Partially Symmetric Functions are Efficiently Isomorphism-Testable

Given a function f: {0,1}^n \to {0,1}, the f-isomorphism testing problem requires a randomized algorithm to distinguish functions that are identical to f up to relabeling of the input variables from functions that are far from being so. An important open question in property testing is to determine for which functions f we can test f-isomorphism with a constant number of queries. Despite much recent attention to this question, essentially only two classes of functions were known to be efficiently isomorphism testable: symmetric functions and juntas. We unify and extend these results by showing that all partially symmetric functions---functions invariant to the reordering of all but a constant number of their variables---are efficiently isomorphism-testable. This class of functions, first introduced by Shannon, includes symmetric functions, juntas, and many other functions as well. We conjecture that these functions are essentially the only functions efficiently isomorphism-testable. To prove our main result, we also show that partial symmetry is efficiently testable. In turn, to prove this result we had to revisit the junta testing problem. We provide a new proof of correctness of the nearly-optimal junta tester. Our new proof replaces the Fourier machinery of the original proof with a purely combinatorial argument that exploits the connection between sets of variables with low influence and intersecting families. Another important ingredient in our proofs is a new notion of symmetric influence. We use this measure of influence to prove that partial symmetry is efficiently testable and also to construct an efficient sample extractor for partially symmetric functions. We then combine the sample extractor with the testing-by-implicit-learning approach to complete the proof that partially symmetric functions are efficiently isomorphism-testable.Comment: 22 page

Partially Symmetric Functions Are Efficiently Isomorphism Testable

Given a Boolean function f, the f-isomorphism testing problem requires a randomized algorithm to distinguish functions that are identical to f up to relabeling of the input variables from functions that are far from being so. An important open question in property testing is to determine for which functions f we can test f-isomorphism with a constant number of queries. Despite much recent attention to this question, essentially only two classes of functions were known to be efficiently isomorphism testable: symmetric functions and juntas. We unify and extend these results by showing that all partially symmetric functions---functions invariant to the reordering of all but a constant number of their variables---are efficiently isomorphism testable. This class of functions, first introduced by Shannon, includes symmetric functions, juntas, and many other functions as well. We conjecture that these functions are essentially the only functions efficiently isomorphism-testable. To prove our main result, we also show that partial symmetry is efficiently testable. In turn, to prove this result we had to revisit the junta testing problem. We provide a new proof of correctness of the nearly optimal junta tester. Our new proof replaces the Fourier machinery of the original proof with a purely combinatorial argument that exploits the connection between sets of variables with low influence and intersecting families. Another important ingredient in our proofs is a new notion of symmetric influence. We use this measure of influence to prove that partial symmetry is efficiently testable and also to construct an efficient sample extractor for partially symmetric functions. We then combine the sample extractor with the testing-by-implicit-learning approach to complete the proof that partially symmetric functions are efficiently isomorphism testable.Simons Foundation (Postdoctoral Fellowship

A High Level Teleoperation Platform for Space Robotic Mission

Proceedings of the 2nd IEEE International Conference on Space Mission Challenges for Information Technology (SMC-IT\u2706

Strong Correlation Between Noise Features at Low Frequency and the Kilohertz QPOs in the X-Ray Binary 4U 1728-34

