correlation spectrum
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2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Suman Dutta ◽  
Subhamoy Maitra ◽  
Chandra Sekhar Mukherjee

<p style='text-indent:20px;'>Here we revisit the quantum algorithms for obtaining Forrelation [Aaronson et al., 2015] values to evaluate some of the well-known cryptographically significant spectra of Boolean functions, namely the Walsh spectrum, the cross-correlation spectrum, and the autocorrelation spectrum. We introduce the existing 2-fold Forrelation formulation with bent duality-based promise problems as desirable instantiations. Next, we concentrate on the 3-fold version through two approaches. First, we judiciously set up some of the functions in 3-fold Forrelation so that given oracle access, one can sample from the Walsh Spectrum of <inline-formula><tex-math id="M1">\begin{document}$ f $\end{document}</tex-math></inline-formula>. Using this, we obtain improved results than what one can achieve by exploiting the Deutsch-Jozsa algorithm. In turn, it has implications in resiliency checking. Furthermore, we use a similar idea to obtain a technique in estimating the cross-correlation (and thus autocorrelation) value at any point, improving upon the existing algorithms. Finally, we tweak the quantum algorithm with the superposition of linear functions to obtain a cross-correlation sampling technique. This is the first cross-correlation sampling algorithm with constant query complexity to the best of our knowledge. This also provides a strategy to check if two functions are uncorrelated of degree <inline-formula><tex-math id="M2">\begin{document}$ m $\end{document}</tex-math></inline-formula>. We further modify this using Dicke states so that the time complexity reduces, particularly for constant values of <inline-formula><tex-math id="M3">\begin{document}$ m $\end{document}</tex-math></inline-formula>.</p>


2021 ◽  
Vol 26 (4) ◽  
pp. 314-325
Author(s):  
S. V. Stepkin ◽  
◽  
O. O. Konovalenko ◽  
Y. V. Vasylkivskyi ◽  
D. V. Mukha ◽  
...  

Purpose: The analytical review of the main results of research in the new direction of the low-frequency radio astronomy, the interstellar medium radio spectroscopy at decameter waves, which had led to astrophysical discovery, recording of the radio recombination lines in absorption for highly excited states of interstellar carbon atoms (more than 600). Design/methodology/approach: The UTR-2 world-largest broadband radio telescope of decameter waves optimally connected with the digital correlation spectrum analyzers has been used. Continuous modernization of antenna system and devices allowed increasing the analysis band from 100 kHzto 24 MHz and a number of channels from 32 to 8192. The radio telescope and receiving equipment with appropriate software allowed to have a long efficient integration time enough for a large line series simultaneously with high resolution, noise immunity and relative sensitivity. Findings: A new type of interstellar spectral lines has been discovered and studied, the interstellar carbon radio recombination lines in absorption for the record high excited atoms with principal quantum numbers greater than 1000. The line parameters (intensity, shape, width, radial velocity) and their relation ship with the interstellar medium physical parameters have been determined. The temperature of line forming regions is about 100 K, the electron concentration up to 0.1 cm–3 and the size of a line forming region is about 10 pc. For the first time, radio recombination lines were observed in absorption. They have significant broadening and are amplified by the dielectronic-like recombination mechanism and are also the lowest frequency lines in atomic spectroscopy. Conclusions: The detected low-frequency carbon radio recombination lines and their observations have become a new highly effective tool for the cold partially ionized interstellar plasma diagnostics. Using them allows obtaining the information which is not available with the other astrophysical methods. For almost half a century of their research, a large amount of hardware-methodical and astrophysical results have been obtained including a record number of Galaxy objects, where there levant lines have been recorded. The domestic achievements have stimulated many theoretical and experimental studies in other countries, but the scientific achievements of Ukrainian scientists prove the best prospects for further development of this very important area of astronomical science. Key words: low-frequency radio astronomy; radio telescope; interstellar medium; radio recombination lines; carbon; hydrogen; spectral analyzer


Materials ◽  
2021 ◽  
Vol 14 (19) ◽  
pp. 5672
Author(s):  
Xuewen Zheng ◽  
Wenyuan Xu ◽  
Shuangrui Xie

In order to explore the influence mechanism of carbon nanotubes on the ultraviolet (UV) aging properties of the SBS-modified asphalt binder, the changes of functional groups in the one-dimensional infrared spectrum and two-dimensional infrared correlation spectrum are studied in this paper. The results show that the UV aging process of the SBS-modified asphalt binder is the process of alkane chain cleavage and reorganization, the formation of oxygen-containing functional groups and decomposition of SBS. The incorporation of carbon nanotubes can reduce the mutual conversion of methyl and methylene functional groups, inhibit the decomposition of butadiene and the destruction of C = C double bonds in SBS. The degradation of SBS during the process of UV aging leads to the change of many functional groups and acceleration of the aging of the SBS-modified asphalt binder. The addition of carbon nanotubes can effectively alleviate the degradation of SBS and the formation of oxygen-containing functional groups at the early stage of UV aging, and reduce the influence of these two changes on other functional groups; thus, improving the anti-aging performance of the SBS-modified asphalt binder.


