Point Correlation Research Articles

Fusion rules and structure constants of E-series minimal models

In the ADE classification of Virasoro minimal models, the E-series is the sparsest: their central charges c=1-6\frac{(p-q)^2}{pq}c=1−6(p−q)2pq are not dense in the half-line c∈ (-∞,1)c∈(−∞,1), due to q=12,18,30q=12,18,30 taking only 3 values — the Coxeter numbers of E_6, E_7, E_8E6,E7,E8. The E-series is also the least well understood, with few known results beyond the spectrum. Here, we use a semi-analytic bootstrap approach for numerically computing 4-point correlation functions. We deduce non-chiral fusion rules, i.e. which 3-point structure constants vanish. These vanishings can be explained by constraints from null vectors, interchiral symmetry, simple currents, extended symmetries, permutations, and parity, except in one case for q=30q=30. We conjecture that structure constants are given by a universal expression built from the double Gamma function, times polynomial functions of \cos(\pi\frac{p}{q})cos(πpq) with values in \mathbb{Q}\big(\cos(\frac{\pi}{q})\big)ℚ(cos(πq)), which we work out explicitly for q=12q=12. We speculate on generalizing E-series minimal models to generic integer values of qq, and recovering loop CFTs as p,q\to ∞p,q→∞.

Average mutual information for random fermionic Gaussian quantum states

Abstract Studying the typical entanglement entropy of a bipartite system when averaging over different ensembles of pure quantum states has been instrumental in different areas of physics, ranging from many-body quantum chaos to black hole evaporation. We extend such analysis to open quantum systems and mixed states, where we compute the typical mutual information in a bipartite system averaged over the ensemble of mixed Gaussian states with a fixed spectrum. Tools from random matrix theory and determinantal point processes allow us to compute arbitrary k-point correlation functions of the singular values of the corresponding complex structure in a subsystem for a given spectrum in the full system. In particular, we evaluate the average von Neumann entropy in a subsystem based on the level density and the average mutual information. Those results are given for finite system size as well as in the thermodynamic limit.

Massive νs through the CNN lens:interpreting the field-level neutrino mass information in weak lensing

Modern cosmological surveys probe the Universe deep into the nonlinear regime, where massive neutrinos suppress cosmic structure. Traditional cosmological analyses, which use the 2-point correlation function to extract information, are no longer optimal in the nonlinear regime, and there is thus much interest in extracting beyond-2-point information to improve constraints on neutrino mass. Quantifying and interpreting the beyond-2-point information is thus a pressing task. We study the field-level information in weak lensing convergence maps using convolution neural networks. We find that the network performance increases as higher source redshifts and smaller scales are considered — investigating up to a source redshift of 2.5 and ℓmax ≃ 104 — verifying that massive neutrinos leave a distinct effect on weak lensing. However, the performance of the network significantly drops after scaling out the 2-point information from the maps, implying that most of the field-level information can be found in the 2-point correlation function alone. We quantify these findings in terms of the likelihood ratio and also use Integrated Gradient saliency maps to interpret which parts of the map the network is learning the most from. We find that, in the absence of noise, the network extracts a similar amount of information from the most overdense and underdense regions. However, upon adding noise, the information in underdense regions is distorted as noise disproportionately washes out void-like structures.

The cusp limit of correlators and: anew graphical bootstrap for correlators/amplitudes to eleven loops

We consider the universal behavior of half-BPS correlators in N = 4 super-Yang-Mills in the cusp limit where two consecutive separations x122, x232 become lightlike. Through the Lagrangian insertion procedure, the Sudakov double-logarithmic divergence of the n-point correlator is related to the (n + 1)-point correlator where the inserted Lagrangian “pinches” to the soft-collinear region of the cusp. We formulate this constraint as a new graphical rule for the f-graphs of the four-point correlator, which turns out to be the most constraining rule known so far. By exploiting this single graphical rule, we bootstrap the planar integrand of the four-point correlator up to ten loops (n = 14) and fix all 22024902 but one coefficient at eleven loops (n = 15); the remaining coefficient is then fixed using the triangle rule. We verify the “Catalan conjecture” for the coefficients of the family of f-graphs known as “anti-prisms” where the coefficient of the twelve-loop (n = 16) anti-prism is found to be −42 by a local analysis of the bootstrap equations. We also comment on the implication of our graphical rule for the non-planar contributions.