We study the timing properties of the low mass X-ray binary 4U 1728-34 using recently released data from the Rossi X-Ray Timing Explorer. This binary, like many others with accreting neutron stars, is known to exhibit strong quasi-periodic oscillations (QPOs) of its X-ray flux near 1 kHz. In addition to the kilohertz QPOs, the Fourier power spectra show a broken power law noise component, with a break frequency between 1 and 50 Hz, and a Lorentzian between 10 and 50 Hz. We find that the frequencies of the break and the low-frequency Lorentzian are well correlated with the frequencies of the kilohertz QPOs. The slope of the correlation is similar to that expected if the oscillations are due to relativistic frame dragging (Lense-Thirring precession) in the inner accretion disk (Stella & Vietri 1998). The correlation is also nearly identical to the one found in Z-sources between the the well known QPOs on the horizontal branch and the kilohertz QPOs, suggesting that the low frequency oscillations are a similar phenomenon in these sources. The frequency of the break in the power spectra is also correlated with the frequencies of the kilohertz QPOs. As previously noted for the similar binaries 4U 1608-50 and 4U 1705-44, this broken power law component closely resembles that of black hole candidates in the low state, where the break frequency is taken as an indicator of mass accretion rate. The relation between break frequency and kilohertz QPO frequency thus provides additional proof that the frequency of the kilohertz QPOs increases with mass accretion rate.Comment: ApJL in press, see the 'QPO page' at http://www.astro.uva.nl/ecford/qpos.htm

Annals Impact Factor 1.67. Welcome to the IF club: achievement and challenges

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A support vector machine based test for incongruence between sets of trees in tree space

BACKGROUND: The increased use of multi-locus data sets for phylogenetic reconstruction has increased the need to determine whether a set of gene trees significantly deviate from the phylogenetic patterns of other genes. Such unusual gene trees may have been influenced by other evolutionary processes such as selection, gene duplication, or horizontal gene transfer. RESULTS: Motivated by this problem we propose a nonparametric goodness-of-fit test for two empirical distributions of gene trees, and we developed the software GeneOut to estimate a p-value for the test. Our approach maps trees into a multi-dimensional vector space and then applies support vector machines (SVMs) to measure the separation between two sets of pre-defined trees. We use a permutation test to assess the significance of the SVM separation. To demonstrate the performance of GeneOut, we applied it to the comparison of gene trees simulated within different species trees across a range of species tree depths. Applied directly to sets of simulated gene trees with large sample sizes, GeneOut was able to detect very small differences between two set of gene trees generated under different species trees. Our statistical test can also include tree reconstruction into its test framework through a variety of phylogenetic optimality criteria. When applied to DNA sequence data simulated from different sets of gene trees, results in the form of receiver operating characteristic (ROC) curves indicated that GeneOut performed well in the detection of differences between sets of trees with different distributions in a multi-dimensional space. Furthermore, it controlled false positive and false negative rates very well, indicating a high degree of accuracy. CONCLUSIONS: The non-parametric nature of our statistical test provides fast and efficient analyses, and makes it an applicable test for any scenario where evolutionary or other factors can lead to trees with different multi-dimensional distributions. The software GeneOut is freely available under the GNU public license

The Santa Fe Light Cone Simulation Project: II. The Prospects for Direct Detection of the WHIM with SZE Surveys

Detection of the Warm-Hot Intergalactic Medium (WHIM) using Sunyaev-Zeldovich effect (SZE) surveys is an intriguing possibility, and one that may allow observers to quantify the amount of "missing baryons" in the WHIM phase. We estimate the necessary sensitivity for detecting low density WHIM gas with the South Pole Telescope (SPT) and Planck Surveyor for a synthetic 100 square degree sky survey. This survey is generated from a very large, high dynamic range adaptive mesh refinement cosmological simulation performed with the Enzo code. We find that for a modest increase in the SPT survey sensitivity (a factor of 2-4), the WHIM gas makes a detectable contribution to the integrated sky signal. For a Planck-like satellite, similar detections are possible with a more significant increase in sensitivity (a factor of 8-10). We point out that for the WHIM gas, the kinematic SZE signal can sometimes dominate the thermal SZE where the thermal SZE decrement is maximal (150 GHz), and that using the combination of the two increases the chance of WHIM detection using SZE surveys. However, we find no evidence of unique features in the thermal SZE angular power spectrum that may aid in its detection. Interestingly, there are differences in the power spectrum of the kinematic SZE, which may not allow us to detect the WHIM directly, but could be an important contaminant in cosmological analyses of the kSZE-derived velocity field. Corrections derived from numerical simulations may be necessary to account for this contamination.Comment: 9 pages, submitted to Astrophysical Journa