scholarly journals Gaussian Process Regression for foreground removal in HI intensity mapping experiments

2021 ◽  
Author(s):  
Paula S Soares ◽  
Catherine A Watkinson ◽  
Steven Cunnington ◽  
Alkistis Pourtsidou
Keyword(s):  
Power Spectrum ◽  
Gaussian Process ◽  
Low Frequency ◽  
Gaussian Process Regression ◽  
Principal Component ◽  
Frequency Range ◽  
Intensity Mapping ◽  
Removal Technique ◽  
First Time ◽  
Foreground Removal

Abstract We apply for the first time Gaussian Process Regression (GPR) as a foreground removal technique in the context of single-dish, low redshift H i intensity mapping, and present an open-source python toolkit for doing so. We use MeerKAT and SKA1-MID-like simulations of 21cm foregrounds (including polarisation leakage), H i cosmological signal and instrumental noise. We find that it is possible to use GPR as a foreground removal technique in this context, and that it is better suited in some cases to recover the H i power spectrum than Principal Component Analysis (PCA), especially on small scales. GPR is especially good at recovering the radial power spectrum, outperforming PCA when considering the full bandwidth of our data. Both methods are worse at recovering the transverse power spectrum, since they rely on frequency-only covariance information. When halving our data along frequency, we find that GPR performs better in the low frequency range, where foregrounds are brighter. It performs worse than PCA when frequency channels are missing, to emulate RFI flagging. We conclude that GPR is an excellent foreground removal option for the case of single-dish, low redshift H i intensity mapping in the absence of missing frequency channels. Our python toolkit gpr4im and the data used in this analysis are publicly available on GitHub.

scholarly journals Gaussian process foreground subtraction and power spectrum estimation for 21 cm cosmology

2020 ◽  
Vol 501 (1) ◽  
pp. 1463-1480
Author(s):  
Nicholas S Kern ◽  
Adrian Liu
Keyword(s):  
Power Spectrum ◽  
Gaussian Process ◽  
Signal To Noise Ratio ◽  
Low Frequency ◽  
Gaussian Process Regression ◽  
Spectrum Estimation ◽  
Signal Loss ◽  
Intensity Mapping ◽  
Quadratic Estimator ◽  
Window Functions

ABSTRACT One of the primary challenges in enabling the scientific potential of 21 cm intensity mapping at the epoch of reionization (EoR) is the separation of astrophysical foreground contamination. Recent works have claimed that Gaussian process regression (GPR) can robustly perform this separation, particularly at low Fourier k wavenumbers where the EoR signal reaches its peak signal-to-noise ratio. We revisit this topic by casting GPR foreground subtraction (GPR-FS) into the quadratic estimator formalism, thereby putting its statistical properties on stronger theoretical footing. We find that GPR-FS can distort the window functions at these low k modes, which, without proper decorrelation, make it difficult to probe the EoR power spectrum. Incidentally, we also show that GPR-FS is in fact closely related to the widely studied inverse covariance weighting of the optimal quadratic estimator. As a case study, we look at recent power spectrum upper limits from the Low-Frequency Array (LOFAR) that utilized GPR-FS. We pay close attention to their normalization scheme, showing that it is particularly sensitive to signal loss when the EoR covariance is misestimated. This has possible ramifications for recent astrophysical interpretations of the LOFAR limits, because many of the EoR models ruled out do not fall within the bounds of the covariance models explored by LOFAR. Being more robust to this bias, we conclude that the quadratic estimator is a more natural framework for implementing GPR-FS and computing the 21 cm power spectrum.

scholarly journals A census of the pulsar population observed with the international LOFAR station FR606 at low frequencies (25–80 MHz)

2020 ◽  
Vol 635 ◽  
pp. A76 ◽  
Author(s):  
L. Bondonneau ◽  
J.-M. Grießmeier ◽  
G. Theureau ◽  
A. V. Bilous ◽  
V. I. Kondratiev ◽  
...  
Keyword(s):  
Low Frequency ◽  
Frequency Range ◽  
Radio Pulsars ◽  
Low Frequencies ◽  
Radio Observatory ◽  
Future Studies ◽  
New Information ◽  
Upper Limits ◽  
Widespread Phenomenon ◽  
First Time

