Using reservoir computing to construct scarred wavefunctions

Scar theory is one of the fundamental pillars in the field of quantum chaos, and scarred functions a superb tool to carry out studies in it. Several methods, usually semiclassical, have been described to cope with these two phenomena. In this paper, we present an alternative method, based on the novel machine learning algorithm known as Reservoir Computing, to calculate such scarred wavefunctions together with the associated eigenstates of the system. The resulting methodology achieves outstanding accuracy while reducing execution times by a factor of ten. As an illustration of the effectiveness of this method, we apply it to the widespread chaotic two-dimensional coupled quartic oscillator.Comment: arXiv admin note: text overlap with arXiv:2310.0745

Anticipating food price crises by reservoir computing

Anticipating price crises in the market of agri-commodities is critical to guarantee both the sustainability of the food system and to ensure food security. However, this is not an easy task, since the problem implies analyzing small and very volatile time series, which are highly influenced by external factors. In this paper, we show that suitable reservoir computing algorithms can be developed that outperform traditional approaches, by reducing the Mean Absolute Error and, more importantly, increasing the Market Direction Accuracy. For this purpose, the applicability of five variants of such method to forecast this market is explored, and their performance evaluated by comparing the results with those obtained with the standard LSTM and SARIMA benchmarks. We conclude that decomposing the time series and modeling each component with a separate RC is essential to successfully anticipate price trends, and that this method works even in the complex changing temporal scenario of the Covid-19 pandemic, when part of the data were collectedThe project that gave rise to these results received the support of a fellowship from ‘‘la Caixa’’ Foundation (ID 100010434). The fellowship code is LCF/BQ/DR20/11790028. This work has also been partially supported by the Spanish Ministry of Science, Innovation and Universities, Gobierno de España, under Contract No. PID2021-122711NB-C21; and by DG of Research and Technological Innovation of the Community of Madrid (Spain) under Contract No. IND2022/TIC-2371

Efficiency of Human Activity on Information Spreading on Twitter

Understanding the collective reaction to individual actions is key to effectively spread information in social media. In this work we define efficiency on Twitter, as the ratio between the emergent spreading process and the activity employed by the user. We characterize this property by means of a quantitative analysis of the structural and dynamical patterns emergent from human interactions, and show it to be universal across several Twitter conversations. We found that some influential users efficiently cause remarkable collective reactions by each message sent, while the majority of users must employ extremely larger efforts to reach similar effects. Next we propose a model that reproduces the retweet cascades occurring on Twitter to explain the emergent distribution of the user efficiency. The model shows that the dynamical patterns of the conversations are strongly conditioned by the topology of the underlying network. We conclude that the appearance of a small fraction of extremely efficient users results from the heterogeneity of the followers network and independently of the individual user behavior.Comment: 29 pages, 10 figure

To each according to its degree: The meritocracy and topocracy of embedded markets

A system is said to be meritocratic if the compensation and power available to individuals is determined by their abilities and merits. A system is topocratic if the compensation and power available to an individual is determined primarily by her position in a network. Here we introduce a model that is perfectly meritocratic for fully connected networks but that becomes topocratic for sparse networks-like the ones in society. In the model, individuals produce and sell content, but also distribute the content produced by others when they belong to the shortest path connecting a buyer and a seller. The production and distribution of content defines two channels of compensation: a meritocratic channel, where individuals are compensated for the content they produce, and a topocratic channel, where individual compensation is based on the number of shortest paths that go through them in the network. We solve the model analytically and show that the distribution of payoffs is meritocratic only if the average degree of the nodes is larger than a root of the total number of nodes. We conclude that, in the light of this model, the sparsity and structure of networks represents a fundamental constraint to the meritocracy of societiesSupport from the MIT Media Lab Consortia, Fundación Caja Madrid (Spain), UAM-Santander (Spain) and CONICYT grants: Anillo en Complejidad Social SOC-1101 and Fondecyt 1110351 is gratefully acknowledge

To Each According to its Degree: The Meritocracy and Topocracy of Embedded Markets

A system is said to be meritocratic if the compensation and power available to individuals is determined by their abilities and merits. A system is topocratic if the compensation and power available to an individual is determined primarily by her position in a network. Here we introduce a model that is perfectly meritocratic for fully connected networks but that becomes topocratic for sparse networks-like the ones in society. In the model, individuals produce and sell content, but also distribute the content produced by others when they belong to the shortest path connecting a buyer and a seller. The production and distribution of content defines two channels of compensation: a meritocratic channel, where individuals are compensated for the content they produce, and a topocratic channel, where individual compensation is based on the number of shortest paths that go through them in the network. We solve the model analytically and show that the distribution of payoffs is meritocratic only if the average degree of the nodes is larger than a root of the total number of nodes. We conclude that, in the light of this model, the sparsity and structure of networks represents a fundamental constraint to the meritocracy of societies.MIT Media Lab Consortiu

Disentangling Jenny’s equation by machine learning

The so-called soil-landscape model is the central paradigm which relates soil types to their forming factors through the visionary Jenny’s equation. This is a formal mathematical expression that would permit to infer which soil should be found in a specific geographical location if the involved relationship was sufficiently known. Unfortunately, Jenny’s is only a conceptual expression, where the intervening variables are of qualitative nature, not being then possible to work it out with standard mathematical tools. In this work, we take a first step to unlock this expression, showing how Machine Learning can be used to predictably relate soil types and environmental factors. Our method outperforms other conventional statistical analyses that can be carried out on the same forming factors defined by measurable environmental variablesThis work has been partially supported by the Spanish Ministry of Science, Innovation and Universities, Gobierno de España, under Contract No. PID2021-122711NB-C21. The authors wish to thank Ricardo Pérez-Ochoa (Government of Asturias) and José Gumuzzio, for facilitating access to basic soil information, and Javier Rodríguez Alonso (INIA, Madrid), for managing georeferenced dat

Order-chaos transition in correlation diagrams and quantization of period orbits

Eigenlevel correlation diagrams has proven to be a very useful tool to understand eigenstate characteristics of classically chaotic systems. In particular, we showed in a previous publication [Phys. Rev. Lett. 80, 944 (1998)] how to unveil the scarring mechanism, a cornerstone in the theory of quantum chaos, using the Planck constant as the correlation parameter. By increasing Planck constant, we induced a transition from order to chaos, in which scarred wavefunctions appeared as the interaction of pairs of eigenstates in broad avoided crossings, forming a well defined frontier in the correlation diagram. In this paper, we demonstrate that this frontier can be obtained by means of the semiclassical quantization of the involved scarring periodic orbits. Additionally, in order to calculate the Maslov index of each scarring periodic orbit, which is necessary for the semiclassical quantization procedure, we introduce a novel straightforward method based on Lagrangian descriptors. We illustrate the theory using the vibrational eigenstates of the LiCN molecular system.Comment: 12 pages, 7 figure