Correction Vector Research Articles

Weld seam positioning method for structural reinforcement based on 3D point cloud

Abstract Machine vision technology assists welding robot weld positioning, which can significantly improve welding accuracy and efficiency. This paper delves into a 3D point cloud-based positioning technique specifically tailored for structural reinforcement welds, utilizing the high-precision 3D structured light camera to get 3D point cloud data from the surface of the reinforcement structures, subsequently conducting a comprehensive analysis of the weld’s geometric characteristics. When the weld seam position can be directly collected, the side plate plane and the bottom plate plane of the reinforcement can be divided by the random sample consensus method. The weld points with rich curvature characteristics can be quickly and reliably selected according to the plane constraint. When the weld position cannot be measured directly, the prediction of the weld position is realized by extracting the edge of the upper surface of the reinforcing rib in the depth map and combining the plane normal vector of the base plate and the point laser correction vector. The experimental results show that this method can accurately locate the weld seam with high accuracy in both working scenarios.

Exchange Rate Pass-Through into Import Prices: Evidence from Türkiye during 2010-2020 Period

This article analyses pass through of exchange rates into the import prices for an emerging economy, Türkiye, which faced severe fluctuations in the nominal exchange rate in the recent years, and experienced significant increases in domestic prices. The Turkish economy continues to struggle due to high inflationary pressures and a steep Turkish Lira (TL) devaluation particularly after 2017. This study aimed at examining the relationship between exchange rate and import prices using quarterly data for the period of 2010q1-2019q1, while the empirical methodology is framed in the multivariate cointegration analysis, along with the application of the Johansen cointegration test and the development of an autoregressive error correction vector for the determination of the pass-through in the long term. Our findings show that 85.6% of the fluctuations of the nominal exchange rate are transmitted to the import prices in the mentioned period, slower than the findings of the study by Akgunduz and his colleagues as the difference of import prices from its long-run relationship implied by the real exchange rate is likely dominated by energy prices in a strong manner. Second significant finding derives from the parameter that measures the speed of the pass-through, whose estimate has been found as -0.0125, inferring that the adjustment in short-term imbalances between import prices and the nominal exchange rate through changes in import prices is rather slow.

Accurate surface profile measurement using CMM without estimating tip correction vectors

Detailed measurement of the curved surface of an industrial product with a radius of curvature of less than a few millimeters is a challenging task for tactile coordinate measuring machines. To estimate a surface profile, tip radius correction is typically performed by estimating the tip correction vector direction. However, a substantial measurement error is introduced by the error in estimating the tip correction vector direction under measurement conditions such as a large position measurement error of an indicated measured point or a short sampling interval, In this study, a method that can estimate a surface profile by calculating the envelope of a probe tip path was proposed. The proposed method was experimentally and numerically confirmed to be able to estimate surface profiles with sub-micrometer accuracy under such measurement conditions.

Measuring and Analysis the Relationship between the Internal Public Debt and the Exchange Rate in the Iraqi Economy for The Period 2004 – 2022

The scholastic view of public religion differed, and this difference was on two extremes. Alleconomic schools agreed that public debt is a monetary liquidity that was unjustly deductedfrom the income and output cycle as a result of the imbalance in the economic balance and thedeparture from the conditions of balance between aggregate demand and aggregate supply.Debt is a waste of financial resources allocated to productive accumulation. Except for theKeynesian school, which considers public debt to be an addition to aggregate demand after thedecline in the role of the private sector in investment as a result of pessimistic expectations thatwarn of signs of economic contraction. Public debt is linked to the exchange rate through theinterest rate channel, so that public debt causes competition for financial resources. Thiscompetition results in an increase in the local interest rate, which results in an increase indemand for the local currency with the aim of increasing investment, and the demand for thelocal currency raises the price of the local currency. Which means that there is an indirectrelationship between public debt and the exchange rate, but this relationship may create damagein the balance of payments in the near future. They assumed the existence of a long-term causalrelationship between internal public debt and the exchange rate. The main goal of this researchis to verify the economic relationship between the investigated variables, using thecointegration model and the error term correction vector model to prove the researchhypothesis. And the Kranger model of causality between the variables. The research reachedthe most prominent conclusion, which is that individual expectations for the internal publicdebt after each annual deficit in the state’s general budget cause a decrease in the value of thelocal currency due to the increase in demand for the dollar and the decrease in demand for thedinar, which means that there is causality in one direction. From internal public debt to theexchange rate, this is what was proven by the results of Kranger’s causality test.