Improved attention mechanism-based transformer model for time series data-anomaly detection

Detection of anomalies present in time series data is a crucial task in diverse realistic applications. Existing approaches exhibited prominent outcomes in this domain, though they face challenges in imbalanced datasets. The novelty of this work lies in the introduction of an Improved Attention Mechanism-based Transformer model, which uniquely integrates advanced attention mechanisms tailored for time series data to enhance anomaly detection capabilities. This approach effectively captures both short- and long-term dependencies, addressing limitations in handling imbalanced datasets. Here, the implemented approach is the Improved Attention Mechanism-based Transformer model, which involves preprocessing, information extraction and anomaly detection. Initially, input time series data undergoes preprocessing, where improved z-score normalization approach is utilized. Subsequently, the preprocessed data is employed to retrieve information for anomaly detection, which is carried out in Improved Attention Mechanism-based Transformer model that retrieves the correlation of every time point as well as relationship through long-distance time information among distinct positions in the sequence. Also, an improved loss function is employed during training of Improved Attention Mechanism-based Transformer model. Finally, in contrast to conventional methods, the proposed model achieves a detection accuracy exceeding 0.968 at a training percentage of 90 while existing models obtain lower ratings.

Manipulating Hydrogen-Bonding Donor/Acceptor in Ultra-Robust Isoreticular Zr(IV) Metal-Organic Frameworks for Efficient Regulation of Water Sorption Inflection Point and Steepness.

The development of porous materials exhibiting steep and stepwise adsorption of water vapor at desired humidity is crucial for implementing diverse applications such as humidity control, heat allocation, and atmospheric water harvesting. The precise molecular-level elucidation of structural characteristics and chemical components that dictate the water sorption behaviors in confined nanospaces, metal-organic frameworks (MOFs) in particular, is fundamentally important, but this has yet to be largely explored. In this work, by leveraging the isoreticular principle, we crafted two pairs of isostructural Zr-MOFs with linker backbones of benzene and pyrazine acting as hydrogen-bonding donor and acceptor, respectively. The outstanding water sorption cyclic durability of the four Zr-MOFs permits persuasive investigation of the correlation of the water sorption inflection point and steepness (the two central figures-of-merit for water sorption) with the linker functionality. The two pyrazine-carrying Zr-MOFs both show steep water uptake at lower relative pressure and slightly decreased steepness, which are quantitatively described by the Dubinin-Astakhov relation. We deciphered the privileged water clusters through single-crystal X-ray diffraction studies in which the pyrazine moiety formed stronger hydrogen-bonding interactions with guest water molecules and favored the formation of water pentamers instead of hexamers that are observed in the benzene analog. The hydrogen-bonding donor/acceptor manipulation approach presented in this work may facilitate future research endeavors focusing on molecular attribute engineering in predeterminedly ultrawater-resistant MOF platforms for efficient regulation of water sorption behaviors toward customized applications.

