Pub Date : 2024-12-01Epub Date: 2024-10-17DOI: 10.1088/2632-072X/ad83a5
Faisal Suwayyid, Guo-Wei Wei
Topological data analysis (TDA) has made significant progress in developing a new class of fundamental operators known as the Dirac operator, particularly in topological signals and molecular representations. However, the current approaches being used are based on the classical case of chain complexes. The present study establishes Mayer Dirac operators based on N-chain complexes. These operators interconnect an alternating sequence of Mayer Laplacian operators, providing a generalization of the classical result . Furthermore, the research presents an explicit formulation of the Laplacian for N-chain complexes induced by vertex sequences on a finite set. Weighted versions of Mayer Laplacian and Dirac operators are introduced to expand the scope and improve applicability, showcasing their effectiveness in capturing physical attributes in various practical scenarios. The study presents a generalized version for factorizing Laplacian operators as an operator's product and its 'adjoint'. Additionally, the proposed persistent Mayer Dirac operators and extensions are applied to biological and chemical domains, particularly in the analysis of molecular structures. The study also highlights the potential applications of persistent Mayer Dirac operators in data science.
拓扑数据分析（TDA）在开发一类新的基本算子（即狄拉克算子）方面取得了重大进展，特别是在拓扑信号和分子表征方面。然而，目前使用的方法都是基于链复合物的经典情况。本研究建立了基于 N 链复合物的梅耶-狄拉克算子。这些算子与梅耶拉普拉斯算子的交替序列相互连接，从而对经典结果 D 2 = L 进行了概括。此外，研究还提出了有限集顶点序列诱导的 N 链复数拉普拉斯的明确表述。研究还引入了梅耶拉普拉斯算子和狄拉克算子的加权版本，以扩大范围和提高适用性，展示它们在各种实际场景中捕捉物理属性的有效性。研究提出了将拉普拉斯算子因数化为算子乘积及其 "邻接 "的通用版本。此外，还将提出的持久性梅耶狄拉克算子及其扩展应用于生物和化学领域，特别是分子结构分析。研究还强调了持久性梅耶-狄拉克算子在数据科学中的潜在应用。
{"title":"Persistent Mayer Dirac.","authors":"Faisal Suwayyid, Guo-Wei Wei","doi":"10.1088/2632-072X/ad83a5","DOIUrl":"10.1088/2632-072X/ad83a5","url":null,"abstract":"<p><p>Topological data analysis (TDA) has made significant progress in developing a new class of fundamental operators known as the Dirac operator, particularly in topological signals and molecular representations. However, the current approaches being used are based on the classical case of chain complexes. The present study establishes Mayer Dirac operators based on <i>N</i>-chain complexes. These operators interconnect an alternating sequence of Mayer Laplacian operators, providing a generalization of the classical result <math> <mrow><msup><mi>D</mi> <mn>2</mn></msup> <mo>=</mo> <mi>L</mi></mrow> </math> . Furthermore, the research presents an explicit formulation of the Laplacian for <i>N</i>-chain complexes induced by vertex sequences on a finite set. Weighted versions of Mayer Laplacian and Dirac operators are introduced to expand the scope and improve applicability, showcasing their effectiveness in capturing physical attributes in various practical scenarios. The study presents a generalized version for factorizing Laplacian operators as an operator's product and its 'adjoint'. Additionally, the proposed persistent Mayer Dirac operators and extensions are applied to biological and chemical domains, particularly in the analysis of molecular structures. The study also highlights the potential applications of persistent Mayer Dirac operators in data science.</p>","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"5 4","pages":"045005"},"PeriodicalIF":2.6,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11488505/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142480552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-10DOI: 10.1088/2632-072x/ad744e
Niall Rodgers, Peter Tiňo and Samuel Johnson
Growing attention has been brought to the fact that many real directed networks exhibit hierarchy and directionality as measured through techniques like trophic analysis and non-normality. We propose a simple growing network model where the probability of connecting to a node is defined by a preferential attachment mechanism based on degree and the difference in fitness between nodes. In particular, we show how mechanisms such as degree-based preferential attachment and node fitness interactions can lead to the emergence of the spectrum of hierarchy and directionality observed in real networks. In this work, we study various features of this model relating to network hierarchy, as measured by trophic analysis. This includes (I) how preferential attachment can lead to network hierarchy, (II) how scale-free degree distributions and network hierarchy can coexist, (III) the correlation between node fitness and trophic level, (IV) how the fitness parameters can predict trophic incoherence and how the trophic level difference distribution compares to the fitness difference distribution, (V) the relationship between trophic level and degree imbalance and the unique role of nodes at the ends of the fitness hierarchy and (VI) how fitness interactions and degree-based preferential attachment can interplay to generate networks of varying coherence and degree distribution. We also provide an example of the intuition this work enables in the analysis of a real historical network. This work provides insight into simple mechanisms which can give rise to hierarchy in directed networks and quantifies the usefulness and limitations of using trophic analysis as an analysis tool for real networks.
