A dynamic programming—integer programming algorithm for allocating touristic investments

Swart, William; Gearing, Charles E.; Var, Turgut

doi:10.1108/eb059970

Cited by 8 publications

(5 citation statements)

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“…Q * (k−1) makes up the first k steps of Q * (k) . This is a special case of the Principle of Optimality [60]: if Q * (k) is optimal, then all subpaths within Q * (k) must be optimal too. In other words, given the optimal…”

Section: Viterbi Algorithmmentioning

confidence: 99%

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Hidden Markov model tracking of continuous gravitational waves from a neutron star with wandering spin

et al. 2016

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Gravitational wave searches for continuous-wave signals from neutron stars are especially challenging when the star's spin frequency is unknown a priori from electromagnetic observations and wanders stochastically under the action of internal (e.g. superfluid or magnetospheric) or external (e.g. accretion) torques. It is shown that frequency tracking by hidden Markov model (HMM) methods can be combined with existing maximum likelihood coherent matched filters like the F-statistic to surmount some of the challenges raised by spin wandering. Specifically it is found that, for an isolated, biaxial rotor whose spin frequency walks randomly, HMM tracking of the F-statistic output from coherent segments with duration T drift = 10 d over a total observation time of T obs = 1 yr can detect signals with wave strains h0 > 2 × 10 −26 at a noise level characteristic of the Advanced Laser Interferometer Gravitational Wave Observatory (Advanced LIGO). For a biaxial rotor with randomly walking spin in a binary orbit, whose orbital period and semi-major axis are known approximately from electromagnetic observations, HMM tracking of the Bessel-weighted F-statistic output can detect signals with h0 > 8 × 10 −26 . An efficient, recursive, HMM solver based on the Viterbi algorithm is demonstrated, which requires ∼ 10 3 CPU-hours for a typical, broadband (0.5-kHz) search for the low-mass X-ray binary Scorpius X-1, including generation of the relevant F-statistic input. In a "realistic" observational scenario, Viterbi tracking successfully detects 41 out of 50 synthetic signals without spin wandering in Stage I of the Scorpius X-1 Mock Data Challenge convened by the LIGO Scientific Collaboration down to a wave strain of h0 = 1.1×10 −25 , recovering the frequency with a root-mean-square accuracy of ≤ 4.3 × 10 −3 Hz.

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Section: Viterbi Algorithmmentioning

confidence: 99%

“…The search space and prior are the same as those in Section V A. In this stage 23 extra injections are successfully detected: 2,5,11,14,17,19,23,26,29,36,44,47,51,60,61,67,68,76,79,83,85, 95, and 98.…”

Section: B T Obs = 1 Yr Two Interferometersmentioning

confidence: 99%

Hidden Markov model tracking of continuous gravitational waves from a neutron star with wandering spin

et al. 2016

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“…The principle of optimality [74] demonstrates that in our special case, all subpaths Q * (k) made up of the first k steps in Q * (O) are optimal for 1 ≤ k ≤ N T . In that sense, the classic Viterbi algorithm [43] provides a recursive, computationally efficient solution to computing Q * (O) in a HMM, reducing the number of operations from N N T +1 Q to (N T + 1)N Q ln N Q by binary maximization [42].…”

Section: Appendix A: Viterbi Algorithmmentioning

confidence: 83%

Hidden Markov model tracking of continuous gravitational waves from young supernova remnants

et al. 2018

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Searches for persistent gravitational radiation from nonpulsating neutron stars in young supernova remnants (SNRs) are computationally challenging because of rapid stellar braking. We describe a practical, efficient, semi-coherent search based on a hidden Markov model (HMM) tracking scheme, solved by the Viterbi algorithm, combined with a maximum likelihood matched filter, the F-statistic. The scheme is well suited to analyzing data from advanced detectors like the Advanced Laser Interferometer Gravitational Wave Observatory (Advanced LIGO). It can track rapid phase evolution from secular stellar braking and stochastic timing noise torques simultaneously without searching second-and higher-order derivatives of the signal frequency, providing an economical alternative to stack-slide-based semi-coherent algorithms. One implementation tracks the signal frequency alone. A second implementation tracks the signal frequency and its first time derivative. It improves the sensitivity by a factor of a few upon the first implementation, but the cost increases by two to three orders of magnitude.PACS numbers: 95.85.Sz, 97.60.Jd

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“…One difficulty of analyzing high-dimensional data is the so-called "curse of dimensionality" (Bellman, 1957), which describes how, as the number of dimensions increases, the difference in distances between different pairs of points in the sample get smaller, and distance functions become less useful in distinguishing between points. A rule of thumb when trying to detect clusters in dimensions is that a sample size on the order of ~ 2 is required (Formann, 1984).…”

Section: Attitudinal Factorsmentioning

confidence: 99%

Describing and Mapping the Interactions between Student Affective Factors Related to Persistence in Science, Physics, and Engineering

Doyle¹

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This dissertation explores how students' beliefs and attitudes interact with their identities as physics people, motivated by calls to increase participation in science, technology, engineering, and mathematics (STEM) careers. This work combines several theoretical frameworks, including Identity theory, Future Time Perspective theory, and other personality traits to investigate associations between these factors. An enriched understanding of how these attitudinal factors are associated with each other extends prior models of identity and link theoretical frameworks used in psychological and educational research. The research uses a series of quantitative and qualitative methodologies, including linear and logistic regression analysis, thematic interview analysis, and an innovative analytic technique adapted for use with student educational data for the first time: topological data analysis via the Mapper algorithm. Engineering students were surveyed in their introductory engineering courses.

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A dynamic programming—integer programming algorithm for allocating touristic investments

Cited by 8 publications

References 0 publications

Hidden Markov model tracking of continuous gravitational waves from a neutron star with wandering spin

Hidden Markov model tracking of continuous gravitational waves from a neutron star with wandering spin

Hidden Markov model tracking of continuous gravitational waves from young supernova remnants

Describing and Mapping the Interactions between Student Affective Factors Related to Persistence in Science, Physics, and Engineering

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