Journal of Physics Complexity最新文献

{"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}

{"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}

{"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}

{"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}

{"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}

{"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}

{"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}

{"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}

{"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}

{"title":"Dynamics and sorting of run-and-tumble particles in fluid flows with transport barriers","authors":"Rafael Dias Vilela, Alfredo J Grados and Jean-Régis Angilella","doi":"10.1088/2632-072x/ad5bb2","DOIUrl":"https://doi.org/10.1088/2632-072x/ad5bb2","url":null,"abstract":"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.","PeriodicalId":53211,"journal":{"name":"Journal of Physics Complexity","volume":"5 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141586518","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}