Smooth Distribution Research Articles

New graphical models for sequential data and the improved state estimations by data-conditioned driving noises

A prevalent problem in statistical signal processing, applied statistics, and time series analysis arises from the attempt to identify the hidden state of Markov process based on a set of available noisy observations. In the context of sequential data, filtering refers to the probability distribution of the underlying Markovian system given the measurements made at or before the time of the estimated state. In addition to the filtering, the smoothing distribution is obtained from incorporating measurements made after the time of the estimated state into the filtered solution. This work proposes a number of new filters and smoothers that, in contrast to the traditional schemes, systematically make use of the process noises to give rise to enhanced performances in addressing the state estimation problem. In doing so, our approaches for the resolution are characterized by the application of the graphical models; the graph-based framework not only provides a unified perspective on the existing filters and smoothers but leads us to design new algorithms in a consistent and comprehensible manner. Moreover, the graph models facilitate the implementation of the suggested algorithms through message passing on the graph.

Diagnosis of Al-CFRTP TA-FSLW defect using acoustic emission signal based on SPWVD and ResNet

As one of the important development directions in modern railway and automobile, lightweight requires reliable connection technology of dissimilar materials. Thermal-assisted friction stir lap welding (TA-FSLW) is an available welding technology for the joining of dissimilar materials, which can solve the problems of physical and chemical properties in the welding process of dissimilar materials. Unfortunately, defects may occur during the welding process. This paper proposes a defect diagnosis method based on smooth pseudo Wigner-Ville distribution (SPWVD) and ResNet18 for Al-CFRTP TA-FSLW. Firstly, the acoustic emission (AE) signal and the temperature of the weld nugget are acquired by the AE sensor and thermography camera in the FSLW process. Then, the time–frequency domain features of AE signal are extracted by SPWVD, and the maximum temperature of the weld nugget is extracted by exponential moving average (EMA) from thermography. Moreover, the dataset is established by SPWVD features, maximum temperature of welding nugget, and several time–frequency features. Finally, the ResNet18-attention network is employed to classify welding defects and stages. The Al-CFRTP TA-FSLW experiments are carried out based on the proposed method. Experimental result indicates that the SPWVD spectrum can effectively extract the feature frequency of deep and shallow hole defects in the welding process. In the section of classification, the accuracy of the dataset with SPWVD features is improved by 2% to 4% compared to other methods, which demonstrates that the SPWVD feature is superior in defect feature extraction.

Learning Deformable Hypothesis Sampling for Accurate PatchMatch Multi-View Stereo

This paper introduces a learnable Deformable Hypothesis Sampler (DeformSampler) to address the challenging issue of noisy depth estimation in faithful PatchMatch multi-view stereo (MVS). We observe that the heuristic depth hypothesis sampling modes employed by PatchMatch MVS solvers are insensitive to (i) the piece-wise smooth distribution of depths across the object surface and (ii) the implicit multi-modal distribution of depth prediction probabilities along the ray direction on the surface points. Accordingly, we develop DeformSampler to learn distribution-sensitive sample spaces to (i) propagate depths consistent with the scene's geometry across the object surface and (ii) fit a Laplace Mixture model that approaches the point-wise probabilities distribution of the actual depths along the ray direction. We integrate DeformSampler into a learnable PatchMatch MVS system to enhance depth estimation in challenging areas, such as piece-wise discontinuous surface boundaries and weakly-textured regions. Experimental results on DTU and Tanks & Temples datasets demonstrate its superior performance and generalization capabilities compared to state-of-the-art competitors. Code is available at https://github.com/Geo-Tell/DS-PMNet.

Sensitivity of Phonation Onset Pressure to Vocal Fold Stiffness Distribution.

