Two-dimensional Correlation Function Research Articles

Celestial gluon amplitudes from the outside in

We show that, given a two-dimensional realization of the celestial OPE in self-dual Yang-Mills, we can find a scalar source around which scattering amplitudes replicate correlation functions computed from the 2D ‘gluon’ operators in a limit where a dynamic massless scalar decouples. We derive conditions on the two-dimensional three-point correlation function so that such a source exists and give two particular examples of this construction, one in which gluons are constructed from vertex operators in the semiclassical limit of Liouville theory and another in which the soft gluons arise from generalized free fields. Finally, we identify a bulk dual to the level of the boundary Kac-Moody algebra and discuss moving beyond the decoupling limit.

Low-False-Alarm-Rate Timing and Duration Estimation of Noisy Frequency Agile Signal by Image Homogeneous Detection and Morphological Signature Matching Schemes.

Frequency hopping spread spectrum (FHSS) applies widely to communication and radar systems to ensure communication information and channel signal quality by tuning frequency within a wide frequency range in a random sequence. An efficient signal processing scheme to resolve the timing and duration signature from an FHSS signal provides crucial information for signal detection and radio band management purposes. In this research, hopping time was first identified by a two-dimensional temporal correlation function (TCF). The timing information was shown at TCF phase discontinuities. To enhance and resolve the timing signature of TCF in a noisy environment, three stages of signature enhancement and morphological matching processes were applied: first, computing the TCF of the FHSS signal and enhancing discontinuities via wavelet transform; second, a dual-diagonal edge finding scheme to extract the timing pattern signature and eliminate mismatching distortion morphologically; finally, Hough transform resolved the agile frequency timing from purified line segments. A grand-scale Monte Carlo simulation of the FHSS signals with additive white Gaussian noise was carried out in the research. The results demonstrated reliable hopping time estimation obtained in SNR at 0 dB and above, with a minimal false detection rate of 1.79%, while the prior related research had an unattended false detection rate of up to 35.29% in such a noisy environment.

STATISTICAL CHARACTERISTICS OF TWO-DIMENSIONAL AUTOCORRELATION FUNCTIONS IN NOISE-LIKE COMPLEX SIGNALS

For various terrestrial and satellite radio systems, the task of detecting complex signals under conditions of a priori uncertainty, when their parameters, including the modulation law, is unknown, is relevant. Detection of such signals can be combined with estimation (measurement) of their parameters, such as carrier frequency and delay time. A method for calculating two-dimensional autocorrelation functions of noise-like complex signals has been developed and their types have been studied depending on the type of pseudo-random sequences on the basis of which they are formed, as well as the modes of emission of these signals in radio systems. Regularities have been revealed in the statistical characteristics of side peaks of various types of complex signals depending on the length of pseudo-random sequences and radiation modes. The developed methodology for calculating the two-dimensional correlation function of complex signals made it possible to identify the relationship between the values of the side peaks of the correlation functions of pseudo-random sequences used in their formation and the peaks of the modules of their two-dimensional correlation function. This approach allows, without a detailed calculation of the two-dimensional correlation functions themselves in various modes of emission of complex signals, to determine their statistical characteristics using the corresponding parameters of the distribution functions of the side peaks of the correlation functions. The two-dimensional correlation function of various complex signals was calculated and their statistical characteristics were studied.

Shape-induced superstructure formation in concentrated ferrofluids under applied magnetic fields.

The field-induced ordering of concentrated ferrofluids based on spherical and cuboidal maghemite nanoparticles is studied using small-angle neutron scattering, revealing a qualitative effect of the faceted shape on the interparticle interactions as shown in the structure factor and correlation lengths. Whereas a spatially disordered hard-sphere interaction potential with a short correlation length is found for ∼9 nm spherical nanoparticles, nanocubes of a comparable particle size exhibit a more pronounced interparticle interaction and the formation of linear arrangements. Analysis of the anisotropic two-dimensional pair distance correlation function gives insight into the real-space arrangement of the nanoparticles. On the basis of the short interparticle distances found here, oriented attachment, i.e. a face-to-face arrangement of the nanocubes, is likely. The unusual field dependence of the interparticle correlations suggests a field-induced structural rearrangement.