Improved Landslide Deformation Prediction Using Convolutional Neural Network–Gated Recurrent Unit and Spatial–Temporal Data

As one of the major forms of geological disaster, landslides cause huge casualties and economic losses in China every year. Given the importance of landslide prediction, it is a challenging task due to difficulties in efficiently leveraging the spatial–temporal information for enhanced prediction. This paper presents a novel spatial–temporal enhanced CNN-GRU model to improve landslide predictions with the following contributions. First, this paper explicitly models the spatial correlation in the dataset and constructs a spatial–temporal time-sequence deformation prediction model that greatly improves landslide predictions. This model integrates the spatial correlation of monitoring points into time-series deformation prediction to improve the prediction of landslide deformation trends. Second, we develop a complete data processing pipeline involving SBAS-InSAR, time-series data preprocessing, spatial–temporal homogeneous point selection and weighting, as well as CNN-GRU model training. The pipeline is tailor-designed to leverage the spatial–temporal correlation in the data to enhance the prediction performance. Third, we apply the proposed model to monitor landslide deformation around Woda Village, Chamdo City, Tibet. The results show that the root mean square error (RMSE) of the monitoring points in the landslide area is reduced by about 20.9% and the number of points with an RMSE of less than 3 mm is increased by 12.9%, leading to a significant improvement in prediction accuracy.

Sequence-Aware Vision Transformer with Feature Fusion for Fault Diagnosis in Complex Industrial Processes.

Industrial fault diagnosis faces unique challenges with high-dimensional data, long time-series, and complex couplings, which are characterized by significant information entropy and intricate information dependencies inherent in datasets. Traditional image processing methods are effective for local feature extraction but often miss global temporal patterns, crucial for accurate diagnosis. While deep learning models like Vision Transformer (ViT) capture broader temporal features, they struggle with varying fault causes and time dependencies inherent in industrial data, where adding encoder layers may even hinder performance. This paper proposes a novel global and local feature fusion sequence-aware ViT (GLF-ViT), modifying feature embedding to retain sampling point correlations and preserve more local information. By fusing global features from the classification token with local features from the encoder, the algorithm significantly enhances complex fault diagnosis. Experimental analyses on data segment length, network depth, feature fusion and attention head receptive field validate the approach, demonstrating that a shallower encoder network is better suited for high-dimensional time-series fault diagnosis in complex industrial processes compared to deeper networks. The proposed method outperforms state-of-the-art algorithms on the Tennessee Eastman (TE) dataset and demonstrates excellent performance when further validated on a power transmission fault dataset.

Superspace invariants and correlators in 4dN = 1 superconformal field theories

Using polarization spinor methods in conjunction with the superspace formalism, we construct 3-point superconformal invariants that are used to determine the form of 3-point correlators of spinning superfield operators in N = 1 superconformal field theories (SCFTs) in 4-dimensions. We enumerate the structural form of various spinning 3-point correlators using these invariants and find additional constraints on their form when the operators are conserved supercurrents. For these purposes, we first construct the invariants and 3-point correlators in non-supersymmetric 4d CFTs which are then extended using superspace methods to 4d SCFTs.

Measuring the matter fluctuations in the Local Universe with the ALFALFA catalogue

Abstract The standard model of cosmology describes the matter fluctuations through the matter power spectrum, where σ8 ≡ σ8, 0 ≡ σ8(z = 0), defined at the scale of 8 h−1 Mpc, acts as a normalisation parameter. Currently, the literature reports measurements of σ8 analysing different cosmic tracers, where some of these results were obtained assuming a fiducial cosmology. In this study we measure, in a model-independent approach, the matter fluctuations in the Local Universe using HI extragalactic sources mapped by the ALFALFA survey. Our analyses allow us to test the standard cosmological model under extreme conditions in the highly non-linear Local Universe, quantifying the amplitude of the matter fluctuations there. Our work directly measures σ8 using the 3-dimensional distances of the HI sources determined by the ALFALFA survey without assuming a fiducial cosmology, resulting in a robust model-independent measurement of σ8. Our methodology involves the construction of suitable mock catalogues to simulate the large scale structure features observed in the data, applying the 2-point correlation function, and making use of Markov Chain Monte Carlo methods to estimate the parameters. Analysing these data we measure σ8 = 0.78 ± 0.04 for h = 0.6727, σ8 = 0.80 ± 0.05 for h = 0.698, and σ8 = 0.83 ± 0.05 for h = 0.7304. Considering the data pairs (σ8, H0) from the Planck CMB and ACT CMB-lensing analyses, our measurement agrees with them within 1 σ confidence level. From a model-independent perspective, we find that the scale where the matter fluctuation is 1, is R = 7.2 ± 1.5 Mpc.

