great accuracy. Also, the prediction is made in the presence of noise and found to closely agree with the target. Remarkably, the logistic map performs well and predicts close to the actual or target values. The low values of the root mean square error confirm the accuracy of this method in terms of efficiency. Our approach removes the necessity of continuous dynamical systems for constructing the reservoir in reservoir computing. Moreover, the accurate prediction for the three different nonlinear systems suggests that this method can be considered a general one and can be applied to predict many systems. Finally, we show that the method also accurately anticipates the time series of the all the three variable of Rössler system for the future (self-prediction).
{"title":"Reservoir computing with logistic map","authors":"R. Arun, M. Sathish Aravindh, A. Venkatesan, M. Lakshmanan","doi":"10.1103/physreve.110.034204","DOIUrl":"https://doi.org/10.1103/physreve.110.034204","url":null,"abstract":"Recent studies on reservoir computing essentially involve a high-dimensional dynamical system as the reservoir, which transforms and stores the input as a higher-dimensional state for temporal and nontemporal data processing. We demonstrate here a method to predict temporal and nontemporal tasks by constructing virtual nodes as constituting a reservoir in reservoir computing using a nonlinear map, namely, the logistic map, and a simple finite trigonometric series. We predict three nonlinear systems, namely, Lorenz, Rössler, and Hindmarsh-Rose, for temporal tasks and a seventh-order polynomial for nontemporal tasks with great accuracy. Also, the prediction is made in the presence of noise and found to closely agree with the target. Remarkably, the logistic map performs well and predicts close to the actual or target values. The low values of the root mean square error confirm the accuracy of this method in terms of efficiency. Our approach removes the necessity of continuous dynamical systems for constructing the reservoir in reservoir computing. Moreover, the accurate prediction for the three different nonlinear systems suggests that this method can be considered a general one and can be applied to predict many systems. Finally, we show that the method also accurately anticipates the time series of the all the three variable of Rössler system for the future (self-prediction).","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"27 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-09DOI: 10.1103/physreve.110.034119
Guoxing Lin
The general theoretical description of spin self-diffusion under a nonlinear gradient magnetic field is proposed, which extends the effective phase diffusion method for a linear gradient field. Based on the phase diffusion, the proposed method reveals the general features of phase evolutions in nonlinear gradient fields. There are three types of phase evolutions: phase diffusion, float phase evolution, and shift evolution based on the starting position. For spin diffusion near the origin of the nonlinear field, these three phase evolutions significantly affect the nuclear magnetic resonance (NMR) signal. The traditional methods have difficulties in handling these three-phase evolutions. Notably, the phase from float phase evolution is missed or misplaced in traditional methods, which leads to incorrect NMR signal attenuation or phase shift. The method here shows that the diffusing and float phase evolutions come from the first and second derivatives of the gradient field. Based on these three phase evolutions, the phase variance and corresponding NMR signal attenuation are obtained, as demonstrated by calculating the phase diffusions under both parabolic and cubic fields. The results indicate that signal attenuation obeys Gaussian attenuation for a short time, then changes to follow Lorentzian or Mittag-Leffler function attenuations as time increases, significantly different from Gaussian attenuation. For spins starting diffusion far away from the origin of the field gradient, the signal attenuation is Gaussian, but the float phase still has an important effect on the total phase shift of even-order gradient fields, which could be used to measure the diffusion coefficient directly. Random walk simulations were performed, which support the obtained theoretical results. General theoretical expressions are obtained, which can handle random order nonlinear gradient fields. The results could help develop advanced experimental techniques based on a nonlinear gradient field in NMR and magnetic resonance imaging.
