Boltzmann distributions are used in statistical mechanics to describe how the states of a system are distributed at a given temperature. We give a novel characterization of this family as the unique one satisfying independence for uncoupled systems. The theorem boils down to a statement about endomorphisms of the convolution semi-group of finitely supported probability measures on the natural numbers, or, alternatively, about endomorphisms of the multiplicative semi-group of polynomials with non-negative coefficients.
", "doi": "10.1007/s00208-025-03263-x", "issn": "0025-5831", "publisher": "Springer Science and Business Media LLC", "publication": "Mathematische Annalen", "publication_date": "2025-08", "series_number": "4", "volume": "392", "issue": "4", "pages": "5617-5638" }, { "id": "authors:kvvgy-5r797", "collection": "authors", "collection_id": "kvvgy-5r797", "cite_using_url": "https://authors.library.caltech.edu/records/kvvgy-5r797", "type": "conference_item", "title": "Robust Market Interventions", "book_title": "Proceedings of the 26th ACM Conference on Economics and Computation", "author": [ { "family_name": "Galeotti", "given_name": "Andrea", "orcid": "0000-0002-3071-9767" }, { "family_name": "Golub", "given_name": "Benjamin", "orcid": "0009-0002-6743-8018" }, { "family_name": "Goyal", "given_name": "Sanjeev", "orcid": "0000-0002-9827-5998" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" }, { "family_name": "Talamas", "given_name": "Eduard", "orcid": "0000-0002-9128-0532" } ], "abstract": "We study when interventions can robustly increase market surplus despite imprecise information about economic primitives, in a setting with many strategic firms possessing market power. The key sufficient condition, recoverable structure, requires large-scale product complementarities. The analysis works by decomposing the incidence of interventions in terms of principal components of a Slutsky matrix. Under recoverable structure, a noisy signal of this matrix reveals enough about these principal components to design robust interventions. Our results demonstrate the utility of spectral methods for analyzing imperfectly observed strategic interactions with many agents. We model n strategic firms pricing differentiated products. Consumer demand, a vector of quantities q(p) \u2208 \u211dn demanded at a vector of prices p \u2208 \u211dn, is captured by a Slutsky matrix D (Dij = \u2202qi/\u2202pj). An authority implements per-unit subsidies \u03c3 \u2208 \u211dn with the goal of increasing total surplus, possessing only noisy signals of market primitives: [EQUATION] = D + E and [EQUATION]. The error matrix E has spectral norm bounded by b (n) in expectation, and \u03b5 are i.i.d. An intervention rule maps signals to interventions, and is \u03f5-robust if its chosen intervention achieves a desired property (e.g., surplus increase) with probability \u2265 1 - \u03f5 for any true market state (D, q0) in a pre-specified set \u0398. A property called (M(n), \u03b4)-recoverable structure is sufficient for robust interventions: D has eigenvalues \u03bb\u2113 with |\u03bb\u2113| \u2265 M(n), and the initial quantity vector q0 must have a substantial projection (norm \u2265 \u03b4 > 0) onto the eigenspace \u2112(D, M(n)) of these dominant eigenvectors u\u2113. Economically, such large eigenvalues signify extensive complementarities. The method uses the spectral decomposition of D. Intervention effects are analyzed via eigenvector projections. Our main result assumes that the market has (M(n), \u03b4)-recoverable structure and bounded observational noise: M(n)/b(n) \u2192 \u221e, which requires a high signal-to-noise ratio for dominant eigenvalues. In that case, under some further technical conditions, robust interventions are possible in the following sense. For any target expenditure s > 0, an intervention rule can \u03f5-robustly achieve total surplus (consumer plus producer) increasing by approximately twice the expenditure s on the intervention, while leaving consumers approximately indifferent. The Davis-Kahan theorem allows reliable estimation of \u2112(D, M(n)) from the noisy [EQUATION], and the claimed intervention outcome is achieved by targeting this recovered subspace. This outcome is nearly the maximum possible total surplus gain for the same expenditure, subject to the requirement of not harming consumers. We also exhibit several classes of environments that demonstrate the tightness of our results, e.g., showing that recoverable structure cannot be completely dispensed with. A full version of the paper can be found at https://arxiv.org/abs/2411.03026.", "doi": "10.1145/3736252.3742556", "isbn": "9798400719431", "publisher": "Association for Computing Machinery", "place_of_publication": "New York", "publication_date": "2025-07-02", "pages": "385" }, { "id": "authors:jhp7z-fw809", "collection": "authors", "collection_id": "jhp7z-fw809", "cite_using_url": "https://authors.library.caltech.edu/records/jhp7z-fw809", "type": "conference_item", "title": "The Hazards and Benefits of Condescension in Social Learning", "book_title": "EC '23: Proceedings of the 24th ACM Conference on Economics and Computation", "author": [ { "family_name": "Arieli", "given_name": "Itai", "orcid": "0000-0002-4548-4585" }, { "family_name": "Babichenkoyako", "given_name": "Yakov", "orcid": "0000-0002-6970-1601" }, { "family_name": "M\u00fcller", "given_name": "Stephan", "orcid": "0000-0001-8077-9015" }, { "family_name": "Pourbabaee", "given_name": "Farzad", "orcid": "0000-0001-5259-9690", "clpid": "Pourbabaee-Farzad" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "In a misspecified social learning setting, agents are condescending if they perceive their peers as having private information that is of lower quality than it is in reality. Applying this to a standard sequential model, we show that outcomes improve when agents are mildly condescending. In contrast, too much condescension leads to worse outcomes, as does anti-condescension.
", "doi": "10.1145/3580507.3597752", "isbn": "9798400701047", "publisher": "ACM", "place_of_publication": "New York, NY", "publication_date": "2023-07", "pages": "119" }, { "id": "authors:bxbqn-1de28", "collection": "authors", "collection_id": "bxbqn-1de28", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220707-170550926", "type": "book_section", "title": "Learning in Repeated Interactions on Networks", "book_title": "Proceedings of the 23rd ACM Conference on Economics and Computation", "author": [ { "family_name": "Huang", "given_name": "Wanying", "clpid": "Huang-Wanying" }, { "family_name": "Strack", "given_name": "Philipp", "orcid": "0000-0002-7960-9243", "clpid": "Strack-Philipp" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "We study how long-lived, rational, exponentially discounting agents learn in a social network. In every period, each agent observes the past actions of his neighbors, receives a private signal, and chooses an action with the objective of matching the state. Since agents behave strategically, and since their actions depend on higher order beliefs, it is difficult to characterize equilibrium behavior. Nevertheless, we show that regardless of the size and shape of the network, and the patience of the agents, the equilibrium speed of learning is bounded from above by a constant that only depends on the private signal distribution.", "doi": "10.1145/3490486.3538307", "isbn": "978-1-4503-9150-4", "publisher": "Association for Computing Machinery", "place_of_publication": "New York, NY", "publication_date": "2022-07-11", "pages": "325" }, { "id": "authors:qks6c-x6q46", "collection": "authors", "collection_id": "qks6c-x6q46", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210303-154811036", "type": "book_section", "title": "Monotone Additive Statistics", "book_title": "Proceedings of the 23rd ACM Conference on Economics and Computation", "author": [ { "family_name": "Mu", "given_name": "Xiaosheng", "orcid": "0000-0002-2868-5182", "clpid": "Mu-Xiaosheng" }, { "family_name": "Pomatto", "given_name": "Luciano", "orcid": "0000-0002-4331-8436", "clpid": "Pomatto-L" }, { "family_name": "Strack", "given_name": "Philipp", "orcid": "0000-0002-7960-9243", "clpid": "Strack-Philipp" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "The expectation is an example of a descriptive statistic that is monotone with respect to stochastic dominance, and additive for sums of independent random variables. We provide a complete characterization of such statistics, and explore a number of applications to models of individual and group decision-making. These include a representation of stationary, monotone time preferences, extending the work of Fishburn and Rubinstein (1982) to time lotteries, as well as a characterization of risk-averse preferences over monetary gambles that are invariant to mean-zero background risks.", "doi": "10.1145/3490486.3538318", "isbn": "978-1-4503-9150-4", "publisher": "Association for Computing Machinery", "place_of_publication": "New York, NY", "publication_date": "2022-07-11", "pages": "34" }, { "id": "authors:7pf6j-r2e27", "collection": "authors", "collection_id": "7pf6j-r2e27", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220707-170554297", "type": "book_section", "title": "Private Private Information", "book_title": "Proceedings of the 23rd ACM Conference on Economics and Computation", "author": [ { "family_name": "He", "given_name": "Kevin", "orcid": "0000-0001-5806-0370", "clpid": "He-Kevin" }, { "family_name": "Sandomirskiy", "given_name": "Fedor", "orcid": "0000-0001-9886-3688", "clpid": "Sandomirskiy-Fedor" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "In a private private information structure, agents' signals contain no information about the signals of their peers. We study how informative such structures can be, and characterize those that are on the Pareto frontier, in the sense that it is impossible to give more information to any agent without violating privacy. In our main application, we show how to optimally disclose information about an unknown state under the constraint of not revealing anything about a correlated variable that contains sensitive information.", "doi": "10.1145/3490486.3538348", "isbn": "978-1-4503-9150-4", "publisher": "Association for Computing Machinery", "place_of_publication": "New York, NY", "publication_date": "2022-07-11", "pages": "1145" }, { "id": "authors:5qyvs-abm77", "collection": "authors", "collection_id": "5qyvs-abm77", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220707-170547552", "type": "monograph", "title": "Taxes and Market Power: A Principal Components Approach", "author": [ { "family_name": "Galeotti", "given_name": "Andrea", "orcid": "0000-0002-3071-9767", "clpid": "Galeotti-Andrea" }, { "family_name": "Golub", "given_name": "Benjamin", "clpid": "Golub-Benjamin" }, { "family_name": "Goyal", "given_name": "Sanjeev", "clpid": "Goyal-Sanjeev" }, { "family_name": "Talam\u00e0s", "given_name": "Eduard", "orcid": "0000-0002-9128-0532", "clpid": "Talam\u00e0s-Eduard" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "Suppliers of differentiated goods make simultaneous pricing decisions, which are strategically linked. Because of market power, the equilibrium is inefficient. We study how a policymaker should target a budget-balanced tax-and-subsidy policy to increase welfare. A key tool is a certain basis for the goods space, determined by the network of interactions among suppliers. It consists of eigenbundles -- orthogonal in the sense that a tax on any eigenbundle passes through only to its own price -- with pass-through coefficients determined by associated eigenvalues. Our basis permits a simple characterization of optimal interventions. A planner maximizing consumer surplus should tax eigenbundles with low pass-through and subsidize ones with high pass-through. The Pigouvian leverage of the system -- the gain in consumer surplus achievable by an optimal tax scheme -- depends only on the dispersion of the eigenvalues of the matrix of strategic interactions. We interpret these results in terms of the network structure of the market.", "doi": "10.48550/arXiv.2112.08153", "publisher": "arXiv", "publication_date": "2021-12-15" }, { "id": "authors:gzavk-dpt69", "collection": "authors", "collection_id": "gzavk-dpt69", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200124-084913765", "type": "article", "title": "Additive conjugacy and the Bohr compactification of orthogonal representations", "author": [ { "family_name": "Chase", "given_name": "Zachary", "orcid": "0000-0001-7015-3537", "clpid": "Chase-Zachary" }, { "family_name": "Hann-Caruthers", "given_name": "Wade", "clpid": "Hann-Caruthers-Wade" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "We say that two unitary or orthogonal representations of a finitely generated group G are additive conjugates if they are intertwined by an additive map, which need not be continuous. We associate to each representation of G a topological action that is a complete additive conjugacy invariant: the action of G by group automorphisms on the Bohr compactification of the underlying Hilbert space. Using this construction we show that the property of