Representation Of Curves Research Articles

NOISE PROTECTION PRINCIPLES OF HIGHWAY CONSTRUCTION

According to the results of scientific research, it was established that the noise generated by vehicles has a negative impact on people's health, therefore, effective solutions in the field of construction and planning are needed to reduce the noise load on residential areas. Usually, noise is produced by the movement of cars, their engines and road surfaces. Noise can have a negative impact on people's health, leading to stress, sleep problems, impaired concentration and other physical and psychological health problems. The most important noise protection principles are the selection of a suitable place for the construction of a road, the use of special geometric solutions that can help reduce the noise load on the surrounding areas, and the installation of soundproof barriers. A fairly effective means of combating the noise load from the highway is the installation of noise protection screens along the highway. They can be made of different materials, different in structural and geometric perspective. It has been studied that the most effective way to protect rural areas from traffic noise is the construction of screen houses along transport highways. According to the data, the noise level behind such buildings decreases to 23 dBA compared to the noise level on the transport highway itself. A noise map is used to determine the noise level in built-up areas as a whole and in individual sections of microdistricts, which is a graphical representation of sound pressure level curves plotted on a plan diagram. These maps make it possible to estimate the reduction of the noise level with distance from the transport highway.

Characteristics of planar sextic indirect-PH curves

<abstract><p>By a fractional quadratic transformation, an indirect-PH curve can have rational offsets. In this paper, I study properties of planar sextic indirect-PH curves, in terms of their Bézier control polygon legs. With our results, sextic Bézier curves can be efficiently tested whether they are indirect-PH curves. The main strategy to achieve our results is using complex representation of planar parametric curve. Sextic indirect-PH curves can be classified into three classes according to different factorizations of their hodographs. Necessary and sufficient conditions for all classes of sextic indirect-PH curves can be described by non-linear complex systems. By analyzing these non-linear systems, algebraic conditions for a sextic Bézier curve to be an indirect-PH curve are first discussed, then geometric characteristics in terms of legs of its control polygon are revealed.</p></abstract>

Brachistochrone Curve Representation via Transition Curve

The brachistochrone curve is an optimal curve that allows the fastest descent path of an object to slide frictionlessly under the influence of a uniform gravitational field. In this paper, the Brachistochrone curve will be reconstructed using two different basis functions, namely Bézier curve and trigonometric Bézier curve with shape parameters. The Brachistochrone curve between two points will be approximated via a C-shape transition curve. The travel time and curvature will be evaluated and compared for each curve. This research revealed that the trigonometric Bézier curve provides the closest approximation of Brachistochrone curve in terms of travel time estimation, and shape parameters in trigonometric Bézier curve provide better shape adjustability than Bézier curve.

INVESTIGATION OF FINANCIAL BUBBLE MATHEMATICAL MODEL UNDER FRACTAL-FRACTIONAL CAPUTO DERIVATIVE

In this study, we proposed a novel approach for modeling the dynamics of a three-agent financial bubble using the fractal-fractional (FF) derivative of the Caputo sense. This new concept was developed to deal with the complex geometry of any dynamical system, and it utilizes both the fractional derivative for the order and the fractal term for the order of the independent variables. The model was investigated using the conformable order derivative of the Caputo operator, with a focus on the fractal dimension and fractional order. The existence and uniqueness of the solution were tested using a FF global derivative, and the approximate root of the system was calculated using the numerically iterative technique of the Newton polynomial. To verify the accuracy of the approximate root scheme, we applied the power singular law with two fractional parameters in the developed numerical technique. The curve representation of the system was also verified by applying the data for the fractals and different conformable orders. Additionally, we tested the sensitivities of the fractional parameters and dynamical system parameters by varying the parameter values. This allowed us to gain a better understanding of how changes in these parameters affect the system’s behavior and stability. As a result, this study presents an innovative and effective approach for modeling the dynamics of financial bubbles using the FF derivative of the Caputo sense. The results of this research contribute to the ongoing efforts to develop more accurate and comprehensive models of complex systems in economics and finance.

