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1
Li, Yunyue, Yang Zhang, and Jon Claerbout. "Hyperbolic estimation of sparse models from erratic data." GEOPHYSICS 77, no. 1 (2012): V1—V9. http://dx.doi.org/10.1190/geo2011-0099.1.
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We have developed a hyperbolic penalty function for image estimation. The center of a hyperbola is parabolic like that of an [Formula: see text] norm fitting. Its asymptotes are similar to [Formula: see text] norm fitting. A transition threshold must be chosen for regression equations of data fitting and another threshold for model regularization. We combined two methods: Newton’s and a variant of conjugate gradient method to solve this problem in a manner we call the hyperbolic conjugate direction (HYCD) method. We tested examples of (1) velocity transform with strong noise (2) migration of aliased data, and (3) blocky interval velocity estimation. For the linear experiments we performed in this study, nonlinearity is introduced by the hyperbolic objective function, but the convexity of the sum of the hyperbolas assures the convergence of gradient methods. Because of the sufficiently reliable performance obtained on the three mainstream geophysical applications, we expect the HYCD solver method to become our default method.
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Miguel, E. San, S. Monserrat, C. Fernández, et al. "Growth models and longevity of freshwater pearl mussels (Margaritifera margaritifera) in Spain." Canadian Journal of Zoology 82, no. 8 (2004): 1370–79. http://dx.doi.org/10.1139/z04-113.
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Growth rates of populations of the freshwater pearl mussel, Margaritifera margaritifera (L., 1758), in northwestern Spain were analysed based on measurements of annual annuli and using two nonlinear functions for length-at-age data sets: von Bertalanffy's growth model and a hyperbolic function. These populations reach the smallest maximum shell length (90.5 mm) and have the shortest life-span (35 years) and the highest growth rate (k in von Bertalanffy's model >0.1·year–1, on average) known for this species. The two models were similar in performance and were well fitted (around 99%) to shell-length-at-age data, although the hyperbolic function appears to be applicable only from 6 years of age. The growth rate (either k or k' from the hyperbolic function) showed a large and significant variation across populations, both among and within drainages.
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Cahyono, Muhammad. "Hybrid Models for Solving the Colebrook–White Equation Using Artificial Neural Networks." Fluids 7, no. 7 (2022): 211. http://dx.doi.org/10.3390/fluids7070211.
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This study proposes hybrid models to solve the Colebrook–White equation by combining explicit equations available in the literature to solve the Colebrook–White equation with an error function. The hybrid model is in the form of fH=fo−eA. fH is the friction factor value f predicted by the hybrid model, fo is the value of f calculated using several explicit formulas for the Colebrook–White equation, and eA is the error function determined using the neural network procedures. The hybrid equation consists of a series of hyperbolic tangent functions whose number corresponds to the number of neurons in the hidden layer. The simulation results showed that the hybrid models using five hyperbolic tangent functions could produce reasonable predictions of friction factors, with the maximum absolute relative error (MAXRE) around one tenth, or ten times lower than that produced by the corresponding existing formula. The simplified hybrid models are also given using four and three tangent hyperbolic functions. These simplified models still provide accurate results with MAXRE of less than 0.1%.
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Safak, Suleyman. "A New Hyperbolic Function Approach of Rock Fragmentation Size Distribution Prediction Models." Symmetry 16, no. 8 (2024): 979. http://dx.doi.org/10.3390/sym16080979.
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It is well known that the first stage of mine-to-mill optimization is rock fragmentation by blasting. The degree of rock fragmentation can be expressed in terms of average grain (X50) size and size distribution. There are approaches in which exponential functions are used to estimate the size distribution of the pile that will be formed before blasting. The most common of these exponential functions used to estimate the average grain size is the Kuz–Ram and KCO functions. The exponential functions provide a curve from 0% to 100% using the mean grain size (X50), characteristic size (XC), and uniformity index (n) parameters. This distribution curve can make predictions in the range of fine grains and coarse grains outside the acceptable error limits in some cases. In this article, the usability of the hyperbolic tangent function, which is symmetrical at origin, in the estimation of the size distribution as an alternative to the exponential distribution functions used in almost all estimation models is investigated. As with exponential functions, the hyperbolic tangent function can express the aggregated size distribution as a percentage with reference to the variables X50 and XC. It has been shown that the hyperbolic tangent function provides 99% accuracy to the distribution of fine grains and coarse grains of the pile formed as a result of blasting data for the characteristic size (XC) parameter and the uniformity index (n).
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Ivanov, Roman V. "The Semi-Hyperbolic Distribution and Its Applications." Stats 6, no. 4 (2023): 1126–46. http://dx.doi.org/10.3390/stats6040071.
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This paper studies a subclass of the class of generalized hyperbolic distribution called the semi-hyperbolic distribution. We obtain analytical expressions for the cumulative distribution function and, specifically, their first and second lower partial moments. Using the received formulas, we compute the value at risk, the expected shortfall, and the semivariance in the semi-hyperbolic model of the financial market. The formulas depend on the values of generalized hypergeometric functions and modified Bessel functions of the second kind. The research illustrates the possibility of analysis of generalized hyperbolic models using the same methodology as is employed for the well-established variance-gamma model.
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PARISI, J., and R. STOOP. "THE GENERALIZED THERMODYNAMIC FORMALISM APPLIED TO HYPERBOLIC AND NONHYPERBOLIC MODELS." Modern Physics Letters B 06, no. 24 (1992): 1513–18. http://dx.doi.org/10.1142/s0217984992001216.