Time and Frequency Synchronization for OTFS

In this letter, we propose timing offset (TO) and carrier frequency offset (CFO) estimators for orthogonal time frequency space modulation (OTFS). The proposed estimators do not require any additional training overheads as they deploy the same pilot signal that is used for channel estimation. Hence, no additional training overhead is required for synchronization, thanks to the periodic properties of the pilot signal in the delay-time domain. Our proposed TO estimator finds the start of each OTFS block by searching for a periodic sequence in delay and time dimensions. The CFO is then estimated by finding the mean of the angles of a two-dimensional correlation function at the best timing instant. As a novel aspect of these estimators, the multipath diversity of the channel is exploited to achieve a high estimation accuracy. Finally, we show the efficacy of our proposed synchronization techniques through extensive simulations.

New bounds of wide‐gap frequency‐hopping sequences with frequency shift

With the rapid development of radar, the phenomenon of Doppler frequency shift is not rare. Frequency shift needs to be considered in order to accurately calculate the mutual interference between signals. Meanwhile, to reduce interference to the received signal, each user's frequency hopping sequence shall have wide frequency hopping gap. The authors introduce the time-frequency two-dimensional Hamming correlation function and extend the bounds for wide-gap frequency-hopping sequences. The Li–Fan–Yang–Wang bounds are the special cases of our bounds for frequency shift is zero.

The Spectrum Power of Interstellar Plasma Inhomogeneities in the Direction of Eleven Radio Pulsars

We have analyzed two-dimensional correlation functions from the dynamic spectra of 11 pulsars using the archival data of the “Radioastron” project. The time-sections of these functions were approximated by exponential functions with a power alpha . It is shown that this approximation describes the shape of the correlation function much better than the Gaussian. The temporal structure function D(Delta t) for small values of the delay Delta tis a power law with an index alpha . The spectrum power of spatial inhomogeneities of the interstellar plasma is related to the power of the structure function as n = alpha + 2. We have determined the characteristic scintillation time and the power n in the direction of 11 pulsars. In the direction of three pulsars (B0329+54, B0823+26, and B1929+10), the spectrum power of spatial inhomogeneities of the interstellar plasma turned out to be very close to the value for the Kolmogorov spectrum (n = 3.67). For other pulsars, it ranges from 3.18 to 3.86. It is shown that the measured scintillation parameters are significantly influenced by the duration of the observation session, expressed by its ratio to the characteristic scintillation time. If this parameter is less than 10, the parameter estimates may be biased: the values of alpha and the characteristic scintillation time {{t}_{{{text{scint}}}}} may decrease.

Cyclostationary Approach to the Analysis of the Power in Electric Circuits under Periodic Excitations

This paper proposes a cyclostationary based approach to power analysis carried out for electric circuits under arbitrary periodic excitation. Instantaneous power is considered to be a particular case of the two-dimensional cross correlation function (CCF) of the voltage across, and current through, an element in the electric circuit. The cyclostationary notation is used for deriving the frequency domain counterpart of CCF—voltage–current cross spectrum correlation function (CSCF). Not only does the latter exhibit the complete representation of voltage–current interaction in the element, but it can be systematically exploited for evaluating all commonly used power measures, including instantaneous power, in the form of Fourier series expansion. Simulation examples, which are given for the parallel resonant circuit excited by the periodic currents expressed as a finite sum of sinusoids and periodic train of pulses with distorted edges, numerically illustrate the components of voltage–current CSCF and the characteristics derived from it. In addition, the generalization of Tellegen’s theorem, suggested in the paper, leads to the immediate formulation of the power conservation law for each CSCF component separately.

Holographic soft S -matrix in QED and gravity

At leading order, the $S$-matrices in QED and gravity are known to factorize, providing unambiguous determinations of the parts divergent due to infrared contributions. The soft $S$-matrices defined in this fashion are shown to be defined entirely in terms of two-dimensional models on the celestial sphere, involving two real scalar fields, allowing us to express the soft $S$-matrices for real as well as virtual divergences as two-dimensional correlation functions. We discuss what this means for finding holographic representations of scattering amplitudes in QED and gravity and comment on simple double copy structures that arise during the analysis.

