Continuity Constraints Research Articles

Routing Algorithms for SDM Flexible Optical Networks

This paper considers the online routing, modulation, spectrum, and core allocation problem in elastic optical networks. Three algorithms are proposed to minimize the bandwidth blocking probability while taking into account the impact of interference from established lightpaths. These algorithms are based on a sequence of alternative paths, ordered in terms of increasing lengths, determined by Yen’s algorithm. Each of the algorithms for the selected single or dual lightpath enforces the constraints of spectrum continuity, contiguity of the slots, and non-overlapping of the spectra with the established lightpaths, maximizes the number of bits per symbol, and selects a specific core on each link of the path. Simulation studies performed for two sample networks showed that the crosstalk has a significant impact on the bandwidth blocking probability. The best results were obtained by iterating over all paths and all slots, selecting the lightpath with the lowest average crosstalk per slot, consisting of the most loaded cores.

Novel Application of Quantum Computing for Routing and Spectrum Assignment in Flexi-Grid Optical Networks

Flexi-grid technology has revolutionized optical networking by enabling Elastic Optical Networks (EONs) that offer greater flexibility and dynamism compared to traditional fixed-grid systems. As data traffic continues to grow exponentially, the need for efficient and scalable solutions to the routing and spectrum assignment (RSA) problem in EONs becomes increasingly critical. The RSA problem, being NP-Hard, requires solutions that can simultaneously address both spatial routing and spectrum allocation. This paper proposes a novel quantum-based approach to solving the RSA problem. By formulating the problem as a Quadratic Unconstrained Binary Optimization (QUBO) model, we employ the Quantum Approximate Optimization Algorithm (QAOA) to effectively solve it. Our approach is specifically designed to minimize end-to-end delay while satisfying the continuity and contiguity constraints of frequency slots. Simulations conducted using the Qiskit framework and IBM-QASM simulator validate the effectiveness of our method. We applied the QAOA-based RSA approach to small network topology, where the number of nodes and frequency slots was constrained by the limited qubit count on current quantum simulator. In this small network, the algorithm successfully converged to an optimal solution in less than 30 iterations, with a total runtime of approximately 10.7 s with an accuracy of 78.8%. Additionally, we conducted a comparative analysis between QAOA, integer linear programming, and deep reinforcement learning methods to evaluate the performance of the quantum-based approach relative to classical techniques. This work lays the foundation for future exploration of quantum computing in solving large-scale RSA problems in EONs, with the prospect of achieving quantum advantage as quantum technology continues to advance.

Three-dimensional Change Detection and Description in Complex Construction Scenarios

Abstract. In large-scale engineering construction scenarios, construction objects and equipment are numerous; their spatial positions and postures change frequently and are complex and varied. Describing the changes between construction entities and the entities themselves in a three-dimensional (3D) geometric space and functional semantic space is challenging. In response to this challenging, we propose a novel workflow to detect and describe the changes in a construction site. First, we add the constraint of object surface continuity to the octree change detection (OCD), exclude the independently changing cells, and improve the change detection robustness. Second, based on the changes in entity elements that occur in the 3D geometric space, we introduce six-type semantics to characterize the changes that occur. Differing from existing change detection semantic description methods that focus on the attribute semantics of changed entity elements, our method focuses on the semantic description of the change process. Finally, for the variations in different semantic types, we propose specific quantization methods that can better quantify the variations in entity elements in 3D geometric space. For the proposed solution, we tested it using two sets of multi-period time-series point cloud data, which can accurately identify the changing construction entities in space and complete the calculation of bridge construction progress, including the building demolition and construction, and the change in the construction apparatus position.

