Euclidean Correlation Research Articles

Generalized parton distributions from the pseudodistribution approach on the lattice

Generalized parton distributions (GPDs) are key quantities for the description of a hadron’s three-dimensional structure. They are the current focus of all areas of hadronic physics—phenomenological, experimental and theoretical, including lattice QCD. Synergies between these areas are desirable and essential to achieve precise quantification and understanding of the structure of, particularly, nucleons, as the basic ingredients of matter. In this paper, we investigate, for the first time, the numerical implementation of the pseudodistribution approach for the extraction of zero-skewness GPDs for unpolarized quarks. Pseudodistributions are Euclidean parton correlators computable in lattice QCD that can be perturbatively matched to the light-cone parton distributions of interest. Although they are closely related to the quasidistributions and come from the same lattice-extracted matrix elements, they are, however, subject to different systematic effects. We use the data previously utilized for quasi-GPDs and extend it with other momentum transfers and nucleon boosts, in particular a higher one (P3=1.67 GeV) with eightfold larger statistics than the largest one used for quasidistributions (P3=1.25 GeV). We renormalize the matrix elements with a ratio scheme and match the resulting Ioffe time distributions to the light cone in coordinate space. The matched distributions are then used to reconstruct the x dependence with a fitting . We investigate some systematic effects related to this procedure, and we also compare the results with the ones obtained in the framework of quasi-GPDs. Our final results involve the invariant four-momentum transfer squared (−t) dependence of the flavor nonsinglet (u−d) H and E GPDs. Published by the American Physical Society 2024

Euclidean effective theory for partons in the spirit of Steven Weinberg

The standard formulation of parton physics involves light-cone correlations of quark and gluon fields in a hadron, which leads to a widespread impression that it can only be studied through real-time Hamiltonian dynamics or light-front quantization, which are challenged by non-perturbative computations with a pertinent regulator for light-cone/rapidity divergences (or zero modes). As such, standard lattice QCD studies have been limited to indirect parton observables such as first few moments and short-distance correlations, which do not provide the x-distributions without solving the model-dependent inverse problem. Here I describe an alternative formulation of partons in terms of equal-time (or Euclidean) correlators, which allows to compute precision-controlled x-distribution through lattice QCD simulations. This approach is in accord with Weinberg's pioneering idea of effective field theory as well as Wilson's renormalization group, in which the large hadron momentum serves as a natural cut-off for light-cone/rapidity divergences and can ultimately be eliminated through a method like the “perfect action” program in lattice QCD.

A Spatio-temporal Graph Transformer driven model for recognizing fine-grained data human activity

Human activity recognition(HAR) is an important research focus in ubiquitous computing. It has been widely applied in various domains, such as smart homes, healthcare assistance, and sports training. Accurate human activity recognition directly impacts the performance of downstream tasks. Existing methods for human activity recognition primarily rely on extracting temporal or spatial features from the data. These features are used for the task of human activity recognition. The existing methods mainly use CNN or RNN models to model the Euclidean correlations among spatially adjacent sensors or channels. However, non-Euclidean pairwise correlations among all sensors or channels are even critical for accurate classification, which has been ignored by the existing methods. In this paper, we incorporate fine-grained spatial structural data into the model to overcome these limitations. A novel deep learning model for human activity recognition is proposed, which is called the fine-grained data-oriented Spatial-Temporal Graph Transformer network (STGT). The introduction of the STGT model can eliminate the limitations of existing spatial feature extraction methods by leveraging a novel data organization approach proposed in this study. This model enhances the spatial features within the time feature extraction module for effective spatio-temporal feature extraction. We conducted experiments on four large-scale real-world HAR datasets to evaluate its performance. The experimental results demonstrate the superiority of our method over state-of-the-art approaches.