Searching for Aquamelt Behavior among Silklike Biomimetics during Fibrillation under Flow.

In this paper, we elucidate a generic mechanism behind strain-induced phase transition in aqueous solutions of silk-inspired biomimetics by atomistic molecular dynamics simulations. We show the results of modeling of homopeptides polyglycine Gly30 and polyalanine Ala30 and a heteropeptide (Gly-Ala-Gly-Ala-Gly-Ser)5, i.e., the simplest and yet relevant sequences that could mimic the behavior of natural silk under stress conditions. First, we analyze hydrophobicities of the sequences by calculating the Gibbs free energy of hydration and inspecting the interchain hydrogen bonding and hydration by water. Second, the force-extension profiles are scanned and compared with the results for poly(ethylene oxide), the synthetic polymer for which the aquamelt behavior has been proved recently. Additionally, the conformational transitions of oligopeptides from coiled to extended states are characterized by a generalized order parameter and by the dependence of the solvent-accessible surface area of the chains on applied stretching. Fibrillation itself is surveyed using both the two-dimensional interchain pair correlation function and the SAXS/WAXS patterns for the aggregates formed under stress. These are compared with experimental data found in the literature on fibril structure of silk composite materials doped with oligoalanine peptides. Our results show that tensile stress introduced into aqueous oligopeptide solutions facilitates interchain interactions. The oligopeptides display both a greater resistance to extension as compared to poly(ethylene oxide) and a reduced ability for hydrogen bonding of the stretched chains between oligomers and with water. Fiber formation is proved for all simulated objects, but the most structured one is made of a heteropeptide (Gly-Ala-Gly-Ala-Gly-Ser)5: For this sequence, we obtain the highest degree of the secondary structure motifs in the fiber. We conclude that this is the most promising candidate among considered sequences to find the aquamelt behavior in further experimental studies.

Generation Method of Two-Dimensional Optical ZCZ Sequences with High Correlation Peak Value

In this paper, we propose new generation methods of two-dimensional (2D) optical zero-correlation zone (ZCZ) sequences with the high peak autocorrelation amplitude. The 2D optical ZCZ sequence consists of a pair of a binary sequence which takes 1 or 0 and a bi-phase sequence which takes 1 or -1, and has a zero-correlation zone in the two-dimensional correlation function. Because of these properties, the 2D optical ZCZ sequence is suitable for optical code-division multiple access (OCDMA) system using an LED array having a plurality of light-emitting elements arranged in a lattice pattern. The OCDMA system using the 2D optical ZCZ sequence can be increased the data rate and can be suppressed interference by the light of adjacent LEDs. By using the proposed generation methods, we can improve the peak autocorrelation amplitude of the sequence. This means that the BER performance of the OCDMA system using the sequence can be improved.

Two-Dimensional Correlation Function of Binary Black Hole Coalescences

We compute the two-dimensional correlation functions of the binary black hole coalescence detections in LIGO-Virgo’s first and second observation runs. The sky distribution of binary black hole coalescence events is tested for correlations at different angular scales by comparing the observed correlation function to two reference functions that are obtained from mock datasets of localization error regions uniformly distributed in the sky. No excess correlation at any angular scale is found. The power-law slope of the correlation function is estimated to be γ = 2.24 ± 0.33 at the three- σ confidence level, a value consistent with the measured distribution of galaxies.

Anisometric mesoscale nuclear and magnetic texture in sintered Nd-Fe-B magnets

By means of temperature and wavelength-dependent small-angle neutron scattering (SANS) experiments on sintered isotropic and textured Nd-Fe-B magnets we provide evidence for the existence of an anisometric structure in the microstructure of the textured magnets. This conclusion is reached by observing a characteristic cross-shaped angular anisotropy in the total unpolarized SANS cross section at temperatures well above the Curie temperature. Comparison of the experimental SANS data to a microstructural model based on the superquadrics form factor allows us to estimate the shape and lower bounds for the size of the structure. Subtraction of the scattering cross section in the paramagnetic regime from data taken at room temperature provides the magnetic SANS cross section. Surprisingly, the anisotropy of the magnetic scattering is very similar to the nuclear SANS signal, suggesting that the nuclear structure is decorated by the magnetic moments via spin-orbit coupling. Based on the computation of the two-dimensional correlation function we estimate lower bounds for the longitudinal and transversal magnetic correlation lengths.