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In this contribution, scaling properties of hyperbolic and nonhyperbolic model systems are discussed by using the generalized thermodynamic formalism. The central quantity for the investigation is the generalized entropy function. With the help of this approach, insight into the possible occurrence of phase transitions in the various entropy-like scaling functions can be gained. It is shown how this effect is determined by the existence of a critical line in the surface described by the generalized entropy function.
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Al-Amry, M. S., and E. F. Al-Abdali. "New Exact Solutions for Generalized of Combined with Negative Calogero-Bogoyavlenskii Schiff and Generalized Yu–Toda–Sassa–Fukuyama Equations." University of Aden Journal of Natural and Applied Sciences 28, no. 1 (2024): 25–30. http://dx.doi.org/10.47372/uajnas.2024.n1.a04.
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In this paper, we present generalized model of combined Calogero-Bogoyavlenskii Schiff and negative-order Calogero-Bogoyavlenskii Schiff G(CBS-nCBS) equation and generalized Yu–Toda–Sassa–Fukuyama g(YTSF) equation. We apply the extended hyperbolic function method, to solve generalized models. Exact travelling wave solutions are obtained and expressed in terms of hyperbolic functions, trigonometric functions, rational functions solutions of these equations from the method with the aid of the computer program Maple.
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Hoon Lim, Siew. "Accounting for environmental pollution in production function." Management of Environmental Quality: An International Journal 25, no. 6 (2014): 679–95. http://dx.doi.org/10.1108/meq-08-2013-0087.
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Purpose – Traditionally, economic production models consider pollution as bads that may be modeled as either outputs or inputs in economic models. The purpose of this paper is to examine the implications of these modeling choices on the measurements of productive efficiency and private costs of pollution control. Design/methodology/approach – The authors apply the hyperbolic distance functions to measure trucking efficiency and the private costs of pollution control. Findings – The results show: (i) regardless of the choice of modeling, when only one bad was incorporated in hyperbolic distance functions, the efficiency loss and private abatement cost measures derived from the two models were equivalent, but potential pollution reduction and good output expansion differed; (ii) when more than one bad were introduced, the equivalence of efficiency loss measure in (i) did not hold; and (iii) the potential amounts of pollution reduction and good output expansion were larger when bads were modeled as inputs. With multiple bads, private abatement costs varied considerably under the two modeling treatments. Practical implications – From a policy standpoint, the results suggest that one should consider the modeling options with caution when multiple economic bads are involved, because the resulting measures of economic burden of pollution control differ. Originality/value – The paper shows that the traditional conceptual framework for modeling pollution in hyperbolic distance functions could yield inconsistent results.
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AKARÇAY, Özlem, and Nimet YAPICI PEHLİVAN. "FUZZY MULTI-OBJECTIVE NONLINEAR PROGRAMMING PROBLEMS UNDER VARİOUS MEMBERSHIP FUNCTIONS: A COMPARATİVE ANALYSIS." Mühendislik Bilimleri ve Tasarım Dergisi 11, no. 3 (2023): 857–72. http://dx.doi.org/10.21923/jesd.1062118.
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Fuzzy sets have been applied to various decision-making problems when there is uncertainty in real-life problems. In decision-making problems, objective functions and constraints sometimes cannot be expressed linearly. In such cases, the problems discussed are expressed by nonlinear programming models. Fuzzy multi-objective programming models are problems containing multiple objective functions, where objective functions and/or constraints include fuzzy parameters. Membership functions are crucial to obtain optimal solution of fuzzy multi-objective programming model. In this study, a green supply chain network model with fuzzy parameters is proposed. Proposed model with nonlinear constraints is a fuzzy multi-objective nonlinear programming model that minimizes both transportation costs and emissions generated by two vehicle types during transportation. The model is used in Zimmermann's Min-Max approach by considering triangular, hyperbolic and exponential membership functions and optimal solutions are obtained. When optimal solutions are compared, it is seen that optimal solution obtained using the hyperbolic membership function is better than the optimal solutions obtained from triangular and exponential ones. Maximum common satisfaction level calculated using hyperbolic membership function for proposed model is λ=0.97. Sensitivity analysis is also carried out by taking into account distances between suppliers, manufacturers, distribution centers and customers, as well as customer demands.
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Sakai, Motoki. "Estimation of Heart Rate from Vocal Frequency Based on Support Vector Machine." International Journal of Advances in Scientific Research 2, no. 1 (2016): 16. http://dx.doi.org/10.7439/ijasr.v2i1.2849.
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Heart rate (HR) is one of the vital signs used to assess our physical condition; it would be beneficial if HR could easily be obtained without special medical instruments. In this study, a feature of vocal frequency was used to estimate HR, because it can easily be recorded with a common device such as a smartphone. Previous studies proposed that a support vector machine (SVM) that adopted the inner product as the kernel function was efficient for estimating HR to a certain extent. However, these studies did not present the effectiveness of other kernel functions, such as the hyperbolic tangent function. Therefore, this study identified a combination of kernel functions of the kernel ridge regression (KRR). In addition, features of vocal frequency to effectively estimate HR were investigated. To evaluate the effectiveness, experiments were conducted with two subjects. In the experiment, 60 sets of HRs and voice data were measured per subject. To identify the most effective kernel function, four kernel functions (the inner function, Gaussian function, polynomial function, and hyperbolic tangent function) were compared. Moreover, effective features of vocal frequency were selected with the sequential feature selection (SFS) method. As a consequence, the hyperbolic tangent function worked best, and high-frequency components of voice were efficient. However, results of this research indicated that effective vocal spectrum components to estimate HR differ depending on prediction models.
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Syrovátka, Pavel, and Miroslav Navrátil. "Linear models of income patterns in consumer demand for foods and evaluation of its elasticity." Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis 53, no. 6 (2005): 173–88. http://dx.doi.org/10.11118/actaun200553060173.