Resurgence in Liouville theory

Liouville conformal field theory is a prototypical example of an exactly solvable quantum field theory, in the sense that the correlation functions in an arbitrary background can be determined exactly using only the constraints of unitarity and crossing symmetry. For example, the three point correlation functions are given by the famous formula of Dorn-Otto-Zamolodchikov-Zamolodchikov (DOZZ). Unlike many other exactly solvable theories, Liouville theory has a continuously tunable parameter — essentially ℏ — which is related to the central charge of the theory. Here we investigate the nature of the perturbative expansion in powers of ℏ, which is the loop expansion around a semi-classical solution. We show that the perturbative coefficients grow factorially, as expected of a Feynman diagram expansion, and take the form of an asymptotic series. We identify the singularities in the Borel plane, and show that they are associated with complex instanton solutions of Liouville theory; they correspond precisely to the complex solutions described by Harlow, Maltz, and Witten. Both single- and multi-valued solutions of Liouville appear. We show that the perturbative loop expansions around these different saddle points mix in the way expected for a trans-series expansion. Thus Liouville theory provides a calculable example of a quantum field theory where perturbative and instanton contributions can be summed up and assembled into a finite answer.

Correlators of long strings on AdS3×S3×T4

In this work, we calculate correlators of long strings on AdS3×S3×T4 with pure NS-NS flux. We first construct physical vertex operators that correspond to long strings. Due to the GSO projection, they depend on the parity of the spectral flow parameter w. For a given w, we construct the physical operators that have the lowest space-time weights in both the NS and R sector. Then, we calculate three point correlators for each possible type of parities of spectral flows. We find that the recursion relations of correlators in the bosonic SL(2, ℝ) WZW model can be understood from the equivalence of these superstring correlators with different picture choices. Furthermore, after carefully mapping the vertex operators to appropriate operators in the dual CFT, we find that once the fermionic contributions together with the picture changing effects are correctly taken into account, some mathematical identities of covering maps lead to the matching of the correlators of the two sides. We check this explicitly at the leading order in the conformal perturbation computation and conjecture that this remains correct to all orders.

EFFECT OF NOZZLE ORIFICE DIAMETER AND POSITION OF HYDRAULIC JUMP ON STAGNATION POINT HEAT TRANSFER DURING LIQUID JET IMPINGEMENT COOLING

Liquid jets have excellent potential to dissipate high thermal loads while maintaining surface temperatures well below the specified reliability limit of electronic devices. The present study investigates orthogonal liquid jet impingement from a single nozzle over a heated substrate while examining the simultaneous effect of nozzle orifice diameter and the appearance of a hydraulic jump on the stagnation point heat transfer rates. Characteristics of single-phase convective heat transfer are explored for five different nozzle orifice diameters ranging from 0.4 mm to 3 mm and coolant flow rates of 50-350 ml/min (Reynolds number ∼ 1,000-12,000). Using high-speed imaging, liquid jet impingement over the target surface is recorded to estimate the location of the hydraulic jump. The heat transfer coefficient (HTC) is found to be a strong function of the coolant flow rate, nozzle orifice diameter, and the position of the hydraulic jump. The stagnation point heat transfer rate degrades in the presence of hydraulic jump despite always being covered with a thin liquid film. It is enhanced by increasing the jet's Reynolds number at a fixed orifice diameter or by decreasing its diameter while maintaining a constant Reynolds number. In addition, a parametric study of the stagnation point's Nusselt number as a function of the flow variables, including the hydraulic jump, is carried out, and a new correlation is proposed. The Nusselt number correlation for the stagnation point agrees well with the present experimental data within a ± 15% error band, allowing a rational design of a single nozzle liquid jet for various thermal management applications.