Phonation onset is characterized by the unstable growth of vocal fold (VF) vibrations that ultimately results in self-sustained oscillation and the production of modal voice. Motivated by histological studies, much research has focused on the role of the layered structure of the vocal folds in influencing phonation onset, wherein the outer "cover" layer is relatively soft and the inner "body" layer is relatively stiff. Recent research, however, suggests that the body-cover (BC) structure over-simplifies actual stiffness distributions by neglecting important spatial variations, such as inferior-superior (IS) and anterior-posterior gradients and smooth transitions in stiffness from one histological layer to another. Herein, we explore sensitivity of phonation onset to stiffness gradients and smoothness. By assuming no a priori stiffness distribution and considering a second-order Taylor series sensitivity analysis of phonation onset pressure with respect to stiffness, we find two general smooth stiffness distributions most strongly influence onset pressure: a smooth stiffness containing aspects of BC differences and IS gradients in the cover, which plays a role in minimizing onset pressure, and uniform increases in stiffness, which raise onset pressure and frequency. While the smooth stiffness change contains aspects qualitatively similar to layered BC distributions used in computational studies, smooth transitions in stiffness result in higher sensitivity of onset pressure than discrete layering. These two general stiffness distributions also provide a simple, low-dimensional, interpretation of how complex variations in VF stiffness affect onset pressure, enabling refined exploration of the effects of stiffness distributions on phonation onset.

An improved tracking method for bearing characteristic frequencies in the time-frequency representation of vibration signal

Rolling bearing is one of the most critical components for support and energy conversion in machines. The fault characteristic frequency (FCF) of time–frequency representation has received increasing attention in bearing diagnosis under variable speed conditions. However, FCF-extracted methods have poor adaptability to amplitude attenuation and noise interference due to local distortions or even transitions in the estimated instantaneous frequency ridges. Consequently, this paper proposes an improved FCF tracking method for variable speed bearing diagnosis. A strategy for locating distortion intervals is first developed using exponential smoothing and residual distribution. Subsequently, an advanced fast path optimization method, including peak map renewal and curve search optimization, is proposed to extract the ridges of interest. Finally, the probability density function of curve-to-curve ratios is designed to accurately identifying bearing faults. Simulation and experimental results demonstrate the effectiveness of the proposed method.

Experimental study of an enhanced water-cooling technique for interstitial microwave cancer ablation system

The aim of this work is to investigate the behavior of the microwave cancer ablation system under enhanced water-cooling technique. Cooling is too important for the microwave ablation process to remove the heat accumulated on the surface of the antenna shaft due to the mismatching standing waves. Cooling of the antenna shaft prevents the rapid heating which causes carbonization of the tissues under ablation and blocks any more heat transfer to the tissues. Moreover, cooling prevents the back heating of the antenna shaft surface which harms the healthy tissues through which the antenna passes. The experimental ablation process has been conducted on bovines’ liver specimens at 2.45 GHz microwave frequency where the cooling water is circulated through an open flow circuit. The area and shape of the heated zone were taken as a criterion to compare between the performances of different cases of cooling water. To validate the obtained results and prove the death of the ablated cells, histology of liver tissues has been done. The proposed technique improves and tends to a larger ablation zone, smooth heat distribution, and no back heating on the antenna shaft.

Influence of boundary conditions on non-equilibrium heat transport under ultrafast laser action based on the lattice Boltzmann method

Based on the lattice Boltzmann method, this paper simulated the non-equilibrium heat transfer process in nano-silicon thin film under ultrafast laser irradiation. The influence of boundary conditions on heat transport was investigated. Results show that under rebound and diffuse boundary conditions, the energy distribution within the film is non-uniform due to interface effects. However, the specular boundary condition is equivalent to eliminating the interface, resulting in a smooth energy distribution. Under convective boundary conditions, the thermal wave phenomenon disappears owing to the open interface. When the energy tends to be stable, the energy density under convective boundary conditions is reduced to 50% of that under adiabatic boundary conditions. As the film size decreases, the differences between boundary conditions become more significant. Particularly when the film size is smaller than the phonon mean free path, the influence of boundary conditions cannot be neglected. Therefore, boundary conditions and size effects are important for the design of nanodevices. Furthermore, compared with the results obtained by the Cattaneo-Vernotte model, it is found that at smaller Knudsen numbers, the Cattaneo-Vernotte model has a better match with the lattice Boltzmann method.