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The paper is focused on the use of the linear constructions for developing of Engel’s demand models in the field of the food-consumer demand. In the theoretical part of the paper, the linear approximations of this demand models are analysed on the bases of the linear interpolation. In the same part of this text, the hyperbolic elasticity function was defined for the linear Engel model. The behaviour of the hyperbolic elasticity function and its properties were consequently investigated too. The behaviour of the determined elasticity function was investigated according to the values of the intercept point and the direction parameter in the original linear Engel model. The obtained theoretical findings were tested using the real data of Czech Statistical Office. The developed linear Engel model was explicitly dynamised, because the achieved database was formed into the time series. With respect to the two variables definitions of the hyperbolic function in the theoretical part of the text, the determined dynamic model of the Engel demand for food was transformed into the form with parametric intercept point:ret* = At + 0.0946 · rmt*,where the values of absolute member are defined as:At = 1773.0973 + 9.3064 · t – 0.3023 · t2; (t = 1, 2, ... 32).The value of At in the parametric linear model of Engel consumer demand for food was during the observed period (1995–2002) always positive. Thus, the hyperbolic elasticity function achieved the elasticity coefficients from the interval:ηt ∈〈+0; +1).Within quantitative analysis of Engel demand for food in the Czech Republic during the given time period, it was founded, that income elasticity of food expenditures of the average Czech household was moved between +0.4080 and +0.4511. The Czech-household demand for food is thus income inelastic with the normal income reactions.
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Oyamakin, S. O., and A. U. Chukwu. "On Hyperbolic Monomolecular growth model in Height/Diameter growth of PINES." Journal of Applied Mathematics, Statistics and Informatics 11, no. 1 (2015): 5–17. http://dx.doi.org/10.1515/jamsi-2015-0001.
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AbstractThis paper proposed a hyperbolic monomolecular growth model (HMMGM). it came as a solution to the improved monomolecular growth equation which was developed by injecting an allometric parameter θ into the intrinsic rate of growth of the monomolecular growth equation using a hyperbolic sine function. Its ability in model prediction was compared with the classical monomolecular growth model an approach which mimicked the natural variability of height/diameter increment with respect to age and therefore provides a more realistic height/diameter predictions using goodness of fit tests and model selection criteria. The Kolmogorov Smirnov test and Shapiro-Wilk test was also used to test the compliance of the error term to normality assumptions while using testing the independence of the error term using the runs test . The mean function of top height/Dbh over age using the two models under study predicted closely the observed values of top height/Dbh in the hyperbolic monomolecular nonlinear growth models better than the source model (classical monomolecular growth model) while the results of R2, Adj. R2, MSE and AIC confirmed the predictive power of the Hyperbolic Monomolecular growth models over its source model.
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Rai, Swati, and Kirti Jain. "Analysis of Forward Pass RNN with Hyperbolic Tangent Function for Software Defect Prediction." International Journal on Advances in Engineering, Technology and Science (IJAETS) 5, no. 1 (2024): 25–29. https://doi.org/10.5281/zenodo.10666637.
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<em>Abstract</em>– Software failure prediction and proneness have long been considered critical challenges for the IT industry and software professionals. Conventional approaches may detect software defects inside an application, but they need previous knowledge of problems or faulty components. Automated software fault recovery models enable the programme to significantly predict and recover from software issues via the use of machine learning techniques. This feature reduces mistakes, time, and money while also making the programme run more smoothly. A software defect prediction development model was given using machine learning techniques, which could enable the programme to carry out its intended purpose. A range of optimisation evaluation benchmarks, including as accuracy, f1-measure, precision, recall, and specificity, were also used to evaluate the model's performance. The FPRNN-HTF (Forward Pass RNN with Hyperbolic Tangent Function) deep learning prediction model is based on convolutional neural networks and its hyperbolic tangent functions. The evaluation process showed how well CNN algorithms were used and how accurate they were. Additionally, a comparative metric is used to assess the proposed prediction model in comparison to other approaches. The collected data showed how well the FPRNN-HTF approach performed. Keywords– FPRNN-HTF (Forward Pass RNN with Hyperbolic Tangent Function), precision, recall, specificity, F1-measure, and accuracy.
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YU, Ya Jun. "Analytical solutions to hyperbolic heat conductive models using Green's function method." Journal of Thermal Science and Technology 13, no. 1 (2018): JTST0012. http://dx.doi.org/10.1299/jtst.2018jtst0012.
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Jia, Chun-Sheng, Liang-Zhong Yi, and Shi-Wen Long. "Relationship of the deformed hyperbolic Kratzer-like and Tietz potential energy models for diatomic molecules." Canadian Journal of Physics 92, no. 10 (2014): 1258–61. http://dx.doi.org/10.1139/cjp-2013-0684.
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Taking the dissociation energy and the equilibrium bond length as explicit parameters, we construct an improved form of the deformed hyperbolic Kratzer-like potential function for diatomic molecules. We show that the deformed hyperbolic Kratzer-like potential model is equivalent to the Tietz potential model for diatomic molecules. We observe that the Tietz potential is superior to the Morse potential in reproducing the interaction potential energy curve for the 23Πg state of the 7Li2 molecule.
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Bazeia, D., Elisama E. M. Lima, and L. Losano. "Kinks and branes in models with hyperbolic interactions." International Journal of Modern Physics A 32, no. 26 (2017): 1750163. http://dx.doi.org/10.1142/s0217751x17501639.