A scalable convolutional neural network approach to fluid flow prediction in complex environments

We evaluate the capability of convolutional neural networks (CNNs) to predict a velocity field as it relates to fluid flow around various arrangements of obstacles within a two-dimensional, rectangular channel. We base our network architecture on a gated residual U-Net template and train it on velocity fields generated from computational fluid dynamics (CFD) simulations. We then assess the extent to which our model can accurately and efficiently predict steady flows in terms of velocity fields associated with inlet speeds and obstacle configurations not included in our training set. Real-world applications often require fluid-flow predictions in larger and more complex domains that contain more obstacles than used in model training. To address this problem, we propose a method that decomposes a domain into subdomains for which our model can individually and accurately predict the fluid flow, after which we apply smoothness and continuity constraints to reconstruct velocity fields across the whole of the original domain. This piecewise, semicontinuous approach is computationally more efficient than the alternative, which involves generation of CFD datasets required to retrain the model on larger and more spatially complex domains. We introduce a local orientational vector field entropy (LOVE) metric, which quantifies a decorrelation scale for velocity fields in geometric domains with one or more obstacles, and use it to devise a strategy for decomposing complex domains into weakly interacting subsets suitable for application of our modeling approach. We end with an assessment of error propagation across modeled domains of increasing size.

A fourth-order compact finite volume method on unstructured grids for simulation of two-dimensional incompressible flow

This paper introduces a novel and efficient compact reconstruction procedure for high-order finite volume methods applied to unstructured grids. In this procedure, we establish a set of constitutive relations that ensure the continuity of the reconstruction polynomial and its normal derivatives between adjacent elements at control points. The paper delves into the details of the fourth-order compact reconstruction method specifically designed for two-dimensional triangular grids. This method can be considered an extension of the one-dimensional compact scheme and cubic spline interpolation methods to two-dimensional triangular unstructured grids. In the cubic polynomial reconstruction, a two-dimensional cubic polynomial is reconstructed using the cell averages of elements in the standard stencil and the function values at control points. The determination of function values at control points is achieved by adhering to the constraint of normal derivative continuity. This reconstruction is solved using a relaxation iteration method and has been verified to be solvable for triangular grids. Compared to other fourth-order implicit compact polynomial reconstructions, our method requires solving a smaller number of unknowns, which means less computational cost in reconstruction. By applying this method to solve the Poisson equation, the linear convection equation, and incompressible flow benchmarks, it demonstrates that the proposed method exhibits the expected high-order accuracy and performs well in incompressible flow problems.

Joint PP and PS AVA inversion using an acceleration algorithm and a multi-trace strategy

Abstract Exploration utilizing converted wave (PS) technology has garnered considerable interest in recent years owing to its ability to provide distinct insights into subsurface properties compared to compressional waves (PP). PS wave is particularly advantageous for accurately determining S-wave velocity (${V}_S$) and bulk density ($\rho $), whereas PP wave is better suited for assessing P-wave velocity (${V}_P$). Thus, theoretically, joint PP and PS AVA inversion can yield precise results for ${V}_P$, ${V}_S$, and $\rho $. However, a critical step before joint inversion is PP and PS registration, which is prone to causing lateral discontinuity in the inversion outcomes. To mitigate this issue, we present a simultaneous multi-trace joint inversion method. The method can improve the lateral consistency of inversion results by imposing lateral continuity constraints on the elastic parameters being inverted. Nevertheless, this simultaneous multi-trace inversion method inherently increases computational burden. To enhance algorithmic efficiency without sacrificing inversion precision, we implement an acceleration strategy. Synthetic and real data examples demonstrate that the proposed method offers remarkable performance in enhancing computational efficiency and lateral continuity compared to the conventional methods.

Dynamic Responses in a Pipe Surrounded by Compacted Soil Suffering from Water Hammer with Fluid–Structure–Soil Interactions

The current literature analyzing the dynamic response of coupled pipelines neglects the crucial interplay between the pipelines themselves and these constraints. This overlooked interaction has substantial influence on the fluid–structure coupling response, particularly in scenarios involving continuous constraints. We focus on a piping system surrounded by compacted soil, which is regarded as unbounded homogeneous elastic soil that suffers from water hammer. This study established a one-dimensional model for water pipe-embedded compacted soil with fluid–structure–soil interaction. Taking fluid–structure–soil interaction into account, fluid–structure interactions (FSIs) include Poisson coupling, junction coupling emerging at the fluid–structure interface, and pipe–soil coupling (PSC) emerging at the pipe–soil interface. In this study, as soil is assumed to be a homogeneous, isotropic elastic material, the coupling responses are more complex than those of an exposed pipe, and the relevant mechanisms justify further exploration to obtain well-predicted results. To mathematically describe this system considering fluid–structure–soil interaction, the four-equation FSI model was modified to accommodate the piping system surrounded by unbounded homogeneous elastic soil, employing the finite volume method (FVM) as a means to tackle and solve the dynamic problems with FSI and PSC, which partitions the computational domain into a finite number of control volumes and discretizes governing equations within each volume. The results were validated by the experimental and numerical results. Then, dynamic FSI responses to water hammer were studied in a reservoir–pipe–reservoir physical system. The hydraulic pressure, pipe wall stress, and axial motion were discussed with respect to different parameters. With the PSC and FSI taken into account, fluid, soil, and pipe signals were obviously observed. The results revealed the structural and fluid modes. Dynamic responses have been proven to be difficult to understand and predict. Despite this, this study provides a tractable method to capture more accurate systematic characteristics of a water pipe embedded in soil.