having almost invariant vectors is an additive conjugacy invariant. As an application we show that G is amenable if and only if there is a nonzero homomorphism from L\u00b2(G) into R/Z that is invariant to the G-action.", "doi": "10.1007/s00208-021-02191-w", "issn": "0025-5831", "publisher": "Springer Verlag", "publication": "Mathematische Annalen", "publication_date": "2021-10", "series_number": "1-2", "volume": "381", "issue": "1-2", "pages": "319-333" }, { "id": "authors:xww49-kn658", "collection": "authors", "collection_id": "xww49-kn658", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210727-175655408", "type": "article", "title": "Feasible Joint Posterior Beliefs", "author": [ { "family_name": "Arieli", "given_name": "Itai", "orcid": "0000-0001-8663-5776", "clpid": "Arieli-Itai" }, { "family_name": "Babichenko", "given_name": "Yakov", "orcid": "0000-0002-6970-1601", "clpid": "Babichenko-Yakov" }, { "family_name": "Sandomirskiy", "given_name": "Fedor", "orcid": "0000-0001-9886-3688", "clpid": "Sandomirskiy-Fedor" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "We study the set of possible joint posterior belief distributions of a group of agents who share a common prior regarding a binary state and who observe some information structure. For two agents, we introduce a quantitative version of Aumann's agreement theorem and show that it is equivalent to a characterization of feasible distributions from a 1995 work by Dawid and colleagues. For any number of agents, we characterize feasible distributions in terms of a \"no-trade\" condition. We use these characterizations to study information structures with independent posteriors. We also study persuasion problems with multiple receivers, exploring the extreme feasible distributions.", "doi": "10.1086/714993", "issn": "0022-3808", "publisher": "University of Chicago Press", "publication": "Journal of Political Economy", "publication_date": "2021-09", "series_number": "9", "volume": "129", "issue": "9", "pages": "2546-2594" }, { "id": "authors:qye4a-re870", "collection": "authors", "collection_id": "qye4a-re870", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220707-170537442", "type": "monograph", "title": "Information Cascades and Social Learning", "author": [ { "family_name": "Bikhchandani", "given_name": "Sushil", "orcid": "0000-0003-0554-072X", "clpid": "Bikhchandani-Sushil" }, { "family_name": "Hirshleifer", "given_name": "David", "orcid": "0000-0003-0280-8882", "clpid": "Hirshleifer-David" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" }, { "family_name": "Welch", "given_name": "Ivo", "orcid": "0000-0002-4347-7250", "clpid": "Welch-Ivo" } ], "abstract": "We review the theory of information cascades and social learning. Our goal is to describe in a relatively integrated and accessible way the more important themes, insights and applications of the literature as it has developed over the last thirty years. We also highlight open questions and promising directions for further theoretical and empirical exploration.", "doi": "10.48550/arXiv.2105.11044", "publisher": "arXiv", "publication_date": "2021-05-23" }, { "id": "authors:54q7t-dfp96", "collection": "authors", "collection_id": "54q7t-dfp96", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210414-131421263", "type": "article", "title": "Equitable Voting Rules", "author": [ { "family_name": "Bartholdi", "given_name": "Laurent", "clpid": "Bartholdi-Laurent" }, { "family_name": "Hann-Caruthers", "given_name": "Wade", "clpid": "Hann-Caruthers-Wade" }, { "family_name": "Josyula", "given_name": "Maya", "clpid": "Josyula-Maya" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" }, { "family_name": "Yariv", "given_name": "Leeat", "clpid": "Yariv-L" } ], "abstract": "May's theorem (1952), a celebrated result in social choice, provides the foundation for majority rule. May's crucial assumption of symmetry, often thought of as a procedural equity requirement, is violated by many choice procedures that grant voters identical roles. We show that a weakening of May's symmetry assumption allows for a far richer set of rules that still treat voters equally. We show that such rules can have minimal winning coalitions comprising a vanishing fraction of the population, but not less than the square root of the population size. Methodologically, we introduce techniques from group theory and illustrate their usefulness for the analysis of social choice questions.", "doi": "10.3982/ecta17032", "issn": "0012-9682", "publisher": "Blackwell Publishing", "publication": "Econometrica", "publication_date": "2021-03-15", "series_number": "2", "volume": "89", "issue": "2", "pages": "563-589" }, { "id": "authors:c9dkm-rs921", "collection": "authors", "collection_id": "c9dkm-rs921", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161111-135545798", "type": "article", "title": "Rational Groupthink", "author": [ { "family_name": "Harel", "given_name": "Matan", "clpid": "Harel-Matan" }, { "family_name": "Mossel", "given_name": "Elchanan", "orcid": "0000-0001-7812-7886", "clpid": "Mossel-Elchanan" }, { "family_name": "Strack", "given_name": "Philipp", "orcid": "0000-0002-7960-9243", "clpid": "Strack-Philipp" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "We study how long-lived rational agents learn from repeatedly observing a private signal and each others' actions. With normal signals, a group of any size learns more slowly than just four agents who directly observe each others' private signals in each period. Similar results apply to general signal structures. We identify rational groupthink\u2014in which agents ignore their private signals and choose the same action for long periods of time\u2014as the cause of this failure of information aggregation.", "doi": "10.1093/qje/qjaa026", "issn": "0033-5533", "publisher": "Oxford University Press", "publication": "Quarterly Journal of Economics", "publication_date": "2021-02", "series_number": "1", "volume": "136", "issue": "1", "pages": "621-668" }, { "id": "authors:x70d0-23195", "collection": "authors", "collection_id": "x70d0-23195", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200124-080643011", "type": "article", "title": "From Blackwell Dominance in Large Samples to R\u00e9nyi Divergences and Back Again", "author": [ { "family_name": "Mu", "given_name": "Xiaosheng", "orcid": "0000-0002-2868-5182", "clpid": "Mu-Xiaosheng" }, { "family_name": "Pomatto", "given_name": "Luciano", "orcid": "0000-0002-4331-8436", "clpid": "Pomatto-L" }, { "family_name": "Strack", "given_name": "Philipp", "clpid": "Strack-Philipp" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "We study repeated independent Blackwell experiments; standard examples include drawing multiple samples from a population, or performing a measurement in different locations. In the baseline setting of a binary state of nature, we compare experiments in terms of their informativeness in large samples. Addressing a question due to Blackwell (1951), we show that generically an experiment is more informative than another in large samples if and only if it has higher R\u00e9nyi divergences.", "doi": "10.3982/ECTA17548", "issn": "1468-0262", "publisher": "Econometric Society", "publication": "Econometrica", "publication_date": "2021-01", "series_number": "1", "volume": "89", "issue": "1", "pages": "475-506" }, { "id": "authors:6590x-xqw57", "collection": "authors", "collection_id": "6590x-xqw57", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190628-075628753", "type": "article", "title": "Repeated Coordination with Private Learning", "author": [ { "family_name": "Basu", "given_name": "Pathikrit", "clpid": "Basu-Pathikrit" }, { "family_name": "Chatterjee", "given_name": "Kalyan", "clpid": "Chatterjee-Kalyan" }, { "family_name": "Hoshino", "given_name": "Tetsuya", "clpid": "Hoshino-Tetsuya" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "We study a repeated game with payoff externalities and observable actions where two players receive information over time about an underlying payoff-relevant state, and strategically coordinate their actions. Players learn about the true state from private signals, as well as the actions of others. They commonly learn the true state (Cripps et al., 2008), but do not coordinate in every equilibrium. We show that there exist stable equilibria in which players can overcome unfavorable signal realizations and eventually coordinate on the correct action, for any discount factor. For high discount factors, we show that in addition players can also achieve efficient payoffs.", "doi": "10.1016/j.jet.2020.105106", "issn": "0022-0531", "publisher": "Elsevier", "publication": "Journal of Economic Theory", "publication_date": "2020-11", "volume": "190", "pages": "Art. No. 105106" }, { "id": "authors:2wy8c-yg798", "collection": "authors", "collection_id": "2wy8c-yg798", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210303-154333226", "type": "monograph", "title": "Background Risk and Small-Stakes Risk Aversion", "author": [ { "family_name": "Mu", "given_name": "Xiaosheng", "orcid": "0000-0002-2868-5182", "clpid": "Mu-Xiaosheng" }, { "family_name": "Pomatto", "given_name": "Luciano", "orcid": "0000-0002-4331-8436", "clpid": "Pomatto-L" }, { "family_name": "Strack", "given_name": "Philipp", "orcid": "0000-0002-7960-9243", "clpid": "Strack-Philipp" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "We show that under plausible levels of background risk, no theory of choice under risk---such as expected utility theory, prospect theory, or rank dependent utility---can simultaneously satisfy the following three economic postulates: (i) Decision makers are risk-averse over small gambles, (ii) they respect stochastic dominance, and (iii) they account for background risk.", "doi": "10.48550/arXiv.2010.08033", "publisher": "arXiv", "publication_date": "2020-10-15" }, { "id": "authors:ya229-k3e62", "collection": "authors", "collection_id": "ya229-k3e62", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200124-090354536", "type": "article", "title": "Unfriendly colorings of graphs with finite average degree", "author": [ { "family_name": "Conley", "given_name": "Clinton T.", "clpid": "Conley-C-T" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "In an unfriendly coloring of a graph the color of every node mismatches that of the majority of its neighbors. We show that every probability measure preserving Borel graph with finite average degree admits a Borel unfriendly coloring almost everywhere. We also show that every bounded degree Borel graph of subexponential growth admits a Borel unfriendly coloring.", "doi": "10.1112/plms.12345", "issn": "0024-6115", "publisher": "London Mathematical Society", "publication": "Proceedings of the London Mathematical Society", "publication_date": "2020-10", "series_number": "4", "volume": "121", "issue": "4", "pages": "828-832" }, { "id": "authors:r0r4n-zhw14", "collection": "authors", "collection_id": "r0r4n-zhw14", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200615-155012317", "type": "book_section", "title": "Feasible Joint Posterior Beliefs", "book_title": "Proceedings of the 21st ACM Conference on Economics and Computation", "author": [ { "family_name": "Arieli", "given_name": "Itai", "orcid": "0000-0001-8663-5776", "clpid": "Arieli-Itai" }, { "family_name": "Babichenko", "given_name": "Yakov", "orcid": "0000-0002-6970-1601", "clpid": "Babichenko-Yakov" }, { "family_name": "Sandomirskiy", "given_name": "Fedor", "orcid": "0000-0001-9886-3688", "clpid": "Sandomirskiy-Fedor" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "We study the set of possible joint posterior belief distributions of a group of agents who share a common prior regarding a binary state and who observe some information structure. Our main result is that, for the two agent case, a quantitative version of Aumann's Agreement Theorem provides a necessary and sufficient condition for feasibility. For any number of agents, a related \"no trade\" condition likewise provides a characterization of feasibility. We use our characterization to construct joint belief distributions in which agents are informed regarding the state, and yet receive no information regarding the other's posterior. We study a related class of Bayesian persuasion problems with a single sender and multiple receivers, and explore the extreme points of the set of feasible distributions.", "doi": "10.1145/3391403.3399505", "isbn": "978-1-4503-7975-5", "publisher": "Association for Computing Machinery", "place_of_publication": "New York, NY", "publication_date": "2020-07", "pages": "643" }, { "id": "authors:m9xak-tca52", "collection": "authors", "collection_id": "m9xak-tca52", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190405-101226198", "type": "article", "title": "Stochastic Dominance Under Independent Noise", "author": [ { "family_name": "Pomatto", "given_name": "Luciano", "orcid": "0000-0002-4331-8436", "clpid": "Pomatto-L" }, { "family_name": "Strack", "given_name": "Philipp", "clpid": "Strack-P" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "Stochastic dominance is a crucial tool for the analysis of choice under risk. It is typically analyzed as a property of two