Constrain the Dark-matter Distribution of Ultra-diffuse Galaxies with Globular-cluster Mass Segregation: A Case Study with NGC5846-UDG1

The properties of globular clusters (GCs) contain valuable information of their host galaxies and dark-matter halos. In the remarkable example of ultra-diffuse galaxy, NGC5846-UDG1, the GC population exhibits strong radial mass segregation, indicative of dynamical-friction-driven orbital decay, which opens the possibility of using imaging data alone to constrain the dark-matter content of the galaxy. To explore this possibility, we develop a semianalytical model of GC evolution, which starts from the initial mass, structural, and spatial distributions of the GC progenitors, and follows the effects of dynamical friction, tidal evolution, and two-body relaxation. Using Markov Chain Monte Carlo, we forward-model the GCs in a UDG1-like potential to match the observed GC statistics, and to constrain the profile of the host halo and the origin of the GCs. We find that, with the assumptions of zero mass segregation when the star clusters were born, UDG1 is relatively dark-matter-poor compared to what is expected from stellar-to-halo–mass relations, and its halo concentration is lower than the cosmological average, irrespective of having a cuspy or a cored profile. Its GC population has an initial spatial distribution more extended than the smooth stellar distribution. We discuss the results in the context of scaling laws of galaxy–halo connections, and warn against naively using the GC-abundance–halo–mass relation to infer the halo mass of ultra-diffuse galaxies. Our model is generally applicable to GC-rich dwarf galaxies, and is publicly available.

Euler’s First-Order Explicit Method–Peridynamic Differential Operator for Solving Two-Dimensional Population Balance Equations in Crystallization

The population balance equations (PBEs) serve as the primary governing equations for simulating the crystallization process. Two-dimensional (2D) PBEs pertain to crystals that exhibit anisotropic growth, which is characterized by changes in two internal coordinates. Because PBEs are the hyperbolic equations, it becomes imperative to establish a high-resolution scheme to reduce numerical diffusion and numerical dispersion, thereby ensuring accurate crystal size distribution. This paper uses Euler’s first-order explicit (EE) method–Peridynamic Differential Operator (PDDO) to solve 2D PBE, namely, the EE method for discretizing the time derivative and the PDDO for discretizing the internal crystal-size derivative. Five examples, including size-independent growth with smooth and non-smooth distributions, size-dependent growth, nucleation, and size-independent/dependent growth for batch crystallization are considered. The results show that the EE–PDDO method is more accurate than the HR method and that it is as good as the fifth-order Weighted Essential Non-Oscillatory (WENO) method in solving 2D PBE. This study extends the EE–PDDO method to the simulation of 2D PBE, and the advantages of the EE-PDDO method in dealing with discontinuous and sharp front problems are demonstrated.

High-resolution EEG source localization in personalized segmentation-free head model with multi-dipole fitting

Objective. Electroencephalograms (EEGs) are often used to monitor brain activity. Several source localization methods have been proposed to estimate the location of brain activity corresponding to EEG readings. However, only a few studies evaluated source localization accuracy from measured EEG using personalized head models in a millimeter resolution. In this study, based on a volume conductor analysis of a high-resolution personalized human head model constructed from magnetic resonance images, a finite difference method was used to solve the forward problem and to reconstruct the field distribution. Approach. We used a personalized segmentation-free head model developed using machine learning techniques, in which the abrupt change of electrical conductivity occurred at the tissue interface is suppressed. Using this model, a smooth field distribution was obtained to address the forward problem. Next, multi-dipole fitting was conducted using EEG measurements for each subject (N = 10 male subjects, age: 22.5 ± 0.5), and the source location and electric field distribution were estimated. Main results. For measured somatosensory evoked potential for electrostimulation to the wrist, a multi-dipole model with lead field matrix computed with the volume conductor model was found to be superior than a single dipole model when using personalized segmentation-free models (6/10). The correlation coefficient between measured and estimated scalp potentials was 0.89 for segmentation-free head models and 0.71 for conventional segmented models. The proposed method is straightforward model development and comparable localization difference of the maximum electric field from the target wrist reported using fMR (i.e. 16.4 ± 5.2 mm) in previous study. For comparison, DUNEuro based on sLORETA was (EEG: 17.0 ± 4.0 mm). In addition, somatosensory evoked magnetic fields obtained by Magnetoencephalography was 25.3 ± 8.5 mm using three-layer sphere and sLORETA. Significance. For measured EEG signals, our procedures using personalized head models demonstrated that effective localization of the somatosensory cortex, which is located in a non-shallower cortex region. This method may be potentially applied for imaging brain activity located in other non-shallow regions.