Pan-chromatic photometric classification of supernovae from multiple surveys and transfer learning for future surveys

ABSTRACTTime-domain astronomy is entering a new era as wide-field surveys with higher cadences allow for more discoveries than ever before. The field has seen an increased use of machine learning and deep learning for automated classification of transients into established taxonomies. Training such classifiers requires a large enough and representative training set, which is not guaranteed for new future surveys such as the Vera Rubin Observatory, especially at the beginning of operations. We present the use of Gaussian processes to create a uniform representation of supernova light curves from multiple surveys, obtained through the Open Supernova Catalog for supervised classification with convolutional neural networks. We also investigate the use of transfer learning to classify light curves from the Photometric LSST Astronomical Time Series Classification Challenge (PLAsTiCC) data set. Using convolutional neural networks to classify the Gaussian process generated representation of supernova light curves from multiple surveys, we achieve an Area Under the Receiver Operating Characteristic curve (AUC) score of 0.859 for classification into Types Ia, Ibc, and II. We find that transfer learning improves the classification accuracy for the most under-represented classes by up to 18 per cent when classifying PLAsTiCC light curves, and is able to achieve an AUC score of 0.946 ± 0.001 when including photometric redshifts for classification into six classes (Ia, Iax, Ia-91bg, Ibc, II, and SLSN-I). We also investigate the usefulness of transfer learning when there is a limited labelled training set to see how this approach can be used for training classifiers in future surveys at the beginning of operations.

Comparative analysis of Fuzzy Tsukamoto's membership functions for determining irrigated rice field feasibility status

The representation of the fuzzy set membership curve consisting of trapezoidal, triangular, and linear shapes, has an important role in the fuzzy logic system. The selection of the curve's shapes determines the useable membership function and affects the fuzzy output value. Previous studies generally used curves that had been employed in predecessors or other studies that did not explain the reason for choosing a fuzzy member curve. This condition became problem because there was not a guide in selecting the appropriate membership function model for the parameters used in the fuzzy process so that most researchers only use membership functions that are commonly used in previous studies or in the same case as their research. The purpose of this study was to determine the effect of selecting trapezoidal and triangular curves on the performance of Tsukamoto's fuzzy logic for determining the rice-fields suitability status. The research methodology comprised 3 main stages. The first stage was data collecting, to collect soil pH values, soil moisture, and air temperature in rice fields. The second stage was the implementation of the Tsukamoto fuzzy. At this stage, two membership function curves were used. The third stage was a comparative analysis of Tsukamoto's fuzzy's output of trapezoidal and triangular curves. The results obtained indicate that there is no significant performance difference between the two different membership functions. The results of the research with the trapezoidal membership function have a better accuracy rate of 93% while the triangular membership function has an accuracy rate of 90%.

CuPARE: parametric reconstruction of curved fibres from glass fibre-reinforced composites

ABSTRACT A new framework for the parametric reconstruction of curved fibres from glass fibre-reinforced composite X-ray computed tomography data is proposed. It allows us to detect fibres in a fibre-reinforced polymer sample from a low-dose, low resolution computed tomography scan. An efficient curve representation is then used for each detected fibre, of which the parameters are estimated directly from few 2D high-resolution projection images. The framework is validated on both simulated and real data of glass fibre-reinforced polymers. The generated results demonstrate that it is robust to noise and requires less than 10 high-resolution projections to obtain reasonable fibre estimates. The method can also improve upon existing estimation frameworks relying on full 3D scans.

Penentuan Status Penularan COVID-19 di Jawa Timur Menggunakan Metode Fuzzy Tsukamoto

The COVID-19 pandemic is not over, the Coronavirus Disease 19 Pandemic due to the SARS-CoV-2 virus is spreading very quickly in almost every country in the world because of its human-to-human nature. The COVID-19 pandemic in Indonesia was detected in Depok, West Java on March 2, 2020. To deal with this, the government must decide on an efficient policy by observing the atmosphere and situation in each region. The way is through determining the risk status of COVID-19 transmission in an area in order to break the chain of transmission of COVID-19. In Indonesia, it is up to each local government to determine the risk status of Covid-19 transmission at the regional level. This has led to subjective evaluations by local leaders and introduced many unclear definitions and boundaries when determining the risk status of COVID-19 transmission. This is the reason behind this research, where the Tsukamoto Algorithm mathematical calculation form is based on the official variables and regulations in the area concerned in determining the risk status of COVID-19 transmission. The data used is the daily data for COVID-19 districts or cities in East Java. The data used are 38 district or city data groups consisting of 4 variables. The input variables are COVID-19 positive cases, Supek cases, and Probabe cases, and each variable is defined as 3 fuzzy sets, namely Low, Medium, and High. The output variables are defined in 4 fuzzy sets regarding the Risk Status for COVID-19 Transmission, such as the East Java Government regulations, namely the status of green, yellow, orange, and red. All variables use membership function of triangular curve representation. How to analyze data using the SPK-COVID application using the Codeigniter Framework. The success of the estimation form of the percentage of conformity status generated by comparing the results of the Tsukamoto Algorithm analysis with real COVID-19 transmission risk status data. After doing 4 repetitions of the analysis, in which each analysis tries to change the area in the fuzzy set, we get a structure with a percentage of status conformity that is usually 95.51%, on data from 38 districts or cities in East Java.