Context. To date, only 69 pulsars have been identified with a detected pulsed radio emission below 100 MHz. A LOFAR-core LBA census and a dedicated campaign with the Nançay LOFAR station in stand-alone mode were carried out in the years 2014–2017 in order to extend the known population in this frequency range. Aims. In this paper, we aim to extend the sample of known radio pulsars at low frequencies and to produce a catalogue in the frequency range of 25–80 MHz. This will allow future studies to probe the local Galactic pulsar population, in addition to helping explain their emission mechanism, better characterising the low-frequency turnover in their spectra, and obtaining new information about the interstellar medium through the study of dispersion, scattering, and scintillation. Methods. We observed 102 pulsars that are known to emit radio pulses below 200 MHz and with declination above −30°. We used the Low Band Antennas (LBA) of the LOw Frequency ARray (LOFAR) international station FR606 at the Nançay Radio Observatory in stand-alone mode, recording data between 25 and 80 MHz. Results. Out of our sample of 102 pulsars, we detected 64. We confirmed the existence of ten pulsars detected below 100 MHz by the LOFAR LBA census for the first time (Bilous et al. 2020, A&A, 635, A75) and we added two more pulsars that had never before been detected in this frequency range. We provided average pulse profiles, DM values, and mean flux densities (or upper limits in the case of non-detections). The comparison with previously published results allows us to identify a hitherto unknown spectral turnover for five pulsars, confirming the expectation that spectral turnovers are a widespread phenomenon.

Gaussian Process Regression – A tool for improved climate index reconstructions

2021 ◽  
Author(s):  
Marlene Klockmann ◽  
Eduardo Zorita
Keyword(s):  
Climate Variability ◽  
Gaussian Process ◽  
Climate Model ◽  
Model Simulation ◽  
Gaussian Process Regression ◽  
Principal Component ◽  
Climate Index ◽  
Test Environment ◽  
Past Climate ◽  
Noisy Input

<p><span>We present a flexible non-linear framework of Gaussian Process Regression (GPR) for the reconstruction of past climate indexes such as the Atlantic Multidecadal Variability (AMV). These reconstructions are needed because the historical observation period is too short to provide a long-term perspective on climate variability. Climate indexes can be reconstructed from proxy data (e.g. tree rings) with the help of statistical models. Previous reconstructions of climate indexes mostly used some form of linear regression methods, which are known to underestimate the true amplitude of variability and perform poorly if noisy input data is used. </span></p><p><span>We implement the machine-learning method GPR for climate index reconstruction with the goal of preserving the amplitude of past climate variability. To test the framework in a controlled environment, we create pseudo-proxies from a coupled climate model simulation of the past 2000 years. In our test environment, the GPR strongly improves the reconstruction of the AMV with respect to a multi-linear Principal Component Regression. The amplitude of reconstructed variability is very close to the true variability even if non-climatic noise is added to the pseudo-proxies. In addition, the framework can directly take into account known proxy uncertainties and fit data-sets with a variable number of records in time. Thus, the GPR framework seems to be a highly suitable tool for robust and improved climate index reconstructions.</span></p>

Gaussian process NARX model for damage detection in composite aircraft structures

2021 ◽  
pp. 1-10
Author(s):  
Samuel da Silva ◽  
Luis G G Villani ◽  
Marc Rebillat ◽  
Nazih Mechbal
Keyword(s):  
Gaussian Process ◽  
Gaussian Process Regression ◽  
Principal Component ◽  
False Alarms ◽  
Confidence Bounds ◽  
Model Uncertainties ◽  
Bottom Part ◽  
Number Of False Alarms ◽  
Simulation Errors ◽  
Nonlinear Autoregressive

Abstract This paper demonstrates the Gaussian process regression model's applicability combined with a nonlinear autoregressive exogenous (NARX) framework using experimental data measured with PZTs' patches bonded in a composite aeronautical structure for concerning a novel SHM strategy. A stiffened carbon-epoxy plate regarding a healthy condition and simulated damage on the center of the bottom part of the stiffener is utilized. Comparing the performance in terms of simulation errors is made to observe if the identified models can represent and predict the waveform with confidence bounds considering the confounding effect produced by noise or possible temperature variations assuming a dataset preprocessed using principal component analysis. The results of the GP-NARX identified model have attested correct classification with a reduced number of false alarms, even with model uncertainties propagation regarding healthy and damaged conditions.

Empirical and theoretical analysis of the extremely low frequency arterial blood pressure power spectrum in unanesthetized rat

2006 ◽  
Vol 291 (6) ◽  
pp. H2816-H2824 ◽  
Author(s):  
David R. Brown ◽  
Lisa A. Cassis ◽  
Dennis L. Silcox ◽  
Laura V. Brown ◽  
David C. Randall
Keyword(s):  
Blood Pressure ◽  
Time Series ◽  
Power Spectrum ◽  
Arterial Blood Pressure ◽  
Low Frequency ◽  
Absolute Difference ◽  
Frequency Range ◽  
Low Frequencies ◽  
Extremely Low Frequency ◽  
Arterial Blood

