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Journal ArticleDOI

maxsmooth: Derivative Constrained Function Fitting

01 Oct 2020-The Journal of Open Source Software (The Open Journal)-Vol. 5, Iss: 54, pp 2596
TL;DR: Maxsmooth is an optimisation routine written in Python (supporting version ≥ 3.6) for fitting Derivative Constrained Functions (DCFs) to data that can produce perfectly smooth fits to data and reveal non-smooth signals of interest in the residuals.
Abstract: maxsmooth is an optimisation routine written in Python (supporting version ≥ 3.6) for fitting Derivative Constrained Functions (DCFs) to data. DCFs are a family of functions which have derivatives that do not cross zero in the band of interest. Two special cases of DCF are Maximally Smooth Functions (MSFs) which have derivatives with order m ≥ 2 constrained and Completely Smooth Functions (CSFs) with m ≥ 1 constrained. Alternatively, we can constrain an arbitrary set of derivatives and we refer to these models as Partially Smooth Functions. Due to their constrained nature, DCFs can produce perfectly smooth fits to data and reveal non-smooth signals of interest in the residuals.

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Citations
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Journal ArticleDOI
TL;DR: The Radio Experiment for the Analysis of Cosmic Hydrogen (REACH) is a sky-averaged 21 cm experiment aiming at improving the current observations by tackling the issues faced by current instruments related to residual systematic signals in the data as mentioned in this paper .
Abstract: Observations of the 21-cm line from primordial hydrogen promise to be one of the best tools to study the early epochs of the Universe: the dark ages, the cosmic dawn and the subsequent epoch of reionization. In 2018, the Experiment to Detect the Global Epoch of Reionization Signature (EDGES) caught the attention of the cosmology community with a potential detection of an absorption feature in the sky-averaged radio spectrum centred at 78 MHz. The feature is deeper than expected, and, if confirmed, would call for new physics. However, different groups have re-analysed the EDGES data and questioned the reliability of the signal. The Radio Experiment for the Analysis of Cosmic Hydrogen (REACH) is a sky-averaged 21-cm experiment aiming at improving the current observations by tackling the issues faced by current instruments related to residual systematic signals in the data. The novel experimental approach focuses on detecting and jointly explaining these systematics together with the foregrounds and the cosmological signal using Bayesian statistics. To achieve this, REACH features simultaneous observations with two different antennas, an ultra-wideband system (redshift range about 7.5 to 28) and a receiver calibrator based on in-field measurements. Simulated observations forecast percent-level constraints on astrophysical parameters, potentially opening up a new window to the infant Universe. The Radio Experiment for the Analysis of Cosmic Hydrogen (REACH) aims to detect the sky-averaged 21-cm neutral hydrogen line from the early Universe by jointly analysing the cosmological signal, foreground emission and systematic effects.

18 citations

Journal ArticleDOI
TL;DR: In this paper , a Bayesian re-analysis of the sky-averaged 21-cm experimental data from SARAS2 using nested sampling implemented with polychord, spectrally smooth foreground modelling implemented with max-smooth, detailed systematic modelling and rapid signal emulation with globalemu is presented.
Abstract: We present a Bayesian re-analysis of the sky-averaged 21-cm experimental data from SARAS2 using nested sampling implemented with polychord, spectrally smooth foreground modelling implemented with maxsmooth, detailed systematic modelling and rapid signal emulation with globalemu. Our analysis differs from previous analysis of the SARAS2 data through the use of a full Bayesian framework and separate modelling of the foreground and non-smooth systematics. We use the most up-to-date signal models including Lyman- 𝛼 and CMB heating parameterised by astrophysical parameters such as star formation efficiency, X-ray heating efficiency, minimal virial circular velocity of star forming galaxies, CMB optical depth and the low energy cutoff of the X-ray spectral energy distribution. We consider models with an excess radio background above the CMB produced via radio emission from early galaxies and parameterised by a radio production efficiency. A non-smooth systematic is identified and modelled as both a frequency damped sinusoid introduced by the electronics and separately from the sky. The latter is modulated by the total efficiency of the antenna and marginally favoured by the data. We consider three different models for the noise in the data. The SARAS2 constraints on individual astrophysical parameters are extremely weak however we identify classes of disfavoured signals. We weakly disfavour standard astrophysical models with high Lyman- 𝛼 fluxes and weak heating and more confidently disfavour exotic models with high Lyman- 𝛼 fluxes, low X-ray efficiencies and high radio production efficiencies in early galaxies.

