Search results for: curve number hydrology

Authors: K. Sanjayani, C. Saraswathy, S. Sreenivasan, S. Sudhahar, D. Suganya, K. S. Neelukumari, N. Vijayarangan

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Double Base Number System (DBNS) is an imminent system of representing a number using two bases namely 2 and 3, which has its application in Elliptic Curve Cryptography (ECC) and Digital Signature Algorithm (DSA).The previous binary method representation included only base 2. DBNS uses an approximation algorithm namely, Greedy Algorithm. By using this algorithm, the number of digits required to represent a larger number is less when compared to the standard binary method that uses base 2 algorithms. Hence, the computational speed is increased and time being reduced. The standard binary method uses binary digits 0 and 1 to represent a number whereas the DBNS method uses binary digit 1 alone to represent any number (canonical form). The greedy algorithm uses two ways to represent the number, one is by using only the positive summands and the other is by using both positive and negative summands. In this paper, arithmetic operations are used for elliptic curve cryptography. Elliptic curve discrete logarithm problem is the foundation for most of the day to day elliptic curve cryptography. This appears to be a momentous hard slog compared to digital logarithm problem. In elliptic curve digital signature algorithm, the key generation requires 160 bit of data by usage of standard binary representation. Whereas, the number of bits required generating the key can be reduced with the help of double base number representation. In this paper, a new technique is proposed to generate key during encryption and extraction of key in decryption.

Keywords: cryptography, double base number system, elliptic curve cryptography, elliptic curve digital signature algorithm

Procedia PDF Downloads 364

Authors: Lívia B. Meirelles, Erika C. A. N. Chrisman, Flávia B. de Andrade, Lilian C. M. de Oliveira

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True Boiling Point distillation (TBP) is one of the most common experimental techniques for the determination of petroleum properties. This curve provides information about the performance of petroleum in terms of its cuts. The experiment is performed in a few days. Techniques are used to determine the properties faster with a software that calculates the distillation curve when a little information about crude oil is known. In order to evaluate the accuracy of distillation curve prediction, eight points of the TBP curve and specific gravity curve (348 K and 523 K) were inserted into the HYSYS Oil Manager, and the extended curve was evaluated up to 748 K. The methods were able to predict the curve with the accuracy of 0.6%-9.2% error (Software X ASTM), 0.2%-5.1% error (Software X Spaltrohr).

Keywords: distillation curve, petroleum distillation, simulation, true boiling point curve

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Authors: Amit K. Singh, Subhankar Sen

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The bifurcation curve of separation in steady two-dimensional viscous flow past an elliptic cylinder is studied by varying the angle of incidence (α) with different aspect ratio (ratio of minor to major axis). The solutions are based on numerical investigation, using finite element analysis, of the Navier-Stokes equations for incompressible flow. Results are presented for Reynolds number up to 50 and angle of incidence varies from 0° to 90°. Range of aspect ratio (Ar) is from 0.1 to 1 (in steps of 0.1) and flow is considered as unbounded flow. Bifurcation curve represents the locus of Reynolds numbers (Res) at which flow detaches or separates from the surface of the body at a given α and Ar. In earlier studies, effect of Ar on laminar separation curve or bifurcation curve is limited for Ar = 0.1, 0.2, 0.5 and 0.8. Some results are also available at α = 90° and 45°. The present study attempts to provide a systematic data and clear understanding on the effect of Ar at bifurcation curve and its point of maxima. In addition, issues regarding location of separation angle and maximum ratio of coefficient of lift to drag are studied. We found that nature of curve, separation angle and maximum ratio of lift to drag changes considerably with respect to change in Ar.