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In this work, we investigate several models described by a single real scalar field with nonpolynomial interactions, constructed to support topological solutions. We do this using the deformation procedure to introduce a function which allows to construct two distinct families of hyperbolic potentials, controlled by three distinct parameters, in the standard formalism. In this way, the procedure allows us to get analytical solutions, and then investigate the energy density, linear stability and zero mode. We move on and introduce a nonstandard formalism to obtain compact solutions, analytically. We also investigate these hyperbolic models in the braneworld context, considering both the standard and nonstandard possibilities. The results show how to construct distinct braneworld models which are implemented via the first-order formalism and are stable against fluctuation of the metric tensor.
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Harlan, William S. "Simultaneous velocity filtering of hyperbolic reflections and balancing of offset‐dependent wavelets." GEOPHYSICS 54, no. 11 (1989): 1455–65. http://dx.doi.org/10.1190/1.1442609.
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Hyperbolic reflections and convolutional wavelets are fundamental models for seismic data processing. Each sample of a “stacked” zero‐offset section can parameterize an impulsive hyperbolic reflection in a midpoint gather. Convolutional wavelets can model source waveforms and near‐surface filtering at the shot and geophone positions. An optimized inversion of the combined modeling equations for hyperbolic traveltimes and convolutional wavelets makes explicit any interdependence and nonuniqueness in these two sets of parameters. I first estimate stacked traces that best model the recorded data and then find nonimpulsive wavelets to improve the fit with the data. These wavelets are used for a new estimate of the stacked traces, and so on. Estimated stacked traces model short average wavelets with a superposition of approximately parallel hyperbolas; estimated wavelets adjust the phases and amplitudes of inconsistent traces, including static shifts. Deconvolution of land data with estimated wavelets makes wavelets consistent over offset; remaining static shifts are midpoint‐consistent. This phase balancing improves the resolution of stacked data and of velocity analyses. If precise velocity functions are not known, then many stacked traces can be inverted simultaneously, each with a different velocity function. However, the increased number of overlain hyperbolas can more easily model the effects of inconsistent wavelets. As a compromise, I limit velocity functions to reasonable regions selected from a stacking velocity analysis—a few functions cover velocities of primary and multiple reflections. Multiple reflections are modeled separately and then subtracted from marine data. The model can be extended to include more complicated amplitude changes in reflectivity. Migrated reflectivity functions would add an extra constraint on the continuity of reflections over midpoint. Including the effect of dip moveout in the model would make stacking and migration velocities equivalent.
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Yenish, Joseph P., Beverly R. Durgan, Douglas W. Miller, and Donald L. Wyse. "Wheat (Triticum aestivum) yield reduction from common milkweed (Asclepias syriaca) competition." Weed Science 45, no. 1 (1997): 127–31. http://dx.doi.org/10.1017/s0043174500092572.
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Yield loss of hard red spring wheat due to competition from common milkweed was measured in grower fields in Minnesota. Wheat yield loss was measured using the area of influence and additive competitive methods. Simple linear regression of wheat yield and percentage wheat yield loss against distance from a common milkweed shoot gaver2values of 0.013 and 0.015, respectively, indicating limited value of the area of influence model for common milkweed in spring wheat. In an additive competition model, wheat yield was reduced 47% at the highest density of 12 common milkweed shoots m−2. Coefficients of determination for percentage yield loss regressed against common milkweed shoot density were 0.548, 0.547, and 0.529 for simple linear, nonlinear rectangular hyperbolic, and linear square root function models, respectively. Regression of percentage yield loss against common milkweed biomass resulted inr2values of 0.566, 0.645, and 0.658 for simple linear, nonlinear rectangular hyperbolic, and linear square root function models, respectively. Restrictions of common milkweed density due to factors other than competition limited yield loss response to the simple linear phase of both the nonlinear rectangular hyperbolic and the linear square root function models previously described.
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Antonides, Gerrit, and Sophia R. Wunderink. "Subjective Time Preference and Willingness to Pay for an Energy-Saving Durable Good." Zeitschrift für Sozialpsychologie 32, no. 3 (2001): 133–41. http://dx.doi.org/10.1024//0044-3514.32.3.133.
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Summary: Different shapes of individual subjective discount functions were compared using real measures of willingness to accept future monetary outcomes in an experiment. The two-parameter hyperbolic discount function described the data better than three alternative one-parameter discount functions. However, the hyperbolic discount functions did not explain the common difference effect better than the classical discount function. Discount functions were also estimated from survey data of Dutch households who reported their willingness to postpone positive and negative amounts. Future positive amounts were discounted more than future negative amounts and smaller amounts were discounted more than larger amounts. Furthermore, younger people discounted more than older people. Finally, discount functions were used in explaining consumers' willingness to pay for an energy-saving durable good. In this case, the two-parameter discount model could not be estimated and the one-parameter models did not differ significantly in explaining the data.
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Xue, Yangkai, Jindou Dai, Zhipeng Lu, Yuwei Wu, and Yunde Jia. "Residual Hyperbolic Graph Convolution Networks." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 15 (2024): 16247–54. http://dx.doi.org/10.1609/aaai.v38i15.29559.