Behind-the-horizon excitations from a single 2d CFT

In this work, we consider the atypical non-equilibrium state found in [1708.06328] which holographically represents a behind-the-horizon excitation in a black hole spacetime. The special feature of this state is that it looks like an equilibrium state when probed by a class of low-energy operators. First, we retrieve this property using the uniformization mapping in the limit of a large central charge, in the process we are able to derive rather than presume approximate thermal physics. Furthermore, in the large-c and high-energy limit, we realize these excitations as elements of the commutant algebra of a GNS-representation of the light operator algebra. Instead of analytically continuing a mixed heavy-light Euclidean correlator to a Lorentzian correlator, we identify the Euclidean correlator as a GNS-linear form and interpret the Lorentzian correlator as a vacuum expectation value of representatives of the light operator algebra on the GNS-vacuum.

Non-hydrodynamic response in QCD-like plasma

Quark-gluon plasma’s (QGP) properties at non-hydrodynamic and non-perturbative regimes remain largely unexplored. Here, we examine the response functions describing how a QGP-like plasma responds to initial energy-momentum disturbance in both static and Bjorken-expanding plasma at non-hydrodynamic gradient using the Boltzmann equation in the relaxation-time approximation (RTA). We show that the resulting response functions are remarkably similar in both static and expanding backgrounds at non-hydrodynamic gradients. While non-hydrodynamic response can not be described by the conventional first-order and second-order theories, its behavior is reasonably captured by the extended version of hydrodynamics proposed by us [1]. The potential sensitivity of the Euclidean correlator to non-hydrodynamic response is also illustrated.

Towards the computation of inclusive decay rates using lattice QCD

We present a non-perturbative computation of inclusive rates of semileptonic decays of heavy mesons from lattice QCD simulations. The calculation is based on the extraction of smeared spectral functions obtained from four-point Euclidean correlation functions computed on configuration ensembles of the JLQCD and ETM collaborations. We compare our results for the inclusive decay rates with analytical predictions from the operator-product expansion, finding a good agreement for the calculation of the inclusive decay rate. This opens the path to the theoretical determination of the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element V_{cb}Vcb to a level of precision competitive with the present experimental uncertainty.

Quantitative characterization of vascular targeted photodynamic therapy efficiency for port-wine stains using image processing techniques

SignificanceVascular targeted photodynamic therapy (V-PDT) is a clinically approved therapeutic approach for treating vascular-related diseases, such as port-wine stains (PWS). For accurate treatment, various light doses are required for different lesions due to the irregularity of vascular size, shape, degree of disease, which commonly alters during different stages of V-PDT, making quantitative analysis of treatment efficiency is highly needed. ApproachLesion images before and after V-PDT treatment of patients with PWS were used to construct a quantitative method to characterize the differences among lesions. Image analysis techniques were applied to calculate Euclidean distances and two-dimensional correlation coefficients for V-PDT efficiency evaluation. ResultsAccording to the image analysis, V-PDT with good treatment efficiency resulted in a larger Euclidean distance and a smaller correlation coefficient, in comparison with the case having lower V-PDT efficiency. ConclusionsThe new method to quantify the Euclidean distances and correlation coefficients is developed, which is promising for the quantitative analysis of V-PDT efficiency for PWS.

Reconstructing lattice QCD spectral functions with stochastic pole expansion and Nevanlinna analytic continuation

The reconstruction of spectral functions from Euclidean correlation functions is a well-known, yet ill-conditioned inverse problem in the fields of many-body and high-energy physics. In this paper, we present a comprehensive investigation of two recently developed analytic continuation methods, namely stochastic pole expansion and Nevanlinna analytic continuation, for extracting spectral functions from mock lattice QCD data. We examine a range of Euclidean correlation functions generated by representative models, including the Breit-Wigner model, the Gaussian mixture model, the resonance-continuum model, and the bottomonium model. Then, we apply the two methods to reconstruct spectral functions from charmonium correlation functions computed using lattice QCD simulations at a finite temperature. Our findings demonstrate that the stochastic pole expansion method, when combined with the constrained sampling algorithm and the self-adaptive sampling algorithm, successfully recovers the essential features of the spectral functions and exhibits excellent resilience to noise of input data. In contrast, the Nevanlinna analytic continuation method suffers from numerical instability, often resulting in the emergence of spurious peaks and significant oscillations in the high-energy regions of the spectral functions, even with the application of the Hardy basis function optimization algorithm. Published by the American Physical Society 2024