Keywords: aspect ratio, bifurcation curve, elliptic cylinder, GMRES, stabilized finite-element

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Authors: Hamed K. Arzani, Hamid K. Arzani, S.N. Kazi, A. Badarudin

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Numerical investigation into convective heat transfer of CuO-Water based nanofluid in a pipe with return bend under laminar flow conditions has been done. The impacts of Reynolds number and the volume concentration of nanoparticles on the flow and the convective heat transfer behaviour are investigated. The results indicate that the increase in Reynolds number leads to the enhancement of average Nusselt number, and the increase in specific heat in the presence of the nanofluid results in improvement in heat transfer. Also, the presence of the secondary flow in the curve plays a key role in increasing the average Nusselt number and it appears higher than the inlet and outlet tubes. However, the pressure drop curve increases significantly in the tubes with the increase in nanoparticles concentration.

Keywords: laminar forced convection, curve pipe, return bend, nanufluid, CFD

Procedia PDF Downloads 263

Authors: Lee Feng Koo, Tze Jin Wong, Pang Hung Yiu, Nik Mohd Asri Nik Long

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Greater common divisor (GCD) attack is an attack that relies on the polynomial structure of the cryptosystem. This attack required two plaintexts differ from a fixed number and encrypted under same modulus. This paper reports a security reaction of Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field under GCD attack. Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field was exposed mathematically to the GCD attack using GCD and Dickson polynomial. The result shows that the cryptanalyst is able to get the plaintext without decryption by using GCD attack. Thus, the study concluded that it is highly perilous when two plaintexts have a slight difference from a fixed number in the same Elliptic curve group over finite field.

Keywords: decryption, encryption, elliptic curve, greater common divisor

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Authors: Jean-Pierre Lomaliza, Kwang-Seok Moon, Hanhoon Park

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It is well-known that Ramer Douglas Peucker (RDP) algorithm greatly depends on the method of choosing starting points. Therefore, this paper focuses on finding such starting points that will optimize the results of RDP algorithm. Specifically, this paper proposes a curve approximation algorithm that finds flat points, called essential points, of an input curve, divides the curve into corner-like sub-curves using the essential points, and applies the RDP algorithm to the sub-curves. The number of essential points play a role on optimizing the approximation results by balancing the degree of shape information loss and the amount of data reduction. Through experiments with curves of various types and complexities of shape, we compared the performance of the proposed algorithm with three other methods, i.e., the RDP algorithm itself and its variants. As a result, the proposed algorithm outperformed the others in term of maintaining the original shapes of the input curve, which is important in various applications like pattern recognition.

Keywords: curve approximation, essential point, RDP algorithm

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Authors: Umar Javed, Kristen Blann, Philip Adalikwu, Maryam Sahraei, John McMaine

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The soil conservation service curve number (SCS-CN) is a widely used method to assess direct runoff depth based on specific rainfall events. “Actual” estimated runoff depth was estimated by subtracting the change in soil moisture from the depth of precipitation for each discrete rain event during the growing seasons from 2021 to 2023. Fields under investigation were situated in a HUC-12 watershed in southeastern South Dakota selected for a common soil series (Nora-Crofton complex and Moody-Nora complex) to minimize the influence of soil texture on soil moisture. Two soil moisture probes were installed from May 2021 to October 2023, with exceptions during planting and harvest periods. For each field, “Textbook” CN estimates were derived from the TR-55 table based on corresponding mapped land use land cover LULC class and hydrologic soil groups from web soil survey maps. The TR-55 method incorporated HSG and crop rotation within the study area fields. These textbook values were then compared to actual CN values to determine the impact of tillage practices on CN and runoff. Most fields were mapped as having a textbook C or D HSG, but the HSG of actual CNs was that of a B or C hydrologic group. Actual CNs were consistently lower than textbook CNs for all management practices, but actual CNs in conventionally tilled fields were the highest (and closest to textbook CNs), while actual CNs in no-till fields were the lowest. Preliminary results suggest that no-till practice reduces runoff compared to conventional till. This research highlights the need to use CNs that incorporate agricultural management to more accurately estimate runoff at the field and watershed scale.