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Hyperbolic graph convolutional networks (HGCNs) have demonstrated representational capabilities of modeling hierarchical-structured graphs. However, as in general GCNs, over-smoothing may occur as the number of model layers increases, limiting the representation capabilities of most current HGCN models. In this paper, we propose residual hyperbolic graph convolutional networks (R-HGCNs) to address the over-smoothing problem. We introduce a hyperbolic residual connection function to overcome the over-smoothing problem, and also theoretically prove the effectiveness of the hyperbolic residual function. Moreover, we use product manifolds and HyperDrop to facilitate the R-HGCNs. The distinctive features of the R-HGCNs are as follows: (1) The hyperbolic residual connection preserves the initial node information in each layer and adds a hyperbolic identity mapping to prevent node features from being indistinguishable. (2) Product manifolds in R-HGCNs have been set up with different origin points in different components to facilitate the extraction of feature information from a wider range of perspectives, which enhances the representing capability of R-HGCNs. (3) HyperDrop adds multiplicative Gaussian noise into hyperbolic representations, such that perturbations can be added to alleviate the over-fitting problem without deconstructing the hyperbolic geometry. Experiment results demonstrate the effectiveness of R-HGCNs under various graph convolution layers and different structures of product manifolds.
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Alqahtani, Abdullah, and Frederick T. Sheldon. "eMIFS: A Normalized Hyperbolic Ransomware Deterrence Model Yielding Greater Accuracy and Overall Performance." Sensors 24, no. 6 (2024): 1728. http://dx.doi.org/10.3390/s24061728.
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Early detection of ransomware attacks is critical for minimizing the potential damage caused by these malicious attacks. Feature selection plays a significant role in the development of an efficient and accurate ransomware early detection model. In this paper, we propose an enhanced Mutual Information Feature Selection (eMIFS) technique that incorporates a normalized hyperbolic function for ransomware early detection models. The normalized hyperbolic function is utilized to address the challenge of perceiving common characteristics among features, particularly when there are insufficient attack patterns contained in the dataset. The Term Frequency–Inverse Document Frequency (TF–IDF) was used to represent the features in numerical form, making it ready for the feature selection and modeling. By integrating the normalized hyperbolic function, we improve the estimation of redundancy coefficients and effectively adapt the MIFS technique for early ransomware detection, i.e., before encryption takes place. Our proposed method, eMIFS, involves evaluating candidate features individually using the hyperbolic tangent function (tanh), which provides a suitable representation of the features’ relevance and redundancy. Our approach enhances the performance of existing MIFS techniques by considering the individual characteristics of features rather than relying solely on their collective properties. The experimental evaluation of the eMIFS method demonstrates its efficacy in detecting ransomware attacks at an early stage, providing a more robust and accurate ransomware detection model compared to traditional MIFS techniques. Moreover, our results indicate that the integration of the normalized hyperbolic function significantly improves the feature selection process and ultimately enhances ransomware early detection performance.
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Abdul Ghaffar, Abdul Razzaq, Md Gulzarul Hasan, Zubair Ashraf, and Mohammad Faisal Khan. "Fuzzy Goal Programming with an Imprecise Intuitionistic Fuzzy Preference Relations." Symmetry 12, no. 9 (2020): 1548. http://dx.doi.org/10.3390/sym12091548.
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Fuzzy goal programming (FGP) is applied to solve fuzzy multi-objective optimization problems. In FGP, the weights are associated with fuzzy goals for the preference among them. However, the hierarchy within the fuzzy goals depends on several uncertain criteria, decided by experts, so the preference relations are not always easy to associate with weight. Therefore, the preference relations are provided by the decision-makers in terms of linguistic relationships, i.e., goal A is slightly or moderately or significantly more important than goal B. Due to the vagueness and ambiguity associated with the linguistic preference relations, intuitionistic fuzzy sets (IFSs) are most efficient and suitable to handle them. Thus, in this paper, a new fuzzy goal programming with intuitionistic fuzzy preference relations (FGP-IFPR) approach is proposed. In the proposed FGP-IFPR model, an achievement function has been developed via the convex combination of the sum of individual grades of fuzzy objectives and amount of the score function of IFPRs among the fuzzy goals. As an extension, we presented the linear and non-linear, namely, exponential and hyperbolic functions for the intuitionistic fuzzy preference relations (IFPRs). A study has been made to compare and analyze the three FGP-IFPR models with intuitionistic fuzzy linear, exponential, and hyperbolic membership and non-membership functions. For solving all three FGP-IFPR models, the solution approach is developed that established the corresponding crisp formulations, and the optimal solution are obtained. The validations of the proposed FGP-IFPR models have been presented with an experimental investigation of a numerical problem and a banking financial statement problem. A newly developed distance measure is applied to compare the efficiency of proposed models. The minimum value of the distance function represents a better and efficient model. Finally, it has been found that for the first illustrative problem considered, the exponential FGP-IFPR model performs best, whereas for the second problem, the hyperbolic FGP-IFPR model performs best and the linear FGP-IFPR model shows worst in both cases.
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Lee, Junhwan, Rodrigo Salgado, and J. Antonio H. Carraro. "Stiffness degradation and shear strength of silty sands." Canadian Geotechnical Journal 41, no. 5 (2004): 831–43. http://dx.doi.org/10.1139/t04-034.
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Soils behave nonlinearly from very early loading stages. When granular soils contain a certain amount of fines, the degree of nonlinearity also changes, as stiffness and strength characteristics vary with fines content. Hyperbolic stressstrain models and variations of these models are often used for description of the nonlinear behavior. A modified hyperbolic stressstrain relationship is used in this paper for representing the degradation of the elastic modulus of silty sands. The model is based on two modulus degradation parameters that determine the magnitude and rate of modulus degradation as a function of stress level. Realistic representation of soil behavior using this nonlinear relationship requires estimation of the degradation parameters as a function of silt content and relative density DR. A series of triaxial test results on sands containing different amounts of nonplastic silt were analyzed with this purpose. Relationships between the degradation parameters and cone penetration test (CPT) cone resistance qc are also proposed.Key words: hyperbolic model, silty sands, triaxial tests, modulus degradation, stressstrain response, shear strength, Gmax.