Flux correlators and semiclassics

We consider correlators for the flux of energy and charge in the background of operators with large global U(1) charge in conformal field theory (CFT). It has recently been shown that the corresponding Euclidean correlators generically admit a semiclassical description in terms of the effective field theory (EFT) for a conformal superfluid. We adapt the semiclassical description to Lorentzian observables and compute the leading large charge behavior of the flux correlators in general U(1) symmetric CFTs. We discuss the regime of validity of the large charge EFT for these Lorentzian observables and the subtleties in extending the EFT approach to subleading corrections. We also consider the Wilson-Fisher fixed point in d = 4 − ϵ dimensions, which offers a specific weakly coupled realization of the general setup, where the subleading corrections can be systematically computed without relying on an EFT.

Holographic Euclidean thermal correlator

In this paper, we compute holographic Euclidean thermal correlators of the stress tensor and U(1) current from the AdS planar black hole. To this end, we set up perturbative boundary value problems for Einstein’s gravity and Maxwell theory in the spirit of Gubser-Klebanov-Polyakov-Witten, with appropriate gauge fixing and regularity boundary conditions at the horizon of the black hole. The linearized Einstein equation and Maxwell equation in the black hole background are related to the Heun equation of degenerate local monodromy. Leveraging the connection relation of local solutions of the Heun equation, we partly solve the boundary value problem and obtain exact two-point thermal correlators for U(1) current and stress tensor in the scalar and shear channels.

Adiabatic Evolution of Low-Temperature Many-Body Systems

We consider finite-range, many-body fermionic lattice models and we study the evolution of their thermal equilibrium state after introducing a weak and slowly varying time-dependent perturbation. Under suitable assumptions on the external driving, we derive a representation for the average of the evolution of local observables via a convergent expansion in the perturbation, for small enough temperatures. Convergence holds for a range of parameters that is uniform in the size of the system. Under a spectral gap assumption on the unperturbed Hamiltonian, convergence is also uniform in temperature. As an application, our expansion allows us to prove closeness of the time-evolved state to the instantaneous Gibbs state of the perturbed system, in the sense of expectation of local observables, at zero and at small temperatures. As a corollary, we also establish the validity of linear response. Our strategy is based on a rigorous version of the Wick rotation, which allows us to represent the Duhamel expansion for the real-time dynamics in terms of Euclidean correlation functions, for which precise decay estimates are proved using fermionic cluster expansion.

Sphaleron Rate of N_{f}=2+1 QCD.

We compute the sphaleron rate of N_{f}=2+1 QCD at the physical point for a range of temperatures 200 MeV≲T≲600 MeV. We adopt a strategy recently applied in the quenched case, based on the extraction of the rate via a modified version of the Backus-Gilbert method from finite-lattice-spacing and finite-smoothing-radius Euclidean topological charge density correlators. The physical sphaleron rate is finally computed by performing a continuum limit at fixed physical smoothing radius, followed by a zero-smoothing extrapolation. Dynamical fermions were discretized using the staggered formulation, which is known to yield large lattice artifacts for the topological susceptibility. However, we find them to be rather mild for the sphaleron rate.

Fourier Analysis of the Vertical Ground Reaction Force During Walking: Applications for Quantifying Differences in Gait Strategies.