{"title":"Effective phase diffusion for spin phase evolution under random nonlinear magnetic field","authors":"Guoxing Lin","doi":"10.1103/physreve.110.034119","DOIUrl":"https://doi.org/10.1103/physreve.110.034119","url":null,"abstract":"The general theoretical description of spin self-diffusion under a nonlinear gradient magnetic field is proposed, which extends the effective phase diffusion method for a linear gradient field. Based on the phase diffusion, the proposed method reveals the general features of phase evolutions in nonlinear gradient fields. There are three types of phase evolutions: phase diffusion, float phase evolution, and shift evolution based on the starting position. For spin diffusion near the origin of the nonlinear field, these three phase evolutions significantly affect the nuclear magnetic resonance (NMR) signal. The traditional methods have difficulties in handling these three-phase evolutions. Notably, the phase from float phase evolution is missed or misplaced in traditional methods, which leads to incorrect NMR signal attenuation or phase shift. The method here shows that the diffusing and float phase evolutions come from the first and second derivatives of the gradient field. Based on these three phase evolutions, the phase variance and corresponding NMR signal attenuation are obtained, as demonstrated by calculating the phase diffusions under both parabolic and cubic fields. The results indicate that signal attenuation obeys Gaussian attenuation for a short time, then changes to follow Lorentzian or Mittag-Leffler function attenuations as time increases, significantly different from Gaussian attenuation. For spins starting diffusion far away from the origin of the field gradient, the signal attenuation is Gaussian, but the float phase still has an important effect on the total phase shift of even-order gradient fields, which could be used to measure the diffusion coefficient directly. Random walk simulations were performed, which support the obtained theoretical results. General theoretical expressions are obtained, which can handle random order nonlinear gradient fields. The results could help develop advanced experimental techniques based on a nonlinear gradient field in NMR and magnetic resonance imaging.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"4 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-09DOI: 10.1103/physreve.110.034203
Taylor J. Whitney, Kevin A. Mitchell
We study the transport of rigid ellipsoidal swimmers in a periodic vortex array via numerical simulation and dynamical systems analysis. Via ensemble simulations, we show the counterintuitive result that slower swimming speeds can generate fast ballistic transport, while faster swimming speeds generate chaotic and diffusive transport, which is inherently slower in the long run. To explain this, we use the symmetry of the flow to construct a time-reversible Poincaré return map on a two-dimensional surface of section in phase space. For sufficiently small swimming speeds, we find stable periodic orbits on the surface of section surrounded by invariant tori, similar to Kolmogorov-Arnold-Moser curves. Trajectories within these tori are ballistic. As the swimming speed is increased, the periodic orbits undergo a sequence of period-doubling bifurcations that destroys the ballistic tori. These bifurcations exactly match the ballistic to diffusive transition from the ensemble simulations. Additional ensemble simulations are used to test the robustness of these results to noise. The ballistic behavior is destroyed as the strength of rotational diffusion increases. However, we estimate that the ballistic tori might still be seen in experiments.
{"title":"Ballistic to diffusive transition for swimmers in a periodic vortex array","authors":"Taylor J. Whitney, Kevin A. Mitchell","doi":"10.1103/physreve.110.034203","DOIUrl":"https://doi.org/10.1103/physreve.110.034203","url":null,"abstract":"We study the transport of rigid ellipsoidal swimmers in a periodic vortex array via numerical simulation and dynamical systems analysis. Via ensemble simulations, we show the counterintuitive result that slower swimming speeds can generate fast ballistic transport, while faster swimming speeds generate chaotic and diffusive transport, which is inherently slower in the long run. To explain this, we use the symmetry of the flow to construct a time-reversible Poincaré return map on a two-dimensional surface of section in phase space. For sufficiently small swimming speeds, we find stable periodic orbits on the surface of section surrounded by invariant tori, similar to Kolmogorov-Arnold-Moser curves. Trajectories within these tori are ballistic. As the swimming speed is increased, the periodic orbits undergo a sequence of period-doubling bifurcations that destroys the ballistic tori. These bifurcations exactly match the ballistic to diffusive transition from the ensemble simulations. Additional ensemble simulations are used to test the robustness of these results to noise. The ballistic behavior is destroyed as the strength of rotational diffusion increases. However, we estimate that the ballistic tori might still be seen in experiments.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"47 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-09DOI: 10.1103/physreve.110.035203
Andrey V. Zobnin, Andrey M. Lipaev, Roman A. Syrovatka, Alexandr D. Usachev, Vadim N. Naumkin, Oleg F. Petrov, Markus H. Thoma, Oleg V. Novitsky, Sergey N. Ryzhikov
Fragmentation of a suspension of micron-sized plastic microparticles and their contraction into dense globules was experimentally obtained in a gas discharge plasma, when the plasma density was deliberately and abruptly increased. The globules took up spherical shapes 0.14–1.1 mm in diameters and contained from tens to thousands microparticles. The fragmentation and globule formation appears to be similar to the development of gravitational instability. This process is attributed to the Le Sage's like attraction among microparticles in a dense plasma due to the plasma losses inside a globule hypothesized theoretically in the middle of the 1990s. The key role of plasma flows in the attraction was prominently demonstrated in the same experiment by the distinctly visible disintegration of the globules when we reduced the density of the surrounding plasma to the initial one. Also molecular dynamics simulations of fragmentation of microparticle clouds and globules formation qualitatively resemble typical patterns of the fragmentation and collapse of interstellar nebulae.