Galois representations of superelliptic curves

AbstractA superelliptic curve over a discrete valuation ring $\mathscr{O}$ of residual characteristic p is a curve given by an equation $\mathscr{C}\;:\; y^n=\,f(x)$ , with $\textrm{Disc}(\,f)\neq 0$ . The purpose of this article is to describe the Galois representation attached to such a curve under the hypothesis that f(x) has all its roots in the fraction field of $\mathscr{O}$ and that $p \nmid n$ . Our results are inspired on the algorithm given in Bouw and WewersGlasg (Math. J.59(1) (2017), 77–108.) but our description is given in terms of a cluster picture as defined in Dokchitser et al. (Algebraic curves and their applications, Contemporary Mathematics, vol. 724 (American Mathematical Society, Providence, RI, 2019), 73–135.).

Z-Transform-Based Profile Matching to Develop a Learning-Free Keyword Spotting Method for Handwritten Document Images

For easy accessibility of the information from the digitized document images, optical character recognition (OCR)-based software can be used. But in the case of handwritten documents, the performance of the state-of-the-art OCR systems is not satisfactory owing to the complexity of the unconstrained handwriting. Hence, research affinity comes up with an alternative solution for this problem called keyword spotting (KWS) which is much more practical than an OCR-based solution. This work proposes a novel learning-free KWS method that can be applied to a heterogeneous collection of handwritten documents. In this work, we introduce a new way of profile matching to compare the query word profiles (i.e., both upper and lower) with the target words’ profiles. At first, both query and target words are binarized, and then two profiles from each such word are generated. Next, we formulate rules to filter out the irrelevant words concerning the query word and obtain the probable candidate query (i.e., target) words. Then we compare the profiles of the query and candidate query words in the Z-transform domain using the condition of resonance for the damped oscillator. However, before the match, we perform an affine transformation on the Bezier curve representation of the profiles of the candidate query words to reduce the effects like scaling, rotation, and shearing which might occur due to the variant writing styles of individuals. The proposed method achieves satisfactory performance compared to state-of-the-art learning-free methods when applied to four publicly available standard datasets namely ICFHR 2014 H-KWS competition Modern, IAM, ICFHR 2016 H-KWS competition Botany and ICFHR 2016 H-KWS competition Konzilsprotokolle datasets.

Deep Learning Extraction of the Temperature-Dependent Parameters of Bulk Defects.

Bulk defects in silicon solar cells are a key contributor to loss of efficiency. To detect and identify those defects, temperature- and injection-dependent lifetime spectroscopy is usually used, and the defect parameters are traditionally extracted using fitting methods to the Shockley-Read-Hall recombination statistics. In this study, we propose a deep learning-based extraction technique that is based on an alternative representation of the lifetime curves: lifetime mapping in the temperature and minority carrier concentration space. The deep learning approach successfully predicts all the defect parameters while addressing one of the main limitations of the traditional approach of locating the defect in the energy spectrum, which usually outputs two possible solutions. Furthermore, the approach is applied to temperature-dependent defect parameters where the traditional approach is not applicable, achieving satisfying levels of prediction of the defect parameters. Image representation and deep learning have the potential to bolster solar cell characterization techniques by extracting more insights from the characterization data.

Compact and accurate models for the diatomic potential energy

Two compact analytical models for the diatomic potential energy are presented and tested. The first (6-parameter) model represents a significant improvement on the extended Lennard-Jones (ELJ) function proposed by Hajigeorgiou [J. Mol. Spectrosc. 263, 101 (2010)], and the second (7-parameter) model is a modified Hulburt-Hirschfelder function. The adjustable parameters of the two functions can be determined either by an algebraic scheme that employs semiclassical expressions in terms of vibrational-rotational molecular constants, or by direct nonlinear least-squares fits to available numerical potential functions. Accuracy tests are carried out for a set of ground electronic states of 30 diatomic molecules. The two potential energy functions give accurate representations of the available numerical potential energy curves with average deviations over the 30 molecules of approximately 0.06% of D e, or 1 meV (∼ 8 cm−1). The best cases give average absolute deviations of 0.0002% of D e, or 0.007 meV (∼ 0.06 cm−1). Quantum-mechanical vibrational eigenvalues of the new potential representations are shown for selected molecules to agree very well with the experimental vibrational energies, with average absolute deviations of much less than 1 cm−1.