Solving nonlinear structural problems by associating line-search and path-following techniques

The demand for computational tools to simulate the nonlinear behavior of structures has intensified. Regarding nonlinear static or dynamic analysis, it is fundamental to use numerical strategies to trace the structure equilibrium paths, overcoming critical points (limit and bifurcations points). The nonlinear solvers must have a high level of efficiency in the two phases of the solution process (predictor and corrector), for each load step. In solving the nonlinear equations, it is quite common that Newton-Raphson's iterations do not converge or require an excessive number of iterations near equilibrium path critical points. Therefore, the line-search optimization technique appears as an additional sophistication. Basically, this technique aims to stagger the corrective displacements vector in the iterative phase, seeking to guarantee and accelerate the convergence of the process. This paper aims to verify the efficiency of the line-search technique coupled with Newton-Raphson iterations and different path-following methods and to verify their influence on the efficiency of the nonlinear solver. The effectiveness of the implemented line-search algorithm is verified by solving two slender structures with accentuated geometric nonlinearity. Such a resource is perceived to be triggered near load limit points (with more success when applied to structures with these critical points), accelerate the iterative process and increase the chances of convergence.

Personalized Setup Optimization Strategies to Improve Clinical Workflow in Image-Guided Pediatric Particle Therapy

The purpose of this retrospective study was to simulate a daily pre-alignment strategy to mitigate systematic positioning errors in image-guided pediatric hadron therapy. All pediatric patients (32 patients, 853 fractions) treated from December 2021 and September 2022 at our Institution were retrospectively considered. For all fractions, daily correction vectors (CVs) resulting from image registration for patient positioning were retrieved in the form of txt files from the hospital database. For each fraction, an adjusted correction vector (V′) was then computed as the difference between the actual one (V) and the algebraic average of the previous ones, as to simulate patient pre-alignment before imaging. The Euclidean norm of each V′ was computed and normalized with respect to that of the corresponding V to derive N. Pre-correcting all the coordinate values led to a 46% average reduction (min 20%, max 60%) in CVs, considering the first 27 fractions (average value in this cohort of patients). Such a potential improvement (N < 1) was observed for the most patients’ fractions (781/853, 91.6%). For the remaining 72/853 cases (8.4%), a remarkable worsening (N > 2) involved only 7/853 (0.82%) fractions. The presented strategy shows promising outcomes in order to ameliorate pediatric patient setup before imaging. However, further investigations to identify patients most likely to benefit from this approach are warranted.

Joint track initiation of resolvable group target

This paper studies the problem of resolvable group target track initiation (RGTI) and proposes a novel method to obtain the discrete association vectors and continuous trajectory parameters of individual targets within the group, which benefits from the fitting representations of target tracks and the utilization of group target motion constraint. Specifically, every target track within the group is modeled as a weighted sum of a same set of time basis functions with different weights, and the aim is to solve multiple pairs of association vectors and trajectory parameters, i.e., unknown weights, according to the measurement equation and group target motion constraint. Next, a joint RGTI framework, which includes track extraction, track purification, trajectory parameter and association vector correction, is proposed to transform the original complex constraint set solving problem into multiple solvable sub-problems. And the convergence of RGTI is ensured through iterative optimization of track purification, trajectory parameter correction and association vector correction. Finally, simulation example demonstrates the superiority of the proposed method compared with existing multi-target track initiation methods.

ConvMatch: Rethinking Network Design for Two-View Correspondence Learning.

Multilayer perceptron (MLP) has become the de facto backbone in two-view correspondence learning, for it can extract effective deep features from unordered correspondences individually. However, the problem of natively lacking context information limits its performance although many context-capturing modules are appended in the follow-up studies. In this paper, from a novel perspective, we design a correspondence learning network called ConvMatch that for the first time can leverage a convolutional neural network (CNN) as the backbone, inherently capable of context aggregation. Specifically, with the observation that sparse motion vectors and a dense motion field can be converted into each other with interpolating and sampling, we regularize the putative motion vectors by estimating the dense motion field implicitly, then rectify the errors caused by outliers in local areas with CNN, and finally obtain correct motion vectors from the rectified motion field. Moreover, we propose global information injection and bilateral convolution, to fit the overall spatial transformation better and accommodate the discontinuities of the motion field in case of large scene disparity. Extensive experiments reveal that ConvMatch consistently outperforms state-of-the-arts for relative pose estimation, homography estimation, and visual localization.