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Kocaoğlu, Aykut. "Efficient Optimization of a Support Vector Regression Model with Natural Logarithm of the Hyperbolic Cosine Loss Function for Broader Noise Distribution." Applied Sciences 14, no. 9 (2024): 3641. http://dx.doi.org/10.3390/app14093641.
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While traditional support vector regression (SVR) models rely on loss functions tailored to specific noise distributions, this research explores an alternative approach: ε-ln SVR, which uses a loss function based on the natural logarithm of the hyperbolic cosine function (lncosh). This function exhibits optimality for a broader family of noise distributions known as power-raised hyperbolic secants (PHSs). We derive the dual formulation of the ε-ln SVR model, which reveals a nonsmooth, nonlinear convex optimization problem. To efficiently overcome these complexities, we propose a novel sequential minimal optimization (SMO)-like algorithm with an innovative working set selection (WSS) procedure. This procedure exploits second-order (SO)-like information by minimizing an upper bound on the second-order Taylor polynomial approximation of consecutive loss function values. Experimental results on benchmark datasets demonstrate the effectiveness of both the ε-ln SVR model with its lncosh loss and the proposed SMO-like algorithm with its computationally efficient WSS procedure. This study provides a promising tool for scenarios with different noise distributions, extending beyond the commonly assumed Gaussian to the broader PHS family.
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Yaghoobi, Tahere, and Man-Fai Leung. "Modeling Software Reliability with Learning and Fatigue." Mathematics 11, no. 16 (2023): 3491. http://dx.doi.org/10.3390/math11163491.
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Software reliability growth models (SRGMs) based on the non-homogeneous Poisson process have played a significant role in predicting the number of remaining errors in software, enhancing software reliability. Software errors are commonly attributed to the mental errors of software developers, which necessitate timely detection and resolution. However, it has been observed that the human error-making mechanism is influenced by factors such as learning and fatigue. In this paper, we address the issue of integrating the fatigue factor of software testers into the learning process during debugging, leading to the development of more realistic SRGMs. The first model represents the software tester’s learning phenomenon using the tangent hyperbolic function, while the second model utilizes an exponential function. An exponential decay function models fatigue. We investigate the behavior of our proposed models by comparing them with similar SRGMs, including two corresponding models in which the fatigue factor is removed. Through analysis, we assess our models’ quality of fit, predictive power, and accuracy. The experimental results demonstrate that the model of tangent hyperbolic learning with fatigue outperforms the existing ones regarding fit, predictive power, or accuracy. By incorporating the fatigue factor, the models provide a more comprehensive and realistic depiction of software reliability.
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Hidayat, Raymundus Lullus Lambang Govinda, Wibowo, Budi Santoso, Fitrian Imaddudin, and Ubaidillah. "Selection of MR damper model suitable for SMC applied to semi-active suspension system by using similarity measures." Open Engineering 12, no. 1 (2022): 1005–12. http://dx.doi.org/10.1515/eng-2022-0367.
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Abstract This article discusses the research to determine the suitable magnetorheological (MR) damper model to produce the damping force generated by the sliding mode control (SMC) strategy. The MR damper models studied are parametric, i.e., the Bingham model, the Bouc-Wen model, and the Bouc-Wen model with a hyperbolic tangent function. The damping force of SMC usually includes sudden changes in the force and chattering. The research was carried out by calculating the value of the similarity measure of the damping force of the controller and the damping force of each model. The results show that the two Bouc Wen models had a high similarity measure. The Bouc Wen model with the hyperbolic tangent function was selected because it provides a sudden change of force and reasonable force tracking needed to develop the inverse MR damper model.
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De Godoi, Felipe Augusto Paes, Fran Sérgio Lobato, and João Jorge Ribeiro Damasceno. "Solution of inverse anomalous mass transfer problems using a hyperbolic space-fractional model and differential evolution." OBSERVATÓRIO DE LA ECONOMÍA LATINOAMERICANA 21, no. 12 (2023): 26050–75. http://dx.doi.org/10.55905/oelv21n12-140.
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The study of anomalous diffusion phenomenon characterizes an important field of science due to limitations of traditional laws considered to represent the conduction term found in mass and heat transfer models. Mathematically, this phenomenon can be represented by empirical and phenomenological models with different levels of complexity. For the latter, differential models with fractional order have been considered. In addition, based on hyperbolic diffusion theory, this fractional differential model can be represented by a second-order derivative on time. This fractional hyperbolic differential model presents two new parameters (fractional order and time relaxation factor) that should be estimated. For this purpose, an inverse problem considering experimental data needs to be formulated and solved. In this context, the present contribution aims to formulate and solve two inverse anomalous diffusion problems considering a fractional hyperbolic advection-dispersion model to obtain the fractional order and the time relaxation tensor using real experimental data sets. To solve the direct problem the Finite Difference Method is extended for fractional context by using Grünwald-Letnikov Derivative. To solve each inverse problem, the Differential Evolution algorithm is considered as an optimization tool. The obtained results are compared with those found considering the simplification of the hyperbolic space-fractional model. In all analyzed cases, the DE algorithm was able to find good estimates for both parameters and it was demonstrated that the objective function considering the fractional hyperbolic advection-dispersion resulted in lower residual values.
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Stoop, R., and J. Parisi. "On the Scaling Function of Lyapunov Exponents for Intermittent Maps." Zeitschrift für Naturforschung A 48, no. 5-6 (1993): 641–42. http://dx.doi.org/10.1515/zna-1993-5-609.