Estimates of Equivalence scale for Iranian Households

Despite its vast natural resources of oil, gas and minerals (mining), dealing with the problem of poverty  and inequality  is a serious challenge for policy makers. This challenge becomes increasingly acute as the authorities succumb, inevitably, to pressures to liberalise the economy by implementing free market principles and similar reforms. The welfare system in the Islamic Republic of Iran is quite complex with various governmental, non-governmental and para-governmental welfare organizations operating side by side. The Subsidy Targetization Act was the biggest of its kind in the history of the Islamic Republic, and that it is bound to affect the well-being of a large proportion of the population, it is rather surprising that it was introduced in such haste and without thorough planning. An equivalence scale is a measure of the cost of living of a household of a given size and demographic composition relative to the cost of living of a reference household when both households attain the same level of utility or standard of living (Lewbel and Pendakur, 2006). The method of calculating the equivalence scale is based on the Engel curve which can be argued to be a specific, restricted, representation of the Marshallian demand curve where prices are held constant and demand varies with income. We have argued, as an example of application of this approach, that this approach provides a more efficient and equitable way of compensating the consumers for the impact of the removal of price subsidies.

Multi-Class Classification using Mixtures of Univariate and Multivariate ROC Curves

Introduction: Receiver Operating Characteristic (ROC) curve is one of the widely used supervised classification technique to allocate/classify the individuals and also instrumental in comparing diagnostic tests. Generally, to deal with classification problems we need to have knowledge on class labels. In most of the medical scenarios, most of data sets exhibit multi-model patterns in class labels which leads to multi-class classification problems. The main aim of this study is to address on the issue of constructing ROC models when there exists multimodel patterns in the class labels further, to classify the individuals for better diagnosis and also to reduce the complexity of graphical representation of ROC curves in such classification problems. Methods: A new version of univariate and multivariate ROC models are proposed in the framework of Finite Mixtures, due to the flexibility of identifying and modelling the subcomponents in the heterogeneous populations. Results: Oral Glucose Tolerance Test and Disk Hernia datasets are used and simulation studies are also performed. Results show that the proposed models possess better accuracy when compared with Bi-Normal and MROC models with reasonable low 1-Specificity and higher Sensitivity. The ROC curves are depicted in a 2D space rather than higher dimension for multi-class classification problem. Conclusion: It is suggested that before one proceeds to model ROC curves, it is better to take a look at the density patterns of the study variable(s), which in turn help in explaining the true information between the classes and also provides good amount of “true” accuracy.

Analytical enclosure of the set of solutions of the three-species multivariate curve resolution problem

In 1985 Borgen and Kowalski published a geometry-based mathematical approach in order to determine the set of feasible solutions of the multivariate curve resolution problem for chemical systems with three species. Twenty years later Rajkó and István devised an algorithm for the analytical derivation of the feasible regions. They showed that the precise boundary of the solution set is piecewise representable in terms of analytical expressions for the boundary curve. This paper generalizes the approach for finding analytical boundary curves by means of duality arguments, provides the precise functional form of the curves in detail, shows how to determine the contact change values and suggests improved analytical expressions which can numerically be evaluated in a stable way. Additionally, it offers detailed instructions for an algorithmic solution and provides the underlying analysis. A program code is presented which generates a piecewise functional representation of the boundary curve.

ℚ-Curves, Hecke characters and some Diophantine equations

In this article we study the equations x 4 + d y 2 = z p x^4+dy^2=z^p and x 2 + d y 6 = z p x^2+dy^6=z^p for positive square-free values of d d . A Frey curve over Q ( − d ) \mathbb {Q}(\sqrt {-d}) is attached to each primitive solution, which happens to be a Q \mathbb {Q} -curve. Our main result is the construction of a Hecke character χ \chi satisfying that the Frey elliptic curve representation twisted by χ \chi extends to G a l Q Gal_\mathbb {Q} , therefore (by Serre’s conjectures) corresponds to a newform in S 2 ( Γ 0 ( n ) , ε ) S_2(\Gamma _0(n),\varepsilon ) for explicit values of n n and ε \varepsilon . Following some well known results and elimination techniques (together with some improvements) our result provides a systematic procedure to study solutions of the above equations and allows us to prove non-existence of non-trivial primitive solutions for large values of p p of both equations for new values of d d .