Keywords: curve number hydrology, hydrologic soil groups, runoff, tillage practices

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Authors: Suzana Ramli, Wardah Tahir

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Estimation of surface runoff depth is a vital part in any rainfall-runoff modeling. It leads to stream flow calculation and later predicts flood occurrences. GIS (Geographic Information System) is an advanced and opposite tool used in simulating hydrological model due to its realistic application on topography. The paper discusses on calculation of surface runoff depth for two selected events by using GIS with Curve Number method for Upper Klang River basin. GIS enables maps intersection between soil type and land use that later produces curve number map. The results show good correlation between simulated and observed values with more than 0.7 of R2. Acceptable performance of statistical measurements namely mean error, absolute mean error, RMSE, and bias are also deduced in the paper.

Keywords: surface runoff, geographic information system, curve number method, environment

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Authors: M. Yushalify Misro, Ahmad Ramli, Jamaludin M. Ali

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Bezier curves have useful properties for path generation problem, for instance, it can generate the reference trajectory for vehicles to satisfy the path constraints. Both algorithms join cubic Bezier curve segment smoothly to generate the path. Some of the useful properties of Bezier are curvature. In mathematics, the curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line. Another extrinsic example of curvature is a circle, where the curvature is equal to the reciprocal of its radius at any point on the circle. The smaller the radius, the higher the curvature thus the vehicle needs to bend sharply. In this study, we use Bezier curve to fit highway-like curve. We use the different approach to finding the best approximation for the curve so that it will resemble highway-like curve. We compute curvature value by analytical differentiation of the Bezier Curve. We will then compute the maximum speed for driving using the curvature information obtained. Our research works on some assumptions; first the Bezier curve estimates the real shape of the curve which can be verified visually. Even, though, the fitting process of Bezier curve does not interpolate exactly on the curve of interest, we believe that the estimation of speed is acceptable. We verified our result with the manual calculation of the curvature from the map.

Keywords: speed estimation, path constraints, reference trajectory, Bezier curve

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Authors: E. K. Naseela, B. M. Dodamani, Chaithra Chandran

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The GIS and remote sensing techniques facilitate accurate estimation of surface runoff from watershed. In the present study an attempt has been made to evaluate the applicability of Natural Resources Service Curve Number method using GIS and Remote sensing technique in the upper Krishna basin (69,425 Sq.km). Landsat 7 (with resolution 30 m) satellite data for the year 2012 has been used for the preparation of land use land cover (LU/LC) map. The hydrologic soil group is mapped using GIS platform. The weighted curve numbers (CN) for all the 5 subcatchments calculated on the basis of LU/LC type and hydrologic soil class in the area by considering antecedent moisture condition. Monthly rainfall data was available for 58 raingauge stations. Overlay technique is adopted for generating weighted curve number. Results of the study show that land use changes determined from satellite images are useful in studying the runoff response of the basin. The results showed that there is no significant difference between observed and estimated runoff depths. For each subcatchment, statistically positive correlations were detected between observed and estimated runoff depth (0.6Keywords: curve number, GIS, remote sensing, runoff

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Authors: Shao-Yuan Huang

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We study the shape of the bifurcation curve of positive solutions for the semipositone problem with the Minkowski-curvature operator. The Minkowski-curvature problem plays an important role in certain fundamental issues in differential geometry and in the special theory of relativity. In addition, it is well known that studying the multiplicity of positive solutions is equivalent to studying the shape of the bifurcation curve. By the shape of the bifurcation curve, we can understand the change in the multiplicity of positive solutions with varying parameters. In this paper, our main technique is a time-map method used in Corsato's PhD Thesis. By this method, studying the shape of the bifurcation curve is equivalent to studying the shape of a certain function T with improper integral. Generally speaking, it is difficult to study the shape of T. So, in this paper, we consider two cases that the nonlinearity is convex or concave. Thus we obtain the following results: (i) If f''(u) < 0 for u > 0, then the bifurcation curve is C-shaped. (ii) If f''(u) > 0 for u > 0, then there exists η>β such that the bifurcation curve does not exist for 0 η. Furthermore, we prove that the bifurcation is C-shaped for L > η under a certain condition.