{"title":"Fitness-based growth of directed networks with hierarchy","authors":"Niall Rodgers, Peter Tiňo and Samuel Johnson","doi":"10.1088/2632-072x/ad744e","DOIUrl":"https://doi.org/10.1088/2632-072x/ad744e","url":null,"abstract":"Growing attention has been brought to the fact that many real directed networks exhibit hierarchy and directionality as measured through techniques like trophic analysis and non-normality. We propose a simple growing network model where the probability of connecting to a node is defined by a preferential attachment mechanism based on degree and the difference in fitness between nodes. In particular, we show how mechanisms such as degree-based preferential attachment and node fitness interactions can lead to the emergence of the spectrum of hierarchy and directionality observed in real networks. In this work, we study various features of this model relating to network hierarchy, as measured by trophic analysis. This includes (I) how preferential attachment can lead to network hierarchy, (II) how scale-free degree distributions and network hierarchy can coexist, (III) the correlation between node fitness and trophic level, (IV) how the fitness parameters can predict trophic incoherence and how the trophic level difference distribution compares to the fitness difference distribution, (V) the relationship between trophic level and degree imbalance and the unique role of nodes at the ends of the fitness hierarchy and (VI) how fitness interactions and degree-based preferential attachment can interplay to generate networks of varying coherence and degree distribution. We also provide an example of the intuition this work enables in the analysis of a real historical network. This work provides insight into simple mechanisms which can give rise to hierarchy in directed networks and quantifies the usefulness and limitations of using trophic analysis as an analysis tool for real networks.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"9 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-01Epub Date: 2024-08-08DOI: 10.1088/2632-072X/ad679e
Jordan C Rozum, Luis M Rocha
Minimum spanning trees and forests are powerful sparsification techniques that remove cycles from weighted graphs to minimize total edge weight while preserving node reachability, with applications in computer science, network science, and graph theory. Despite their utility and ubiquity, they have several limitations, including that they are only defined for undirected networks, they significantly alter dynamics on networks, and they do not generally preserve important network features such as shortest distances, shortest path distribution, and community structure. In contrast, distance backbones, which are subgraphs formed by all edges that obey a generalized triangle inequality, are well defined in directed and undirected graphs and preserve those and other important network features. The backbone of a graph is defined with respect to a specified path-length operator that aggregates weights along a path to define its length, thereby associating a cost to indirect connections. The backbone is the union of all shortest paths between each pair of nodes according to the specified operator. One such operator, the max function, computes the length of a path as the largest weight of the edges that compose it (a weakest link criterion). It is the only operator that yields an algebraic structure for computing shortest paths that is consistent with De Morgan's laws. Applying this operator yields the ultrametric backbone of a graph in that (semi-triangular) edges whose weights are larger than the length of an indirect path connecting the same nodes (i.e. those that break the generalized triangle inequality based on max as a path-length operator) are removed. We show that the ultrametric backbone is the union of minimum spanning forests in undirected graphs and provides a new generalization of minimum spanning trees to directed graphs that, unlike minimum equivalent graphs and minimum spanning arborescences, preserves all shortest paths and De Morgan's law consistency.