Time series biomechanical data inform our understanding of normal gait mechanics and pathomechanics. This study examines the utility of different quantitative methods to distinguish vertical ground reaction forces (VGRFs) from experimentally distinct gait strategies. The goals of this study are to compare measures of VGRF data-using the shape factor method and a Fourier series-based analysis-to (1)describe how these methods reflect and distinguish gait patterns and (2)determine which Fourier series coefficients discriminate normal walking, with a relatively stiff-legged gait, from compliant walking, using deep knee flexion and limited vertical oscillation. This study includes a reanalysis of previously presented VGRF data. We applied the shape factor method and fit 3- to 8-term Fourier series to zero-padded VGRF data. We compared VGRF renderings using Euclidean L2 distances and correlations stratified by gait strategy. Euclidean L2 distances improved with additional harmonics, with limited improvement after the seventh term. Euclidean L2 distances were greater in shape factor versus Fourier series renderings. In the 8 harmonic model, amplitudes of 9 Fourier coefficients-which contribute to VGRF features including peak and local minimum amplitudes and limb loading rates-were different between normal and compliant walking. The results suggest that Fourier series-based methods distinguish between gait strategies.

EV charging load profile identification and seasonal difference analysis via charging sessions data of charging stations

The popularity of electric vehicles (EVs) brings environmental benefits, but their hard-to-estimate stochastic charging behaviors places additional diversity on grid load management. This paper proposes a procedure to identify typical charging load profiles (CLPs) via large scale charging session data from charging stations (CSs). The daily CLPs are computed from charging sessions, and a comprehensive similarity metric based on the weighting of Euclidean and Pearson correlation coefficient is proposed to achieve better clustering. The clustering is performed using the Clustering LARge Applications (CLARA) algorithm to accommodate large sample scenarios. Subsequently, hierarchical clustering of CSs is performed based on possible CLPs，and their CLPs are estimated by Monte Carlo simulation. The performance of the proposed method is tested and evaluated with over 340,000 charging sessions from 109 CSs in Wuhan at central China, and seasonal differences in CLPs are explored. The results show that the method of mining typical CLPs from charging sessions is effective, 17 typical CLPs are identified in different seasons, which provide effective information on the fluctuation and magnitude of daily power demand, the charging power demand also shows significant seasonal differences, and good accuracy is achieved by dividing the CSs into different groups for load estimation.

Connecting Euclidean to light-cone correlations: from flavor nonsinglet in forward kinematics to flavor singlet in non-forward kinematics

We present a unified framework for the perturbative factorization connecting Euclidean correlations to light-cone correlations. Starting from nonlocal quark and gluon bilinear correlators, we derive the relevant hard-matching kernel up to the next-to-leading-order, both for the flavor singlet and non-singlet combinations, in non-forward and forward kinematics, and in coordinate and momentum space. The results for the generalized distribution functions (GPDs), parton distribution functions (PDFs), and distribution amplitudes (DAs) are obtained by choosing appropriate kinematics. The renormalization and matching are done in a state-of-the-art scheme. We also clarify some issues raised on the perturbative matching of GPDs in the literature. Our results provide a complete manual for extracting all leading-twist GPDs, PDFs as well as DAs from lattice simulations of Euclidean correlations in a state-of-the-art strategy, either in coordinate or in momentum space factorization approach.

Large p SYK from chord diagrams

The p-body SYK model at finite temperature exhibits submaximal chaos and contains stringy-like corrections to the dual JT gravity. It can be solved exactly in two different limits: “large p” SYK 1 ≪ p ≪ N and “double-scaled” SYK N, p → ∞ with λ = 2p2/N fixed. We clarify the relation between the two. Starting from the exact results in the double-scaled limit, we derive several observables in the large p limit. We compute euclidean 2n-point correlators and out-of-time-order four-point function at long lorentzian times. To compute the correlators we find the relevant asymptototics of the Uqsu11\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{U}}_q\\left( su\\left(1,1\\right)\\right) $$\\end{document} 6j-symbol.

