Cross-correlation Distribution Research Articles

Distributed High-Temperature Sensing Based on Non-Local Haar Transform in OFDR

We demonstrate a short-time long distance distributed high-temperature sensing by non-local Haar transform (NLH) in optical frequency domain reflectometry (OFDR). By searching similar pixels across a non-local region, NLH makes good use of incomplete space similarity of information contained in 3D cross-correlation distribution of local Rayleigh scattering spectra measured by OFDR, which can be used to enhance image denoising performance and retain rare details of original spectra data. With the proposed method, we have achieved a short-time distributed high-temperature sensing ranging from 950°C to 1050°C over 102 m by reduced-cladding single mode fiber (RC-SMF) with a sensing spatial resolution of 2 cm. Compared with traditional image denoising methods including Gaussian filter (GF), block-matching three dimensional filter (BM3D) and wavelet denoising (WD), the proposed NLH method has a best performance to restore the consistency of spectral shift distribution caused by the same temperature change without deterioration of sensing spatial resolution.

Three-dimensional hydraulic tomography analyses to investigate commingling issues of reproducibility, data density, and geological prior models

Over the past two decades, geostatistics-based hydraulic tomography (HT) has been proven to be a robust method for subsurface heterogeneity characterization. However, the reproducibility of estimated parameter fields, namely the hydraulic conductivity (K) and specific storage (Ss), obtained over different data collection periods and under different flow scenarios have been rarely studied. In this study, we investigate the reproducibility and predictivity of HT estimates using data collected in 2019 and 2020 at a field site of varying boundary conditions underlain by sedimentary units in Japan, with different data density and prior geological information. Model performance of each case is evaluated qualitatively and quantitatively by examining results from model calibration, self-validation and cross-validation, in terms of parameter fields comparison, drawdown matches and cross-correlation distributions. Results of this study reveal that: 1) overall, the parameter fields for 2019 and 2020 HT estimates are generally reproducible, while fine-scale discrepancy exists; 2) they are also found to be reproducible in terms of consistency of estimated geostatistical parameters; 3) higher levels of reproducibility and predictivity associated with estimated K and Ss fields are obtained when higher data density is included for geostatistical inverse modeling with more accurate prior geological information; and 4) the different spatial distributions of cross-correlation between head and parameter fields induced through the significant variation of the groundwater flow field from 2019 to 2020 strengthen the notion of reproducibility of HT results. These results collectively suggest that HT has the potential for mapping changes to K and Ss heterogeneity over time broadening its future applications to various practical problems.

Two-valued cross correlation distributions between binary m sequences and their decimation sequences

Two-valued cross correlation distributions between binary m sequences and their decimation sequences

Time-domain based evaluation of detection efficiency in liquid scintillation counting

This work explores the distribution of time intervals between signals from the photomultiplier tubes (PMTs) of a liquid scintillation counting (LSC) system when a scintillation burst caused by an ionizing particle is detected. This distribution is termed the cross-correlation distribution and it is shown that it contains information about the probability to detect a scintillation event. A theoretical model that describes the cross-correlation distribution is derived. The model can be used to estimate the mean number of detected photons in a LSC measurement, which allows the calculation of the detection efficiency. The theoretical findings are validated by Monte Carlo simulations and by experiments with low-energy beta-emitting and electron-capture radionuclides (^3hbox {H}, ^{14}hbox {C}, ^{63}hbox {Ni} and ^{55}hbox {Fe}), with dedicated LSC systems and several commercial LSC cocktails. The results show that some of the parameters of the cross-correlation distribution such as the peak height or the kurtosis can be used as detection efficiency estimators or quenching indicators in LSC. Thus, although the time domain and the cross-correlation distribution have received little to no attention in the practice of LSC, they have the capacity to bring significant improvements in almost all LSC applications related to activity determination of low-energy beta-emitting and electron-capture radionuclides. The results also suggest concepts for the development of innovative LSC systems.

Nonlinear Quasi-Synchronous Multi User Chirp Spread Spectrum Signaling

Multi user orthogonal chirp spread spectrum (OCSS) can improve the spectral inefficiency of chirp spread spectrum (CSS) but is only feasible with perfect synchronism and without any channel dispersion. Asynchronism, channel dispersion, or unexpectedly large Doppler shifts can cause multiple access interference (MAI), which degrades performance. Conditions with small timing offsets we term quasi-synchronous (QS). In this paper, we propose two new sets of nonlinear chirps to improve CSS system performance in QS conditions. We analytically and numerically evaluate cross-correlation distributions. We also derive the bit error probability for Binary CSS analytically and validate our theoretical result with both numerical and simulation results; our error probability expression is applicable to any binary time-frequency (TF) chirp waveform. Finally, we show that in QS conditions our two new nonlinear chirp designs outperform the classical linear chirp and all existing nonlinear chirps from the literature. To complete our analysis, we demonstrate that our nonlinear CSS designs outperform existing chirps in two realistic (empirically modeled) dispersive air to ground channels.