The slope of the log of power versus the log of frequency in the arterial blood pressure (BP) power spectrum is classically considered constant over the low-frequency range (i.e., “fractal” behavior), and is quantified by β in the relationship “1/ fβ.” In practice, the fractal range cannot extend to indefinitely low frequencies, but factor(s) that terminate this behavior, and determine β, are unclear. We present 1) data in rats ( n = 8) that reveal an extremely low frequency spectral region (0.083–1 cycle/h), where β approaches 0 (i.e., the “shoulder”); and 2) a model that 1) predicts realistic values of β within that range of the spectrum that conforms to fractal dynamics (∼1–60 cycles/h), 2) offers an explanation for the shoulder, and 3) predicts that the “successive difference” in mean BP (mBP) is an important parameter of circulatory function. We recorded BP for up to 16 days. The absolute difference between successive mBP samples at 0.1 Hz (the successive difference, or Δ) was 1.87 ± 0.21 mmHg (means ± SD). We calculated β for three frequency ranges: 1) 0.083–1; 2) 1–6; and 3) 6–60 cycles/h. The β for all three regions differed ( P < 0.01). For the two higher frequency ranges, β indicated a fractal relationship (β6–60/h = 1.27 ± 0.01; β1–6/h = 1.80 ± 0.16). Conversely, the slope of the lowest frequency region (i.e., the shoulder) was nearly flat (β0.083–1 /h = 0.32 ± 0.28). We simulated the BP time series as a random walk about 100 mmHg with ranges above and below of 10, 30, and 50 mmHg and with Δ from 0.5 to 2.5. The spectrum for the conditions mimicking actual BP time series (i.e., range, 85–115 mmHg; Δ, 2.00) resembled the observed spectra, with β in the lowest frequency range = 0.207 and fractal-like behavior in the two higher frequency ranges (β = 1.707 and 2.057). We suggest that the combined actions of mechanisms limiting the excursion of arterial BP produce the shoulder in the spectrum and that Δ contributes to determining β.

scholarly journals Mild poikilocapnic hypoxia increases very low frequency haemoglobin oxygenation oscillations in prefrontal cortex

2021 ◽  
Vol 54 (1) ◽  
Author(s):  
Agnieszka Gruszecka ◽  
Monika Waskow ◽  
Marta A. Malkiewicz ◽  
J. Patrick Neary ◽  
Jyotpal Singh ◽  
...  
Keyword(s):  
Prefrontal Cortex ◽  
Healthy Subjects ◽  
Right Hemisphere ◽  
Low Frequency ◽  
Cerebrospinal Fluid Dynamics ◽  
Frequency Range ◽  
Brain Response ◽  
Very Low Frequency ◽  
First Time ◽  
Insight Into

Abstract Background The aim of the study was to investigate the effect of mild cerebral hypoxia on haemoglobin oxygenation (HbO2), cerebrospinal fluid dynamics and cardiovascular physiology. To achieve this goal, four signals were recorded simultaneously: blood pressure, heart rate / electrocardiogram, HbO2 from right hemisphere and changes of subarachnoid space (SAS) width from left hemisphere. Signals were registered from 30 healthy, young participants (2 females and 28 males, body mass index = 24.5 ± 2.3 kg/m2, age 30.8 ± 13.4 years). Results We analysed the recorded signals using wavelet transform and phase coherence. We demonstrated for the first time that in healthy subjects exposed to mild poikilokapnic hypoxia there were increases in very low frequency HbO2 oscillations (< 0.052 Hz) in prefrontal cortex. Additionally, SAS fluctuation diminished in the whole frequency range which could be explained by brain oedema. Conclusions Consequently the study provides insight into mechanisms governing brain response to a mild hypoxic challenge. Our study supports the notion that HbO2 and SAS width monitoring might be beneficial for patients with acute lung disease.

scholarly journals Robust Foregrounds Removal for 21-cm Experiments

2017 ◽  
Vol 12 (S333) ◽  
pp. 284-287
Author(s):  
F. Mertens ◽  
A. Ghosh ◽  
L. V. E. Koopmans
Keyword(s):  
Maximum Likelihood ◽  
Power Spectrum ◽  
Gaussian Process ◽  
Structure Formation ◽  
Early Universe ◽  
Direct Detection ◽  
Gaussian Process Regression ◽  
New Method ◽  
Imaging Method ◽  
Order Of Magnitude

AbstractDirect detection of the Epoch of Reionization via the redshifted 21-cm line will have unprecedented implications on the study of structure formation in the early Universe. To fulfill this promise current and future 21-cm experiments will need to detect the weak 21-cm signal over foregrounds several order of magnitude greater. This requires accurate modeling of the galactic and extragalactic emission and of its contaminants due to instrument chromaticity, ionosphere and imperfect calibration. To solve for this complex modeling, we propose a new method based on Gaussian Process Regression (GPR) which is able to cleanly separate the cosmological signal from most of the foregrounds contaminants. We also propose a new imaging method based on a maximum likelihood framework which solves for the interferometric equation directly on the sphere. Using this method, chromatic effects causing the so-called “wedge” are effectively eliminated (i.e. deconvolved) in the cylindrical (k⊥, k∥) power spectrum.