gambles that are taken in isolation. We study how additional independent sources of risk (e.g., uninsurable labor risk, house price risk) can affect the ordering of gambles. We show that, perhaps surprisingly, background risk can be strong enough to render lotteries that are ranked by their expectation ranked in terms of first-order stochastic dominance. We extend our results to second-order stochastic dominance and show how they lead to a novel and elementary axiomatization of mean-variance preferences.", "doi": "10.1086/705555", "issn": "0022-3808", "publisher": "University of Chicago Press", "publication": "Journal of Political Economy", "publication_date": "2020-05", "series_number": "5", "volume": "128", "issue": "5", "pages": "1877-1900" }, { "id": "authors:yz2f6-maw09", "collection": "authors", "collection_id": "yz2f6-maw09", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200521-152747894", "type": "article", "title": "Social Learning Equilibria", "author": [ { "family_name": "Mossel", "given_name": "Elchanan", "orcid": "0000-0001-7812-7886", "clpid": "Mossel-E" }, { "family_name": "Mueller-Frank", "given_name": "Manuel", "clpid": "Mueller-Frank-M" }, { "family_name": "Sly", "given_name": "Allan", "clpid": "Sly-A" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "We consider a large class of social learning models in which a group of agents face uncertainty regarding a state of the world, share the same utility function, observe private signals, and interact in a general dynamic setting. We introduce social learning equilibria, a static equilibrium concept that abstracts away from the details of the given extensive form, but nevertheless captures the corresponding asymptotic equilibrium behavior. We establish general conditions for agreement, herding, and information aggregation in equilibrium, highlighting a connection between agreement and information aggregation.", "doi": "10.3982/ecta16465", "issn": "0012-9682", "publisher": "Econometric Society", "publication": "Econometrica", "publication_date": "2020-05", "series_number": "3", "volume": "88", "issue": "3", "pages": "1235-1267" }, { "id": "authors:nm5e3-25081", "collection": "authors", "collection_id": "nm5e3-25081", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170712-084843331", "type": "article", "title": "Invariant random subgroups of semidirect products", "author": [ { "family_name": "Biringer", "given_name": "Ian", "clpid": "Biringer-I" }, { "family_name": "Bowen", "given_name": "Lewis", "clpid": "Bowen-L" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "We study invariant random subgroups (IRSs) of semidirect products G=A\u22ca\u0393. In particular, we characterize all IRSs of parabolic subgroups of SL_d(R), and show that all ergodic IRSs of R^d\u22caSL_d(R) are either of the form R^d\u22caK for some IRS of SL_d(R), or are induced from IRSs of \u039b\u22caSL(\u039b), where \u039b", "doi": "10.1017/etds.2018.46", "issn": "0143-3857", "publisher": "Cambridge University Press", "publication": "Ergodic Theory and Dynamical Systems", "publication_date": "2020-02", "series_number": "2", "volume": "40", "issue": "2", "pages": "353-366" }, { "id": "authors:z89d1-ffk59", "collection": "authors", "collection_id": "z89d1-ffk59", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200123-105749369", "type": "monograph", "title": "There are no monotone homomorphisms out of the convolution semigroup", "author": [ { "family_name": "Fritz", "given_name": "Tobias", "clpid": "Fritz-Tobias" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "We prove that there is no nonzero way of assigning real numbers to probability measures on R in a way which is monotone under first-order stochastic dominance and additive under convolution.", "doi": "10.48550/arXiv.1912.01733", "publisher": "arXiv", "publication_date": "2019-12-03" }, { "id": "authors:1f0pv-rf491", "collection": "authors", "collection_id": "1f0pv-rf491", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20191114-102021413", "type": "article", "title": "Strong amenability and the infinite conjugacy class property", "author": [ { "family_name": "Frisch", "given_name": "Joshua", "clpid": "Frisch-J" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" }, { "family_name": "Vahidi Ferdowsi", "given_name": "Pooya", "clpid": "Vahidi-Ferdowsi-P" } ], "abstract": "A group is said to be strongly amenable if each of its proximal topological actions has a fixed point. We show that a finitely generated group is strongly amenable if and only if it is virtually nilpotent. More generally, a countable discrete group is strongly amenable if and only if none of its quotients have the infinite conjugacy class property.", "doi": "10.1007/s00222-019-00896-z", "issn": "0020-9910", "publisher": "Springer", "publication": "Inventiones Mathematicae", "publication_date": "2019-12", "series_number": "3", "volume": "218", "issue": "3", "pages": "833-851" }, { "id": "authors:2rh1h-48t12", "collection": "authors", "collection_id": "2rh1h-48t12", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200615-160518971", "type": "monograph", "title": "Characteristic measures of symbolic dynamical systems", "author": [ { "family_name": "Frisch", "given_name": "Joshua", "clpid": "Frisch-J" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "A probability measure is a characteristic measure of a topological dynamical system if it is invariant to the automorphism group of the system. We show that zero entropy shifts always admit characteristic measures. We use similar techniques to show that automorphism groups of minimal zero entropy shifts are sofic.", "doi": "10.48550/arXiv.1908.02930", "publisher": "arXiv", "publication_date": "2019-08-08" }, { "id": "authors:t636j-2fq90", "collection": "authors", "collection_id": "t636j-2fq90", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190725-090144871", "type": "article", "title": "Choquet-Deny groups and the infinite conjugacy class property", "author": [ { "family_name": "Frisch", "given_name": "Joshua", "clpid": "Frisch-J" }, { "family_name": "Hartman", "given_name": "Yair", "clpid": "Hartman-Y" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" }, { "family_name": "Vahidi Ferdowsi", "given_name": "Pooya", "clpid": "Vahidi-Ferdowsi-P" } ], "abstract": "A countable discrete group G is called Choquet-Deny if for every non-degenerate probability measure \u03bc on G, it holds that all bounded \u03bc-harmonic functions are constant. We show that a finitely generated group G is Choquet-Deny if and only if it is virtually nilpotent. For general countable discrete groups, we show that G is Choquet-Deny if and only if none of its quotients has the infinite conjugacy class property. Moreover, when G is not Choquet-Deny, then this is witnessed by a symmetric, finite entropy, non-degenerate measure.", "doi": "10.4007/annals.2019.190.1.5", "issn": "0003-486X", "publisher": "Princeton University", "publication": "Annals of Mathematics", "publication_date": "2019-07", "series_number": "1", "volume": "190", "issue": "1", "pages": "307-320" }, { "id": "authors:8mk1w-9ze73", "collection": "authors", "collection_id": "8mk1w-9ze73", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190625-114737785", "type": "book_section", "title": "Equitable Voting Rules", "book_title": "Proceedings of the 2019 ACM Conference on Economics and Computation", "author": [ { "family_name": "Bartholdi", "given_name": "Laurent", "clpid": "Bartholdi-L" }, { "family_name": "Hann-Caruthers", "given_name": "Wade", "clpid": "Hann-Caruthers-W" }, { "family_name": "Josyula", "given_name": "Maya", "clpid": "Josyula-M" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" }, { "family_name": "Yariv", "given_name": "Leeat", "clpid": "Yariv-L" } ], "abstract": "A celebrated result in social choice is May's Theorem (1952), providing the foundation for majority rule. May's crucial assumption of symmetry, often thought of as a procedural equity requirement, is violated by many choice procedures that grant voters identical roles. We show that a modification of May's symmetry assumption allows for a far richer set of rules that still treat voters equally, but have minimal winning coalitions comprising a vanishing fraction of the population. We conclude that procedural fairness can coexist with the empowerment of a small minority of individuals. Methodologically, we introduce techniques from discrete mathematics and illustrate their usefulness for the analysis of social choice questions.", "doi": "10.1145/3328526.3329551", "isbn": "978-1-4503-6792-9", "publisher": "Association for Computing Machinery", "place_of_publication": "New York, NY", "publication_date": "2019-06", "pages": "315" }, { "id": "authors:dkhn3-n3274", "collection": "authors", "collection_id": "dkhn3-n3274", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161111-133444186", "type": "article", "title": "Normal amenable subgroups of the automorphism group of the full shift", "author": [ { "family_name": "Frisch", "given_name": "Joshua", "clpid": "Frisch-J" }, { "family_name": "Schlank", "given_name": "Tomer", "clpid": "Schlank-T" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "We show that every normal amenable subgroup of the automorphism group of the full shift is contained in its center. This follows from the analysis of this group's Furstenberg topological boundary, through the construction of a minimal and strongly proximal action. We extend this result to higher dimensional full shifts. This also provides a new proof of Ryan's theorem and of the fact that these groups contain free groups.", "doi": "10.1017/etds.2017.72", "issn": "0143-3857", "publisher": "Cambridge University Press", "publication": "Ergodic Theory and Dynamical Systems", "publication_date": "2019-05", "series_number": "5", "volume": "39", "issue": "5", "pages": "1290-1298" }, { "id": "authors:5edh3-kv125", "collection": "authors", "collection_id": "5edh3-kv125", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161111-131006027", "type": "article", "title": "Thompson's group F is not strongly amenable", "author": [ { "family_name": "Hartman", "given_name": "Yair", "clpid": "Hartman-Y" }, { "family_name": "Juschenko", "given_name": "Kate", "clpid": "Juschenko-K" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" }, { "family_name": "Vahidi Ferdowsi", "given_name": "Pooya", "clpid": "Vahidi-Ferdowsi-P" } ], "abstract": "We show that Thompson's group has a topological action on a compact metric space that is proximal and has no fixed points.", "doi": "10.1017/etds.2017.49", "issn": "0143-3857", "publisher": "Cambridge University Press", "publication": "Ergodic Theory and Dynamical Systems", "publication_date": "2019-04", "series_number": "4", "volume": "39", "issue": "4", "pages": "925-929" }, { "id": "authors:hr7ja-y2861", "collection": "authors", "collection_id": "hr7ja-y2861", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200124-085648355", "type": "monograph", "title": "On the spectrum of asymptotic entropies of random walks", "author": [ { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" }, { "family_name": "Zheng", "given_name": "Tianyi", "clpid": "Zheng-Tianyi" } ], "abstract": "Given a random walk on a free group, we study the random walks it induces on the group's quotients. We show that the spectrum of asymptotic entropies of the induced random walks has no isolated points, except perhaps its maximum.", "doi": "10.48550/arXiv.1903.01312", "publisher": "arXiv", "publication_date": "2019-03-04" }, { "id": "authors:yrhbn-2yz42", "collection": "authors", "collection_id": "yrhbn-2yz42", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190404-161816718", "type": "publication_workingpaper", "title": "The cost of information", "author": [ { "family_name": "Pomatto", "given_name": "Luciano", "orcid": "0000-0002-4331-8436", "clpid": "Pomatto-L" }, { "family_name": "Strack", "given_name": "Philipp", "clpid": "Strack-P" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "We develop an axiomatic theory of information acquisition that captures the idea of constant marginal costs in information production: the cost of generating two independent signals is the sum of their costs, and generating a signal with probability half costs half its original cost. Together with a monotonicity and a continuity conditions, these axioms determine the cost of a signal up to a vector of parameters. These parameters have a clear economic interpretation and determine the difficulty of distinguishing states. We argue that this cost function is a versatile modeling tool that leads to more realistic predictions than mutual information.", "doi": "10.48550/arXiv.1812.04211", "publication_date": "2019-02-04" }, { "id": "authors:s2z9p-cek47", "collection": "authors", "collection_id": "s2z9p-cek47", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181126-153354872", "type": "book_section", "title": "A Deterministic Protocol for Sequential Asymptotic Learning", "book_title": "2018 IEEE International Symposium on Information Theory (ISIT)", "author": [ { "family_name": "Cheng", "given_name": "Yu", "clpid": "Cheng-Yu" }, { "family_name": "Hann-Caruthers", "given_name": "Wade", "clpid": "Hann-Caruthers-W" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "In the classic herding model, agents receive private signals about an underlying binary state of nature, and act sequentially to choose one of two possible actions, after observing the actions of their predecessors. We investigate what types of behaviors lead to asymptotic learning, where agents will eventually converge to the right action in probability. It is known that for rational agents and bounded signals, there will not be asymptotic learning. Does it help if the agents can be cooperative rather than act selfishly? This is simple to achieve if the agents are allowed to use randomized protocols. In this paper, we provide the first deterministic protocol under which asymptotic learning occurs. In addition, our protocol has the advantage of being much simpler than previous protocols.", "doi": "10.1109/ISIT.2018.8437859", "isbn": "978-1-5386-4780-6", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2018-06", "pages": "1735-1738" }, { "id": "authors:ays2h-xav26", "collection": "authors", "collection_id": "ays2h-xav26", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161111-104138106", "type": "book_section", "title": "Social Learning Equilibria", "book_title": "Proceedings of the 2018 ACM Conference on Economics and Computation", "author": [ { "family_name": "Mossel", "given_name": "Elchanan", "orcid": "0000-0001-7812-7886", "clpid": "Mossel-E" }, { "family_name": "Mueller-Frank", "given_name": "Manuel", "clpid": "Mueller-Frank-M" }, { "family_name": "Sly", "given_name": "Allan", "clpid": "Sly-A" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "We consider social learning settings in which a group of agents face uncertainty regarding a state of the world, observe private signals, share the same utility function, and act in a general dynamic setting. We introduce Social Learning Equilibria, a static equilibrium concept that abstracts away from the details of the given dynamics, but nevertheless captures the corresponding asymptotic equilibrium behavior. We establish strong equilibrium properties on agreement, herding, and information aggregation.", "doi": "10.1145/3219166.3219207", "isbn": "978-1-4503-5829-3", "publisher": "Association for Computing Machinery", "place_of_publication": "New York, NY", "publication_date": "2018-06", "pages": "639" }, { "id": "authors:899h4-y2s31", "collection": "authors", "collection_id": "899h4-y2s31", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20191010-132749128", "type": "book_section", "title": "Non-Exploitable Protocols for Repeated Cake Cutting", "author": [ { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" }, { "family_name": "Vardi", "given_name": "Shai", "clpid": "Vardi-S" }, { "family_name": "Ziani", "given_name": "Juba", "orcid": "0000-0002-3324-4349", "clpid": "Ziani-Juba" } ], "abstract": "We introduce the notion of exploitability in cut-and-choose protocols for repeated cake cutting. If a cut-and-choose protocol is repeated, the cutter can possibly gain information about the chooser from her previous actions, and exploit this information for her own gain, at the expense of the chooser. We define a generalization of cut-and-choose protocols - forced-cut protocols - in which some cuts are made exogenously while others are made by the cutter, and show that there exist non-exploitable forced-cut protocols that use a small number of cuts per day: When the cake has at least as many dimensions as days, we show a protocol that uses a single cut per day. When the cake is 1-dimensional, we show an adaptive non-exploitable protocol that uses 3 cuts per day, and a non-adaptive protocol that uses n cuts per day (where n is the number of days). In contrast, we show that no non-adaptive non-exploitable forced-cut protocol can use a constant number of cuts per day. Finally, we show that if the cake is at least 2-dimensional, there is a non-adaptive non-exploitable protocol that uses 3 cuts per day.", "publisher": "Association for the Advancement of Artificial Intelligence", "publication_date": "2018-02" }, { "id": "authors:tgbga-5zw88", "collection": "authors", "collection_id": "tgbga-5zw88", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170712-081145954", "type": "article", "title": "The speed of sequential asymptotic learning", "author": [ { "family_name": "Hann-Caruthers", "given_name": "Wade", "clpid": "Hann-Caruthers-W" }, { "family_name": "Martynov", "given_name": "Vadim V.", "clpid": "Martynov-V-V" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "In the classical herding literature, agents receive a private signal regarding a binary state of nature, and sequentially choose an action, after observing the actions of their predecessors. When the informativeness of private signals is unbounded, it is known that agents converge to the correct action and correct belief. We study how quickly convergence occurs, and show that it happens more slowly than it does when agents observe signals. However, we also show that the speed of learning from actions can be arbitrarily close to the speed of learning from signals. In particular, the expected time until the agents stop taking the wrong action can be either finite or infinite, depending on the private signal distribution. In the canonical case of Gaussian private signals we calculate the speed of convergence precisely, and show explicitly that, in this case, learning from actions is significantly slower than learning from signals.", "doi": "10.1016/j.jet.2017.11.009", "issn": "0022-0531", "publisher": "Elsevier", "publication": "Journal of Economic Theory", "publication_date": "2018-01", "volume": "173", "pages": "383-409" }, { "id": "authors:x2458-79e56", "collection": "authors", "collection_id": "x2458-79e56", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180410-145958889", "type": "book_section", "title": "Quasi-regular sequences and optimal schedules for security games", "book_title": "Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms", "author": [ { "family_name": "Kempe", "given_name": "David", "clpid": "Kempe-D" }, { "family_name": "Schulman", "given_name": "Leonard J.", "orcid": "0000-0001-9901-2797", "clpid": "Schulman-L-J" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "contributor": [ { "family_name": "Czumaj", "given_name": "Artur", "clpid": "Czumaj-A" } ], "abstract": "We study security games in which a defender commits to a mixed strategy for protecting a finite set of targets of different values. An attacker, knowing the defender's strategy, chooses which target to attack and for how long. If the attacker spends time t at a target i of value \u03b1_i, and if he leaves before the defender visits the target, his utility is t \u00b7 \u03b1_i; if the defender visits before he leaves, his utility is 0. The defender's goal is to minimize the attacker's utility. The defender's strategy consists of a schedule for visiting the targets; it takes her unit time to switch between targets. Such games are a simplified model of a number of real-world scenarios such as protecting computer networks from intruders, crops from thieves, etc.\n\nWe show that optimal defender play for such security games, although played in continuous time, reduces to the solution of a combinatorial question regarding the existence of infinite sequences over a finite alphabet, with the following properties for each symbol i: (1) i constitutes a prescribed limiting fraction p_i of the sequence. (2) The occurrences of i are spread apart close to evenly, in that the ratio of the longest to shortest interval between consecutive occurrences is bounded by a parameter K. We call such sequences K-quasi-regular; a 1-quasi-regular sequence is one in which the occurrences of each symbol form an arithmetic sequence. \n\nAs we show, a 1-quasi-regular sequence ensures an optimal defender strategy for these security games: the intuition for this fact lies in the famous \"inspection paradox.\" However, as we demonstrate, for K < 2 and general p_i, K-quasi-regular sequences may not exist. Fortunately, this does not turn out to be an obstruction: we show that, surprisingly, 2-quasi-regular sequences also suffice for optimal defender play. What is more, even randomized 2-quasi-regular sequences suffice for optimality. We show that such sequences always exist, and can be calculated efficiently. Thus, we can ensure optimal defender play for these security games. \n\nThe question of the least K for which deterministic K-quasi-regular sequences exist is fascinating. Using an ergodic theoretical approach, we proceed to show that deterministic 3-quasi-regular sequences always exist (and can be calculated efficiently). We also show that these deterministic 3-regular sequences give rise to a \u2248 1.006-approximation algorithm for the defender's optimal strategy. For 2 \u2264 K < 3 we do not know whether deterministic K-quasi-regular sequences always exist; however, when the pi are all small, improved bounds are possible, and in fact, (1 + \u220a)-quasi-regular deterministic sequences exist for any \u220a > 0 for sufficiently small p_i.", "doi": "10.1137/1.9781611975031.106", "isbn": "978-1-6119-7503-1", "publisher": "Society for Industrial and Applied Mathematics", "place_of_publication": "Philadelphia, PA", "publication_date": "2018-01", "pages": "1625-1644" }, { "id": "authors:2wjwa-cq465", "collection": "authors", "collection_id": "2wjwa-cq465", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161114-092928470", "type": "article", "title": "Generic Stationary Measures and Actions", "author": [ { "family_name": "Bowen", "given_name": "Lewis", "clpid": "Bowen-L" }, { "family_name": "Hartman", "given_name": "Yair", "clpid": "Hartman-Y" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "Let G be a countably infinite group, and let \u03bc be a generating probability measure on G. We study the space of \u03bc-stationary Borel probability measures on a topological G space, and in particular on Z^G, where Z is any perfect Polish space. We also study the space of \u03bc-stationary, measurable G-actions on a standard, nonatomic probability space.\nEquip the space of stationary measures with the weak* topology. When \u03bc has finite entropy, we show that a generic measure is an essentially free extension of the Poisson boundary of (G, \u03bc). When Z is compact, this implies that the simplex of \u03bc-stationary \nmeasures on Z^G is a Poulsen simplex. We show that this is also the case for the simplex of stationary measures on {0, 1}^G.\nWe furthermore show that if the action of G on its Poisson boundary is essentially free then a generic measure is isomorphic to the Poisson boundary. \nNext, we consider the space of stationary actions, equipped with a standard topology known as the weak topology. Here we show that when G has property (T), the \nergodic actions are meager. We also construct a group G without property (T) such that the ergodic actions are not dense, for some \u03bc.\nFinally, for a weaker topology on the set of actions, which we call the very weak topology, we show that a dynamical property (e.g., ergodicity) is topologically generic if and only if it is generic in the space of measures. There we also show a Glasner-King type 0-1 law stating that every dynamical property is either meager or residual.", "doi": "10.1090/tran/6803", "issn": "0002-9947", "publisher": "American Mathematical Society", "publication": "Transactions of the American Mathematical Society", "publication_date": "2017-07", "series_number": "7", "volume": "369", "issue": "7", "pages": "4889-4929" }, { "id": "authors:tw0pb-nsv65", "collection": "authors", "collection_id": "tw0pb-nsv65", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161111-150254761", "type": "article", "title": "Opinion Exchange Dynamics", "author": [ { "family_name": "Mossel", "given_name": "Elchanan", "orcid": "0000-0001-7812-7886", "clpid": "Mossel-E" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "The exchange of opinions between individuals is a fundamental social interaction that plays a role in nearly any social, political and economic process. While it is unlikely that a simple mathematical model can accurately describe the exchange of opinions between two people, one could hope to gain some insights on emergent phenomena that affect large groups of people.", "doi": "10.1214/14-PS230", "issn": "1549-5787", "publisher": "Institute of Mathematical Statistics", "publication": "Probability Surveys", "publication_date": "2017-06-27", "volume": "14", "pages": "155-204" }, { "id": "authors:njjv8-zag17", "collection": "authors", "collection_id": "njjv8-zag17", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200124-092403035", "type": "monograph", "title": "Invariant random subgroups of semidirect products", "author": [ { "family_name": "Biringer", "given_name": "Ian", "clpid": "Biringer-I" }, { "family_name": "Bowen", "given_name": "Lewis", "clpid": "Bowen-L" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "We study invariant random subgroups (IRSs) of semidirect products G = A\u22ca\u0393. In particular, we characterize all IRSs of parabolic subgroups of SL_d(R), and show that all ergodic IRSs of R^d\u22caSL_d(R) are