Target shape approximation of funicular surfaces by load control using RBF interpolation

Existing methods for form-finding prioritize discovering optimal shapes under design load conditions, often overlooking the designer’s shape preferences. To address this problem, this research relaxes the load condition and develops a user-friendly form-finding tool that encapsulates a new method for obtaining funicular surfaces that pass through user-prescribed points through load control. The method involves generating smooth load distributions via RBF interpolation of nodal loads, which are repeatedly adjusted so that the equilibrium shape is close enough to the target points. For faster convergence, the step size of the load adjustment is automatically determined through a coarse line search, and a warm start is introduced in form-finding with the dynamic relaxation method. Despite uneven load distributions, the method ensures high accuracy in approximating the surface shape to the desired points while preserving funicularity against the load distributions. Additionally, the resulting load distribution gives designers valuable feedback on the specified target points, as the degree of load non-uniformity indicates the deviation from the equilibrium shape for uniformly distributed loads.

Characterization and thermo-mechanical analysis of centrifugally fabricated aluminium-boron carbide functionally graded composites

This research focuses on developing lightweight functionally gradient composites (FGCs) having graded distribution B4C in aluminium matrix by employing centrifugal casting technique. Two different sizes of reinforcement, that is, 100 and 50 μm was chosen to analyse its effect on the thermo mechanical properties and its distribution were analysed in this study. Advanced characterization revealed smooth graded distribution of the reinforcement across the thickness of the fabricated FGCs. The density and micro Vickers hardness test showed that they are 1.5% higher at outer periphery ensuring the graded distribution of B4C. The tensile strength was 31% higher for 50 μm sized reinforcement in the FGC, due to the increased surface area-to-volume ratio of the reinforcement. The thermal properties like thermal conductivity was 46.4% higher, thermal diffusivity was 27.8% higher for 100 μm sized reinforcement than for 50 μm sized reinforcement in the FGC. The above research work provides a new perspective on deploying aluminium based B4C graded composites for heat exchangers or fins subjected to varying thermal loads.

High performance epoxy soybean oil-based composite reinforced by wood powder

A novel bio-based composite, called the ESO-1,6-hexanediamine-ADP-wood (EHAW) composite, was created using epoxy soybean oil (ESO), 1,6-hexanediamine, and ammonium dihydrogen phosphate (ADP) co-condensed resin as matrix and wood powder as aggregate. The cross-linking was achieved through the ring opening polymerization of 1,6-hexanediamine and ESO, which was then esterified and condensed with ADP to form a network structure. The effects of mass ratio of wood powder to soybean oil-hexamethylene diamine-ammonium dihydrogen phosphate (EHA) resin on the performance of the composite were investigated. The mass ratio of wood powder to EHA resin was 0.25, 0.5 and 0.75, respectively. The results revealed that composite with the wood powder/EHA resin of 0.5 (EHAW2) had the best performance indicates by its smooth and uniform distribution under SEM observations. In addition, EHAW2 showed better Brinell hardness, compressive strength, UV resistance as well as water absorption properties than the other two ratios. It also showed better thermal conductivity and flame retardancy. The total heat released during combustion is low, and there are no collapse and shape change during the combustion process, making it an ideal material for building applications.