Binary and ternary sequences with a few cross correlations

Let m be a positive integer, r ≡ 1 (mod 3) be a prime number, and the order of p modulo rm be $\frac {\phi (r^{m})}3$, where ϕ is the Euler function. Let $q=p^{\frac {\phi (r^{m})}3}$ and $d=\frac {q-1}{r^{m}}$. We investigate the cross correlation distribution between a p-ary m-sequence and its d-decimated sequences. In this paper, we deal with the cases of p = 2 and p = 3. Our results show that the binary sequences have two-valued cross correlations and the ternary sequences have at most three-valued cross correlations, see Theorems 3.2 and 4.2. As a byproduct, we also explicitly compute the Gauss periods $\eta _{0}^{(\frac {q-1}{r^{m}},q)}$.

Measuring the Sum-of-Squares Indicator of Boolean Functions in Encryption Algorithm for Internet of Things

Encryption algorithm has an important application in ensuring the security of the Internet of Things. Boolean function is the basic component of symmetric encryption algorithm, and its many cryptographic properties are important indicators to measure the security of cryptographic algorithm. This paper focuses on the sum-of-squares indicator of Boolean function; an upper bound and a lower bound of the sum-of-squares on Boolean functions are obtained by the decomposition Boolean functions; some properties and a search algorithm of Boolean functions with the same autocorrelation (or cross-correlation) distribution are given. Finally, a construction method to obtain a balanced Boolean function with small sum-of-squares indicator is derived by decomposition Boolean functions. Compared with the known balanced Boolean functions, the constructed functions have the higher nonlinearity and the better global avalanche characteristics property.

Comparison of noise reduction methods in radiometric correlation measurements of two-phase liquid-gas flows

Two-phase liquid-gas flows occur frequently in the mining, energy, chemical, and petrochemical industries. One of non-contact methods used to analyse these flows is the gamma ray absorption method. However, the signals received from radiation detectors contain a significant stochastic noise, which makes them difficult to analyse. The article describes four methods of noise reduction in cross-correlation measurements of water-air mixture flows in a horizontal pipeline. In addition to the classical method of digital filtering of signals, the methods consisting in signal spectrum filtering, discrete wavelet transformation, and Nadaraya-Watson kernel estimator are described. Sample results of the measurements carried out in the horizontal pipe having the inner diameter of 30 mm for the air bubbles velocity ranging from 0.7 to 1.4 m/s are presented. In the research, the absorption set composed of two linear Am-241 gamma-ray sources and two scintillation NaI(Tl) probes was used. It was found that the lowest measurement uncertainty of the dispersed phase flow velocity is obtained when the cross-correlation distributions of the recorded signals are smoothed using the Discrete Wavelet Transform or the Nadaraya-Watson kernel estimator.

Binary Sequences With Three-Valued Cross Correlations of Different Lengths

In general, it is hard to find the cross correlation distribution between two sequences. In particular, there are only few cases that the cross correlation is three-valued. In this paper, new pairs of binary sequences with three cross correlation values are presented. These two sequences have different lengths: $2^{2k}-1$ and $3(2^{k}-1)$ , respectively. We determine the cross correlation distribution between these two sequences. We also give the possible correlation values for the shift decimated sequences. The magnitude of cross correlation values is shown to be low. The techniques presented in this paper may be useful to handle other similar cases.

Automated detection of Martian water ice clouds using Support Vector Machine and simple feature vectors

We present a method for evaluating the presence of Martian water ice clouds using difference images and cross-correlation distributions calculated from blue band images of the Valles Marineris obtained by the Mars Orbiter Camera onboard the Mars Global Surveyor (MGS/MOC). We derived one subtracted image and one cross-correlation distribution from two reflectance images. The difference between the maximum and the average, variance, kurtosis, and skewness of the subtracted image were calculated. Those of the cross-correlation distribution were also calculated. These eight statistics were used as feature vectors for training Support Vector Machine because they were the simplest of features that was expected to be closely associated with the physical properties of water ice clouds. The generalization ability was tested using 10-fold cross-validation. F-measure and accuracy tended to be approximately 0.8 if the maximum in the normalized reflectance and the difference of the maximum and the average in the cross-correlation were selected as features. This result can be physically explained because the blue band as well as the red band is sensitive to water ice clouds. A simple and low-dimensional feature vector enables us to understand the detected water ice clouds physically and presents the lower bound of the score that classifiers trained using more sophisticated feature vectors have to achieve.