either of the form R^d\u22caK for some IRS of SL_d(R), or are induced from IRSs of \u039b\u22caSL(\u039b), where \u039b < R^d is a lattice.", "doi": "10.48550/arXiv.1703.01282", "publisher": "arXiv", "publication_date": "2017-03-03" }, { "id": "authors:2bwkj-kyf78", "collection": "authors", "collection_id": "2bwkj-kyf78", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161111-145903029", "type": "article", "title": "Unimodularity of Invariant Random Subgroups", "author": [ { "family_name": "Biringer", "given_name": "Ian", "clpid": "Biringer-I" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "An invariant random subgroup H\u2264G is a random closed subgroup whose law is invariant to conjugation by all elements of G. When G is locally compact and second countable, we show that for every invariant random subgroup H\u2264G there almost surely exists an invariant measure on G/H. Equivalently, the modular function of H is almost surely equal to the modular function of G, restricted to H. \n\nWe use this result to construct invariant measures on orbit equivalence relations of measure preserving actions. Additionally, we prove a mass transport principle for discrete or compact invariant random subgroups.", "doi": "10.1090/tran/6755", "issn": "0002-9947", "publisher": "American Mathematical Society", "publication": "Transactions of the American Mathematical Society", "publication_date": "2016-10-28", "volume": "369", "pages": "4043-4061" }, { "id": "authors:qpymd-ajt43", "collection": "authors", "collection_id": "qpymd-ajt43", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161109-132848541", "type": "article", "title": "Stabilizer rigidity in irreducible group actions", "author": [ { "family_name": "Hartman", "given_name": "Yair", "clpid": "Hartman-Y" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "We consider irreducible actions of locally compact product groups, and of higher rank semi-simple Lie groups. Using the intermediate factor theorems of Bader\u2013Shalom and Nevo\u2013Zimmer, we show that the action stabilizers, and all irreducible invariant random subgroups, are co-amenable in their normal closure. As a consequence, we derive rigidity results on irreducible actions that generalize and strengthen the results of Bader\u2013Shalom and Stuck\u2013Zimmer.", "doi": "10.1007/s11856-016-1424-4", "issn": "0021-2172", "publisher": "Springer", "publication": "Israel Journal of Mathematics", "publication_date": "2016-10", "series_number": "2", "volume": "216", "issue": "2", "pages": "679-705" }, { "id": "authors:sg4gy-p6629", "collection": "authors", "collection_id": "sg4gy-p6629", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161110-074103834", "type": "book_section", "title": "Efficient Bayesian Learning in Social Networks with Gaussian Estimators", "book_title": "54th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2016", "author": [ { "family_name": "Mossel", "given_name": "Elchanan", "orcid": "0000-0001-7812-7886", "clpid": "Mossel-E" }, { "family_name": "Olsman", "given_name": "Noah", "orcid": "0000-0002-4351-3880", "clpid": "Olsman-N" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "We consider a group of Bayesian agents who try to estimate a state of the world \u03b8 through interaction on a social\nnetwork. Each agent v initially receives a private measurement of \u03b8: a number S_v picked from a Gaussian distribution with mean \u03b8 and standard deviation one. Then, in each discrete time iteration, each reveals its estimate of \u03b8 to its neighbors, and, observing its neighbors' actions, updates its belief using Bayes' Law. This process aggregates information efficiently, in the sense that all the agents converge to the belief that they would have,\nhad they access to all the private measurements. We show that this process is computationally efficient, so that each agent's calculation can be easily carried out. We also show that on any graph the process converges after at most 2N \u00b7 D steps, where N is the number of agents and D is the diameter of the network. Finally, we show that on trees and on distance transitive-graphs the process converges after D steps, and that it preserves privacy, so that agents learn very little about the private signal of most other agents, despite the efficient aggregation of information. Our results extend those in an unpublished manuscript of the first and last authors.", "doi": "10.1109/ALLERTON.2016.7852341", "isbn": "978-1-5090-4551-8", "publisher": "IEEE", "place_of_publication": "Piscataway, NJ", "publication_date": "2016-09-30", "pages": "425-432" }, { "id": "authors:4ps3z-8tg56", "collection": "authors", "collection_id": "4ps3z-8tg56", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160603-083016959", "type": "article", "title": "Graphical potential games", "author": [ { "family_name": "Babichenko", "given_name": "Yakov", "clpid": "Babichenko-Y" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "We study the class of potential games that are also graphical games with respect to a given graph G of connections between the players. We show that, up to strategic equivalence, this class of games can be identified with the set of Markov random fields on G. From this characterization, and from the Hammersley\u2013Clifford theorem, it follows that the potentials of such games can be decomposed into local potentials.", "doi": "10.1016/j.jet.2016.03.010", "issn": "0022-0531", "publisher": "Elsevier", "publication": "Journal of Economic Theory", "publication_date": "2016-05", "volume": "163", "pages": "889-899" }, { "id": "authors:3xbk1-zwt83", "collection": "authors", "collection_id": "3xbk1-zwt83", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161111-141028249", "type": "article", "title": "Transitive graphs uniquely determined by their local structure", "author": [ { "family_name": "Frisch", "given_name": "Joshua", "clpid": "Frisch-J" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "We give an example of an infinite, vertex transitive graph that has the following property: it is the unique completion to a transitive graph of a large enough finite subgraph of itself.", "doi": "10.1090/proc/12901", "issn": "0002-9939", "publisher": "American Mathematical Society", "publication": "Proceedings of the American Mathematical Society", "publication_date": "2016-05", "series_number": "5", "volume": "144", "issue": "5", "pages": "1913-1918" }, { "id": "authors:1fbtx-nyk67", "collection": "authors", "collection_id": "1fbtx-nyk67", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161111-122744051", "type": "monograph", "title": "Weak equivalence of stationary actions and the entropy realization problem", "author": [ { "family_name": "Burton", "given_name": "Peter", "clpid": "Burton-P" }, { "family_name": "Lupini", "given_name": "Martino", "orcid": "0000-0003-1588-7057", "clpid": "Lupini-M" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "We introduce the notion of weak containment for stationary actions of a countable group and define a natural topology on the space of weak equivalence classes. We prove that Furstenberg entropy is an invariant of weak equivalence, and moreover that it descends to a continuous function on the space of weak equivalence classes.", "doi": "10.48550/arXiv.1603.05013", "publication_date": "2016-03-16" }, { "id": "authors:d3khd-chq05", "collection": "authors", "collection_id": "d3khd-chq05", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161111-141359999", "type": "article", "title": "Property (T) and the Furstenberg Entropy of Nonsingular Actions", "author": [ { "family_name": "Bowen", "given_name": "Lewis", "clpid": "Bowen-L" }, { "family_name": "Hartman", "given_name": "Yair", "clpid": "Hartman-Y" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "We establish a new characterization of property (T) in terms of the Furstenberg entropy of nonsingular actions. Given any generating measure \u03bc on a countable group G, A. Nevo showed that a necessary condition for G to have property (T) is that the Furstenberg \u03bc-entropy values of the ergodic, properly nonsingular G-actions are bounded away from zero. We show that this is also a sufficient condition.", "doi": "10.1090/proc/12685", "issn": "0002-9939", "publisher": "American Mathematical Society", "publication": "Proceedings of the American Mathematical Society", "publication_date": "2016-01", "series_number": "1", "volume": "144", "issue": "1", "pages": "31-39" }, { "id": "authors:ze2wh-d0577", "collection": "authors", "collection_id": "ze2wh-d0577", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20151029-144956303", "type": "article", "title": "Strategic Learning and the Topology of Social Networks", "author": [ { "family_name": "Mossel", "given_name": "Elchanan", "orcid": "0000-0001-7812-7886", "clpid": "Mossel-E" }, { "family_name": "Sly", "given_name": "Allan", "clpid": "Sly-A" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "We consider a group of strategic agents who must each repeatedly take one of two possible actions. They learn which of the two actions is preferable from initial private signals and by observing the actions of their neighbors in a social network.", "doi": "10.3982/ECTA12058", "issn": "0012-9682", "publisher": "Econometric Society", "publication": "Econometrica", "publication_date": "2015-09", "series_number": "5", "volume": "83", "issue": "5", "pages": "1755-1794" }, { "id": "authors:yr4pm-hz383", "collection": "authors", "collection_id": "yr4pm-hz383", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161114-085457028", "type": "article", "title": "Furstenberg entropy realizations for virtually free groups and lamplighter groups", "author": [ { "family_name": "Hartman", "given_name": "Yair", "clpid": "Hartman-Y" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "Let (G,\u00b5) be a discrete group with a generating probability measure. Nevo showed that if G has Kazhdan's property (T), then there exists \u025b > 0 such that the Furstenberg entropy of any (G,\u00b5)-stationary ergodic space is either 0 or larger than \u025b. Virtually free groups, such as SL_2(\u2124), do not have property (T), and neither do their extensions, such as surface groups. For virtually free groups, we construct stationary actions with arbitrarily small, positive entropy. The construction involves building and lifting spaces of lamplighter groups. For some classical lamplighter gropus, these spaces realize a dense set of entropies between 0 and the Poisson boundary entropy.", "doi": "10.1007/s11854-015-0016-2", "issn": "0021-7670", "publisher": "Hebrew University Magnes Press", "publication": "Journal d'Analyse Math\u00e9matique", "publication_date": "2015-04", "series_number": "1", "volume": "126", "issue": "1", "pages": "227-257" }, { "id": "authors:tkvca-n5335", "collection": "authors", "collection_id": "tkvca-n5335", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161111-134938105", "type": "monograph", "title": "Symbolic dynamics on amenable groups: the entropy of generic shifts", "author": [ { "family_name": "Frisch", "given_name": "Joshua", "clpid": "Frisch-J" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "Let G be a finitely generated amenable group. We study the space of shifts on G over a given finite alphabet A. We show that the zero entropy shifts are generic in this space, and that more generally the shifts of entropy c are generic in the space of shifts with entropy at least c. The same is shown to hold for the space of transitive shifts and for the space of weakly mixing shifts. \nAs applications of this result, we show that for every entropy value c\u2208[0,log|A|] there is a weakly mixing subshift of A^G with entropy c. We also show that the set of strongly irreducible shifts does not form a G_\u03b4 in the space of shifts, and that all non-trivial, strongly irreducible shifts are non-isolated points in this space.", "doi": "10.48550/arXiv.1503.06251", "publication_date": "2015-03-21" }, { "id": "authors:sehfj-w7m20", "collection": "authors", "collection_id": "sehfj-w7m20", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161114-074309531", "type": "article", "title": "Majority Dynamics and the Retention of Information", "author": [ { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" }, { "family_name": "Tessler", "given_name": "Ran J.", "clpid": "Tessler-R-J" } ], "abstract": "We consider a group of agents connected by a social network who participate in majority dynamics: each agent starts with an opinion in {\u22121, +1} and repeatedly updates it to match the opinion of the majority of its neighbors.\n\nWe assume that one of {\u22121, +1} is the \"correct\" opinion S, and consider a setting in which the initial opinions are independent conditioned on S, and biased towards it. They hence contain enough information to reconstruct S with high probability. We ask whether it is still possible to reconstruct S from the agents' opinions after many rounds of updates.\n\nWhile this is not the case in general, we show that indeed, for a large family of bounded degree graphs, information on S is retained by the process of majority dynamics.