Numerical Solution of Two-Dimensional Nonlinear Unsteady Advection-Diffusion-Reaction Equations with Variable Coefficients

The advection-diffusion-reaction (ADR) equation is a fundamental mathematical model used to describe various processes in many different areas of science and engineering. Due to wide applicability of the ADR equation, finding accurate solution is very important to better understand a physical phenomenon represented by the equation. In this study, a numerical scheme for solving two-dimensional unsteady ADR equations with spatially varying velocity and diffusion coefficients is presented. The equations include nonlinear reaction terms. To discretize the ADR equations, the Crank–Nicolson finite difference method is employed with a uniform grid. The resulting nonlinear system of equations is solved using Newton’s method. At each iteration of Newton’s method, the Gauss–Seidel iterative method with sparse matrix computation is utilized to solve the block tridiagonal system and obtain the error correction vector. The consistency and stability of the numerical scheme are investigated. MATLAB codes are developed to implement this combined numerical approach. The validation of the scheme is verified by solving a two-dimensional advection-diffusion equation without reaction term. Numerical tests are provided to show the good performances of the proposed numerical scheme in simulation of ADR problems. The numerical scheme gives accurate results. The obtained numerical solutions are presented graphically. The result of this study may provide insights to apply numerical methods in solving comprehensive models of physical phenomena that capture the underlying situations.

A modified atmospheric scattering model and degradation image clarification algorithm for haze environments

Addressing the limitation of existing image dehazing algorithms based on atmospheric scattering models, which often overlook the underlying physical causes of color distortion in hazy images, resulting in suboptimal algorithm robustness and image clarity when faced with varying levels of haze pollution, this study introduces a refined atmospheric scattering model. It also presents a haze image clarity algorithm based on this modified atmospheric scattering model by analyzing the fundamental factors contributing to image degradation and distortion caused by haze. Initially, the hazy image undergoes conversion to a new HSI color space. The hazy image is aligned more closely with human visual perception characteristics by implementing an adaptive saturation enhancement technique and adjusting contribution coefficients for the three RGB channels to the luminance component. Subsequently, the hazy image is partitioned into dense haze and non-dense haze regions based on haze distribution characteristics within the image. A global light intensity computation method is devised for the hazy image utilizing a quad-tree segmentation algorithm. Following this, calculations are performed to determine the atmospheric light value and transmittance for dense and non-dense haze regions separately. The global atmospheric light and transmittance values are then derived based on the probability density function of the dense haze region using Alpha Fusion. Finally, corrections are applied to the global atmospheric light values using an atmospheric light correction vector, while denoising the global transmittance is achieved through a fast non-local mean filtering algorithm. Experimental findings demonstrate that the proposed haze image clarity algorithm, grounded in the modified atmospheric scattering model, exhibits adaptability across various degrees and types of haze images. Comparative analysis against other prominent image dehazing algorithms reveals its efficacy in addressing severe color distortion in dense haze scenarios, achieving a more natural clarity effect, and showcasing superior performance across all numerical evaluation metrics.

Non-uniformity correction algorithm for DoFP adapted to integration time variations.

Division of the focal plane (DoFP) polarization detector is a pivotal technology in real-time polarization detection. This technology integrates a micropolarization array (MPA) onto the conventional focal plane, introducing a more intricate non-uniformity than traditional focal plane detectors. Current non-uniformity correction algorithms for DoFP are difficult to adapt to changes in integration time and perform poorly in low-polarization scenarios. Analyzing the characteristics of DoFP, formulating a pixel response model, and introducing an adaptive non-uniformity correction algorithm tailored for varying integration time. The DoFP analysis vectors are decomposed into average polarization response and unit analysis vectors for correction separately to improve the performance of the correction algorithm in different polarization scenarios. The performance of modern correction algorithms was tested and evaluated using standard uniform images, and the proposed method outperformed existing algorithms in terms of polarization measurement accuracy under the root mean square error (RMSE) metric. Moreover, in natural scene images, our proposed algorithm shows favorable visual effects and distinguishes itself from its superior stability amid changes in the integration time.