{"title":"Observation of Le Sage gravity analog in complex plasma","authors":"Andrey V. Zobnin, Andrey M. Lipaev, Roman A. Syrovatka, Alexandr D. Usachev, Vadim N. Naumkin, Oleg F. Petrov, Markus H. Thoma, Oleg V. Novitsky, Sergey N. Ryzhikov","doi":"10.1103/physreve.110.035203","DOIUrl":"https://doi.org/10.1103/physreve.110.035203","url":null,"abstract":"Fragmentation of a suspension of micron-sized plastic microparticles and their contraction into dense globules was experimentally obtained in a gas discharge plasma, when the plasma density was deliberately and abruptly increased. The globules took up spherical shapes 0.14–1.1 mm in diameters and contained from tens to thousands microparticles. The fragmentation and globule formation appears to be similar to the development of gravitational instability. This process is attributed to the Le Sage's like attraction among microparticles in a dense plasma due to the plasma losses inside a globule hypothesized theoretically in the middle of the 1990s. The key role of plasma flows in the attraction was prominently demonstrated in the same experiment by the distinctly visible disintegration of the globules when we reduced the density of the surrounding plasma to the initial one. Also molecular dynamics simulations of fragmentation of microparticle clouds and globules formation qualitatively resemble typical patterns of the fragmentation and collapse of interstellar nebulae.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"10 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-09DOI: 10.1103/physreve.110.034118
Kazuaki Murayama
This paper considers similarities between statistical physics and Bayes inference through the Bayesian linear regression model. Some similarities have been discussed previously, such as the analogy between the marginal likelihood in Bayes inference and the partition function in statistical mechanics. In particular, this paper considers the proposal to associate discrete sample size with inverse temperature [C. H. LaMont and P. A. Wiggins, Phys. Rev. E99, 052140 (2019)]. The previous study suggested that incorporating this similarity motivates the derivation of analogs of thermodynamic functions such as energy and entropy. The study also anticipated that those analogous functions have potential to describe Bayes estimation from physical points of view and to provide physical insights into mechanisms of estimation. This paper incorporates a macroscopic perspective as an asymptotics similar to the thermodynamic limit into the previous suggestion. Its motivation stems from the statistical mechanical concept of deriving thermodynamic functions that characterize macroscopic properties of macroscopic systems. This incorporation not only allows analogs of macroscopic thermodynamic functions to be considered but also suggests a candidate for an analog of inverse temperature with continuity, which is partly consistent with the previous proposal to associate the discrete sample size with inverse temperature. On the basis of this suggestion, we analyze analogs of macroscopic thermodynamic functions for a Bayesian linear regression model which is the basis of various machine learning models. We further investigate, through the behavior of these functions, how Bayes estimation is described from the perspective of physics and what kind of physical insight is obtained. As a result, the estimation of regression coefficients, which is the primary task of regression, appears to be described by the physical picture of balance between decreasing energy and increasing entropy as in equilibrium states of thermodynamic systems. More specifically we observe the physical view of Bayes inference as follows: the estimation succeeds where the effect of decreasing energy is dominant at low temperature. On the other hand, the estimation fails where the effect of increasing entropy is dominant at high temperature.