Exponential Sums From Half Quadratic Forms and Their Applications

In this paper, we consider a class of exponential sums from some half quadratic binomials. The exponential sums are proven to be eleven-valued with maximal magnitude $({1}/{2}(q-\sqrt {q}))$ except for the trivial value $q$ . As applications, first, we investigate the autocorrelation and cross-correlation distribution among the sequences in a sequence family. Second, we determine the weight distributions of several classes of linear codes. Some of the dual codes have minimum distance four, which are optimal with respect to the Hamming bound. Our results extend the result by Choi et al. and show that some correlation values in it do not occur.

An Implicit Correlation Method for Cross-Correlation Sampling, with MCNPX-PoliMi Validation

Monte Carlo particle transport codes used to model detector responses are traditionally run in analog mode. However, analog simulations of cross-correlation measurements are extremely time-consuming because the probability of coincident detection is small, approximately equal to the product of the probabilities of a single detection in each detector. The new implicit correlation method described here increases the number of correlated event scores, thereby reducing variance and required computation times. The cost of the implicit correlation method is comparable to the cost of simulating single-event detection for the lowest absolute detector efficiency in the problem. The new method is especially useful in the nuclear nonproliferation and safeguards fields for simulating correlation measurements of shielded special nuclear material.The new method was implemented in MCNPX-PoliMi for neutron-neutron cross-correlations with a 252Cf spontaneous fission source measured by 14 detectors at various angles. The method demonstrated good agreement with analog simulation and reference measurement results. Small differences between nonanalog and analog cross-correlation distributions are attributed to discretization errors that are often not present in practical applications. Improvement in the figure of merit was greater than a factor of 100 in all tested cases.

The cross correlation distribution of a p-ary m-sequence of period [formula omitted] and its decimated sequences by [formula omitted

Let p be an odd prime, m and k be positive integers such that s=m/e is odd and k/e is even, where e=gcd⁡(m,k). In this paper, the value distribution of the exponential sum ∑x∈Fpmχ(αx(pk+1)(pm+1)/4+βx) is completely determined with pm≡1(mod4). As applications, when pm≡1(mod4), the distribution of the cross correlation between a p-ary m-sequence (st) of period pm−1 and its decimated sequence (sdt) with d=(pk+1)(pm+1)/4 is determined. The sequence family F is constructed and the cross correlation distribution among sequences in the family F is also determined. Our result shows that the maximal magnitude of the correlation value is low when e=1.

Some Results on Cross-Correlation Distribution Between a <inline-formula> <tex-math notation="TeX">\(p\) </tex-math></inline-formula>-Ary <inline-formula> <tex-math notation="TeX">\(m\) </tex-math></inline-formula>-Sequence and Its Decimated Sequences

For an odd prime p and two positive integers m, k such that m/gcd(k, m) ≥ 3 is odd, let d be a positive integer satisfying d( p k + 1) ≡ 2(mod p m − 1) .I n this paper, the cross-correlation between a p-ary m-sequence and its d-decimated sequences is investigated, and the cross correlation distribution is completely determined. The relationship between the decimations d considered in this paper and some known ones is also studied. This paper generalizes some previous results, and also gives new decimations, which lead to low cross correlation.

Cross-correlation measurements with the EJ-299-33 plastic scintillator

New organic–plastic scintillation compositions have demonstrated pulse-shape discrimination (PSD) of neutrons and gamma rays. We present cross-correlation measurements of 252Cf and mixed uranium–plutonium oxide (MOX) with the EJ-299-33 plastic scintillator. For comparison, equivalent measurements were performed with an EJ-309 liquid scintillator. Offline, digital PSD was applied to each detector. These measurements show that EJ-299-33 sacrifices a factor of 5 in neutron–neutron efficiency relative to EJ-309, but could still utilize the difference in neutron–neutron efficiency and neutron single-to-double ratio to distinguish 252Cf from MOX.These measurements were modeled with MCNPX-PoliMi, and MPPost was used to convert the detailed collision history into simulated cross-correlation distributions. MCNPX-PoliMi predicted the measured 252Cf cross-correlation distribution for EJ-309 to within 10%. Greater photon uncertainty in the MOX sample led to larger discrepancy in the simulated MOX cross-correlation distribution. The modeled EJ-299-33 plastic also gives reasonable agreement with measured cross-correlation distributions, although the MCNPX-PoliMi model appears to under-predict the neutron detection efficiency.

A Note on the Five Valued Conjectures of Johansen, Helleseth and Kholosha and Zeta Functions

For the complete five-valued cross-correlation distribution between two m-sequences s <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> and s <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dt</sub> of period 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> - 1 that differ by the decimation d = (2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2k</sup> + 1)/(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sup> + 1) where m is odd and gcd(k, m) = 1, Johansen and Helleseth expressed it in terms of some exponential sums. And two conjectures were presented about them. In this correspondence we study these conjectures for the particular case where k = 3, and the cases k = 1, 2 can also be analyzed in a similar process. When k > 3, the degrees of the relevant polynomials will become higher.