INVESTIGATING THE IMPACT OF INNOVATION TECHNOLOGIES IN LOGISTICS (CROSSING TRANSPORTATION MODEL: CASE STUDY OF THE LANGARA - KENDARI ROUTE)

Konawe Islands is a regency in the Southeast Sulawesi Province. This area heavily relies on Kendari City, the provincial capital, to support daily necessities, recreational activities, and higher education pursuits for the people of Konawe Islands. Wooden boats and ferries serve as the primary means of transportation for the locals. However, during harsh weather, only ferries is operational. Yet, there have been loading violations on ferries, increasing the risk to maritime safety. This research aims to formulate ways to address loading issues on ro-ro ferries along the Langara-Kendari route, ensuring compliance with laws and facilitating smooth cargo distribution. The distribution system is structured based on the method persona user and empathy mapping. Research findings indicate that distribution service users require a freight forwarder for large-scale cargo and consolidation for smaller-scale loads. Therefore, the author recommends the use of applications like Uber, Grab, and Uber to resolve this issue.

TOTALLY NONHOLONOMIC DISTRIBUTIONS AND SUB-RIEMANNIAN STRUCTURES

In this paper, we study totally non-holonomic distributions and sub-riemannian structure on Rn (n = 1, 2, 3, 4, ...) and on the manifolds of not null curvature such as Tn and Sn with n more or equal than 3, in order to look at this structure on a manifold like a restricting of a Riemannian metric on a totally non-holonomic distribution of this manifold. On Rn, it always possible to construct this structure thanks to her multitude of smooth distributions and vector elds. On the manifolds of not null curvature, we de ne this structure on the kernel of a non-degenerate 1-form or of contact form on this manifold.

Nanoscale Stolephorus sp. powder fabrication using high-energy milling for bioactive materials in dentistry.

The application of natural products in dentistry has been widely explored. Anchovy (Stolephorus in Latin) has been examined for its bioactive content (calcium, phosphorus and fluoride) as an agent for bone stimulation and tooth development, topical fluoridation and pulp capping. Ball milling has been used to prepare calcium oxide nanoparticles from snakehead fish bone. The aim of the study was to reduce the particle size of Stolephorus sp. powder to the nanoscale using high-energy ball milling for 8, 12 and 24 h, and to analyze the optimal milling time by comparing the powder characteristics. The Stolephorus sp. were oven-dried at 50°C for 6 h, after which the entire fish were crushed into powder. The fish powder was produced by blending the material for 5 min and passing it through a 200-mesh sieve. The remaining dried fish was blended again for 5 min until it passed through the sieve. The top-down approach to the particle size reduction was performed using high-energy milling at 3 distinct time points (8, 12 and 24 h). The characteristics of the powder were evaluated using a particle size analyzer, a Fourier-transform infrared spectrometer (FTIR) and scanning electron microscopy-energy dispersive spectroscopy (SEM-EDS). The Stolephorus sp. powder contained 64.50% protein, 7,420 mg/kg sodium, 28,912 mg/kg calcium, and 1,924 mg/kg magnesium. The high-energy milling process resulted in a reduction of the particle size from the microscale to the nanoscale. The analysis of the average particle size and polydispersity index indicated that 24 h of milling showed the most optimal results. Furthermore, the functional groups exhibited no significant alteration at 3 milling times (p ≥ 0.05, FTIR analysis). The high-energy milling method has the potential to reduce the particle size of Stolephorus sp. powder to the nanoscale at the 8- and 24-h milling periods. The powder resulting from the 24-h milling process had a size of 789.3 ±170.7 nm, smooth size distribution, good size uniformity, a polydispersity index of 0.763, no significant change in organic and inorganic compound content, and a calcium/phosphorus ratio that was the closest to that of hydroxyapatite (HAp).

Quantum state preparation of normal distributions using matrix product states

State preparation is a necessary component of many quantum algorithms. In this work, we combine a method for efficiently representing smooth differentiable probability distributions using matrix product states with recently discovered techniques for initializing quantum states to approximate matrix product states. Using this, we generate quantum states encoding a class of normal probability distributions in a trapped ion quantum computer for up to 20 qubits. We provide an in depth analysis of the different sources of error which contribute to the overall fidelity of this state preparation procedure. Our work provides a study in quantum hardware for scalable distribution loading, which is the basis of a wide range of algorithms that provide quantum advantage.