Two ranges in blood pressure power spectrum with different 1/f characteristics

1994 ◽  
Vol 267 (2) ◽  
pp. H449-H454 ◽  
Author(s):  
C. D. Wagner ◽  
P. B. Persson
Keyword(s):  
Blood Pressure ◽  
Time Series ◽  
Power Spectrum ◽  
Low Frequency ◽  
Frequency Range ◽  
F Region ◽  
Autonomic Blockade ◽  
Beta Receptor Blockade ◽  
The Difference ◽  
Fast Fourier Analysis

Most time series of biological systems contain a considerable amount of 1/f noise. This form of noise is characterized by fluctuations in which power steadily increases at lower frequencies. To determine the origin of 1/f noise, blood pressure (BP) was measured over 4 h in conscious foxhounds. The power spectrum of BP was obtained by fast Fourier analysis. After log-log transformation, the power spectrum (log power vs. log frequency) characteristically revealed a linear regression. Surprisingly, there were two 1/f ranges. The first 1/f region was located within a low-frequency range (< 10(-1.7) Hz; slope -0.9; r = -0.9). The second 1/f range was identified at 10(-1.4) to 10(-1) Hz (slope -1.2; r = -0.7). After baroreceptor denervation (n = 7), the steepness of both slopes increased significantly (P < 0.05 for lower 1/f range, P < 0.001 for higher 1/f range), and the difference in slopes was clearly greater (slope in lower range -1.2; r = 0.96 vs. -3.1, r = -0.92 in the higher range; P < 0.001). Neither alpha-receptor (n = 6) nor beta-receptor blockade (n = 4) considerably changed the slopes after denervation. However, autonomic blockade (n = 5) restored the slope in the low-frequency range (-0.9; r = -0.9). In conclusion, there are two independently modulated 1/f frequency ranges in BP time series. Baroreceptors especially attenuate 1/f noise in the higher frequency range.

scholarly journals Searching for H i imprints in cosmic web filaments with 21-cm intensity mapping

2019 ◽  
Vol 489 (1) ◽  
pp. 385-400 ◽  
Author(s):  
Denis Tramonte ◽  
Yin-Zhe Ma ◽  
Yi-Chao Li ◽  
Lister Staveley-Smith
Keyword(s):  
Principal Component Analysis ◽  
Confidence Level ◽  
Column Density ◽  
Neutral Hydrogen ◽  
Principal Component ◽  
Density Parameter ◽  
Common Reference ◽  
Intensity Mapping ◽  
Upper Limits ◽  
First Time

ABSTRACT We investigate the possible presence of neutral hydrogen (H i) in intergalactic filaments at very low redshift (z ∼ 0.08), by stacking a set of 274 712 2dFGRS galaxy pairs over 21-cm maps obtained with dedicated observations conducted with the Parkes radio telescope, over a total sky area of approximately 1300 deg2 covering two patches in the northern and in the southern Galactic hemispheres. The stacking is performed by combining local maps in which each pair is brought to a common reference frame; the resulting signal from the edge galaxies is then removed to extract the filament residual emission. We repeat the analysis on maps cleaned removing either 10 or 20 foreground modes in a principal component analysis. Our study does not reveal any clear H i excess in the considered filaments in either case; we determine upper limits on the total filament H i brightness temperature at $T_{\rm b} \lesssim 10.3 \, \mu \text{K}$ for the 10-mode and at $T_{\rm b} \lesssim 4.8 \, \mu \text{K}$ for the 20-mode removed maps at the 95 per cent confidence level. These estimates translate into upper limits for the local filament H i density parameter, $\Omega _{\rm HI}^{\rm (f)} \lesssim 7.0\times 10^{-5}$ and $\Omega _{\rm HI}^{\rm (f)} \lesssim 3.2\times 10^{-5}$, respectively, and for the H i column density, $N_{\rm HI} \lesssim 4.6\times 10^{15}\, \text{cm}^{-2}$ and $N_{\rm HI} \lesssim 2.1\times 10^{15}\, \text{cm}^{-2}$, respectively. These column density constraints are consistent with previous detections of H i in the warm-hot intergalactic medium obtained observing broad Ly α absorption systems. This work shows for the first time how such constraints can be achieved using the stacking of galaxy pairs on 21-cm maps.

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