A model for the redshift-space galaxy 4-point correlation function

The field of cosmology is entering an epoch of unparalleled wealth of observational data thanks to galaxy surveys such as DESI, Euclid, and Roman. Therefore, it is essential to have a firm theoretical basis that allows the effective analysis of the data. With this purpose, we compute the nonlinear, gravitationally-induced connected galaxy 4-point correlation function (4PCF) at the tree level in Standard Perturbation Theory (SPT), including redshift-space distortions (RSD). We begin from the trispectrum and take its inverse Fourier transform into configuration space, exploiting the isotropic basis functions of [1]. We ultimately reduce the configuration-space expression to low-dimensional radial integrals of the power spectrum. This model will enable the use of the BAO feature in the connected 4PCF to sharpen our constraints on the expansion history of the Universe. It will also offer an additional avenue for determining the galaxy bias parameters, and thus tighten our cosmological constraints by breaking degeneracies. Survey geometry can be corrected in the 4PCF, and many systematics are localized, which is an advantage over data analysis with the trispectrum.

Visual Simultaneous Localization and Mapping for Highly Dynamic Environments

ABSTRACTThis paper presents a visual simultaneous localization and mapping (SLAM) system designed for highly dynamic environments, capable of eliminating dynamic objects using only visual information. The proposed system integrates learning‐based and geometry‐based methods to address the challenges posed by moving objects. The learning‐based approach leverages image segmentation to remove previously trained objects, whereas the geometry‐based approach utilises point correlation to eliminate unseen objects. By complementing each other, these methods enhance the robustness of the SLAM system in dynamic scenarios. Experimental results demonstrate that the proposed method effectively removes dynamic objects. Comparative studies with state‐of‐the‐art algorithms further show that the proposed method achieves superior accuracy and robustness.

SAEF: Secure Anonymization and Encryption Framework for Open-Access Remote Photoplethysmography Datasets.

The advancement of remote photoplethys-mography (rPPG) technology depends on the availability of comprehensive datasets. However, the reliance on facial features for rPPG signal acquisition poses significant privacy concerns, hindering the development of open-access datasets. This work establishes privacy protection principles for rPPG datasets and introduces the secure anonymization and encryption framework (SAEF) to address these challenges while preserving rPPG data integrity. SAEF first identifies privacy-sensitive facial regions for removal through importance and necessity analysis. The irreversible removal of these regions has an insignificant impact on signal quality, with an R-value deviation of less than 0.06 for BVP extraction and a mean absolute error (MAE) deviation of less than 0.05 for heart rate (HR) calculation. Additionally, SAEF introduces a high efficiency cascade key encryption method (CKEM), achieving encryption in 5.54 × 10-5 seconds per frame, which is over three orders of magnitude faster than other methods, and reducing approximate point correlation (APC) values to below 0.005, approaching complete randomness. These advancements significantly improve real-time video encryption performance and security. Finally, SAEF serves as a preprocessing tool for generating volunteer-friendly, open-access rPPG datasets.

The Clinical Learning Environment Experience of the Student Nurse of the Generation Z: a Convergent Parallel Mixed Method Study