Keywords: bifurcation curve, Minkowski-curvature problem, positive solution, time-map method

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Authors: Shunsuke Miyoshi, Yasuyuki Nogami, Takuya Kusaka, Nariyoshi Yamai

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Elliptic curve discrete logarithm problem (ECDLP) is one of problems on which the security of pairing-based cryptography is based. This paper considers Pollard's rho method to evaluate the security of ECDLP on Barreto-Naehrig (BN) curve that is an efficient pairing-friendly curve. Some techniques are proposed to make the rho method efficient. Especially, the group structure on BN curve, distinguished point method, and Montgomery trick are well-known techniques. This paper applies these techniques and shows its optimization. According to the experimental results for which a large-scale parallel system with MySQL is applied, 94-bit ECDLP was solved about 28 hours by parallelizing 71 computers.

Keywords: Pollard's rho method, BN curve, Montgomery multiplication

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Authors: Fakharuddin Ibrahim, Jamaludin Md. Ali, Ahmad Ramli

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In this paper, we will discuss about the data interpolation by using the rational cubic Ball curve. To generate a curve with a better and satisfactory smoothness, the curve segments must be connected with a certain amount of continuity. The continuity that we will consider is of type G¹ continuity. The conditions considered are known as the G¹ Hermite condition. A simple application of the proposed method is to generate an Arabic font satisfying the required continuity.

Keywords: data interpolation, rational ball curve, hermite condition, continuity

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Authors: F. Esfandyari Darabad, Z. Samadi

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The volume of runoff caused by rainfall in the river basin has enticed the researchers in the fields of the water management resources. In this study, first of the hydrological data such as the rainfall and discharge of the Khiyav river basin of Meshkin city in the northwest of Iran collected and then the process of analyzing and reconstructing has been completed. The soil conservation service (scs) has developed a method for calculating the runoff, in which is based on the curve number specification (CN). This research implemented the following model in the Khiyav river basin of Meshkin city by the GIS techniques and concluded the following fact in which represents the usage of weight model in calculating the curve numbers that provides the possibility for the all efficient factors which is contributing to the runoff creation such as; the geometric characteristics of the basin, the basin soil characteristics, vegetation, geology, climate and human factors to be considered, so an accurate estimation of runoff from precipitation to be achieved as the result. The findings also exposed the accident-prone areas in the output of the Khiyav river basin so it was revealed that the Khiyav river basin embodies a high potential for the flood creation.

Keywords: curve number, khiyav river basin, runoff estimation, SCS

Procedia PDF Downloads 591

Authors: Mohammad Ridzwan Bin Abd Rahim, Siegfried Schmauder, Yupiter HP Manurung, Peter Binkele, Meor Iqram B. Meor Ahmad, Kiarash Dogahe

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This paper deals with the short crack initiation of the material P91 under cyclic loading at two different temperatures, concluded with the estimation of the short crack initiation Wöhler (S/N) curve. An artificial but representative model microstructure was generated using Voronoi tessellation and the Finite Element Method, and the non-uniform stress distribution was calculated accordingly afterward. The number of cycles needed for crack initiation is estimated on the basis of the stress distribution in the model by applying the physically-based Tanaka-Mura model. Initial results show that the number of cycles to generate crack initiation is strongly correlated with temperature.