本文通过贝叶斯线性回归模型，探讨了统计物理学与贝叶斯推理之间的相似之处。有些相似之处之前已经讨论过，如贝叶斯推理中的边际似然与统计力学中的分区函数之间的类比。本文特别考虑了将离散样本大小与逆温度相关联的提议[C. H. LaMont and P. A. Wiggins, Phys. Rev. E 99, 052140 (2019)]。之前的研究表明，结合这种相似性可以推导出热力学函数的类似物，如能量和熵。该研究还预计，这些类似函数有可能从物理角度描述贝叶斯估计，并为估计机制提供物理见解。本文将宏观视角作为与热力学极限类似的渐近线纳入了前述建议。其动机源于统计力学概念，即导出表征宏观系统宏观特性的热力学函数。这种纳入不仅允许考虑宏观热力学函数的类似物，而且还提出了具有连续性的逆温度类似物的候选方案，这与之前提出的将离散样本大小与逆温度联系起来的建议在一定程度上是一致的。根据这一建议，我们分析了贝叶斯线性回归模型的宏观热力学函数类似物，该模型是各种机器学习模型的基础。通过这些函数的行为，我们进一步研究了如何从物理学的角度描述贝叶斯估计，以及获得了什么样的物理启示。结果发现，回归的主要任务--回归系数的估计，似乎可以用热力学系统平衡状态下能量递减和熵增加之间平衡的物理图景来描述。更具体地说，我们观察到贝叶斯推理的物理观点如下：在低温时，当能量递减效应占主导地位时，估计就会成功。另一方面，当高温时熵增效应占主导地位时，估计就会失败。
{"title":"Statistical physical view of statistical inference in Bayesian linear regression model","authors":"Kazuaki Murayama","doi":"10.1103/physreve.110.034118","DOIUrl":"https://doi.org/10.1103/physreve.110.034118","url":null,"abstract":"This paper considers similarities between statistical physics and Bayes inference through the Bayesian linear regression model. Some similarities have been discussed previously, such as the analogy between the marginal likelihood in Bayes inference and the partition function in statistical mechanics. In particular, this paper considers the proposal to associate discrete sample size with inverse temperature [C. H. LaMont and P. A. Wiggins, <span>Phys. Rev. E</span> <b>99</b>, 052140 (2019)]. The previous study suggested that incorporating this similarity motivates the derivation of analogs of thermodynamic functions such as energy and entropy. The study also anticipated that those analogous functions have potential to describe Bayes estimation from physical points of view and to provide physical insights into mechanisms of estimation. This paper incorporates a macroscopic perspective as an asymptotics similar to the thermodynamic limit into the previous suggestion. Its motivation stems from the statistical mechanical concept of deriving thermodynamic functions that characterize macroscopic properties of macroscopic systems. This incorporation not only allows analogs of macroscopic thermodynamic functions to be considered but also suggests a candidate for an analog of inverse temperature with continuity, which is partly consistent with the previous proposal to associate the discrete sample size with inverse temperature. On the basis of this suggestion, we analyze analogs of macroscopic thermodynamic functions for a Bayesian linear regression model which is the basis of various machine learning models. We further investigate, through the behavior of these functions, how Bayes estimation is described from the perspective of physics and what kind of physical insight is obtained. As a result, the estimation of regression coefficients, which is the primary task of regression, appears to be described by the physical picture of balance between decreasing energy and increasing entropy as in equilibrium states of thermodynamic systems. More specifically we observe the physical view of Bayes inference as follows: the estimation succeeds where the effect of decreasing energy is dominant at low temperature. On the other hand, the estimation fails where the effect of increasing entropy is dominant at high temperature.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"21 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-09DOI: 10.1103/physreve.110.034307
Khadija Khatun, Chen Shen, Lei Shi, Jun Tanimoto
Destructive agents, who opt out of the game and indiscriminately harm others, paradoxically foster cooperation, representing an intriguing variant of the voluntary participation strategy. Yet, their impact on cooperation remains inadequately understood, particularly in the context of pairwise social dilemma games and in comparison to their counterparts, constructive agents, who opt out of the game but indiscriminately benefit others. Furthermore, little is known about the combined effects of both agent types on cooperation dynamics. Using replicator dynamics in infinite and well-mixed populations, we find that contrary to their role in facilitating cooperation in multiplayer games, destructive agents fail to encourage cooperation in pairwise social dilemmas. Instead, they replace defection in the prisoners' dilemma and stag-hunt games. Similarly, in the chicken game, they can destabilize or replace the mixed equilibrium of cooperation and defection, undermining cooperation in the harmony (trivial) game. Conversely, constructive agents, when their payoffs exceed their contributions to opponents, can exhibit effects similar to destructive agents. However, if their payoffs are lower, while they destabilize defection in prisoners' dilemma and stag-hunt games, they do not disrupt the cooperation equilibrium in harmony games and have a negligible impact on the coexistence of cooperation in chicken games. The combination of destructive and constructive agents does not facilitate cooperation, but instead generates complex evolutionary dynamics, including bistable, tristable, and quadstable states, with outcomes contingent on their relative payoffs and game types. These results, taken together, enhance our understanding of the impact of the voluntary participation mechanism on cooperation, contributing to a more comprehensive understanding of its influence.