Improved Breitung and Roling estimator for mixed-frequency models with application to forecasting inflation rates

Instead of applying the commonly used parametric Almon or Beta lag distribution of MIDAS, Breitung and Roling (J Forecast 34:588–603, 2015) suggested a nonparametric smoothed least-squares shrinkage estimator (henceforth SLS1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${SLS}_{1}$$\\end{document}) for estimating mixed-frequency models. This SLS1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${SLS}_{1}$$\\end{document} approach ensures a flexible smooth trending lag distribution. However, even if the biasing parameter in SLS1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${SLS}_{1}$$\\end{document} solves the overparameterization problem, the cost is a decreased goodness-of-fit. Therefore, we suggest a modification of this shrinkage regression into a two-parameter smoothed least-squares estimator (SLS2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${SLS}_{2}$$\\end{document}). This estimator solves the overparameterization problem, and it has superior properties since it ensures that the orthogonality assumption between residuals and the predicted dependent variable holds, which leads to an increased goodness-of-fit. Our theoretical comparisons, supported by simulations, demonstrate that the increase in goodness-of-fit of the proposed two-parameter estimator also leads to a decrease in the mean square error of SLS2,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${SLS}_{2},$$\\end{document} compared to that of SLS1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${SLS}_{1}$$\\end{document}. Empirical results, where the inflation rate is forecasted based on the oil returns, demonstrate that our proposed SLS2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${SLS}_{2}$$\\end{document} estimator for mixed-frequency models provides better estimates in terms of decreased MSE and improved R2, which in turn leads to better forecasts.

Equações universais para as distribuições de chuva dos métodos SCS e Huff

ABSTRACT The temporal distribution of design rainfall hyetographs can be obtained through various procedures. One such method involves using temporal distribution curves to disaggregate a rainfall value of longer duration into chronological values within shorter time intervals. This is demonstrated by SCS distribution curves for durations of 6 and 24 hours and the well-known Huff curves. Another approach involves deriving temporal distribution using design hyetograph calculation methods, such as the Chicago and alternating block methods, based on Intensity-Duration-Frequency (IDF) equations. This paper aims to combine these approaches and develop universal equations capable of accurately fitting smooth rainfall time distribution curves. The advantage is the replacement of tables, like SCS and Huff, with analytical equations, enhancing usability in spreadsheets. Furthermore, these universal equations can determine the temporal rainfall distribution using an IDF equation or fitting a specified design hyetograph like Euler type II. Four numerical examples are provided.

Tomographic Imaging of the Sagittarius Spiral Arm's Magnetic Field Structure

The Galactic global magnetic field is thought to play a vital role in shaping Galactic structures such as spiral arms and giant molecular clouds. However, our knowledge of magnetic field structures in the Galactic plane at different distances is limited, as measurements used to map the magnetic field are the integrated effect along the line of sight. In this study, we present the first ever tomographic imaging of magnetic field structures in a Galactic spiral arm. Using optical stellar polarimetry over a 17′×10′ field of view, we probe the Sagittarius spiral arm. Combining these data with stellar distances from the Gaia mission, we can isolate the contributions of five individual clouds along the line of sight by analyzing the polarimetry data as a function of distance. The observed clouds include a foreground cloud (d < 200 pc) and four clouds in the Sagittarius arm at 1.23, 1.47, 1.63, and 2.23 kpc. The column densities of these clouds range from 0.5 to 2.8 × 1021 cm−2. The magnetic fields associated with each cloud show smooth spatial distributions within their observed regions on scales smaller than 10 pc and display distinct orientations. The position angles projected on the plane of the sky, measured from the Galactic north to the east, for the clouds in increasing order of distance are 135°, 46°, 58°, 150°, and 40°, with uncertainties of a few degrees. Notably, these position angles deviate significantly from the direction parallel to the Galactic plane.