Keywords: short crack initiation, P91, Wöhler curve, Voronoi tessellation, Tanaka-Mura model

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Authors: Y.J. Wang, C. Q. Ru

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A key issue of cohesive zone models is how to determine the cohesive zone model parameters based on real material test data. In this paper, uniaxial nominal stress-strain curve (SS curve) is used to determine two key parameters of a cohesive zone model (CZM): The maximum traction and the area under the curve of traction-separation law (TSL). To this end, the true SS curve is obtained based on the nominal SS curve, and the relationship between the nominal SS curve and TSL is derived based on an assumption that the stress for cracking should be the same in both CZM and the real material. In particular, the true SS curve after necking is derived from the nominal SS curve by taking the average of the power law extrapolation and the linear extrapolation, and a damage factor is introduced to offset the true stress reduction caused by the voids generated at the necking zone. The maximum traction of the TSL is equal to the maximum true stress calculated based on the damage factor at the end of hardening. In addition, a simple specimen is modeled by Abaqus/Standard to calculate the critical J-integral, and the fracture energy calculated by the critical J-integral represents the stored strain energy in the necking zone calculated by the true SS curve. Finally, the CZM parameters obtained by the present method are compared to those used in a previous related work for a simulation of the drop-weight tear test.

Keywords: dynamic fracture, cohesive zone model, traction-separation law, stress-strain curve, J-integral

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Authors: Abdelghani Qadem

Abstract:

Urbanization in Morocco has ushered in profound shifts in hydrological dynamics, presenting a spectrum of challenges and avenues for sustainable water management. This abstract delves into the nuances of urban hydrology in Morocco, spotlighting the ramifications of rapid urban expansion, the imprint of climate change, and the imperative for cohesive water management strategies. The swift urban sprawl across Morocco has engendered a surge in impermeable surfaces, reshaping the natural hydrological cycle and amplifying quandaries such as urban inundations and water scarcity. Moreover, the specter of climate change looms large, heralding alterations in precipitation regimes and a heightened frequency of extreme meteorological events, thus compounding the hydrological conundrum. However, amidst these challenges, urban hydrology in Morocco also unfolds vistas of innovation and sustainability. The integration of green infrastructure, encompassing solutions like permeable pavements and vegetated roofs, emerges as a linchpin in ameliorating the hydrological imbalances wrought by urbanization, fostering infiltration, and curbing surface runoff. Additionally, embracing the tenets of water-sensitive urban design promises to fortify water efficiency and resilience in urban landscapes. Effectively navigating urban hydrology in Morocco mandates a cross-disciplinary approach that interweaves urban planning, water resource governance, and climate resilience strategies. A collaborative ethos, bridging governmental entities, academic institutions, and grassroots communities, assumes paramount importance in crafting and executing comprehensive solutions that grapple with the intricate interplay of urbanization, hydrology, and climate dynamics. In summation, confronting the labyrinthine challenges of urban hydrology in Morocco necessitates proactive strides toward fostering sustainable urban growth and bolstering resilience to climate vagaries. By embracing cutting-edge technologies and embracing an ethos of integrated water management, Morocco can forge a path toward a more water-secure and resilient urban future.

Keywords: urban hydrology, Morocco, urbanization, climate change, water management, green infrastructure, sustainable development

Procedia PDF Downloads 16

Authors: Y. J. Wang, C. Q. Ru

Abstract:

A key issue of cohesive zone models is how to determine the cohesive zone model (CZM) parameters based on real material test data. In this paper, uniaxial nominal stress-strain curve (SS curve) is used to determine two key parameters of a cohesive zone model: the maximum traction and the area under the curve of traction-separation law (TSL). To this end, the true SS curve is obtained based on the nominal SS curve, and the relationship between the nominal SS curve and TSL is derived based on an assumption that the stress for cracking should be the same in both CZM and the real material. In particular, the true SS curve after necking is derived from the nominal SS curve by taking the average of the power law extrapolation and the linear extrapolation, and a damage factor is introduced to offset the true stress reduction caused by the voids generated at the necking zone. The maximum traction of the TSL is equal to the maximum true stress calculated based on the damage factor at the end of hardening. In addition, a simple specimen is simulated by Abaqus/Standard to calculate the critical J-integral, and the fracture energy calculated by the critical J-integral represents the stored strain energy in the necking zone calculated by the true SS curve. Finally, the CZM parameters obtained by the present method are compared to those used in a previous related work for a simulation of the drop-weight tear test.