{"title":"Stability of pairwise social dilemma games: Destructive agents, constructive agents, and their joint effects","authors":"Khadija Khatun, Chen Shen, Lei Shi, Jun Tanimoto","doi":"10.1103/physreve.110.034307","DOIUrl":"https://doi.org/10.1103/physreve.110.034307","url":null,"abstract":"Destructive agents, who opt out of the game and indiscriminately harm others, paradoxically foster cooperation, representing an intriguing variant of the voluntary participation strategy. Yet, their impact on cooperation remains inadequately understood, particularly in the context of pairwise social dilemma games and in comparison to their counterparts, constructive agents, who opt out of the game but indiscriminately benefit others. Furthermore, little is known about the combined effects of both agent types on cooperation dynamics. Using replicator dynamics in infinite and well-mixed populations, we find that contrary to their role in facilitating cooperation in multiplayer games, destructive agents fail to encourage cooperation in pairwise social dilemmas. Instead, they replace defection in the prisoners' dilemma and stag-hunt games. Similarly, in the chicken game, they can destabilize or replace the mixed equilibrium of cooperation and defection, undermining cooperation in the harmony (trivial) game. Conversely, constructive agents, when their payoffs exceed their contributions to opponents, can exhibit effects similar to destructive agents. However, if their payoffs are lower, while they destabilize defection in prisoners' dilemma and stag-hunt games, they do not disrupt the cooperation equilibrium in harmony games and have a negligible impact on the coexistence of cooperation in chicken games. The combination of destructive and constructive agents does not facilitate cooperation, but instead generates complex evolutionary dynamics, including bistable, tristable, and quadstable states, with outcomes contingent on their relative payoffs and game types. These results, taken together, enhance our understanding of the impact of the voluntary participation mechanism on cooperation, contributing to a more comprehensive understanding of its influence.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"42 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-06DOI: 10.1103/physreve.110.034114
Yuya Shishikura, Hiroki Ohta
We propose a statistical physics model of a neutral community, where each agent can represent identical plant species growing in the vertical direction with sunlight in the form of rich-get-richer competition. Disturbance added to this ecosystem, which makes an agent restart from the lowest growth level, is realized as a stochastic resetting. We show that in this model for sufficiently strong competition, vertical diversity characterized by a family of Hill numbers robustly emerges as a local maximum at intermediate disturbance.
{"title":"Emergence of vertical diversity under disturbance","authors":"Yuya Shishikura, Hiroki Ohta","doi":"10.1103/physreve.110.034114","DOIUrl":"https://doi.org/10.1103/physreve.110.034114","url":null,"abstract":"We propose a statistical physics model of a neutral community, where each agent can represent identical plant species growing in the vertical direction with sunlight in the form of rich-get-richer competition. Disturbance added to this ecosystem, which makes an agent restart from the lowest growth level, is realized as a stochastic resetting. We show that in this model for sufficiently strong competition, vertical diversity characterized by a family of Hill numbers robustly emerges as a local maximum at intermediate disturbance.","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"17 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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