Constraint Maps with Free Boundaries: the Obstacle Case

This paper revives a four-decade-old problem concerning regularity theory for (continuous) constraint maps with free boundaries. Dividing the map into two parts, the distance part and the projected image to the constraint, one can prove various properties for each component. As has already been pointed out in the literature, the distance part falls under the classical obstacle problem, which is well-studied by classical methods. A perplexing issue, untouched in the literature, concerns the properties of the projected image and its higher regularity, which we show to be at most of class C2,1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^{2,1}$$\\end{document}. In arbitrary dimensions, we prove that the image map is globally of class W3,BMO\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W^{3,BMO}$$\\end{document}, and locally of class C2,1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^{2,1}$$\\end{document} around the regular part of the free boundary. The issue becomes more delicate around singular points, and we resolve it in two dimensions. In the appendix, we extend some of our results to what we call leaky maps.

Volumetric Reconstruction of Ionospheric Electric Currents From Tri‐Static Incoherent Scatter Radar Measurements

AbstractWe present a new technique for the upcoming tri‐static incoherent scatter radar system EISCAT 3D (E3D) to perform a volumetric reconstruction of the 3D ionospheric electric current density vector field, focusing on the feasibility of the E3D system. The input to our volumetric reconstruction technique are estimates of the 3D current density perpendicular to the main magnetic field, j⊥, and its covariance, to be obtained from E3D observations based on two main assumptions: (a) Ions fully magnetized above the E region, set to 200 km here. (b) Electrons fully magnetized above the base of our domain, set to 90 km. In this way, j⊥ estimates are obtained without assumptions about the neutral wind field, allowing it to be subsequently determined. The volumetric reconstruction of the full 3D current density is implemented as vertically coupled horizontal layers represented by Spherical Elementary Current Systems with a built‐in current continuity constraint. We demonstrate that our technique is able to retrieve the three dimensional nature of the currents in our idealized setup, taken from a simulation of an active auroral ionosphere using the Geospace Environment Model of Ion‐Neutral Interactions (GEMINI). The vertical current is typically less constrained than the horizontal, but we outline strategies for improvement by utilizing additional data sources in the inversion. The ability to reconstruct the neutral wind field perpendicular to the magnetic field in the E region is demonstrated to mostly be within ±50 m/s in a limited region above the radar system in our setup.

Novel hybrid integrated Pix2Pix and WGAN model with Gradient Penalty for binary images denoising

This paper introduces a novel approach to image denoising that leverages the advantages of Generative Adversarial Networks (GANs). Specifically, we propose a model that combines elements of the Pix2Pix model and the Wasserstein GAN (WGAN) with Gradient Penalty (WGAN-GP). This hybrid framework seeks to capitalize on the denoising capabilities of conditional GANs, as demonstrated in the Pix2Pix model, while mitigating the need for an exhaustive search for optimal hyperparameters that could potentially ruin the stability of the learning process. In the proposed method, the GAN’s generator is employed to produce denoised images, harnessing the power of a conditional GAN for noise reduction. Simultaneously, the implementation of the Lipschitz continuity constraint during updates, as featured in WGAN-GP, aids in reducing susceptibility to mode collapse. This innovative design allows the proposed model to benefit from the strong points of both Pix2Pix and WGAN-GP, generating superior denoising results while ensuring training stability. Drawing on previous work on image-to-image translation and GAN stabilization techniques, the proposed research highlights the potential of GANs as a general-purpose solution for denoising. The paper details the development and testing of this model, showcasing its effectiveness through numerical experiments. The dataset was created by adding synthetic noise to clean images. Numerical results based on real-world dataset validation underscore the efficacy of this approach in image-denoising tasks, exhibiting significant enhancements over traditional techniques. Notably, the proposed model demonstrates strong generalization capabilities, performing effectively even when trained with synthetic noise.