Реєстр перкутанних коронарних втручань: зміни за останні роки (2010–2022)

In 2022, the number of coronary angiograms in Ukrainian clinics was 51 084, which is 27.6 % more than in 2019, the number of stented patients is 27 513 for all forms of coronary artery disease (scheduled and urgent patients), which is 19.7 % more than in 2019 year and 16 847 stenting were performed in STEMI patients in the first day from the onset of symptoms, which is 12.9 % more than in 2019.During the period of the Register operation, the fact of creation of 66 reperfusion centers was recorded, which are the main part of Regional Reperfusion Networks (RRN) and strive to function in accordance with national unified protocols for the treatment of STEMI, NSTEMI and stable coronary syndromes.Today, the distribution of patients by time from the onset of symptoms to mechanical reperfusion in Ukraine is distributed as follows: in the first 12 hours from the onset of STEMI symptoms, 85 % are present (15 % are «late» patients who are hospitalized at 12–24 hours from the onset of symptoms or later, often requiring urgent coronary angiography and possibly primary stenting). Patients arriving in the «ideal» period for reperfusion (in the first 2 hours) is about 15 %, the largest group of STEMI patients who arrived at the clinic in the first 2–4 hours from the onset of symptoms is 30 %, and the number of patients with AMI in the period of 4–6 hours from the onset of symptoms, the average is 25 %, and the 6–12-hour group completes the analysis by 15 %, respectively.The number of procedures in STEMI patients increased annually, which led to a decrease in hospital mortality in reperfusion centers (55–60 % of patients in catheterization laboratories in Ukraine are STEMI patients) to an average of 4.7 %, and in the general group of AMI in Ukraine to 12.3 %. Unfortunately, 40–45 % of patients are currently hospitalized in clinics without the possibility of primary stenting.A ten-year observation of the dynamics of primary stenting revealed changes, which we called the «reperfusion paradox», which occurred in 2015–2016, which fully confirmed the correct vector of technology development and determined the trend of its development. This phenomenon is the beginning of a natural decrease in the number of fibrinolytic procedures from 27 % (2010 year) to 4.6 % (2021 year), respectively, and an increase in the number of primary procedures in STEMI patients from 4.0 % (2010 year) to 56.4 % (2022 year), which is quite natural and confirms the processes of active development and systemic transformations in interventional cardiology in Ukraine and around the world.As a result, it was found that we have increased 17 times the number of primary percutaneous interventions per million population over the last decade, while European countries have increased the number of similar procedures by only 14 %. This fact indicates the correct direction of development and the speed of movement in this direction.

Стратегирование координации организаций строительного комплекса стран БРИКС в условиях экономики данных

In 2024, Russia chairs the BRICS, having defined its global strategy as “strengthening multilateralism for equitable global development and security”. According to the methodology developed by Prof. V.L. Kvint, the global strategy depends on the relevant international, national, and corporate strategies of companies from the BRICS countries. Data economy uses algorithms for data processing and analysis, including AI solutions. Prof. V.L. Kvint defines the strategy as a combination of wisdom, a correct attack vector, and an adequate assessment of resources. Prof. A.A. Romanov and Prof. V.V. Kondratiev used Model-Based Systems Engineering 2.0 to adapt Prof. L.A. Bakhvalov’s methodology of system modeling to the modern conditions. All these principles can yield a new approach to multi-criteria modeling of related cross-country and cross-industry corporate strategies, especially if facilitated by the digital twin method and the interoperability policy. The major construction industry is high on the BRICS agenda in terms of large infrastructure and industrial facilities. Therefore, Model-Based Systems Engineering 2.0 provides good prospects for development strategy modeling.

Credit Channel Transmission of Monetary Policy: How to Promote Growth in Indonesia?