\n\nOur proof technique yields novel combinatorial results on majority dynamics on both finite and infinite graphs, with applications to zero temperature Ising models.", "doi": "10.1007/s11856-014-1148-2", "issn": "0021-2172", "publisher": "Springer", "publication": "Israel Journal of Mathematics", "publication_date": "2015-02", "series_number": "1", "volume": "206", "issue": "1", "pages": "483-507" }, { "id": "authors:g3mvt-q2747", "collection": "authors", "collection_id": "g3mvt-q2747", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161110-120309955", "type": "article", "title": "Scenery Reconstruction on Finite Abelian Groups", "author": [ { "family_name": "Finucane", "given_name": "Hilary", "clpid": "Finucane-H" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" }, { "family_name": "Yaari", "given_name": "Yariv", "clpid": "Yaari-Y" } ], "abstract": "We consider the question of when a random walk on a finite abelian group with a given step distribution can be used to reconstruct a binary labeling of the elements of the group, up to a shift. Matzinger and Lember (2006) give a sufficient condition for reconstructability on cycles. While, as we show, this condition is not in general necessary, our main result is that it is necessary when the length of the cycle is prime and larger than 5, and the step distribution has only rational probabilities. We extend this result to other abelian groups.", "doi": "10.1016/j.spa.2014.03.012", "issn": "0304-4149", "publisher": "Elsevier B.V.", "publication": "Stochastic Processes and their Applications", "publication_date": "2014-08", "series_number": "8", "volume": "124", "issue": "8", "pages": "2754-2770" }, { "id": "authors:av4tc-q2055", "collection": "authors", "collection_id": "av4tc-q2055", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161111-145123837", "type": "monograph", "title": "Convergence, unanimity and disagreement in majority dynamics on unimodular graphs and random graphs", "author": [ { "family_name": "Benjamini", "given_name": "Itai", "clpid": "Benjamini-I" }, { "family_name": "Chan", "given_name": "Siu-On", "clpid": "Chan-Siu-On" }, { "family_name": "O'Donnell", "given_name": "Ryan", "clpid": "O'Donnell-R" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" }, { "family_name": "Tan", "given_name": "Li-Yang", "clpid": "Tan-Li-Yang" } ], "abstract": "In majority dynamics, agents located at the vertices of an undirected simple graph update their binary opinions synchronously by adopting those of the majority of their neighbors. \nOn infinite unimodular transitive graphs (e.g., Cayley graphs), when initial opinions are chosen from a distribution that is invariant with respect to the graph automorphism group, we show that the opinion of each agent almost surely either converges, or else eventually oscillates with period two; this is known to hold for finite graphs, but not for all infinite graphs. \nOn Erd\u0151s-R\u00e9nyi random graphs with degrees \u03a9(n\u221a), we show that when initial opinions are chosen i.i.d. then agents all converge to the initial majority opinion, with constant probability. Conversely, on random 4-regular finite graphs, we show that with high probability different agents converge to different opinions.", "doi": "10.48550/arXiv.1405.2486", "publication_date": "2014-05-11" }, { "id": "authors:1xdge-aph37", "collection": "authors", "collection_id": "1xdge-aph37", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161114-070336278", "type": "article", "title": "Majority Dynamics and Aggregation of Information in Social Networks", "author": [ { "family_name": "Mossel", "given_name": "Elchanan", "orcid": "0000-0001-7812-7886", "clpid": "Mossel-E" }, { "family_name": "Neeman", "given_name": "Joe", "clpid": "Neeman-J" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "Consider n individuals who, by popular vote, choose among q \u2265 2 alternatives, one of which is \"better\" than the others. Assume that each individual votes independently at random, and that the probability of voting for the better alternative is larger than the probability of voting for any other. It follows from the law of large numbers that a plurality vote among the n individuals would result in the correct outcome, with probability approaching one exponentially quickly as n \u2192 \u221e.\nOur interest in this paper is in a variant of the process above where, after forming their initial opinions, the voters update their decisions based on some interaction with their neighbors in a social network. Our main example is \"majority dynamics\", in which each voter adopts the most\npopular opinion among its friends. The interaction repeats for some number of rounds and is then followed by a population-wide plurality vote. The question we tackle is that of \"efficient aggregation of information\": in which cases is the better alternative chosen with probability approaching one as n \u2192 \u221e? Conversely, for which sequences of growing graphs does aggregation fail, so that the wrong alternative gets chosen with probability bounded away from zero? We construct a family of examples in which interaction prevents efficient aggregation of information, and give a condition on the social network which ensures that aggregation occurs. For the case of majority dynamics we also investigate the question of unanimity in the\nlimit. In particular, if the voters' social network is an expander graph, we show that if the initial population is sufficiently biased towards a particular alternative then that alternative will eventually become the unanimous preference of the entire population.", "doi": "10.1007/s10458-013-9230-4", "issn": "1387-2532", "publisher": "Kluwer Academic Publishers", "publication": "Autonomous Agents and Mutli-Agent Systems", "publication_date": "2014-05", "series_number": "3", "volume": "28", "issue": "3", "pages": "408-429" }, { "id": "authors:mftzy-6bb79", "collection": "authors", "collection_id": "mftzy-6bb79", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161114-072802716", "type": "article", "title": "Asymptotic learning on Bayesian social networks", "author": [ { "family_name": "Mossel", "given_name": "Elchanan", "orcid": "0000-0001-7812-7886", "clpid": "Mossel-E" }, { "family_name": "Sly", "given_name": "Allan", "clpid": "Sly-A" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "We study a standard model of economic agents on the nodes of a social network graph who learn a binary \"state of the world\" S, from initial signals, by repeatedly observing each other's best guesses. Asymptotic learning is said to occur on a family of graphs G_n=(V_n,E_n) with |V_n|\u2192\u221e if with probability tending to 1 as n\u2192\u221e all agents in G_n eventually estimate S correctly. We identify sufficient conditions for asymptotic learning and contruct examples where learning does not occur when the conditions do not hold.", "doi": "10.1007/s00440-013-0479-y", "issn": "0178-8051", "publisher": "Springer", "publication": "Probability Theory and Related Fields", "publication_date": "2014-02", "series_number": "1-2", "volume": "158", "issue": "1-2", "pages": "127-157" }, { "id": "authors:5shpz-p9366", "collection": "authors", "collection_id": "5shpz-p9366", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161110-081650257", "type": "article", "title": "Making Consensus Tractable", "author": [ { "family_name": "Mossel", "given_name": "Elchanan", "orcid": "0000-0001-7812-7886", "clpid": "Mossel-E" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "We study a model of consensus decision making in which a finite group of Bayesian agents has to choose between one of two courses of action. Each member of the group has a private and independent signal at his or her disposal, giving some indication as to which action is optimal. To come to a common decision, the participants perform repeated rounds of voting. In each round, each agent casts a vote in favor of one of the two courses of action, reflecting his or her current belief, and observes the votes of the rest. \n\nWe provide an efficient algorithm for the calculation the agents have to perform and show that consensus is always reached and that the probability of reaching a wrong decision decays exponentially with the number of agents.", "doi": "10.1145/2542174.2542176", "issn": "2167-8375", "publisher": "ACM", "publication": "ACM Transactions on Economics and Computation", "publication_date": "2013-12", "series_number": "4", "volume": "1", "issue": "4", "pages": "Art. No. 20" }, { "id": "authors:ex9gs-37q03", "collection": "authors", "collection_id": "ex9gs-37q03", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161110-144803099", "type": "article", "title": "Testing Booleanity and the Uncertainty Principle", "author": [ { "family_name": "Gur", "given_name": "Tom", "clpid": "Gur-Tom" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "Let f : {-1,1}^n \u2192 R be a real function on the hypercube, given by its discrete\nFourier expansion, or, equivalently, represented as a multilinear polynomial. We say that it is\nBoolean if its image is in {-1;1}.\nWe show that every function on the hypercube with a sparse Fourier expansion must\neither be Boolean or far from Boolean. In particular, we show that a multilinear polynomial\nwith at most k terms must either be Boolean, or output values different than -1 or 1 for a\nfraction of at least 2=(k+2)\u00b2 of its domain.\nIt follows that given oracle access to f, together with the guarantee that its representation\nas a multilinear polynomial has at most k terms, one can test Booleanity using O(k\u00b2) queries.\nWe show an \u03a9(k) queries lower bound for this problem.\nOur proof crucially uses Hirschman's entropic version of Heisenberg's uncertainty principle.", "doi": "10.4086/cjtcs.2013.014", "issn": "1073-0486", "publisher": "Theory of Computing Exchange", "publication": "Chicago Journal of Theoretical Computer Science", "publication_date": "2013-11-10", "volume": "2013", "pages": "Art. No. 14" }, { "id": "authors:ee3ak-awj41", "collection": "authors", "collection_id": "ee3ak-awj41", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161114-065718415", "type": "article", "title": "A lower bound on seller revenue in single buyer monopoly auctions", "author": [ { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "We consider a monopoly seller who optimally auctions a single object to a single potential buyer, with a known distribution of valuations. We show that a tight lower bound on the seller's expected revenue is 1/e times the geometric expectation of the buyer's valuation, and that this bound is uniquely achieved for the equal revenue distribution. We show also that when the valuation's expectation and geometric expectation are close, then the seller's expected revenue is close to the expected valuation.", "doi": "10.1016/j.orl.2013.05.011", "issn": "0167-6377", "publisher": "Elsevier", "publication": "Operations Research Letters", "publication_date": "2013-09", "series_number": "5", "volume": "41", "issue": "5", "pages": "474-476" }, { "id": "authors:z6wkq-brk71", "collection": "authors", "collection_id": "z6wkq-brk71", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161114-080916122", "type": "monograph", "title": "Textual Features for Programming by Example", "author": [ { "family_name": "Menon", "given_name": "Aditya Krishna", "clpid": "Menon-A-K" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" }, { "family_name": "Gulwani", "given_name": "Sumit", "clpid": "Gulwani-S" }, { "family_name": "Lampson", "given_name": "Butler", "clpid": "Lampson-B" }, { "family_name": "Kalai", "given_name": "Adam Tauman", "clpid": "Kalai-A-T" } ], "abstract": "In Programming by Example, a system attempts to infer a program from input and output examples, generally by searching for a composition of certain base functions. Performing a na\u0457ve brute force search is infeasible for even mildly involved tasks. We note that the examples themselves often present clues as to which\nfunctions to compose, and how to rank the resulting programs. In text processing, which is our domain of interest, clues arise from simple textual features: for example, if parts of the input and output strings are permutations of one another, this suggests that sorting may be useful. We describe a system that learns the reliability of such clues, allowing for faster search and a principled ranking over programs. Experiments on a prototype of this system show that this learning scheme facilitates efficient inference on a range of text processing tasks.", "doi": "10.48550/arXiv.1209.3811", "publication_date": "2012-09-17" }, { "id": "authors:148nq-15p36", "collection": "authors", "collection_id": "148nq-15p36", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161110-073042338", "type": "article", "title": "Complete Characterization of Functions Satisfying the Conditions of Arrow's Theorem", "author": [ { "family_name": "Mossel", "given_name": "Elchanan", "orcid": "0000-0001-7812-7886", "clpid": "Mossel-E" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "Arrow's theorem implies that a social welfare function satisfying Transitivity, the Weak Pareto Principle (Unanimity), and Independence of Irrelevant Alternatives (IIA) must be