Using unsupervised learning based convolutional neural networks to solve Digital Image Correlation

Digital Image Correlation (DIC) is a robust, non-contact method for full-field deformation measurement widely used in photomechanics. Based on subset image matching and an iterative optimization architecture, traditional DIC deformation field analysis requires manual selection of such calculation parameters as subset size, rendering it challenging to balance spatial resolution and measurement resolution in non-uniform field measurements. The requirement of manual parameter adjustment is lowered by a recently emerged supervised learning-based neural network DIC method, as it establishes a direct correlation between images and deformation fields using deep neural networks (DNN). However, its generalization and accuracy are contingent on the scope and variety of the dataset because it requires training with a large number of simulated speckle images of deformation fields with known standards. This paper proposes an unsupervised learning neural network based DIC measurement method that circumvents the need for standard deformation fields and achieves high precision analysis of deformed fields. It constructs a loss function based on the photometric consistency assumption of speckle images before and after deformation and allows the neural network model to directly extract displacement information from the gray data of the “reference image-deformed image” pair. Meanwhile, the model is enhanced accordingly by further introducing displacement continuity constraints to enhance accuracy and mitigate noise interference. Validation through both simulated and real experiments shows that the proposed approach surpasses traditional subset DIC in measuring non-uniform deformation fields with higher precision. It also offers superior flexibility and adaptability over supervised learning-based neural network DIC methods by eliminating the need for a large training dataset, allowing for immediate application in displacement field analysis.

Fast Clustering by Directly Solving Bipartite Graph Clustering Problem.

Spectral clustering (SC) has been widely used in many applications and shows excellent performance. Its high computational cost limits its applications; many strategies including the anchor technique can partly alleviate the high computational cost problem. However, early methods ignore the fact that SC usually involves two stages: relaxation and postprocessing, i.e., it relaxes the discrete constraints to continuous constraints, and then conducts the postprocessing to get the discrete solution, which is time-consuming and deviates from directly solving the primal problem. In this article, we first adopt the bipartite graph strategy to reduce the time complexity of SC, and then an improved coordinate descent (CD) method is proposed to solve the primal problem directly without singular value decomposition (SVD) and postprocessing, i.e., directly solving the primal problem not approximately solving. Experiments on various real-world benchmark datasets show that the proposed method can get better solutions faster with better clustering performance than traditional optimization methods. Furthermore, it can jump out of local minima of traditional methods and continue to obtain better local solutions. Moreover, compared with other clustering methods, it also shows its superiority.

VascuConNet: an enhanced connectivity network for vascular segmentation.

Medical image segmentation commonly involves diverse tissue types and structures, including tasks such as blood vessel segmentation and nerve fiber bundle segmentation. Enhancing the continuity of segmentation outcomes represents a pivotal challenge in medical image segmentation, driven by the demands of clinical applications, focusing on disease localization and quantification. In this study, a novel segmentation model is specifically designed for retinal vessel segmentation, leveraging vessel orientation information, boundary constraints, and continuity constraints to improve segmentation accuracy. To achieve this, we cascade U-Net with a long-short-term memory network (LSTM). U-Net is characterized by a small number of parameters and high segmentation efficiency, while LSTM offers a parameter-sharing capability. Additionally, we introduce an orientation information enhancement module inserted into the model's bottom layer to obtain feature maps containing orientation information through an orientation convolution operator. Furthermore, we design a new hybrid loss function that consists of connectivity loss, boundary loss, and cross-entropy loss. Experimental results demonstrate that the model achieves excellent segmentation outcomes across three widely recognized retinal vessel segmentation datasets, CHASE_DB1, DRIVE, and ARIA.

Generalized Bézier-like model and its applications to curve and surface modeling.