最小生成树和森林是一种功能强大的稀疏化技术，它们可以去除加权图中的循环，从而在保持节点可达性的同时使总边重最小化，在计算机科学、网络科学和图论中都有应用。尽管这些技术非常有用，而且无处不在，但它们也有一些局限性，包括它们只针对无向网络，会显著改变网络的动态性，而且一般不会保留重要的网络特征，如最短距离、最短路径分布和群落结构。与此相反，距离骨干图是由遵守广义三角形不等式的所有边组成的子图，在有向图和无向图中都得到了很好的定义，并保留了这些和其他重要的网络特征。图的主干是根据指定的路径长度算子定义的，该算子汇总路径上的权重来定义路径长度，从而为间接连接设定成本。根据指定的算子，骨干图是每对节点之间所有最短路径的联合。其中一个运算符，即 max 函数，将路径的长度计算为组成路径的边的最大权重（最弱链接标准）。它是唯一能产生与德摩根定律一致的代数结构来计算最短路径的算子。应用此算子可以得到图的超对称主干，即删除权重大于连接相同节点的间接路径长度的（半三角形）边（即那些破坏基于 max 作为路径长度算子的广义三角形不等式的边）。我们证明了超对称骨干图是无向图中最小生成森林的结合，并为有向图提供了最小生成树的新广义，与最小等价图和最小生成树状图不同，它保留了所有最大-最小最短路径和德摩根定律的一致性。
{"title":"The ultrametric backbone is the union of all minimum spanning forests.","authors":"Jordan C Rozum, Luis M Rocha","doi":"10.1088/2632-072X/ad679e","DOIUrl":"10.1088/2632-072X/ad679e","url":null,"abstract":"<p><p>Minimum spanning trees and forests are powerful sparsification techniques that remove cycles from weighted graphs to minimize total edge weight while preserving node reachability, with applications in computer science, network science, and graph theory. Despite their utility and ubiquity, they have several limitations, including that they are only defined for undirected networks, they significantly alter dynamics on networks, and they do not generally preserve important network features such as shortest distances, shortest path distribution, and community structure. In contrast, distance backbones, which are subgraphs formed by all edges that obey a generalized triangle inequality, are well defined in directed and undirected graphs and preserve those and other important network features. The backbone of a graph is defined with respect to a specified path-length operator that aggregates weights along a path to define its length, thereby associating a cost to indirect connections. The backbone is the union of all shortest paths between each pair of nodes according to the specified operator. One such operator, the max function, computes the length of a path as the largest weight of the edges that compose it (a weakest link criterion). It is the only operator that yields an algebraic structure for computing shortest paths that is consistent with De Morgan's laws. Applying this operator yields the ultrametric backbone of a graph in that (semi-triangular) edges whose weights are larger than the length of an indirect path connecting the same nodes (i.e. those that break the generalized triangle inequality based on max as a path-length operator) are removed. We show that the ultrametric backbone is the union of minimum spanning forests in undirected graphs and provides a new generalization of minimum spanning trees to directed graphs that, unlike minimum equivalent graphs and minimum spanning arborescences, preserves all <math><mrow><mo>max</mo> <mo>-</mo> <mo>min</mo></mrow> </math> shortest paths and De Morgan's law consistency.</p>","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"5 3","pages":"035009"},"PeriodicalIF":2.6,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11307140/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141918093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-27DOI: 10.1088/2632-072x/ad679f
Michelle Roost, Karel Devriendt, Giulio Zucal, Jürgen Jost
Discrete curvatures are quantities associated to the nodes and edges of a graph that reflect the local geometry around them. These curvatures have a rich mathematical theory and they have recently found success as a tool to analyze networks across a wide range of domains. In this work, we consider the problem of constructing graphs with a prescribed set of discrete edge curvatures, and explore the space of such graphs. We address this problem in two ways: first, we develop an evolutionary algorithm to sample graphs with discrete curvatures close to a given set. We use this algorithm to explore how other network statistics vary when constrained by the discrete curvatures in the network. Second, we solve the exact reconstruction problem for the specific case of Forman–Ricci curvature. By leveraging the theory of Markov bases, we obtain a finite set of rewiring moves that connects the space of all graphs with a fixed discrete curvature.
