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Optimized hierarchical continuous-wave searches

Optimized hierarchical continuous-wave searches. Badri Krishnan Curt Cutler, Iraj Gholami AEI, Golm. LSC meeting, March 2004 ASIS session. G040155-00-Z. Motivation. Full coherent searches for unknown pulsars not computationally feasible Require incoherent, sub-optimal methods

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Optimized hierarchical continuous-wave searches

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  1. Optimized hierarchical continuous-wave searches Badri Krishnan Curt Cutler, Iraj Gholami AEI, Golm LSC meeting, March 2004 ASIS session G040155-00-Z

  2. Motivation • Full coherent searches for unknown pulsars not computationally feasible • Require incoherent, sub-optimal methods • Illustrative example: The stack slide search Example: Searching for young, fast pulsars over the whole sky and including two spin-down parameters for 10 days data requires a 1017 Flops computer P.Brady and T.Creighton, PRD 61, 082001 (2000)

  3. The Stack-Slide method • Basic idea: Take the Fourier transform of each segment and track the Doppler shift by adding power in the frequency domain (Stack and Slide) • First step : Break up data into N segments • Calculate power spectrum or DeFT for each segment

  4. Frequency Time Add power after frequency bins are shifted according to the time-frequency pattern

  5. General hierarchical pipeline Break data into segments Incoherent stepcan be either stack-slide orHough Analyze eachsegment coherently Acquire more data Combine segments incoherently Select candidates Analyze candidatescoherently using all available data Detection orupper limit

  6. The search parameters Number of incoherent stages : n Variables for each incoherent stage Variables for final coherent stage Ni : Number of stacks Ti : Time-baseline of each stack mi : Mismatch in signal power Xi: Threshold on summed power Tobs : Total observation time mcoh : Mismatch in signal power • Given : • Available computer power C0 • Data of a certain time duration Tobs • Weakest signal strength we wish to detect h0 • Desired confidence level • We want to know: • Optimal values of the search parameters Minimize computational cost subject to constraints

  7. Two different search modes • Take fresh data in each stage • Re-use old data time Ist stage IInd stage IIIrd stage Ist stage IInd stage IIIrd stage

  8. Statistics Summed power follows chi-square distribution with 2N d.o.f False alarm and false dismissal rates : ai : False alarm rate for ith stage Determines number of candidates for next stage to analyze Total false alarm rate always determined by final coherent stage bi : False dismissal rate for ith stage Determines weakest signal that can be detected Choose thresholds for each stage by fixing false dismissal rate

  9. Template counting Parameter space metric calculated by Brady & Creighton Number of points in coarse grid : Number of points in fine grid :

  10. Computational costs Computational cost of each stage is essentially cost of calculating FFTplus cost of summing the power For each point in parameter space, number of floating point operations for first, intermediate and coherent stages: F(i) = Number of candidates which survive the ith stage

  11. Optimization strategy • Basic strategy is to minimize Total computational cost subject to constraint that amount of analyzed data is lesser than available data • False alarm rate is not really a constraint because false alarm rate is set by final coherent step • Computationally limited searches can only see strong signals and when we do see them, it is usually easy to build up confidence • Want to analyze data in (roughly) real time • Function to be optimized is S(x) = 1 if 0 < x < 1 and very large otherwise

  12. Preliminary results • Example of search criteria : • Total observation time : 1 year • Signal strength we wish to detect : • Allowed false dismissal rate for each stage : 1% • Mismatch in coherent stage : 0.10 • Don’t reuse old data • Max number of spindowns included : 3 • All-sky search • Largest frequency searched over : fmax = 1000 Hz • Smallest spindown age : tmin = 40 yr Optimization carried out by simulated annealing and amoeba method

  13. Single stage search with coherent follow-up: • Length of each stack : 1.9 days • Number of stacks : 39 • Observation time : 74 days • Power mismatch : 0.53 • Computational requirement : 6.3 x 1016 Flops • Two stage search with coherent follow-up: • Length of each stack : 0.37 days ; 0.25 days • Number of stacks : 199 ; 956 • Observation time : 73 days ; 240 days • Power mismatch : 0.51 ; 0.23 • Computational requirement : 8.8 x 1013 Flops • Three stage search with coherent follow-up: • Length of each stack : 0.17 days ; 0.15 days ; 0.48 days • Number of stacks : 511; 1028 ; 261 • Observation time : 84 days ; 149 days ; 125 days • Power mismatch : 0.48 ; 0.33 ; 0.02 • Computational requirement : 7.8 x 1012 Flops

  14. Conclusions • Optimization scheme for hierarchical stack-slide search presented • Tells us what the search pipeline parameters must be • Expect similar results for hierarchical Hough search also • Does not consider cost of Monte Carlo simulations or memory issues • Shows that hierarchical schemes are absolutely essential for large parameter space blind searches

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