An Attempt at Describing Learning Curves for a Complex Sub-Task in Reading Acquisition

Learning curves are a well-known phenomenon in learning and describe the oscillation between correct and incorrect performance that precedes mastery. It demonstrates that making mistakes is part of the learning process. It is equally clear that these learning curves are highly individual and therefore pose a challenge in their description and direct comparison. With the ability to collect large amounts of data through learning games with adaptively generated content, it is now possible to take a novel look at this process. Literacy games were deployed in a school setting for the iRead EU Horizon 2020 Project. The Navigo app delivered a complex task of practising to distinguish vowel length in bi-syllabic words in German to pupils in the disguise of a game. Pupils' engagement with the game resulted in the largest longitudinal corpus that has ever been collected for this sort of task from 251 pupils in German elementary schools. The resulting data exhibits learning curves as trajectories, depicting response time and correctness across several weeks for each pupil’s playing sessions. The work presented here attempts to (a) model and parameterise these curves, (b) automate their classification into common forms across a larger population, and (c) detect mastery. In doing so, we propose a method of learning curve representation and interpretation and apply it to the data. A describable pattern of cognitive processing seems to be observable and common to all curves that may allow a prediction of mastery and ability for skill transfer to other environments for a subset of the players. As a result, we were able to describe five general types of common progressions. These findings are in part supported by additional data from pre- and post-tests in the form of paper-and-pencil activities. The work presented here should serve to demonstrate the importance of using large scale input data for training literacy skills rather than a few examples as is the norm in static schoolbooks.

Encoder-X: Solving Unknown Coefficients Automatically in Polynomial Fitting by Using an Autoencoder

Modeling, prediction, and recognition tasks depend on the proper representation of the objective curves and surfaces. Polynomial functions have been proved to be a powerful tool for representing curves and surfaces. Until now, various methods have been used for polynomial fitting. With a recent boom in neural networks, researchers have attempted to solve polynomial fitting by using this end-to-end model, which has a powerful fitting ability. However, the current neural network-based methods are poor in stability and slow in convergence speed. In this article, we develop a novel neural network-based method, called Encoder-X, for polynomial fitting, which can solve not only the explicit polynomial fitting but also the implicit polynomial fitting. The method regards polynomial coefficients as the feature value of raw data in a polynomial space expression and therefore polynomial fitting can be achieved by a special autoencoder. The entire model consists of an encoder defined by a neural network and a decoder defined by a polynomial mathematical expression. We input sampling points into an encoder to obtain polynomial coefficients and then input them into a decoder to output the predicted function value. The error between the predicted function value and the true function value can update parameters in the encoder. The results prove that this method is better than the compared methods in terms of stability, convergence, and accuracy. In addition, Encoder-X can be used for solving other mathematical modeling tasks.

Identifying Pythagorean-Hodograph Curves Closest to Prescribed Planar Bézier Curves

The problem of identifying the planar Pythagorean-hodograph curve that is “closest” to a given Bézier curve, and has the same end points (or end points and tangents), is considered. The “closeness” measure employed in this context is the root-mean-square magnitude of the differences between pairs of corresponding control points for the two curves. The methodology is developed in the context of quintic PH curves, although it readily generalizes to PH curves of higher degree. Using the complex representation for planar curves, it is shown that this problem can be reduced to the minimization of a quartic penalty function in certain real variables, subject to two quadratic constraints, which can be efficiently solved by the Lagrange multiplier method. By expressing the penalty function and constraints in terms of variables that identify a complex pre-image polynomial, the closest solution is guaranteed to be a PH curve. Several computed examples are used to illustrate implementation of the optimization methodology and typical approximation results that can be obtained.

A Data-Driven Representation of Aggregate Efficiency Curves of Hydro Units for the Mid-Term Hydrothermal Coordination Problem

A crucial aspect of the mid-term hydrothermal coordination problem is the nonlinear variation of hydro power with the water head, which can be computed through forebay and tailrace curves of the reservoirs. More accurate representations may also include turbine efficiency curves as a function of head and discharge, and penstock head losses as a function of turbined outflow. Based on large set of historical data for the operation of hydro plants, we propose a data-driven model to obtain such curves, which comprises: interpolation/extrapolation procedures to fill missing data and extreme regions of the curve; computation of average weekly values to avoid an optimistic behavior when using instantaneous curves for larger time intervals; an additive model with polynomial splines for curve fitting. The methodology was applied to the real Brazilian system, showing a significant improvement in the accuracy of the hydro production function, without sensitive changes on CPU time.