Pair Correlation Analysis Maps the Dynamic Two-Dimensional Organization of Natural Killer Cell Receptors at the Synapse.

In living systems, the contact between cells is the basis of recognition, differentiation, and orchestration of an immune response. Obstacles and barriers to biomolecular motion, especially for receptors at cellular synapses, critically control these functions by creating an anisotropic environment. Whereas conventional fluorescence fluctuation methods, such as fluorescence correlation spectroscopy or fluorescence recovery after photobleaching, can only measure the isotropic diffusion of molecules, the two-dimensional pair correlation function (2D-pCF) approach probes the anisotropic paths at different spatial locations within an image, allowing the creation of high-resolution maps that can visualize and quantify how molecules move in a living cell. In this work, we show how the 2D-pCF method maps the environment in cellular synapses as perceived by natural killer (NK) cell receptors. In cultured human HLA null 721.221 cells, 2D-pCF reveals the motion of inhibitory receptor HLA-Cw4-YFP coexpressed with KIR3DL1 to be highly directional around specific loci, while these restrictions were absent in the case of HLA-B51-YFP coexpressed with KIR2DL1. Further, in freshly isolated educated (H-2Dd) and uneducated (MHC–/–) primary murine NK cells, the 2D-pCF method shows significant differences in the paths taken by activating receptor NKp46 and inhibitory receptor Ly49A in educated compared to uneducated cells. Altogether, we demonstrate that the 2D-pCF method is very powerful in informing about the spatial organization of motion in cells. Our data support the hypothesis that flexibility in the spatial arrangement of membrane receptors, that is, the absence of barriers, is crucial for NK cell function.

Primary fields in celestial CFT

The basic ingredient of CCFT holography is to regard four-dimensional amplitudes describing conformal wave packets as two-dimensional conformal correlation functions of the operators associated to external particles. By construction, these operators transform as quasi-primary fields under SL(2, ℂ) conformal symmetry group of the celestial sphere. We derive the OPE of the CCFT energy-momentum tensor with the operators representing gauge bosons and show that they transform as Virasoro primaries under diffeomorphisms of the celestial sphere.

Alcock–Paczynski Test with the Evolution of Redshift-space Galaxy Clustering Anisotropy

Abstract We develop an improved Alcock–Paczynski (AP) test method that uses the redshift-space two-point correlation function (2pCF) of galaxies. Cosmological constraints can be obtained by examining the redshift dependence of the normalized 2pCF, which should not change apart from the expected small nonlinear evolution. An incorrect choice of cosmology used to convert redshift to comoving distance will manifest itself as redshift-dependent 2pCF. Our method decomposes the redshift difference of the two-dimensional correlation function into the Legendre polynomials whose amplitudes are modeled by radial fitting functions. Our likelihood analysis with this 2D fitting scheme tightens the constraints on Ω m and w by ∼40% compared to the method of Li et al. that uses one-dimensional angular dependence only. We also find that the correction for the nonlinear evolution in the 2pCF has a non-negligible cosmology dependence, which has been neglected in previous similar studies by Li et al. With an accurate accounting for the nonlinear systematics and use of full two-dimensional shape information of the 2pCF down to scales as small as 5 h −1 Mpc it is expected that the AP test with redshift-space galaxy clustering anisotropy can be a powerful method to constraining the expansion history of the universe.