{"title":"Exploring the space of graphs with fixed discrete curvatures","authors":"Michelle Roost, Karel Devriendt, Giulio Zucal, Jürgen Jost","doi":"10.1088/2632-072x/ad679f","DOIUrl":"https://doi.org/10.1088/2632-072x/ad679f","url":null,"abstract":"Discrete curvatures are quantities associated to the nodes and edges of a graph that reflect the local geometry around them. These curvatures have a rich mathematical theory and they have recently found success as a tool to analyze networks across a wide range of domains. In this work, we consider the problem of constructing graphs with a prescribed set of discrete edge curvatures, and explore the space of such graphs. We address this problem in two ways: first, we develop an evolutionary algorithm to sample graphs with discrete curvatures close to a given set. We use this algorithm to explore how other network statistics vary when constrained by the discrete curvatures in the network. Second, we solve the exact reconstruction problem for the specific case of Forman–Ricci curvature. By leveraging the theory of Markov bases, we obtain a finite set of rewiring moves that connects the space of all graphs with a fixed discrete curvature.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"20 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217517","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-11DOI: 10.1088/2632-072x/ad64a3
Lukas Fesser, Sergio Serrano de Haro Iváñez, Karel Devriendt, Melanie Weber and Renaud Lambiotte
The notion of curvature on graphs has recently gained traction in the networks community, with the Ollivier–Ricci curvature (ORC) in particular being used for several tasks in network analysis, such as community detection. In this work, we choose a different approach and study augmentations of the discretization of the Ricci curvature proposed by Forman (AFRC). We empirically and theoretically investigate its relation to the ORC and the un-augmented Forman–Ricci curvature. In particular, we provide evidence that the AFRC frequently gives sufficient insight into the structure of a network to be used for community detection, and therefore provides a computationally cheaper alternative to previous ORC-based methods. Our novel AFRC-based community detection algorithm is competitive with an ORC-based approach.
{"title":"Augmentations of Forman’s Ricci curvature and their applications in community detection","authors":"Lukas Fesser, Sergio Serrano de Haro Iváñez, Karel Devriendt, Melanie Weber and Renaud Lambiotte","doi":"10.1088/2632-072x/ad64a3","DOIUrl":"https://doi.org/10.1088/2632-072x/ad64a3","url":null,"abstract":"The notion of curvature on graphs has recently gained traction in the networks community, with the Ollivier–Ricci curvature (ORC) in particular being used for several tasks in network analysis, such as community detection. In this work, we choose a different approach and study augmentations of the discretization of the Ricci curvature proposed by Forman (AFRC). We empirically and theoretically investigate its relation to the ORC and the un-augmented Forman–Ricci curvature. In particular, we provide evidence that the AFRC frequently gives sufficient insight into the structure of a network to be used for community detection, and therefore provides a computationally cheaper alternative to previous ORC-based methods. Our novel AFRC-based community detection algorithm is competitive with an ORC-based approach.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"1 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141932262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-17DOI: 10.1088/2632-072x/ad5ad5
Felippe Alves and David Saad
We study vaccine budget-sharing strategies in the SIR (Susceptible-Infected-Recovered) model given a structured community network to investigate the benefit of sharing vaccine across communities. The network studied comprises two communities, one of which controls vaccine budget and may share it with the other. Different scenarios are considered regarding the connectivity between communities, infection rates and the unvaccinated fraction of the population. Properties of the SIR model facilitates the use of dynamic message passing (DMP) and optimal control methods to investigate preventive and reactive budget-sharing scenarios. Our results show a large set of budget-sharing strategies in which the sharing community benefits from the reduced global infection rates with no detrimental impact on its local infection rate.