8 citations

DOI
01 Jan 2015
TL;DR: In this article, the authors acknowledge partial support from the Spanish Ministerio de Economia y Competitividad (MICINN) through projects AYA2013-48623-C2-2, AYA2007-68058-C03-01 and AYA2010-21766-C 03-02, Aya2012-30789, and the Consolider-Ingenio project CSD2010-00064 (EPI: Exploring the Physics of Inflation).
Abstract: The authors acknowledge partial support from the Spanish Ministerio de Economia y Competitividad (MICINN) through projects AYA2013-48623-C2-2, AYA2007-68058-C03-01, AYA2010-21766-C03-02, AYA2012-30789, and the Consolider-Ingenio project CSD2010-00064 (EPI: Exploring the Physics of Inflation). We also acknowledge the support of the Ramon y Cajal fellowship (RyC 2011 148062) awarded by the Spanish MICINN and the Marie Curie Career Integration Grant (CIG 294183).

5 citations

References
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Journal ArticleDOI
TL;DR: A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n 41) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point.
Abstract: A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n 41) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point. The simplex adapts itself to the local landscape, and contracts on to the final minimum. The method is shown to be effective and computationally compact. A procedure is given for the estimation of the Hessian matrix in the neighbourhood of the minimum, needed in statistical estimation problems.

27,271 citations


Additional excerpts

  • ...…high magnitude smooth signals or foregrounds. maxsmooth DCFs can be fitted with routines such as Basin-hopping (Wales & Doye, 1997) and NelderMead (Nelder & Mead, 1965) and this has been the practice for 21-cm cosmology (Sathyanarayana Rao, Subrahmanyan, Udaya Shankar, & Chluba, 2017; Singh &…...

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  • ...When jointly fitting an MSF and signal model we find that we can accurately recover the signal itself (see Bevins et al. (2020)). maxsmooth is applicable to any experiment in which the signal of interest has to be separated from comparatively high magnitude smooth signals or foregrounds. maxsmooth DCFs can be fitted with routines such as Basin-hopping (Wales & Doye, 1997) and NelderMead (Nelder & Mead, 1965) and this has been the practice for 21-cm cosmology (Sathyanarayana Rao, Subrahmanyan, Udaya Shankar, & Chluba, 2017; Singh & Subrahmanyan, 2019)....

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Journal ArticleDOI
TL;DR: In this paper, the potential energy surface is transformed into a collection of interpenetrating staircases, and the lowest known structures are located for all Lennard-Jones clusters up to 110 atoms, including a number that have never been found before in unbiased searches.
Abstract: We describe a global optimization technique using “basin-hopping” in which the potential energy surface is transformed into a collection of interpenetrating staircases. This method has been designed to exploit the features that recent work suggests must be present in an energy landscape for efficient relaxation to the global minimum. The transformation associates any point in configuration space with the local minimum obtained by a geometry optimization started from that point, effectively removing transition state regions from the problem. However, unlike other methods based upon hypersurface deformation, this transformation does not change the global minimum. The lowest known structures are located for all Lennard-Jones clusters up to 110 atoms, including a number that have never been found before in unbiased searches.

2,637 citations


"maxsmooth: Derivative Constrained F..." refers background in this paper

  • ...…to be separated from comparatively high magnitude smooth signals or foregrounds. maxsmooth DCFs can be fitted with routines such as Basin-hopping (Wales & Doye, 1997) and NelderMead (Nelder & Mead, 1965) and this has been the practice for 21-cm cosmology (Sathyanarayana Rao, Subrahmanyan, Udaya…...

    [...]

  • ...When jointly fitting an MSF and signal model we find that we can accurately recover the signal itself (see Bevins et al. (2020)). maxsmooth is applicable to any experiment in which the signal of interest has to be separated from comparatively high magnitude smooth signals or foregrounds. maxsmooth DCFs can be fitted with routines such as Basin-hopping (Wales & Doye, 1997) and NelderMead (Nelder & Mead, 1965) and this has been the practice for 21-cm cosmology (Sathyanarayana Rao, Subrahmanyan, Udaya Shankar, & Chluba, 2017; Singh & Subrahmanyan, 2019)....