TWO-DIMENSIONAL SIGNAL PROCESSING IN THE DISCRETE FOURIER BASIS

Исследуются проблемы обработки двумерных сигналов в пространственно-частотной области на базе двумерного дискретного преобразования Фурье. Рассмотрено общее определение и математическое описание двумерного дискретного сигнала в пространственной области. Дана алгебраическая форма двумерного дискретного преобразования Фурье, кратко рассмотрены основные свойства двумерного дискретного преобразования Фурье. Проведен (по отечественным и зарубежным информационным источникам) системный анализ дискретных двумерных сигналов (природы их происхождения, источников формирования), а также методов их обработки, основанных на двумерном дискретном преобразовании Фурье. Рассмотрены приложения дискретных двумерных сигналов в различных предметных областях. Рассмотрены достоинства и недостатки цифровых методов дискретной двумерной обработки на основе двумерного дискретного преобразования Фурье. Выдвинута рабочая гипотеза решения проблематики дискретной двумерной обработки сигналов в пространственно-частотной области путем разработки новых двумерных базисных систем, сочетающих преимущества двумерного дискретного базиса Фурье и снижающих (устраняющих) влияние его негативных эффектов. Показано, что двумерный вариант дискретного канонического разложения случайных сигналов, разработанный В. С. Пугачевым, предполагает (по умолчанию) видоизменение стандартной циклической двумерной корреляционной функции исходного сигнала. Предложены пути решения указанной проблемы.

Asymmetric spectral noise correlations in coherent Stokes and anti-Stokes Raman scatterings

As a diagonal projection of the traditional generalized two-dimensional correlation function, a one-dimensional second-order correlation function in the frequency domain is introduced. This function was applied in coherent Stokes and anti-Stokes Raman scattering (CSRS/CARS) processes. The experiment was performed by a high-average-power fiber amplified femtosecond laser system with a 1 MHz repetition rate. To measure spectral noise fluctuations, sets of 30 sample spectra of pyridine solution were recorded in the fast sequence mode. Experimental design combined with the use of appropriate notch filters allowed for simultaneous recording of the CARS/CSRS spectra. Asymmetry in the noise fluctuations between CARS and CSRS processes is revealed by both one- and two-dimensional (synchronous as well as asynchronous) noise correlation calculations, demonstrating a potential for a high-resolution spectroscopic tool.

Interstellar scintillation observations for PSR B0355+54

In this paper, we report our investigation of pulsar scintillation phenomena by monitoring PSR B0355$+$54 at 2.25 GHz for three successive months using \emph{Kunming 40-m radio telescope}. We have measured the dynamic spectrum, the two-dimensional correlation function, and the secondary spectrum. In those observations with high signal-to-noise ratio ($S/N\ge100$), we have detected the scintillation arcs, which are rarely observable using such a small telescope. The sub-microsecond scale width of the scintillation arc indicates that the transverse scale of structures on scattering screen is as compact as AU size. Our monitoring has also shown that both the scintillation bandwidth, timescale, and arc curvature of PSR B0355$+$54 were varying temporally. The plausible explanation would need to invoke multiple-scattering-screen or multiple-scattering-structure scenario that different screens or ray paths dominate the scintillation process at different epochs.

Near-infrared (NIR) disrelation mapping analysis for poly(lactic) acid nanocomposite

Near infrared (NIR) imaging data of poly(lactic) acid (PLA) nanocomposite were analysed by disrelation mapping to prove the possible interaction between PLA matrix and montmorillonite-based nanoclay. The basic concept of disrelation mapping can be viewed as a spatial filter based on two-dimensional (2D) correlation function to elucidate specific areas where disrelated variation between intensities occurs. Correlation intensity develops on disrelation map only if spectral intensities at v1 and v2 within the local spatial area vary in a dissimilar manner. This feature is especially suitable for identifying the area where interaction between components occurs, which is not fully detected by the conventional visualizations based on a single wavenumber. Disrelation maps constructed with NIR bands arising from the crystalline and amorphous components of the PLA. The pattern appearing on the disrelation map indicated different distributions of the crystalline and amorphous components of the nanocomposite sample. In addition, the development of disrelation intensity becomes acute especially at the area adjacent to the clay, revealing that the clay essentially works as nucleating agent to cause the additional development of crystalline structure of PLA by lowering the surface energy barrier.