Background. The internship represents an experience that incorporates numerous meanings and values that involve nursing students globally, particularly for those belonging to Generation Z. Aims. 1) to assess the students' perceptions of the clinical learning environments, 2) to identify the elements that contribute to determining the clinical learning environment, and 3) to compare quantitative and qualitative results to highlight key elements that can support the development of targeted educational strategies for nursing students. Design. Convergent parallel mixed-method study Participants. Students attending the first, second and third years of the bachelor degree in nursing. Methods. Quantitative and socio-demographic data were collected with a questionnaire that included the Clinical Learning Environment and Supervision plus Nurse Teacher (CLES-T) scale. Qualitative data were collected with the internship diaries. The qualitative data transformed into dummy variables were finally correlated with the quantitative data using a biserial point correlation to explore their relationships. Results. We received answers from 63 students, half of them females, who reported experiencing a positive clinical learning environment. Simple linear regressions showed that the variables age, course year, being a student worker or with health care work experience, previous volunteering are all positively correlated with the total scale and with each dimension of the CLES-T. The content analysis of the internship diaries revealed 7 main categories describing the experience of the clinical learning environment of nursing students of Generation Z. Finally, it was possible to outline a summary scheme that describes the key elements that contribute to the success of the internship and the learning experience. Conclusions. The key success factors emerging from the study include meaningful relationships with tutors, staff, and peers, effective management of emotional aspects, development of professional identity, intrinsic motivation, and the acquisition of practical skills through feedback and support. A positive and well-organized clinical learning environment facilitates these outcomes, promoting role awareness and responsibility. These findings can be applied to nursing education by developing targeted educational strategies such as structured mentoring programs, emotional training, and practical simulations. Integrating these elements enables educators and institutions to overcome challenges in clinical internships, enhancing students' preparation and fostering the development of competent and confident nurses.

Classification of conformal carroll algebras

We classify a one-parameter family, confcarrzd+1, of conformal extensions of the Carroll algebra in arbitrary dimension with z being the anisotropic scaling exponent. We further obtain their infinite-dimensional extensions, confcarr~zd+1, and discuss their corresponding finite-dimensional truncated subalgebras when the scaling exponent is integer or half-integer. For all these conformal extensions, we also constrain the 2-point and 3-point correlation functions with electric and/or magnetic features.

GeometryFormer: Semi-Convolutional Transformer Integrated with Geometric Perception for Depth Completion in Autonomous Driving Scenes.

Depth completion is widely employed in Simultaneous Localization and Mapping (SLAM) and Structure from Motion (SfM), which are of great significance to the development of autonomous driving. Recently, the methods based on the fusion of vision transformer (ViT) and convolution have brought the accuracy to a new level. However, there are still two shortcomings that need to be solved. On the one hand, for the poor performance of ViT in details, this paper proposes a semi-convolutional vision transformer to optimize local continuity and designs a geometric perception module to learn the positional correlation and geometric features of sparse points in three-dimensional space to perceive the geometric structures in depth maps for optimizing the recovery of edges and transparent areas. On the other hand, previous methods implement single-stage fusion to directly concatenate or add the outputs of ViT and convolution, resulting in incomplete fusion of the two, especially in complex outdoor scenes, which will generate lots of outliers and ripples. This paper proposes a novel double-stage fusion strategy, applying learnable confidence after self-attention to flexibly learn the weight of local features. Our network achieves state-of-the-art (SoTA) performance with the NYU-Depth-v2 Dataset and the KITTI Depth Completion Dataset. It is worth mentioning that the root mean square error (RMSE) of our model on the NYU-Depth-v2 Dataset is 87.9 mm, which is currently the best among all algorithms. At the end of the article, we also verified the generalization ability in real road scenes.

1d conformal field theory and dispersion relations

We study conformal field theory in d = 1 space-time dimensions. We derive a dispersion relation for the 4-point correlation function of identical bosons and fermions, in terms of the double discontinuity. This extends the conformal dispersion relation of [1], which holds for CFTs in dimensions d ≥ 2, to the case of d = 1. The dispersion relation is obtained by combining the Lorentzian inversion formula with the operator product expansion of the 4-point correlator. We perform checks of the dispersion relation using correlators of generalised free fields and derive an integral relation between the kernel of the dispersion relation and that of the Lorentzian inversion formula. Finally, for 1-d holographic conformal theories, we analytically compute scalar Witten diagrams in AdS2 at tree-level and 1-loop.