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Abstract The scaling function of Lyapunov exponents for intermittent systems is full of particularities if compared with hyperbolic cases or the usual, nonhyperbolic, parabola. One particularity arises when this function is calculated from finite-time Lyapunov exponents: Different scaling properties with respect to the length of the finite-time chains emerge. As expected from random walk models, the scaling of an ensemble with non-Gaussian fluctuations evolves for certain values of the external parameter.
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Chоvniuk, Y., V. V. Kravchuk, A. Moskvitina, and I. Pefteva. "Use of the Method of Integral Relations for the Analytic Solutions of Hyperbolic Models of Thermal Conductivity." Ventilation, Illumination and Heat Gas Supply 38 (July 1, 2021): 6–16. http://dx.doi.org/10.32347/2409-2606.2021.38.6-16.
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The study of the processes of unsteady heat conduction, the calculation of the parameters of media under conditions of unsteady heat conduction of the latter is an important direction, which is used in applied problems of heat and mass transfer. When solving a mathematical model under various boundary conditions, there is a problem of the reliability of numerical calculations, therefore there is a need to solve the mathematical model by an analytical method. For example, a mathematical model of heat and mass transfer processes in a heat accumulator during its charging and discharging is solved analytically by the Green's function method, similarly, a mathematical model of heat carrier heating processes in solar collectors is solved. The specific definition of the Green's function corresponds to a specific problem in mathematical physics. Green's function contains complete information about the studied equation, and with its help one can construct a solution for any inhomogeneity. The development of the method of Green's functions for solving boundary value problems of unsteady heat conduction of generalized type on the basis of the Maxwell-Cattaneo-Lykov law is proposed. On the basis of the introduced Green's function of the differential equation, the Green's function of the boundary value problem is determined. Green's function of a boundary value problem is considered as an element of the set of Green's functions of an equation or a system of equations. Boundary conditions are formulated in accordance with the specified law. When considering specific problems, in a number of cases, it is expedient to transfer the integral form of writing boundary conditions of the second or third kind into a differential form equivalent to the integral one. The proposed integral relations for analytical solutions of boundary value problems of unsteady heat conduction for equations of hyperbolic type. Necessary and sufficient conditions for the existence and uniqueness of the Green's function of the boundary value problem are given and its analytical representation is given in terms of the fundamental system of solutions and boundary conditions. Boundary conditions are formulated for hyperbolic models of heat conduction in integral and differential forms. Boundary value problems for a semi-infinite region are considered, analytical solutions are obtained, their analysis is carried out, and temperature jumps at the heat wave front are calculated. Illustrative problems for a semi-infinite region are considered, and the heat wake region and the unperturbed region are described.
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Hossain, SK Safdar, Bamidele Victor Ayodele, Zaid Abdulhamid Alhulaybi, and Muhammad Mudassir Ahmad Alwi. "Data-Driven Approach to Modeling Biohydrogen Production from Biodiesel Production Waste: Effect of Activation Functions on Model Configurations." Applied Sciences 12, no. 24 (2022): 12914. http://dx.doi.org/10.3390/app122412914.
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Biodiesel production often results in the production of a significant amount of waste glycerol. Through various technological processes, waste glycerol can be sustainably utilized for the production of value-added products such as hydrogen. One such process used for waste glycerol conversion is the bioprocess, whereby thermophilic microorganisms are utilized. However, due to the complex mechanism of the bioprocess, it is uncertain how various input parameters are interrelated with biohydrogen production. In this study, a data-driven machine-learning approach is employed to model the prediction of biohydrogen from waste glycerol. Twelve configurations consisting of the multilayer perceptron neural network (MLPNN) and the radial basis function neural network (RBFNN) were investigated. The effect of using different combinations of activation functions such as hyperbolic tangent, identity, and sigmoid on the model’s performance was investigated. Moreover, the effect of two optimization algorithms, scaled conjugate gradient and gradient descent, on the model performance was also investigated. The performance analysis of the models revealed that the manner in which the activation functions are combined in the hidden and outer layers significantly influences the performance of various models. Similarly, the model performance was also influenced by the nature of the optimization algorithms. The MLPNN models displayed better predictive performance compared to the RBFNN models. The RBFNN model with softmax as the hidden layer activation function and identity as the outer layer activation function has the least predictive performance, as indicated by an R2 of 0.403 and a RMSE of 301.55. While the MLPNN configuration with the hyperbolic tangent as the hidden layer activation function and the sigmoid as the outer layer activation function yielded the best performance as indicated by an R2 of 0.978 and a RMSE of 9.91. The gradient descent optimization algorithm was observed to help improve the model’s performance. All the input variables significantly influence the predicted biohydrogen. However, waste glycerol has the most significant effects.
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Zhang, Xiaoming, Dongjie Tian, and Huiyong Wang. "Knowledge Graph Completion Based on Entity Descriptions in Hyperbolic Space." Applied Sciences 13, no. 1 (2022): 253. http://dx.doi.org/10.3390/app13010253.
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Hyperbolic space has received extensive attention because it can accurately and concisely represent hierarchical data. Currently, for knowledge graph completion tasks, the introduction of exogenous information of entities can enrich the knowledge representation of entities, but there is a problem that entities have different levels under different relations, and the embeddings of different entities in Euclidean space often requires high dimensional space to distinguish. Therefore, in order to solve the above problem, we propose a method that use entity descriptions to complete the knowledge graph in the Poincaré ball model of hyperbolic space. In this method, the text representation of entity descriptions is in Euclidean space and mapped to hyperbolic space through exponential map. Next, the triple embeddings are initialized in hyperbolic space, and the structured representation of the triple is trained by the hyperbolic model. Finally, the text representation and the structured representation of the entity are cross-fused in hyperbolic space, and then the balance factors are used to adjust the unbalanced energy function. Experimental results show that, compared with baseline models, the proposed method can improve the performance of knowledge graphs completion.
