arXiv subjects

Omer Tamuz

Publications and source records attributed to Omer Tamuz.

82 records · Page 5Linked to original sources

arXiv2011

Complete Characterization of Functions Satisfying the Conditions of Arrow's Theorem

Arrow's theorem implies that a social choice function satisfying Transitivity, the Pareto Principle (Unanimity) and Independence of Irrelevant Alternatives (IIA) must be dictatorial. When non-strict preferences are allowed, a dictatorial social choice 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. 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 choice functions satisfying Transitivity, the 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 Pareto Principle). Additionally, we derive formulas for the number of functions satisfying these conditions.

math.CO↗

arXiv2011

Efficient Bayesian Social Learning on Trees

We consider a set of agents who are attempting to iteratively learn the 'state of the world' from their neighbors in a social network. Each agent initially receives a noisy observation of the true state of the world. 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. This model, introduced by Gale and Kariv (2003), is 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. We 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). Under appropriate assumptions on the rate of convergence, we deduce that each agent is only required to spend polylogarithmic (in 1/\eps) computational effort to approximately learn the true state of the world with error probability \eps, on regular trees of degree at least five. We provide numerical and other evidence to justify our assumption on convergence rate. We 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.

cs.SI↗

arXiv2010

Truthful Fair Division

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. We 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.

cs.GT↗

arXiv2009

Iterative Maximum Likelihood on Networks

We consider n agents located on the vertices of a connected graph. Each agent v receives a signal X_v(0)~N(s, 1) where s is an unknown quantity. A natural iterative way of estimating s 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. In 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 s, given X_v(t) and X_w(t) for all neighbors w of v, and the structure of the graph. We give an explicit efficient procedure for calculating X_v(t), study the convergence of the process as t goes to infinity and show that if the limit exists then it is the same 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. The 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.

math.ST↗

arXiv2007

Photometric follow-up of the transiting planet WASP-1b

We report on photometric follow-up of the recently discovered transiting planet WASP-1b. We observed two transits with the Wise Observatory 1m telescope, and used a variant of the EBOP code together with the Sys-Rem detrending approach to fit the light curve. Assuming a stellar mass of 1.15 M_sun, we derived a planetary radius of R_p = 1.40 +- 0.06 R_J and mass of M_p = 0.87 +- 0.07 M_J. An uncertainty of 15% in the stellar mass results in an additional systematic uncertainty of 5% in the planetary radius and of 10% in planetary mass. Our observations yielded a slightly better ephemeris for the center of the transit: T_c [HJD] = (2454013.3127 +- 0.0004) + N_tr * (2.51996 +- 0.00002). The new planet is an inflated, low-density planet, similar to HAT-P-1b and HD209458b.

astro-ph↗

arXiv2006

The Sys-Rem Detrending Algorithm: Implementation and Testing

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.

astro-ph↗

arXiv2006

Analysis of the eclipsing binaries in the LMC discovered by OGLE: Period distribution and frequency of the short-period binaries

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). After 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. Somewhat 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 +- 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.

astro-ph↗

arXiv2006

Automated analysis of eclipsing binary lightcurves. I. EBAS -- a new Eclipsing Binary Automated Solver with EBOP

We present a new algorithm -- Eclipsing Binary Automated Solver (EBAS), to analyse lightcurves of eclipsing binaries. The algorithm is designed to analyse large numbers of lightcurves, 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.

astro-ph↗

arXiv2006

Automated analysis of eclipsing binary lightcurves with EBAS. II. Statistical analysis of OGLE LMC eclipsing binaries

In the first paper of this series we presented EBAS, a new fully automated algorithm to analyse the lightcurves of eclipsing binaries, based on the EBOP code. Here we apply the new algorithm to the whole sample of 2580 binaries found in the OGLE 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 days. 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 +- 0.4 percent of the main-sequence B-type stars in the LMC 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. On the other hand, the binary frequency found by 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.

astro-ph↗

arXiv2005

Correcting systematic effects in a large set of photometric lightcurves

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.

astro-ph↗