Credit plays a significant part in supporting the public economy and as a driver of financial development. Banking facilitates households and companies as deficit spending units to finance their consumption and investment. This encourages the economic growth through increased aggregate demand. This research aims to analyze the transmission of monetary policy in Indonesia through credit channel, how the monetary policy affects economic growth. For monthly data 2017-2022, with the Vector Error Correction Model (VECM) and Vector Auto Regressive (VAR), the research results show that economic growth provides a negative response to consumption shocks on the household liquidity effect credit channel. While through the balance sheet channel, economic growth responds positively to investment shocks. The balance sheet channel is more effective in transmitting monetary policy credit channels targeting economic growth in Indonesia during the research period. Investment as an engine of growth is achieved through optimizing the role of banking intermediation in productive rather than consumer financing because it has a greater multiplier effect on the economy

A comparative analysis of gender diversity in labour participation and growth in Sub-Saharan African countries

In recent years, official statistics on female labour supply in several emerging nations have shown that female labour force participation rates are dropping. Although development organisations have created and implemented non-contextual empowerment initiatives, some of which have improved women's lives, a desirable outcome has not been achieved. A comparative analysis of gender diversity in labour economic participation and growth in sub-Saharan Africa (SSA) was conducted. The study uses pooled least squares, fixed effects, random effects, difference generalised method of moments, and system-generalised method of moments models. Likewise, three models are estimated in the study for disaggregated male and female economic participation factors, respectively, while the third is for aggregate economic participation. In addition, causality was investigated using the panel vector correction model. The findings show that the indicators of human capital and labour economic participation are positive and significant in all three models. However, male human capital and labour economic participation contribute to productivity growth more than aggregate indicators. Also, the female indicators are the lowest contributing factor to growth. Also, the institutional quality is significant in aggregate and male labour economic participation but insignificant in female labour economic participation. The causality result shows one-way causality from female human capital to productivity growth. The study suggests, among others, the need to develop a financing mechanism to expand women-focused human capital interventions in SSA.

주택시장과 거시경제변수들 간의 장기적 균형관계 연구

This paper was empirically conducted to compare the explanatory power of the Vector Error Correction Model (VECM) and Vector Autoregressive Model (VAR Model) in predicting the long-term equilibrium relationship between housing prices and macroeconomic variables. The analysis period spans from January 1987 to July 2023. The analysis results are as follows. First, it is found that there exists one cointegration relationship among housing prices, stock prices, liquidity, 5-year yield of government housing bonds, and income. Therefore, the VECM model can be applied to analyze the long- and short-term equilibrium relationship. Secondly, the estimation results of the VECM model revealed the presence of the following long-term relationships: a negative (-) relationship between housing prices and stock prices, a positive (+) relationship with liquidity, a negative (-) relationship with the 5-year yield of government housing bonds, and a positive (+) relationship with income. This aligns with the expected theoretical signs. Thirdly, the Root Mean Square Error (RMSE) and Theil's Inequality Coefficient, which indicate the predictive and explanatory power of the VECM and VAR models, respectively, showed that the VECM model outperformed the VAR model with smaller values for both metrics. Therefore, when a cointegration relationship exists between housing prices and macroeconomic variables, it is necessary to apply the VECM model rather than the VAR model for analysis.

A Novel OFDM-Based Time Domain Quadrature GSM for Visible Light Communication System

In order to improve the spectral efficiency (SE) as well as the receiver performance of band-limited visible light communications (VLCs), two orthogonal frequency division multiplexing (OFDM)-based quadrature generalized multiple-input multiple-output (QG-MIMO) transmission schemes, including time domain (TD) quadrature generalized spatial modulation (TD-QGSM) and TD quadrature generalized spatial multiplexing (TD-QGSMP), are proposed in this paper. Firstly, the constellation symbols in the frequency domain are split into in-phase and quadrature components to perform the OFDM modulation separately. Then, the corresponding time domain signal is spatially mapped on different light emitting diodes (LEDs) for achieving the diversity or multiplexing. In addition, we also propose an illegal vector correction (IVC)-based orthogonal matching pursuit (OMP) detection algorithm to deal with the error propagation and noise amplification effect, where a novel correction criterion is involved for assisting the index vectors estimation and thus for improving the demodulation performance. The simulation results demonstrate that the SE can be significantly improved by the proposed schemes as compared with the existing OFDM-based generalized MIMO schemes, with the TD-QGSM increasing by at least 56.5% and the TD-QGSMP increasing by at least 72.3%. Moreover, the bit error rate (BER) performance can be further improved when applying the proposed IVC-OMP detection method, which outperforms the traditional maximum-likelihood and maximum ratio combining (ML-MRC) detection by at least 62.5%.