Materials ◽  
2021 ◽  
Vol 14 (19) ◽  
pp. 5479
Author(s):  
Sachikazu Omura ◽  
Yoshinori Kawazoe ◽  
Daisuke Uemura

We developed non-toxic, harmless adhesives composed of all-natural and renewable resources, of which one was composed of tannin and gelatin, which unfortunately was lacking water resistance, and the other of tannin and ε-poly-l-lysine. In this study, we analyzed the chemical structures of these adhesives by two-dimensional nuclear magnetic resonance (2D-NMR) to explain the difference in water-resistance of the two glues. The results showed that only one proton was left in the benzene ring of tannin after mixing. This suggests that the amino group of the protein was directly attached to the benzene ring by a Michael addition-type reaction, and not to the hydroxyl group. In addition, the heteronuclear multiple bond correlation spectrum of the tannin-poly-l-lysine compound indicated that the hydroxyl groups of the tannin oxidized, suggesting the improvement of its water resistance.


2021 ◽  
Author(s):  
Yongxiang Zhang ◽  
Danchen Zhu ◽  
Lei Zhao

Abstract Rolling element bearings are crucial components in all kinds of rotating machinery. Its fault detection is of great importance, as it ensure the performance of the whole machine. Periodic transient impulses caused by bearing defects are usually submerged in strong background noise which poses a challenge for effective fault feature extraction. To detect bearing faults reliably, a new fault feature extraction method is presented. First, the adaptive maximum second-order cyclostationary blind deconvolution (ACYCBD) is utilized to recover bearing fault related impulses, while the optimal filter length is chosen based on the harmonic significance index (HSI) which quantifies the diagnostic information contained in a deconvoluted signal. Second, cross-correlation is calculated between the teager energy operator (TEO) and the envelope of the deconvoluted signal to further eliminate the irrelevant noise. Finally, fast fourier transform (FFT) is employed to acquire the cross-correlation spectrum and the fault features can be extracted successfully. The performance of the proposed method is verified on both simulation signals and experimental signals acquired from a test rig. The superior abilities of noise reduction and fault detection are shown clearly when compared with some traditional method.


Machines ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 123
Author(s):  
Yang Liu ◽  
Jigou Liu ◽  
Ralph Kennel

Precise frequency measurement plays an essential role in many industrial and robotic systems. However, different effects in the application’s environment cause signal noises, which make frequency measurement more difficult. In small signals or rough environments, even negative Signal-to-Noise Ratios (SNRs) are possible. Thus, frequency measuring methods, which are suited for low SNR signals, are in great demand. While denoising methods such as autocorrelation do not suffice for small signal with low SNR, frequency measurement methods such as Fast-Fourier Transformation or Continuous Wavelet Transformation suffer from Heisenberg’s uncertainty principle, which makes simultaneous high frequency and time resolutions impossible. In this paper, the cross-correlation spectrum is presented as a new frequency measuring method. It can be used in any frequency domain, and provides greater denoising than autocorrelation. Furthermore, frequency and time resolutions are independent from one another, and can be set separately by the user. In simulations, it achieves an average deviation of less than 0.1% on sinusoidal signals with a SNR of −10 dB and a signal length of 1000 data points. When applied to “self-mixing”-interferometry signals, the method can reach a normalized root-mean square error of 0.2% with the aid of an estimation method and an averaging algorithm. Therefore, further research of the method is recommended.


2020 ◽  
Vol 21 (24) ◽  
pp. 9545
Author(s):  
Tatiana V. Ilina ◽  
Zhaoyong Xi ◽  
Teresa Brosenitsch ◽  
Nicolas Sluis-Cremer ◽  
Rieko Ishima

NMR studies of large proteins, over 100 kDa, in solution are technically challenging and, therefore, of considerable interest in the biophysics field. The challenge arises because the molecular tumbling of a protein in solution considerably slows as molecular mass increases, reducing the ability to detect resonances. In fact, the typical 1H-13C or 1H-15N correlation spectrum of a large protein, using a 13C- or 15N-uniformly labeled protein, shows severe line-broadening and signal overlap. Selective isotope labeling of methyl groups is a useful strategy to reduce these issues, however, the reduction in the number of signals that goes hand-in-hand with such a strategy is, in turn, disadvantageous for characterizing the overall features of the protein. When domain motion exists in large proteins, the domain motion differently affects backbone amide signals and methyl groups. Thus, the use of multiple NMR probes, such as 1H, 19F, 13C, and 15N, is ideal to gain overall structural or dynamical information for large proteins. We discuss the utility of observing different NMR nuclei when characterizing a large protein, namely, the 66 kDa multi-domain HIV-1 reverse transcriptase that forms a homodimer in solution. Importantly, we present a biophysical approach, complemented by biochemical assays, to understand not only the homodimer, p66/p66, but also the conformational changes that contribute to its maturation to a heterodimer, p66/p51, upon HIV-1 protease cleavage.


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