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Price of information in games of chance: A statistical physics approach.

Physical review research Pub Date : 2024-09-04 DOI: 10.1103/PhysRevResearch.6.033250

Luca Gamberi, Alessia Annibale, Pierpaolo Vivo

{"title":"Price of information in games of chance: A statistical physics approach.","authors":"Luca Gamberi, Alessia Annibale, Pierpaolo Vivo","doi":"10.1103/PhysRevResearch.6.033250","DOIUrl":"https://doi.org/10.1103/PhysRevResearch.6.033250","url":null,"abstract":"Information in the form of data, which can be stored and transferred between users, can be viewed as an intangible commodity, which can be traded in exchange for money. Determining the fair price at which a string of data should be traded is an important and open problem in many settings. In this work we develop a statistical physics framework that allows one to determine analytically the fair price of information exchanged between players in a game of chance. For definiteness, we consider a game where N players bet on the binary outcome of a stochastic process and share the entry fees pot if successful. We assume that one player holds information about past outcomes of the game, which they may either use exclusively to improve their betting strategy or offer to sell to another player. We find a sharp transition as the number of players N is tuned across a critical value, between a phase where the transaction is always profitable for the seller and one where it may not be. In both phases, different regimes are possible, depending on the \"quality\" of information being put up for sale: we observe symbiotic regimes, where both parties collude effectively to rig the game in their favor, competitive regimes, where the transaction is unappealing to the data holder as it overly favors a competitor for scarce resources, and even prey-predator regimes, where an exploitative data holder could be giving away bad-quality data to undercut a competitor. Our analytical framework can be generalized to more complex settings and constitutes a flexible tool to address the rich and timely problem of pricing information in games of chance.","PeriodicalId":520315,"journal":{"name":"Physical review research","volume":"6 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7616869/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142776296","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}

引用次数: 0

Holographic-(V)AE: An end-to-end SO(3)-equivariant (variational) autoencoder in Fourier space.

Physical review research Pub Date : 2024-04-01 DOI: 10.1103/physrevresearch.6.023006

Gian Marco Visani, Michael N Pun, Arman Angaji, Armita Nourmohammad

{"title":"Holographic-(V)AE: An end-to-end SO(3)-equivariant (variational) autoencoder in Fourier space.","authors":"Gian Marco Visani, Michael N Pun, Arman Angaji, Armita Nourmohammad","doi":"10.1103/physrevresearch.6.023006","DOIUrl":"10.1103/physrevresearch.6.023006","url":null,"abstract":"Group-equivariant neural networks have emerged as an efficient approach to model complex data, using generalized convolutions that respect the relevant symmetries of a system. These techniques have made advances in both the supervised learning tasks for classification and regression, and the unsupervised tasks to generate new data. However, little work has been done in leveraging the symmetry-aware expressive representations that could be extracted from these approaches. Here, we present holographic-(variational) autoencoder [H-(V)AE], a fully end-to-end SO(3)-equivariant (variational) autoencoder in Fourier space, suitable for unsupervised learning and generation of data distributed around a specified origin in 3D. H-(V)AE is trained to reconstruct the spherical Fourier encoding of data, learning in the process a low-dimensional representation of the data (i.e., a latent space) with a maximally informative rotationally invariant embedding alongside an equivariant frame describing the orientation of the data. We extensively test the performance of H-(V)AE on diverse datasets. We show that the learned latent space efficiently encodes the categorical features of spherical images. Moreover, the low-dimensional representations learned by H-VAE can be used for downstream data-scarce tasks. Specifically, we show that H-(V)AE's latent space can be used to extract compact embeddings for protein structure microenvironments, and when paired with a random forest regressor, it enables state-of-the-art predictions of protein-ligand binding affinity.","PeriodicalId":520315,"journal":{"name":"Physical review research","volume":"6 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11661850/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142879570","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}

引用次数: 0