{"title":"The futility of being selfish in vaccine distribution","authors":"Felippe Alves and David Saad","doi":"10.1088/2632-072x/ad5ad5","DOIUrl":"https://doi.org/10.1088/2632-072x/ad5ad5","url":null,"abstract":"We study vaccine budget-sharing strategies in the SIR (Susceptible-Infected-Recovered) model given a structured community network to investigate the benefit of sharing vaccine across communities. The network studied comprises two communities, one of which controls vaccine budget and may share it with the other. Different scenarios are considered regarding the connectivity between communities, infection rates and the unvaccinated fraction of the population. Properties of the SIR model facilitates the use of dynamic message passing (DMP) and optimal control methods to investigate preventive and reactive budget-sharing scenarios. Our results show a large set of budget-sharing strategies in which the sharing community benefits from the reduced global infection rates with no detrimental impact on its local infection rate.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"64 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-17DOI: 10.1088/2632-072x/ad5e2e
Megha Suswaram, Uttam Bhat and Justin D Yeakel
Acoustic signaling is employed by many sexually reproducing species to select for mates and enhance fitness. However, signaling in dense populations can create an auditory background, or chorus, which may interfere with a signal receiver’s phonotactic selectivity, or the ability to distinguish individual signals. Feedback between the strength of an individual’s signal, phonotactic selectivity, and population size, may interact in complex ways to impact the evolution of signaling within a population, potentially leading to the emergence of silence. Here we formulate a general model that captures the dynamic feedback between individual acoustic signalers, phonotactic selectivity, and the population-level chorus to explore the eco-evolutionary dynamics of an acoustic trait within a population. We find that population dynamics have a significant influence on the evolutionary dynamics of the signaling trait, and that very sharp transitions separate conspicuous from silent populations. Our framework also reveals that increased phonotactic selectivity promotes the stability of signaling populations, and that transitions from signaling to silence are prone to hysteresis. We suggest that understanding the relationship between factors influencing population size, such as environmental productivity, as well as factors influencing phonotactic selectivity, such as anthropogenic noise, are central to understanding the complex mosaic of acoustically signaling and silent populations.
{"title":"Rising above the noise: the influence of population dynamics on the evolution of acoustic signaling","authors":"Megha Suswaram, Uttam Bhat and Justin D Yeakel","doi":"10.1088/2632-072x/ad5e2e","DOIUrl":"https://doi.org/10.1088/2632-072x/ad5e2e","url":null,"abstract":"Acoustic signaling is employed by many sexually reproducing species to select for mates and enhance fitness. However, signaling in dense populations can create an auditory background, or chorus, which may interfere with a signal receiver’s phonotactic selectivity, or the ability to distinguish individual signals. Feedback between the strength of an individual’s signal, phonotactic selectivity, and population size, may interact in complex ways to impact the evolution of signaling within a population, potentially leading to the emergence of silence. Here we formulate a general model that captures the dynamic feedback between individual acoustic signalers, phonotactic selectivity, and the population-level chorus to explore the eco-evolutionary dynamics of an acoustic trait within a population. We find that population dynamics have a significant influence on the evolutionary dynamics of the signaling trait, and that very sharp transitions separate conspicuous from silent populations. Our framework also reveals that increased phonotactic selectivity promotes the stability of signaling populations, and that transitions from signaling to silence are prone to hysteresis. We suggest that understanding the relationship between factors influencing population size, such as environmental productivity, as well as factors influencing phonotactic selectivity, such as anthropogenic noise, are central to understanding the complex mosaic of acoustically signaling and silent populations.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"10 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-16DOI: 10.1088/2632-072x/ad6051
Nima Dehghani and Gianluca Caterina
This paper introduces a category theory-based framework to redefine physical computing in light of advancements in quantum computing and non-standard computing systems. By integrating classical definitions within this broader perspective, the paper rigorously recontextualizes what constitutes physical computing devices and processes. It demonstrates how the compositional nature and relational structures of physical computing systems can be coherently formalized using category theory. This approach not only encapsulates recent formalisms in physical computing but also offers a structured method to explore the dynamic interactions within these systems.