dictatorial. When non-strict preferences are also allowed, a dictatorial social welfare function is defined as a function for which there exists a single voter whose strict preferences are followed. This definition allows for many different dictatorial functions, since non-strict preferences of the dictator are not necessarily followed. In particular, we construct examples of dictatorial functions which do not satisfy Transitivity and IIA. Thus Arrow's theorem, in the case of non-strict preferences, does not provide a complete characterization of all social welfare functions satisfying Transitivity, the Weak Pareto Principle, and IIA. The main results of this article provide such a characterization for Arrow's theorem, as well as for follow up results by Wilson. In particular, we strengthen Arrow's and Wilson's result by giving an exact if and only if condition for a function to satisfy Transitivity and IIA (and the Weak Pareto Principle). Additionally, we derive formulae for the number of functions satisfying these conditions.", "doi": "10.1007/s00355-011-0547-0", "issn": "0176-1714", "publisher": "Springer", "publication": "Social Choice and Welfare", "publication_date": "2012-06", "series_number": "1", "volume": "39", "issue": "1", "pages": "127-140" }, { "id": "authors:2qapf-ext21", "collection": "authors", "collection_id": "2qapf-ext21", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161114-064703507", "type": "publication_workingpaper", "title": "An Abramov formula for stationary spaces of discrete groups", "author": [ { "family_name": "Hartman", "given_name": "Yair", "clpid": "Hartman-Y" }, { "family_name": "Lima", "given_name": "Yuri", "clpid": "Lima-Y" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "Let (G, \u03bc) be a discrete group equipped with a generating probability measure, and let \u0393 be a finite index subgroup of G. A \u03bc-random walk on G, starting from the identity, returns to \u0393 with probability one. Let \u03b8 be the hitting measure, or the distribution of the position in which the random walk first hits \u0393.\nWe prove that the Furstenberg entropy of a (G, \u03bc)-stationary space, with respect to the induced action of (\u0393, \u03b8), is equal to the Furstenberg entropy with respect to the action of (G, \u03bc), times the index of \u0393 in G. The index is shown to be equal to the expected return time to \u0393.\nAs a corollary, when applied to the Furstenberg-Poisson boundary of (G, \u03bc), we prove that the random walk entropy of (\u0393, \u03b8) is equal to the random walk entropy of (G, \u03bc), times the index of \u0393 in G.", "doi": "10.48550/arXiv.1204.5414", "publication_date": "2012-04-24" }, { "id": "authors:1248d-kht92", "collection": "authors", "collection_id": "1248d-kht92", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161110-143929904", "type": "monograph", "title": "Bundling Customers: How to Exploit Trust Among Customers to Maximize Seller Profit", "author": [ { "family_name": "Mossel", "given_name": "Elchanan", "orcid": "0000-0001-7812-7886", "clpid": "Mossel-E" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "We consider an auction of identical digital goods to customers whose valuations are drawn independently from known distributions. Myerson's classic result identifies the truthful mechanism that maximizes the seller's expected profit. Under the assumption that in small groups customers can learn each others' valuations, we show how Myerson's result can be improved to yield a higher payoff to the seller using a mechanism that offers groups of customers to buy bundles of items.", "doi": "10.48550/arXiv.1202.0969", "publication_date": "2012-04-04" }, { "id": "authors:arwxv-qn786", "collection": "authors", "collection_id": "arwxv-qn786", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161114-082632264", "type": "book_section", "title": "Lower Bounds on Revenue of Approximately Optimal Auctions", "book_title": "Internet and Network Economics", "author": [ { "family_name": "Sivan", "given_name": "Balasubramanian", "clpid": "Sivan-S" }, { "family_name": "Syrgkanis", "given_name": "Vasilis", "clpid": "Syrgkanis-V" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "contributor": [ { "family_name": "Goldberg", "given_name": "Paul W.", "clpid": "Goldberg-P-W" } ], "abstract": "We obtain revenue guarantees for the simple pricing mechanism of a single posted price, in terms of a natural parameter of the distribution of buyers' valuations. Our revenue guarantee applies to the single item n buyers setting, with values drawn from an arbitrary joint distribution. Specifically, we show that a single price drawn from the distribution of the maximum valuation v_(max)\u2009= \u2009max{V_1,V_2,\u2026,V_n} achieves a revenue of at least a 1/e fraction of the geometric expectation of v_(max). This generic bound is a measure of how revenue improves/degrades as a function of the concentration/spread of v_(max).\n\nWe further show that in absence of buyers' valuation distributions, recruiting an additional set of identical bidders will yield a similar guarantee on revenue. Finally, our bound also gives a measure of the extent to which one can simultaneously approximate welfare and revenue in terms of the concentration/spread of v_(max).", "doi": "10.1007/978-3-642-35311-6_42", "isbn": "978-3-642-35310-9", "publisher": "Springer Verlag", "place_of_publication": "New York, NY", "publication_date": "2012", "pages": "526-531" }, { "id": "authors:p4eqg-25p92", "collection": "authors", "collection_id": "p4eqg-25p92", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161110-121844664", "type": "book_section", "title": "Social Learning in a Changing World", "book_title": "Internet and Network Economics", "author": [ { "family_name": "Frongillo", "given_name": "Rafael M.", "clpid": "Frongillo-R-M" }, { "family_name": "Schoenebeck", "given_name": "Grant", "clpid": "Schoenebeck-G" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "contributor": [ { "family_name": "Chen", "given_name": "Ning", "clpid": "Chen-Ning" }, { "family_name": "Elkind", "given_name": "Edith", "clpid": "Elkind-E" }, { "family_name": "Koutsoupias", "given_name": "Elias", "clpid": "Koutsoupias-E" } ], "abstract": "We study a model of learning on social networks in dynamic environments, describing a group of agents who are each trying to estimate an underlying state that varies over time, given access to weak signals and the estimates of their social network neighbors.\n\nWe study three models of agent behavior. In the fixed response model, agents use a fixed linear combination to incorporate information from their peers into their own estimate. This can be thought of as an extension of the DeGroot model to a dynamic setting. In the best response model, players calculate minimum variance linear estimators of the underlying state.\n\nWe show that regardless of the initial configuration, fixed response dynamics converge to a steady state, and that the same holds for best response on the complete graph. We show that best response dynamics can, in the long term, lead to estimators with higher variance than is achievable using well chosen fixed responses.\n\nThe penultimate prediction model is an elaboration of the best response model. While this model only slightly complicates the computations required of the agents, we show that in some cases it greatly increases the efficiency of learning, and on complete graphs is in fact optimal, in a strong sense.", "doi": "10.1007/978-3-642-25510-6_13", "isbn": "978-3-642-25509-0", "publisher": "Springer-Verlag", "place_of_publication": "Berlin Heidelberg", "publication_date": "2011-12", "pages": "146-157" }, { "id": "authors:qq6jx-pzf63", "collection": "authors", "collection_id": "qq6jx-pzf63", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161110-102619803", "type": "book_section", "title": "Adaptively Learning the Crowd Kernel", "book_title": "International Conference on Machine Learning", "author": [ { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" }, { "family_name": "Liu", "given_name": "Ce", "clpid": "Liu-Ce" }, { "family_name": "Belongie", "given_name": "Serge", "orcid": "0000-0002-0388-5217", "clpid": "Belongie-S" }, { "family_name": "Shamir", "given_name": "Ohad", "clpid": "Shamir-O" }, { "family_name": "Kalai", "given_name": "Adam Tauman", "clpid": "Kalai-A-T" } ], "contributor": [ { "family_name": "Getoor", "given_name": "Lise", "clpid": "Getoor-L" }, { "family_name": "Scheffer", "given_name": "Tobias", "clpid": "Scheffer-T" } ], "abstract": "We introduce an algorithm that, given n objects, learns a similarity matrix over all n^2 pairs, from crowdsourced data alone. The algorithm samples responses to adaptively chosen triplet-based relative-similarity queries. Each query has the form \"is object a more similar to b or to c?\" and is chosen to be maximally informative given the preceding responses. The output is an embedding of\nthe objects into Euclidean space (like MDS); we refer to this as the \"crowd kernel.\" SVMs reveal that the crowd kernel captures prominent and subtle features across a number of domains, such as \"is striped\" among neckties\nand \"vowel vs. consonant\" among letters.", "doi": "10.48550/arXiv.1105.1033", "isbn": "978-1-4503-0619-5", "publisher": "ACM", "place_of_publication": "New York, NY", "publication_date": "2011-07", "pages": "673-680" }, { "id": "authors:cazf0-pdg89", "collection": "authors", "collection_id": "cazf0-pdg89", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161110-083842987", "type": "monograph", "title": "Efficient Bayesian Social Learning on Trees", "author": [ { "family_name": "Kanoria", "given_name": "Yashodhan", "clpid": "Kanoria-Y" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "We consider a set of agents who are attempting to\niteratively learn the 'state of the world' from their\nneighbors in a social network. Each agent initially\nreceives a noisy observation of the true state of the\nworld. The agents then repeatedly 'vote' and observe the votes of some of their peers, from which they gain more information. The agents' calculations are Bayesian and aim to myopically maximize the expected utility at each iteration. \nThis model, introduced by Gale and Kariv (2003),\nis a natural approach to learning on networks. However, it has been criticized, chiefly because the agents' decision rule appears to become computationally intractable as the number of iterations advances. For instance, a dynamic programming approach (part of this work) has running time that is exponentially large in min(n; (d - 1)^t), where n is the number of agents. \nWe provide a new algorithm to perform the agents' computations on locally tree-like graphs. Our algorithm uses the dynamic cavity method to drastically reduce computational effort. Let d be the maximum degree and t be the iteration number. The computational effort needed per agent is exponential only in O(td) (note that the number of possible information sets of a neighbor at time t is itself exponential in td).\nUnder appropriate assumptions on the rate of convergence, we deduce that each agent is only required to spend polylogarithmic (in 1=\u0454) computational effort to approximately learn the true state of the world with error probability \u0454, on regular trees of degree at least five. We provide numerical and other evidence to justify our assumption on convergence rate.