Study of Quarkonium in QGP from Unquenched Lattice QCD

This paper discusses the charmonium and bottomonium correlators in the pseudoscalar channel and the corresponding spectral reconstruction on the lattice. The absence of a transport peak in the pseudoscalar channel spectral function allows for an easier study of the in-medium modification of bound states. However, extracting spectral information from Euclidean correlators is still a numerically ill-posed problem. To constrain the spectral reconstruction, we use an ansatz motivated from perturbation theory. The perturbative model spectral function has two main contributions: a thermal part around the threshold obtained from pNRQCD and the vacuum part well above the threshold. These two regions are matched continuously, and the model spectral function is obtained by introducing parameters that control the overall thermal shift of the peak and the overall amplitude. The lattice correlator data is computed using clover-improved Wilson valence fermions on large and fine gauge field configurations generated using N_f=2+1 flavors Highly Improved Staggered Quark action with physical strange quark mass m_s, and slightly heavy degenerate up and down quark masses m_l=m_s/5 that correspond to m_pi simeq 320 MeV. Our results obtained at T=220 MeV and T=251 MeV suggest that no resonance peaks are needed to describe the charmonium lattice data at these temperatures, while for bottomonium thermally broadened resonance peaks persists.

Probing the Energy-Smeared R Ratio Using Lattice QCD.

We present a first-principles lattice QCD investigation of the R ratio between the e^{+}e^{-} cross section into hadrons and into muons. By using the method of Ref.[1], that allows one to extract smeared spectral densities from Euclidean correlators, we compute the R ratio convoluted with Gaussian smearing kernels of widths of about 600MeV and central energies from 220MeV up to 2.5GeV. Our theoretical results are compared with the corresponding quantities obtained by smearing the KNT19 compilation [2] of R-ratio experimental measurements with the same kernels and, by centering the Gaussians in the region around the ρ-resonance peak, a tension of about 3 standard deviations is observed. From the phenomenological perspective, we have not included yet in our calculation QED and strong isospin-breaking corrections, and this might affect the observed tension. From the methodological perspective, our calculation demonstrates that it is possible to study the R ratio in Gaussian energy bins on the lattice at the level of accuracy required in order to perform precision tests of the standard model.

Classification of Cocoa Pod Maturity Using Similarity Tools on an Image Database: Comparison of Feature Extractors and Color Spaces

Côte d’Ivoire, the world’s largest cocoa producer, faces the challenge of quality production. Immature or overripe pods cannot produce quality cocoa beans, resulting in losses and an unprofitable harvest. To help farmer cooperatives determine the maturity of cocoa pods in time, our study evaluates the use of automation tools based on similarity measures. Although standard techniques, such as visual inspection and weighing, are commonly used to identify the maturity of cocoa pods, the use of automation tools based on similarity measures can improve the efficiency and accuracy of this process. We set up a database of cocoa pod images and used two feature extractors: one based on convolutional neural networks (CNN), in particular, MobileNet, and the other based on texture analysis using a gray-level co-occurrence matrix (GLCM). We evaluated the impact of different color spaces and feature extraction methods on our database. We used mathematical similarity measurement tools, such as the Euclidean distance, correlation distance, and chi-square distance, to classify cocoa pod images. Our experiments showed that the chi-square distance measurement offered the best accuracy, with a score of 99.61%, when we used GLCM as a feature extractor and the Lab color space. Using automation tools based on similarity measures can improve the efficiency and accuracy of cocoa pod maturity determination. The results of our experiments prove that the chi-square distance is the most appropriate measure of similarity for this task.

Towards learning optimized kernels for complex Langevin

We present a novel strategy aimed at restoring correct convergence in complex Langevin simulations. The central idea is to incorporate system-specific prior knowledge into the simulations, in order to circumvent the NP-hard sign problem. In order to do so, we modify complex Langevin using kernels and propose the use of modern auto-differentiation methods to learn optimal kernel values. The optimization process is guided by functionals encoding relevant prior information, such as symmetries or Euclidean correlator data. Our approach recovers correct convergence in the non-interacting theory on the Schwinger-Keldysh contour for any real-time extent. For the strongly coupled quantum anharmonic oscillator we achieve correct convergence up to three-times the real-time extent of the previous benchmark study. An appendix sheds light on the fact that for correct convergence not only the absence of boundary terms, but in addition the correct Fokker-Plank spectrum is crucial.