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  • ...We find that the use of quadratic programming makes maxsmooth approximately two orders of magnitude quicker than a Basin-hopping/Nelder-Mead approach. maxsmooth rephrases the above condition such that ±m dmy dxm ≤ 0, where the ± applies to a given m....

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Journal ArticleDOI
TL;DR: In this article, the physics of the 21 cm transition were reviewed, focusing on processes relevant at high redshifts, and the insights to be gained from such observations were described.

1,315 citations

Journal ArticleDOI
28 Feb 2018-Nature
TL;DR: The detection of a flattened absorption profile in the sky-averaged radio spectrum that is largely consistent with expectations for the 21-centimetre signal induced by early stars; however, the best-fitting amplitude of the profile is more than a factor of two greater than the largest predictions.
Abstract: The 21-cm absorption profile is detected in the sky-averaged radio spectrum, but is much stronger than predicted, suggesting that the primordial gas might have been cooler than predicted. As the first stars heated hydrogen in the early Universe, the 21-cm hyperfine line—an astronomical standard that represents the spin-flip transition in the ground state of atomic hydrogen—was altered, causing the hydrogen gas to absorb photons from the microwave background. This should produce an observable absorption signal at frequencies of less than 200 megahertz (MHz). Judd Bowman and colleagues report the observation of an absorption profile centred at a frequency of 78 MHz that is about 19 MHz wide and 0.5 kelvin deep. The profile is generally in line with expectations, although it is deeper than predicted. An accompanying paper by Rennan Barkana suggests that baryons were interacting with cold dark-matter particles in the early Universe, cooling the gas more than had been expected. After stars formed in the early Universe, their ultraviolet light is expected, eventually, to have penetrated the primordial hydrogen gas and altered the excitation state of its 21-centimetre hyperfine line. This alteration would cause the gas to absorb photons from the cosmic microwave background, producing a spectral distortion that should be observable today at radio frequencies of less than 200 megahertz1. Here we report the detection of a flattened absorption profile in the sky-averaged radio spectrum, which is centred at a frequency of 78 megahertz and has a best-fitting full-width at half-maximum of 19 megahertz and an amplitude of 0.5 kelvin. The profile is largely consistent with expectations for the 21-centimetre signal induced by early stars; however, the best-fitting amplitude of the profile is more than a factor of two greater than the largest predictions2. This discrepancy suggests that either the primordial gas was much colder than expected or the background radiation temperature was hotter than expected. Astrophysical phenomena (such as radiation from stars and stellar remnants) are unlikely to account for this discrepancy; of the proposed extensions to the standard model of cosmology and particle physics, only cooling of the gas as a result of interactions between dark matter and baryons seems to explain the observed amplitude3. The low-frequency edge of the observed profile indicates that stars existed and had produced a background of Lyman-α photons by 180 million years after the Big Bang. The high-frequency edge indicates that the gas was heated to above the radiation temperature less than 100 million years later.

992 citations

Journal ArticleDOI
TL;DR: This review detail the physics that governs the 21 cm signal and describe what might be learnt from upcoming observations, and generalize the discussion to intensity mapping of other atomic and molecular lines.
Abstract: Imaging the Universe during the first hundreds of millions of years remains one of the exciting challenges facing modern cosmology. Observations of the redshifted 21 cm line of atomic hydrogen offer the potential of opening a new window into this epoch. This will transform our understanding of the formation of the first stars and galaxies and of the thermal history of the Universe. A new generation of radio telescopes is being constructed for this purpose with the first results starting to trickle in. In this review, we detail the physics that governs the 21 cm signal and describe what might be learnt from upcoming observations. We also generalize our discussion to intensity mapping of other atomic and molecular lines.

720 citations


"maxsmooth: Derivative Constrained F..." refers background in this paper

  • ...During the CD and EoR the first stars formed and the properties of the hydrogen gas changed as it interacted with radiation from these stars (Barkana, 2016; Furlanetto, Oh, & Briggs, 2006; Pritchard & Loeb, 2012)....

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