\nWe extend our results in various directions, including loopy graphs. Our results indicate efficiency of iterative Bayesian social learning in a wide range of situations, contrary to widely held beliefs.", "doi": "10.48550/arXiv.1102.1398", "publication_date": "2011-02" }, { "id": "authors:mr5rg-bsq25", "collection": "authors", "collection_id": "mr5rg-bsq25", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161109-165317769", "type": "article", "title": "Iterative maximum likelihood on networks", "author": [ { "family_name": "Mossel", "given_name": "Elchanan", "orcid": "0000-0001-7812-7886", "clpid": "Mossel-E" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "abstract": "We consider n agents located on the vertices of a connected graph. Each agent v receives a signal X_v(0)\u223cN(\u03bc,1) where \u03bc is an unknown quantity. A natural iterative way of estimating \u03bc is to perform the following procedure. At iteration t+1 let X_v(t+1) be the average of X_v(t) and of X_w(t) among all the neighbors w of v. It is well known that this procedure converges to X(\u221e) = 1/2 |E|^(\u22121) \u03a3 d_v X_v where dv is the degree of v. \n\nIn this paper we consider a variant of simple iterative averaging, which models \"greedy\" behavior of the agents. At iteration t, each agent v declares the value of its estimator X_v(t) to all of its neighbors. Then, it updates X_v(t+1) by taking the maximum likelihood (or minimum variance) estimator of \u03bc, given X_v(t) and X_w(t) for all neighbors w of v, and the structure of the graph. \n\nWe give an explicit efficient procedure for calculating X_v(t), study the convergence of the process as t\u2192\u221e and show that if the limit exists then X_v(\u221e)=X_w(\u221e) for all v and w. For graphs that are symmetric under actions of transitive groups, we show that the process is efficient. Finally, we show that the greedy process is in some cases more efficient than simple averaging, while in other cases the converse is true, so that, in this model, \"greed\" of the individual agents may or may not have an adverse affect on the outcome. \n\nThe model discussed here may be viewed as the maximum likelihood version of models studied in Bayesian Economics. The ML variant is more accessible and allows in particular to show the significance of symmetry in the efficiency of estimators using networks of agents.", "doi": "10.1016/j.aam.2009.11.004", "issn": "0196-8858", "publisher": "Elsevier", "publication": "Advances in Applied Mathematics", "publication_date": "2010-07", "series_number": "1", "volume": "45", "issue": "1", "pages": "36-49" }, { "id": "authors:ge6ta-6sf05", "collection": "authors", "collection_id": "ge6ta-6sf05", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161110-075056609", "type": "book_section", "title": "Truthful Fair Division", "book_title": "Algorithmic Game Theory", "author": [ { "family_name": "Mossel", "given_name": "Elchanan", "orcid": "0000-0001-7812-7886", "clpid": "Mossel-E" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" } ], "contributor": [ { "family_name": "Kontogiannis", "given_name": "S.", "clpid": "Kontogiannis-S" }, { "family_name": "Koutsoupias", "given_name": "Elias", "clpid": "Koutsoupias-E" }, { "family_name": "Spirakis", "given_name": "P. G.", "clpid": "Spirakis-P-G" } ], "abstract": "We address the problem of fair division, or cake cutting, with the goal of finding truthful mechanisms. In the case of a general measure space (\"cake\") and non-atomic, additive individual preference measures - or utilities - we show that there exists a truthful \"mechanism\" which ensures that each of the k players gets at least 1/k of the cake. This mechanism also minimizes risk for truthful players. Furthermore, in the case where there exist at least two different measures we present a different truthful mechanism which ensures that each of the players gets more than 1/k of the cake.\n\nWe then turn our attention to partitions of indivisible goods with bounded utilities and a large number of goods. Here we provide similar mechanisms, but with slightly weaker guarantees. These guarantees converge to those obtained in the non-atomic case as the number of goods goes to infinity.", "doi": "10.1007/978-3-642-16170-4_25", "isbn": "978-3-642-16169-8", "publisher": "Springer-Verlag", "place_of_publication": "Berlin Heidelberg", "publication_date": "2010", "pages": "288-299" }, { "id": "authors:5x592-8wn14", "collection": "authors", "collection_id": "5x592-8wn14", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161109-163957800", "type": "article", "title": "Photometric follow-up of the transiting planet WASP-1b", "author": [ { "family_name": "Shporer", "given_name": "A.", "orcid": "0000-0002-1836-3120", "clpid": "Shporer-A" }, { "family_name": "Tamuz", "given_name": "O.", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" }, { "family_name": "Zucker", "given_name": "S.", "clpid": "Zucker-S" }, { "family_name": "Mazeh", "given_name": "T.", "clpid": "Mazeh-T" } ], "abstract": "We report on photometric follow-up of the recently discovered transiting planet WASP-1b. We observed two transits with the Wise Observatory 1-m telescope, and used a variant of the Eclipsing Binary Orbit Program (EBOP) code together with the Sys-Rem detrending approach to fit the light curve. Assuming a stellar mass of 1.15 M_\u2299, we derived a planetary radius of R_p= 1.40 \u00b1 0.06R_J and mass of M_p= 0.87 \u00b1 0.07M_J. An uncertainty of 15 per cent in the stellar mass results in an additional systematic uncertainty of 5 per cent in the planetary radius and of 10 per cent in planetary mass. Our observations yielded a slightly better ephemeris for the centre of the transit: T_c [HJD]= (245 4013.3127 \u00b1 0.0004) +N_(tr)(2.51996 \u00b1 0.00002). The new planet is an inflated, low-density planet, similar to HAT-P-1b and HD 209458b.", "doi": "10.1111/j.1365-2966.2007.11537.x", "issn": "0035-8711", "publisher": "Royal Astronomical Society", "publication": "Monthly Notices of the Royal Astronomical Society", "publication_date": "2007-04-11", "series_number": "3", "volume": "376", "issue": "3", "pages": "1296-1300" }, { "id": "authors:e707h-hty72", "collection": "authors", "collection_id": "e707h-hty72", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161115-090420610", "type": "monograph", "title": "The Sys-Rem Detrending Algorithm: Implementation and Testing", "author": [ { "family_name": "Mazeh", "given_name": "T.", "clpid": "Mazeh-T" }, { "family_name": "Tamuz", "given_name": "O.", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" }, { "family_name": "Zucker", "given_name": "S.", "clpid": "Zucker-S" } ], "abstract": "Sys-Rem (Tamuz, Mazeh & Zucker 2005) is a detrending algorithm designed to remove systematic effects in a large set of lightcurves obtained by a photometric survey. The algorithm works without any prior knowledge of the effects, as long as they appear in many stars of the sample. This paper presents the basic principles of Sys-Rem and discusses a parameterization used to determine the number of effects removed. We assess the performance of Sys-Rem on simulated transits injected into WHAT survey data. This test is proposed as a general scheme to assess the effectiveness of detrending algorithms. Application of Sys-Rem to the OGLE dataset demonstrates the power of the algorithm. We offer a coded implementation of Sys-Rem to the community.", "doi": "10.48550/arXiv.0612418", "publication_date": "2006-12-15" }, { "id": "authors:2sd25-3ax57", "collection": "authors", "collection_id": "2sd25-3ax57", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161115-085954023", "type": "monograph", "title": "Analysis of the eclipsing binaries in the LMC discovered by OGLE: period distribution and frequency of the short-period binaries", "author": [ { "family_name": "Mazeh", "given_name": "Tsevi", "clpid": "Mazeh-T" }, { "family_name": "Tamuz", "given_name": "Omer", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" }, { "family_name": "North", "given_name": "Pierre", "clpid": "North-P" } ], "abstract": "We review the results of our analysis of the OGLE LMC eclipsing binaries (Mazeh, Tamuz & North 2006), using EBAS -- Eclipsing Binary Automated Solver, an automated algorithm to fit lightcurves of eclipsing binaries (Tamuz, Mazeh & North 2006). \nAfter being corrected for observational selection effects, the set of detected eclipsing binaries yielded the period distribution and the frequency of all LMC short-period binaries, and not just the eclipsing systems. \nSomewhat surprisingly, the period distribution is consistent with a flat distribution in log P between 2 and 10 days. The total number of binaries with periods shorter than 10 days in the LMC was estimated to be about 5000. This figure led us to suggest that (0.7 \u00b1 0.4)% of the main-sequence A- and B-type stars are found in binaries with periods shorter than 10 days. This frequency is substantially smaller than the fraction of binaries found by small Galactic radial-velocity surveys of B stars.", "doi": "10.48550/arXiv.0611482", "publication_date": "2006-11-15" }, { "id": "authors:2fj5e-fqq81", "collection": "authors", "collection_id": "2fj5e-fqq81", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161109-162833455", "type": "article", "title": "Automated analysis of eclipsing binary light curves - I. EBAS - a new Eclipsing Binary Automated Solver with EBOP", "author": [ { "family_name": "Tamuz", "given_name": "O.", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" }, { "family_name": "Mazeh", "given_name": "T.", "clpid": "Mazeh-T" }, { "family_name": "North", "given_name": "P.", "clpid": "North-P" } ], "abstract": "We present a new algorithm, Eclipsing Binary Automated Solver (EBAS), to analyse light curves of eclipsing binaries. The algorithm is designed to analyse large numbers of light curves, and is therefore based on the relatively fast EBOP code. To facilitate the search for the best solution, EBAS uses two parameter transformations. Instead of the radii of the two stellar components, EBAS uses the sum of radii and their ratio, while the inclination is transformed into the impact parameter. To replace human visual assessment, we introduce a new 'alarm' goodness-of-fit statistic that takes into account correlation between neighbouring residuals. We perform extensive tests and simulations that show that our algorithm converges well, finds a good set of parameters and provides reasonable error estimation.", "doi": "10.1111/j.1365-2966.2006.10049.x", "issn": "0035-8711", "publisher": "Royal Astronomical Society", "publication": "Monthly Notices of the Royal Astronomical Society", "publication_date": "2006-04-21", "series_number": "4", "volume": "367", "issue": "4", "pages": "1521-1530" }, { "id": "authors:s5ddn-sc375", "collection": "authors", "collection_id": "s5ddn-sc375", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161109-163450950", "type": "article", "title": "Automated analysis of eclipsing binary light curves - II. Statistical analysis of OGLE LMC eclipsing binaries", "author": [ { "family_name": "Mazeh", "given_name": "T.", "clpid": "Mazeh-T" }, { "family_name": "Tamuz", "given_name": "O.", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" }, { "family_name": "North", "given_name": "P.", "clpid": "North-P" } ], "abstract": "In the first paper of this series, we presented EBAS \u2013 Eclipsing Binary Automated Solver, a new fully automated algorithm to analyse the light curves of eclipsing binaries, based on the EBOP code. Here, we apply the new algorithm to the whole sample of 2580 binaries found in the Optical Gravitational Lensing Experiment (OGLE) Large Magellanic Cloud (LMC) photometric survey and derive the orbital elements for 1931 systems. To obtain the statistical properties of the short-period binaries of the LMC, we construct a well-defined subsample of 938 eclipsing binaries with main-sequence B-type primaries. Correcting for observational selection effects, we derive the distributions of the fractional radii of the two components and their sum, the brightness ratios and the periods of the short-period binaries. Somewhat surprisingly, the results are consistent with a flat distribution in log P between 2 and 10 d. We also estimate the total number of binaries in the LMC with the same characteristics, and not only the eclipsing binaries, to be about 5000. This figure leads us to suggest that (0.7 \u00b1 0.4) per cent of the main-sequence B-type stars in the LMC are found in binaries with periods shorter than 10 d. This frequency is substantially smaller than the fraction of binaries found by small Galactic radial-velocity surveys of B stars. On the other hand, the binary frequency found by Hubble Space Telescope (HST) photometric searches within the late main-sequence stars of 47 Tuc is only slightly higher and still consistent with the frequency we deduced for the B stars in the LMC.", "doi": "10.1111/j.1365-2966.2006.10050.x", "issn": "0035-8711", "publisher": "Royal Astronomical Society", "publication": "Monthly Notices of the Royal Astronomical Society", "publication_date": "2006-04-21", "series_number": "4", "volume": "367", "issue": "4", "pages": "1531-1542" }, { "id": "authors:6t7fq-5s958", "collection": "authors", "collection_id": "6t7fq-5s958", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161109-161950022", "type": "article", "title": "Correcting systematic effects in a large set of photometric light curves", "author": [ { "family_name": "Tamuz", "given_name": "O.", "orcid": "0000-0002-0111-0418", "clpid": "Tamuz-O" }, { "family_name": "Mazeh", "given_name": "T.", "clpid": "Mazeh-T" }, { "family_name": "Zucker", "given_name": "S.", "clpid": "Zucker-S" } ], "abstract": "We suggest a new algorithm to remove systematic effects in a large set of lightcurves obtained by a photometric survey. The algorithm can remove systematic effects, like the ones associated with atmospheric extinction, detector efficiency, or PSF changes over the detector. The algorithm works without any prior knowledge of the effects, as long as they linearly appear in many stars of the sample. The approach, which was originally developed to remove atmospheric extinction effects, is based on a lower rank approximation of matrices, an approach which was already suggested and used in chemometrics, for example. The proposed algorithm is specially useful in cases where the uncertainties of the measurements are unequal. For equal uncertainties the algorithm reduces to the Principal Components Analysis (PCA) algorithm. We present a simulation to demonstrate the effectiveness of the proposed algorithm and point out its potential, in search for transit candidates in particular.", "doi": "10.1111/j.1365-2966.2004.08585.x", "issn": "0035-8711", "publisher": "Royal Astronomical Society", "publication": "Monthly Notices of the Royal Astronomical Society", "publication_date": "2005-02-01", "series_number": "4", "volume": "356", "issue": "4", "pages": "1466-1470" } ]