The subject matter of surfaces in computer aided geometric design (CAGD) is the depiction and design of surfaces in the computer graphics arena. Due to their geometric features, modeling of Bézier curves and surfaces with their shape parameters is the most well-liked topic of research in CAGD/computer-aided manufacturing (CAM). The primary challenges in industries such as automotive, shipbuilding, and aerospace are the design of complex surfaces. In order to address this issue, the continuity constraints between surfaces are utilized to generate complex surfaces. The parametric and geometric continuities are the two metrics commonly used for establishing connections among surfaces. This paper proposes continuity constraints between two generalized Bézier-like surfaces (gBS) with different shape parameters to address the issue of modeling and designing surfaces. Initially, the generalized form of C3 and G3 of generalized Bézier-like curves (gBC) are developed. To check the validity of these constraints, some numerical examples are also analyzed with graphical representations. Furthermore, for a continuous connection among these gBS, the necessary and sufficient G1 and G2 continuity constraints are also developed. It is shown through the use of several geometric designs of gBS that the recommended basis can resolve the shape and position adjustment problems associated with Bézier surfaces more effectively than any other basis. As a result, the proposed scheme not only incorporates all of the geometric features of curve design schemes but also improves upon their faults, which are typically encountered in engineering. Mainly, by changing the values of shape parameters, we can alter the shape of the curve by our choice which is not present in the standard Bézier model. This is the main drawback of traditional Bézier model.

Routing and wavelength assignment for folded hypercube in linear array WDM optical networks

The folded hypercube is one of the hypercube variants and is of great significance in the study of interconnection networks. In a folded hypercube, information can be broadcast using efficient distributed algorithms. In the context of parallel computing, folded hypercube has been studied as a possible network topology as an alternative to the hypercube. The routing and wavelength assignment (RWA) problem is significant, since it improves the performance of wavelength-routed all-optical networks constructed using wavelength division multiplexing approach. Given the physical network topology, the aim of the RWA problem is to establish routes for the connection requests and assign the fewest possible wavelengths in accordance with the wavelength continuity and distinct wavelength constraints. This paper discusses the RWA problem in a linear array for the folded hypercube communication pattern by using the congestion technique.

Coupled vibration analysis of the spacecraft with the flexible shaft and solar panels assembly

Dynamical characteristics of the spacecraft with flexible components are investigated in this paper. The component consists of a flexible shaft and solar panels, where solar panels are completely fixed on the shaft. A novel power series multiplier polynomial method is proposed to describe the connecting condition between the shaft and solar panels. The deformation and force matching conditions between the one dimensional shaft and two dimensional panels are established, which is the major contribution about the multidimensional combined structure of this study. According to constraining boundary conditions of the shaft and solar panels, the bending-torsion coupled deformation of the component is expressed. The attitude maneuvering of the central platform and the elastic vibration of the component cause the rigid-flexible coupled effect. Then the discrete dynamical equation of the spacecraft is obtained by using the rigid-flexible coupled modal shapes. The correctness of the proposed method is verified by comparing the natural characteristics with that of the finite element model. The relative error of the higher order frequency is not more than 4%. Numerical results show that the degree of the bending angle polynomial should be at least quadratic to ensure the accuracy of the calculation. The proposed power series multiplier polynomial breaks through the barriers that the traditional Lagrange multiplier cannot express the continuous constraint. It is an effective method to fit the constrained boundary by the polynomial rather than by the discrete multipoint method.

Vibration Response of Metal Plate and Shell Structure under Multi-Source Excitation with Welding and Bolt Connection

There are many excitation sources and complex vibration environments in combine harvesters. The coupling and superposition of different vibration signals on the plate and shell seriously affect the working parts of the body. This also reduces the reliability of the whole machine. At present, domestic and foreign research on existing harvesters mainly focuses on harvesting performance, with less research on vibration characteristics. Therefore, in this paper, the vibration response of the metal plate–shell under the two connection modes of bolt connection and welding is studied, in order to optimize the design and structure of the plate–shell structure of the combine harvester and improve the overall performance. First, the welded and bolted plates are numerically modeled using Hypermesh pre-processing functions. Then, the boundary conditions are simulated by continuous variable stiffness elastic constraint experiments. Finally, the intrinsic vibration dynamic model of the four-sided simply supported plate and four-sided solidly supported plate is established using the modal superposition method. By analyzing the modal frequencies and vibration patterns, the following results are obtained. The connection method between the plate and the frame has a significant impact on the inherent vibration characteristics of the plate. The bolt connection will make the plate’s intrinsic vibration frequency higher than that of the welding method, but the effect on the plate’s intrinsic vibration pattern is more minor. At the same time, in order to verify the accuracy of the model, the actual modal vibration patterns and frequencies of the same proportion of plates in the modal test are compared with the results of modal vibration patterns and frequencies obtained by Ansys. The errors of the two dynamic model analytical methods are within 1% and 3%, respectively. This result verifies the accuracy of the dynamic model of the metal plate and shell structure under different connection methods.