Foreign Aid and Institutional Quality towards Reducing Gender-Based Violence

Studies have shown a possible link between women achieving some degree of economic independence through empowerment and a decline in gender-based violence (GBV). However, inadequate funding has been a major challenge in developing economies, while foreign aid has been seen as an alternative funding source. Foreign aid for promoting women’s rights and gender equality is improving in African countries. Yet, according to official statistics, the frequency of GBV in Africa is among the highest in the world. Given this, this paper examines the impact of women’s aid and institutional quality on factors that can reduce GBV using both cross-sectional autoregressive lags to investigate short- and long-run implications and the Panel Vector Correction Model to examine the shock effect of aid on other variables. Also, the mediating role of institutional quality and women’s aid are considered. The metrics used for the factors that reduce GBV are female children out of school, the secondary school gender parity index, the genital mutilation prevalence rate, and the metrics for institutional quality are the rules of law and government effectiveness. The implications from the findings show that enhancing the legal structure is very important in Africa, given the low coefficient values to reduce discrimination against the right to education; more should be done to increase the enrolment of female students through the maximisation of women’s aid in order to achieve the short- and long-term objectives of reducing gender violence. The findings also show that the rule of law significantly aids in the reduction of female genital mutilation in the short and long run; government effectiveness is insignificant. Also, they show that women’s aid also reduces female genital mutilation, albeit at a low rate. The results of this study call for strong enhanced government support and funding to end the practice of female genital mutilation and discrimination against female education in the short and long run.

An Ab Initio Correction Vector Restricted Active Space Approach to the L-Edge XAS and 2p3d RIXS Spectra of Transition Metal Complexes.

We describe an ab initio approach to simulate L-edge X-ray absorption (XAS) and 2p3d resonant inelastic X-ray scattering (RIXS) spectroscopies. We model the strongly correlated electronic structure within a restricted active space and employ a correction vector formulation instead of sum-over-state expressions for the spectra, thus eliminating the need to calculate a large number of intermediate and final electronic states. We present benchmark simulations of the XAS and RIXS spectra of the iron complexes [FeCl4]1-/2- and [Fe(SCH3)4]1-/2- and interpret the spectra by deconvolving the correction vectors. Our approach represents a step toward simulating the X-ray spectroscopies of larger metal cluster systems that play a pivotal role in biology.

Multi-order analytical solving computation of rainstorm causal decomposition during typhoons using a designed key–lock quasi-Newton optimizing derivation

To precisely identify multi-dimensional spatiotemporal rain-making parameters, generate an approximate Hessian matrix, and solve the nonlinear ill-posed problem, this study uses composite logical tangent hyperbolic functions to construct the rain-generating simulation model as nonlinear algebraic equations with designed key–lock quasi-Newton optimization for deriving multi-order objective functional derivatives for rainstorm causal decomposition into advanced functional, analytical solution (lock) and Newton's conditional constraints. Specifically, the rank-two approximate structure of the Levenberg–Marquardt and Broyden–Fletcher–Goldfarb–Shanno quasi-Newton algorithms are modified as the symmetric rank-four structure to efficiently calculate a positive definite stable Hessian and solve the constrained nonlinear rain-making threshold. The model projects various rain-making factors into multi-rank loading scores, characterizing rain-generating mechanisms and causal components as associated DNAs. To accelerate/modify directional convergence, avoid local minimum, and detect global optimum, the devised vectorized limited switchable step sizes are optimized using advanced double-bracketing approaches combined with candidate parameters' correction vectors (key) and referenced step-size distributions solved by Newton's constrained analytical solution to reduce heterogeneous differences and eliminate the conventional overestimated Hessian. The identified rain-making DNAs reveal that typhoons with similar DNAs move in similar directions. Specifically, rain-making DNAs in Taipei Category 1 were correlated with wind force/direction and cloud height along PCs 1, 3, 4, and 7, and those in Category 2 were correlated with cloud-cover distribution along PCs 1, 2, and 5. The identified rain-making thresholds of typhoons with constant direction/structure showed a weaker steady state, whereas the unsteady rest produced multi-peak rainfall hydrographs. Rain evolution analysis reveals that cloudy rainbands, carried by the wind field, move along the Tamsui River valley when traveling between northeast and south-southeast of Taipei; converge with gradient and geostrophic winds when traveling between east-northeast and southwest; merge with southwest monsoon when traveling between west-southwest and northeast of Kaohsiung.