{"title":"Physical computing: a category theoretic perspective on physical computation and system compositionality","authors":"Nima Dehghani and Gianluca Caterina","doi":"10.1088/2632-072x/ad6051","DOIUrl":"https://doi.org/10.1088/2632-072x/ad6051","url":null,"abstract":"This paper introduces a category theory-based framework to redefine physical computing in light of advancements in quantum computing and non-standard computing systems. By integrating classical definitions within this broader perspective, the paper rigorously recontextualizes what constitutes physical computing devices and processes. It demonstrates how the compositional nature and relational structures of physical computing systems can be coherently formalized using category theory. This approach not only encapsulates recent formalisms in physical computing but also offers a structured method to explore the dynamic interactions within these systems.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"78 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141722345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-11DOI: 10.1088/2632-072x/ad5e55
L A Hurley, J G Restrepo and S E Shaheen
Reservoir computing is a machine learning framework where the readouts from a nonlinear system (the reservoir) are trained so that the output from the reservoir, when forced with an input signal, reproduces a desired output signal. A common implementation of reservoir computers (RCs) is to use a recurrent neural network as the reservoir. The design of this network can have significant effects on the performance of the RC. In this paper we study the effect of the node activation function on the ability of RCs to learn and predict chaotic time series. We find that the Forecast Horizon (FH), the time during which the reservoir’s predictions remain accurate, can vary by an order of magnitude across a set of 16 activation functions used in machine learning. By using different functions from this set, and by modifying their parameters, we explore whether the entropy of node activation levels or the curvature of the activation functions determine the predictive ability of the reservoirs. We find that the FH is low when the activation function is used in a region where it has low curvature, and a positive correlation between curvature and FH. For the activation functions studied we find that the largest FH generally occurs at intermediate levels of the entropy of node activation levels. Our results show that the performance of RCs is very sensitive to the activation function shape. Therefore, modifying this shape in hyperparameter optimization algorithms can lead to improvements in RC performance.
{"title":"Tuning the activation function to optimize the forecast horizon of a reservoir computer","authors":"L A Hurley, J G Restrepo and S E Shaheen","doi":"10.1088/2632-072x/ad5e55","DOIUrl":"https://doi.org/10.1088/2632-072x/ad5e55","url":null,"abstract":"Reservoir computing is a machine learning framework where the readouts from a nonlinear system (the reservoir) are trained so that the output from the reservoir, when forced with an input signal, reproduces a desired output signal. A common implementation of reservoir computers (RCs) is to use a recurrent neural network as the reservoir. The design of this network can have significant effects on the performance of the RC. In this paper we study the effect of the node activation function on the ability of RCs to learn and predict chaotic time series. We find that the Forecast Horizon (FH), the time during which the reservoir’s predictions remain accurate, can vary by an order of magnitude across a set of 16 activation functions used in machine learning. By using different functions from this set, and by modifying their parameters, we explore whether the entropy of node activation levels or the curvature of the activation functions determine the predictive ability of the reservoirs. We find that the FH is low when the activation function is used in a region where it has low curvature, and a positive correlation between curvature and FH. For the activation functions studied we find that the largest FH generally occurs at intermediate levels of the entropy of node activation levels. Our results show that the performance of RCs is very sensitive to the activation function shape. Therefore, modifying this shape in hyperparameter optimization algorithms can lead to improvements in RC performance.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"244 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141611722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-10DOI: 10.1088/2632-072x/ad5bb2
Rafael Dias Vilela, Alfredo J Grados and Jean-Régis Angilella
We investigate the dynamics of individual run-and-tumble particles in a convective flow which is a prototype of fluid flows with transport barriers. We consider the most prevalent case of swimmers denser than the background fluid. As a result of gravity and the effects of the carrying flow, in the absence of swimming the particles either sediment or remain in a convective cell. When run-and-tumble also takes place, the particles may move to upper convective cells. We derive analytically the probability of uprise. Since that probability in a given fluid flow can vary strongly across species, our findings inspire a purely dynamical mechanism for species extraction in the dilute regime. Numerical simulations support our analytical predictions and demonstrate that a judicious choice of the fluid flow’s parameters can lead to particle sorting with an arbitrary degree of purity.
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