Keywords: dynamic fracture, cohesive zone model, traction-separation law, stress-strain curve, J-integral

Procedia PDF Downloads 478

Authors: Martin Kendra, Jaroslav Mašek, Juraj Čamaj, Matej Babin

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The railway transport is considered as a one of the most environmentally friendly mode of transport. With future prediction of increasing of freight transport there are lines facing problems with demanded capacity. Increase of the track capacity could be achieved by infrastructure constructive adjustments. The contribution shows how the travel time can be minimized and the track capacity increased by changing some of the basic infrastructure and operation parameters, for example, the minimal curve radius of the track, the number of tracks, or the usable track length at stations. Calculation of the necessary parameter changes is based on the fundamental physical laws applied to the train movement, and calculation of the occupation time is dependent on the changes of controlling the traffic between the stations.

Keywords: curve radius, maximum curve speed, track mass capacity, reconstruction

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Authors: Shoujia Fang, Guoqing Ding, Xin Chen

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The quality of press-fit assembly is closely related to reliability and safety of product. The paper proposed a keypoint detection method based on convolutional neural network to improve the accuracy of keypoint detection in press-fit curve. It would provide an auxiliary basis for judging quality of press-fit assembly. The press-fit curve is a curve of press-fit force and displacement. Both force data and distance data are time-series data. Therefore, one-dimensional convolutional neural network is used to process the press-fit curve. After the obtained press-fit data is filtered, the multi-layer one-dimensional convolutional neural network is used to perform the automatic learning of press-fit curve features, and then sent to the multi-layer perceptron to finally output keypoint of the curve. We used the data of press-fit assembly equipment in the actual production process to train CNN model, and we used different data from the same equipment to evaluate the performance of detection. Compared with the existing research result, the performance of detection was significantly improved. This method can provide a reliable basis for the judgment of press-fit quality.

Keywords: keypoint detection, curve feature, convolutional neural network, press-fit assembly

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Authors: Wali Ullah, Muhammad Nishat

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The study investigates the extent to which the so called Nelson-Siegel model (DNS) and its extended version that accounts for time varying volatility (DNS-EGARCH) can optimally fit the yield curve and predict its future path in the context of an emerging economy. For the in-sample fit, both models fit the curve remarkably well even in the emerging markets. However, the DNS-EGARCH model fits the curve slightly better than the DNS. Moreover, both specifications of yield curve that are based on the Nelson-Siegel functional form outperform the benchmark VAR forecasts at all forecast horizons. The DNS-EGARCH comes with more precise forecasts than the DNS for the 6- and 12-month ahead forecasts, while the two have almost similar performance in terms of RMSE for the very short forecast horizons.

Keywords: yield curve, forecasting, emerging markets, Kalman filter, EGARCH

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Authors: Roger L. Goodwin

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This paper presents a rank correlation curve. The traditional correlation coefficient is valid for both continuous variables and for integer variables using rank statistics. Since the correlation coefficient has already been established in rank statistics by Spearman, such a calculation can be extended to the correlation curve. This paper presents two survey questions. The survey collected non-continuous variables. We will show weak to moderate correlation. Obviously, one question has a negative effect on the other. A review of the qualitative literature can answer which question and why. The rank correlation curve shows which collection of responses has a positive slope and which collection of responses has a negative slope. Such information is unavailable from the flat, "first-glance" correlation statistics.

Keywords: Bayesian estimation, regression model, rank statistics, correlation, correlation curve

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Authors: Kushakov Kholmurodjon, Muhammadjonov Akbarshox

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This present paper is devoted to a system of second-order nonlinear differential equations with a special right-hand side, exactly, the linear part and a third-order polynomial of a special form. It is shown that for some relations between the parameters, there is a second-order curve in which trajectories leaving the points of this curve remain in the same place. Thus, the curve is invariant with respect to the given system. Moreover, this system is invariant under a non-degenerate linear transformation of variables. The form of this curve, depending on the relations between the parameters and the eigenvalues of the matrix, is proved. All solutions of this system of differential equations are shown analytically.