TPMS2STEP: Error-Controlled and [formula omitted] Continuity-Preserving Translation of TPMS Models to STEP Files Based on Constrained-PIA

Triply periodic minimal surface (TPMS) is emerging as an important way of designing microstructures. However, there has been limited use of commercial CAD/CAM/CAE software packages for TPMS design and manufacturing. This is mainly because TPMS is consistently described in the functional representation (F-rep) format, while modern CAD/CAM/CAE tools are built upon the boundary representation (B-rep) format. One possible solution to this gap is translating TPMS to STEP, which is the standard data exchange format of CAD/CAM/CAE. Following this direction, this paper proposes a new translation method with error-controlling and C2 continuity-preserving features. It is based on an approximation error-driven TPMS sampling algorithm and a constrained-PIA algorithm. The sampling algorithm controls the deviation between the original and translated models. With it, an error bound of 2ϵ on the deviation can be ensured if two conditions called ϵ-density and ϵ-approximation are satisfied. The constrained-PIA algorithm enforces C2 continuity constraints during TPMS approximation, and meanwhile attaining high efficiency. A theoretical convergence proof of this algorithm is also given. The effectiveness of the translation method has been demonstrated by a series of examples and comparisons. The code will be open-sourced upon publication.

Continuously bounds-preserving discontinuous Galerkin methods for hyperbolic conservation laws

For finite element approximations of transport phenomena, it is often necessary to apply a form of limiting to ensure that the discrete solution remains well-behaved and satisfies physical constraints. However, these limiting procedures are typically performed at discrete nodal locations, which is not sufficient to ensure the robustness of the scheme when the solution must be evaluated at arbitrary locations (e.g., for adaptive mesh refinement, remapping in arbitrary Lagrangian–Eulerian solvers, overset meshes, etc.). In this work, a novel limiting approach for discontinuous Galerkin methods is presented which ensures that the solution is continuously bounds-preserving (i.e., across the entire solution polynomial) for any arbitrary choice of basis, approximation order, and mesh element type. Through a modified formulation for the constraint functionals, the proposed approach requires only the solution of a single spatial scalar minimization problem per element for which a highly efficient numerical optimization procedure is presented. The efficacy of this approach is shown in numerical experiments by enforcing continuous constraints in high-order unstructured discontinuous Galerkin discretizations of hyperbolic conservation laws, ranging from scalar transport with maximum principle preserving constraints to compressible gas dynamics with positivity-preserving constraints.

How word stress is realized in Thai: evidence from the ordering of coordinate compounds

Abstract This study challenges the widespread belief that Thai lacks word stress, demonstrating its pivotal role in morphophonology. Through a Maximum Entropy analysis, we investigated how specific segmental properties statistically influence speakers’ choices of word order in coordinate compounds. Results indicate a significant effect of phonological weight on the ordering patterns. Specifically, the dispreference for stop codas in final positions and the preference for long or low vowels word-finally converge to differentially distribute phonological weight, ensuring that final syllables are heavier in accordance with the Stress-to-Weight Principle. Additionally, a marginal affinity is observed between the final syllable and the (historical) high-register tone, aligning with the well-documented tone-stress interaction where high tones gravitate towards stressed syllables. These findings provide compelling evidence for the existence of word stress in Thai: compound stress necessarily coincides with word stress, as dictated by the Continuous Column Constraint. Thus, this work suggests that relying solely on phonetic cues is insufficient for identifying stress; instead, a comprehensive analysis incorporating “phonological exponents” is essential to capture the greater phonological contrasts licensed in stressed syllables. This study also contributes to a deeper understanding of metrical and prosodic prominence, revealing that word stress can sometimes be masked by higher-level prominence.