X-ray cross-correlation analysis of the low-mass X-ray binary 4U 1636-53

AbstractWe analyze the cross-correlation function of the soft and hard X-rays of the atoll source 4U 1636-53 with RXTE data. The results show that the cross-correlations evolve along the different branches of the color-color diagram. At the lower left banana states, we have both positive and ambiguous correlations, and positive correlations are dominant for the lower banana and the upper banana states. The anti-correlation is detected at the top of the upper banana states. The cross-correlations of two atoll sources 4U 1735-44 and 4U 1608-52 have been studied in previous work, and the anti-correlations are detected at the lower left banana or the top of the upper banana states. Our results show that, in the 4U 1636-53, the distribution of the cross-correlations in the color-color diagram is similar to those of 4U 1735-44 and 4U 1608-52, and confirm further that the distribution of cross-correlations in color-color diagram could be correlated with the luminosity of the source.

Some New Results on the Cross Correlation of &lt;inline-formula&gt; &lt;tex-math notation="TeX"&gt;$m$ &lt;/tex-math&gt;&lt;/inline-formula&gt;-Sequences

The determination of the cross correlation between an m-sequence and its decimated sequence has been a longstanding research problem. Considering a ternary m-sequence of period 33r - 1, we determine the cross correlation distribution for decimations d = 3r + 2 and d = 32r + 2, where gcd(r, 3) = 1. Meanwhile, for a binary m-sequence of period 22lm - 1, we make an initial investigation for the decimation d = (22lm - 1)/(2m + 1) + 2s, where l ≥ 2 is even and 0 <; s <; 2m - 1. It is shown that the cross correlation takes at least four values. Furthermore, we confirm the validity of two famous conjectures due to Sarwate et al. and Helleseth in this case.

Cross-Correlation Distribution between a &lt;i&gt;p&lt;/i&gt;-Ary &lt;i&gt;m&lt;/i&gt;-Sequence and Its Decimated Sequence with Decimation Factor $d=\frac{(p^{m}+1)^2}{2(p^e+1)}$

Let p be an odd prime and m be any positive integer. Assume that n=2m and e is a positive divisor of m with m/e being odd. For the decimation factor $d=\frac{(p^{m}+1)^2}{2(p^e+1)}$, the cross-correlation between the p-ary m-sequence $\{tr_1^n(\alpha^i)\}$ and its decimated sequence $\{tr_1^n(\alpha^{di})\}$ is investigated. The value distribution of the correlation function is completely determined. The results in this paper generalize the previous results given by Choi, Luo and Sun et al., where they considered some special cases of the decimation factor d with a restriction that m is odd. Note that the integer m in this paper can be even or odd. Thus, the decimation factor d here is more flexible than the previous ones. Moreover, our method for determining the value distribution of the correlation function is different from those adopted by Luo and Sun et al. in that we do not need to calculate the third power sum of the correlation function, which is usually difficult to handle.

5-값 상호상관관계를 갖는 비선형 이진수열군의 상호상관관계 빈도 분석

여러 가지 디지털통신 시스템에서 많이 사용되고 있는 의사 난수열을 설계하는데 있어 가장 중요한 문제는 생성된 수열들 사이의 상호상관관계가 낮은 수열을 생성하는 것이다. 또한 설계된 이진수열의 상호상관관계의 빈도분석은 많은 연구자에 의해 연구되어왔다. 본 논문에서는 n=2m, <TEX>$d=2^{n-1}(3{\cdot}2^m-1)$</TEX>일 때 5-값 상호상관관계를 갖는 비선형 이진수열군 <TEX>$S^r=\{Tr^m_1\{[Tr^n_m(a{\alpha}^t+{\alpha}^{dt}</TEX><TEX>]</TEX><TEX>^r\}{\mid}a{\in}GF(2^m),0{\leq}t </TEX><TEX>&</TEX><TEX>lt; 2^n-1\}$</TEX>에 대한 상호상관관계에 대한 빈도 분석과 여러 가지 상호상관관계 성질을 분석한다. 여기서 <TEX>$gcd(r,2^m-1)=1$</TEX>이다. The design of PN(Pseudo Noise) sequences with good cross-correlation properties is important for many research areas in communication systems. Also analyses of cross-correlation frequency between designed sequences have been researched. In this paper we analyze of cross-correlation distribution and properties of non-linear binary sequences family <TEX>$S^r=\{Tr^m_1\{[Tr^n_m(a{\alpha}^t+{\alpha}^{dt}</TEX><TEX>]</TEX><TEX>^r\}{\mid}a{\in}GF(2^m),0{\leq}t </TEX><TEX>&</TEX><TEX>lt; 2^n-1\}$</TEX>, where <TEX>$gcd(r,2^m-1)=1$</TEX> with 5-valued cross-correlation.