Keywords: dynamic system, ellipse, hyperbola, Hess system, polar coordinate system

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Authors: Eduardo C. Guardia, Jose W. M. Lima, Afonso H. M. Santos

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This paper presents a nonparametric method to obtain the hazard rate “Bathtub curve” for power system components. The model is a mixture of the three known phases of a component life, the decreasing failure rate (DFR), the constant failure rate (CFR) and the increasing failure rate (IFR) represented by three parametric Weibull models. The parameters are obtained from a simultaneous fitting process of the model to the Kernel nonparametric hazard rate curve. From the Weibull parameters and failure rate curves the useful lifetime and the characteristic lifetime were defined. To demonstrate the model the historic time-to-failure of distribution transformers were used as an example. The resulted “Bathtub curve” shows the failure rate for the equipment lifetime which can be applied in economic and replacement decision models.

Keywords: bathtub curve, failure analysis, lifetime estimation, parameter estimation, Weibull distribution

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Authors: Salisu ibrahim, Abdalla Rababah

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In this research, we use Weighted G2-Multi-degree reduction of Bezier curve of degree n to a Bezier curve of degree m, m < n. The degree reduction of Bezier curves is used to represent a given Bezier curve of n by a Bezier curve of degree m, m < n. Exact degree reduction is not possible, and degree reduction is approximate process in nature. We derive a weighted degree reducing method that is geometrically continuous at the end points. Different norms will be considered, several error minimizations will be given. The proposed methods produce error function that are less than the errors of existing methods.

Keywords: Bezier curves, multiple degree reduction, geometric continuity, error function

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Authors: D. Sigirli

Abstract:

The Receiver Operating Characteristic (ROC) curve is a commonly used statistical tool for evaluating the diagnostic performance of screening and diagnostic test with continuous or ordinal scale results which aims to predict the presence or absence probability of a condition, usually a disease. When the test results were measured as numeric values, sensitivity and specificity can be computed across all possible threshold values which discriminate the subjects as diseased and non-diseased. There are infinite numbers of possible decision thresholds along the continuum of the test results. The ROC curve presents the trade-off between sensitivity and the 1-specificity as the threshold changes. The empirical ROC curve which is a non-parametric estimator of the ROC curve is robust and it represents data accurately. However, especially for small sample sizes, it has a problem of variability and as it is a step function there can be different false positive rates for a true positive rate value and vice versa. Besides, the estimated ROC curve being in a jagged form, since the true ROC curve is a smooth curve, it underestimates the true ROC curve. Since the true ROC curve is assumed to be smooth, several smoothing methods have been explored to smooth a ROC curve. These include using kernel estimates, using log-concave densities, to fit parameters for the specified density function to the data with the maximum-likelihood fitting of univariate distributions or to create a probability distribution by fitting the specified distribution to the data nd using smooth versions of the empirical distribution functions. In the present paper, we aimed to propose a smooth ROC curve estimation based on the boundary corrected kernel function and to compare the performances of ROC curve smoothing methods for the diagnostic test results coming from different distributions in different sample sizes. We performed simulation study to compare the performances of different methods for different scenarios with 1000 repetitions. It is seen that the performance of the proposed method was typically better than that of the empirical ROC curve and only slightly worse compared to the binormal model when in fact the underlying samples were generated from the normal distribution.

Keywords: empirical estimator, kernel function, smoothing, receiver operating characteristic curve

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Authors: Dariusz Jacek Jakóbczak

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Mathematics and computer science are interested in methods of 2D curve interpolation and extrapolation using the set of key points (knots). A proposed method of Hurwitz- Radon Matrices (MHR) is such a method. This novel method is based on the family of Hurwitz-Radon (HR) matrices which possess columns composed of orthogonal vectors. Two-dimensional curve is interpolated via different functions as probability distribution functions: polynomial, sinus, cosine, tangent, cotangent, logarithm, exponent, arcsin, arccos, arctan, arcctg or power function, also inverse functions. It is shown how to build the orthogonal matrix operator and how to use it in a process of curve reconstruction.

Keywords: 2D data interpolation, hurwitz-radon matrices, MHR method, probabilistic modeling, curve extrapolation

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Authors: Rong Wang, Sandra Hasanefendic, Elizabeth von Hauff, Bart Bossink

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Technological learning and learning curve models have been continuously used to estimate the photovoltaics (PV) cost development over time for the climate mitigation targets. They can integrate a number of technological learning sources which influence the learning process. Yet the accuracy and realistic predictions for cost estimations of PV development are still difficult to achieve. This paper develops four hypothetical-alternative learning curve models by proposing different combinations of technological learning sources, including both local and global technology experience and the knowledge stock. This paper specifically focuses on the non-linear relationship between the costs and technological learning source and their dynamic interaction and uses the system dynamics approach to predict a more accurate PV cost estimation for future development. As the case study, the data from China is gathered and drawn to illustrate that the learning curve model that incorporates both the global and local experience is more accurate and realistic than the other three models for PV cost estimation. Further, absorbing and integrating the global experience into the local industry has a positive impact on PV cost reduction. Although the learning curve model incorporating knowledge stock is not realistic for current PV cost deployment in China, it still plays an effective positive role in future PV cost reduction.

Keywords: photovoltaic, system dynamics, technological learning, learning curve

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Authors: Siti Noor Farwina Anwar, Hailiza Kamarulhaili

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In this paper, we present the idea of implementing the Integer Sub-Decomposition (ISD) method on elliptic curves with j-invariant 1728. The ISD method was proposed in 2013 to compute scalar multiplication in elliptic curves, which remains to be the most expensive operation in Elliptic Curve Cryptography (ECC). However, the original ISD method only works on integer number field and solve integer scalar multiplication. By extending the method into the complex quadratic field, we are able to solve complex multiplication and implement the ISD method on elliptic curves with j-invariant 1728. The curve with j-invariant 1728 has a unique discriminant of the imaginary quadratic field. This unique discriminant of quadratic field yields a unique efficiently computable endomorphism, which later able to speed up the computations on this curve. However, the ISD method needs three endomorphisms to be accomplished. Hence, we choose all three endomorphisms to be from the same imaginary quadratic field as the curve itself, where the first endomorphism is the unique endomorphism yield from the discriminant of the imaginary quadratic field.

Keywords: efficiently computable endomorphism, elliptic scalar multiplication, j-invariant 1728, quadratic field

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Authors: Cyril Hrncar, Jozef Bujko, Widya P. B. Putra

Abstract:

The growth curve of poultry is important to evaluate the farming management system. This study was aimed to estimate the growth curve of body weight in goose. The growth curve in this study was estimated with non-linear Gompertz model through CurveExpert 1.4. software. Three Slovak mixed-sex goose breeds of Landes (L), Pomeranian (P) and Steinbacher (S) were used in this study. Total of 28 geese (10 L, 8 P and 10 S) were used to estimate the growth curve. Research showed that the asymptotic weight (A) in those geese were reached of 5332.51 g (L), 6186.14 g (P) and 5048.27 g (S). Thus, the maturing rate (k) in each breed were similar (0.05 g/day). The weight of inflection was reached of 1960.48 g (L), 2274.32 g (P) and 1855.98 g (S). The time of inflection (ti) was reached of 25.6 days (L), 26.2 days (P) and 27.80 days (S). The maximum growth rate (MGR) was reached of 98.02 g/day (L), 113.72 g/day (P) and 92.80 g/day (S). Hence, the coefficient of determination (R2) in Gompertz model was 0.99 for each breed. It can be concluded that Pomeranian geese had highest of growth trait than the other breeds.

Keywords: body weight, growth curve, inflection, Slovak geese, Gompertz model

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