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Shamseldin, A. Y., A. E. Nasr, and K. M. O’Connor. "Comparison of different forms of the Multi-layer Feed-Forward Neural Network method used for river flow forecasting." Hydrology and Earth System Sciences 6, no. 4 (2002): 671–84. http://dx.doi.org/10.5194/hess-6-671-2002.
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Abstract. The Multi-Layer Feed-Forward Neural Network (MLFFNN) is applied in the context of river flow forecast combination, where a number of rainfall-runoff models are used simultaneously to produce an overall combined river flow forecast. The operation of the MLFFNN depends not only on its neuron configuration but also on the choice of neuron transfer function adopted, which is non-linear for the hidden and output layers. These models, each having a different structure to simulate the perceived mechanisms of the runoff process, utilise the information carrying capacity of the model calibration data in different ways. Hence, in a discharge forecast combination procedure, the discharge forecasts of each model provide a source of information different from that of the other models used in the combination. In the present work, the significance of the choice of the transfer function type in the overall performance of the MLFFNN, when used in the river flow forecast combination context, is investigated critically. Five neuron transfer functions are used in this investigation, namely, the logistic function, the bipolar function, the hyperbolic tangent function, the arctan function and the scaled arctan function. The results indicate that the logistic function yields the best model forecast combination performance. Keywords: River flow forecast combination, multi-layer feed-forward neural network, neuron transfer functions, rainfall-runoff models
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Shweta, Ambuj Kumar Mishra, and Umesh Kumar Sharma. "Traversable wormhole modelling with exponential and hyperbolic shape functions in F(R,T) framework." International Journal of Modern Physics A 35, no. 25 (2020): 2050149. http://dx.doi.org/10.1142/s0217751x20501493.
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The concept of traversable wormhole, a hypothetical tunnel-like structure is initially proposed by Morris and Thorne (Am. J. Phys. 56, 395 (1988)) by using Einstein’s general relativity theory. Harko et al. (Phys. Rev. D 84, 024020 (2011)) defined [Formula: see text] gravity as an extended gravitational theory having terms [Formula: see text] and [Formula: see text] as Ricci scalar and trace of energy momentum respectively. In this article, we explore wormhole models for the framework of [Formula: see text] gravity by using two different shape functions. The first shape function is [Formula: see text], [Formula: see text] (proposed by Mishra and Sharma, arXiv:2003.00298v1 , 2020) and second is a hyperbolic shape function which is of the form [Formula: see text]. Geometrical behavior of wormholes are discussed in anisotropic scenario by using equation of state [Formula: see text]. The stability of models are analyzed by using equilibrium condition and determining gravitational force, anisotropic force, hydrostatic force and force due to modified gravity. For the validation of null energy condition and weak energy condition, significant role of shape function is illustrated for the presence of nonexotic matter.
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Daghistani, Amira F., Ahmed M. T. Abd El-Bar, Ahmed M. Gemeay, Mahmoud A. E. Abdelrahman, and Samia Z. Hassan. "A Hyperbolic Secant-Squared Distribution via the Nonlinear Evolution Equation and Its Application." Mathematics 11, no. 20 (2023): 4270. http://dx.doi.org/10.3390/math11204270.
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In this article, we present a hyperbolic secant-squared distribution via the nonlinear evolution equation. Namely, for this equation, the probability density function of the hyperbolic secant-squared (HSS) distribution has been determined. The density of our model has a variety of shapes, including symmetric, left-skewed, and right-skewed. Eight distinct frequent list estimation methods have been proposed for estimating the parameters of our models. Additionally, these estimation techniques have been used to examine the behavior of the HSS model parameters using data sets that were generated randomly. To demonstrate how the findings may be used to model real data using the HSS distribution, we also use real data. Finally, the proposed justification can be applied to a variety of other complex physical models.
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Lu, Wenlian, Libin Rong, and Tianping Chen. "Global Convergence of Delayed Neural Network Systems." International Journal of Neural Systems 13, no. 03 (2003): 193–204. http://dx.doi.org/10.1142/s0129065703001534.
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In this paper, without assuming the boundedness, strict monotonicity and differentiability of the activation functions, we utilize a new Lyapunov function to analyze the global convergence of a class of neural networks models with time delays. A new sufficient condition guaranteeing the existence, uniqueness and global exponential stability of the equilibrium point is derived. This stability criterion imposes constraints on the feedback matrices independently of the delay parameters. The result is compared with some previous works. Furthermore, the condition may be less restrictive in the case that the activation functions are hyperbolic tangent.
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Arló-Costa, Horacio. "Models of preference reversals and personal rules: Do they require maximizing a utility function with a specific structure?" Behavioral and Brain Sciences 28, no. 5 (2005): 650–51. http://dx.doi.org/10.1017/s0140525x05220113.
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One of the reasons for adopting hyperbolic discounting is to explain preference reversals. Another is that this value structure suggests an elegant theory of the will. I examine the capacity of the theory to solve Newcomb's problem. In addition, I compare Ainslie's account with other procedural theories of choice that seem at least equally capable of accommodating reversals of preference.
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Almotairi, Sultan, Elsayed Badr, M. Elsisy, F. Farahat, and M. El Sayed. "Performance Analysis of Fully Intuitionistic Fuzzy Multi-Objective Multi-Item Solid Fractional Transportation Model." Fractal and Fractional 8, no. 7 (2024): 404. http://dx.doi.org/10.3390/fractalfract8070404.
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An investigation is conducted in this paper into a performance analysis of fully intuitionistic fuzzy multi-objective multi-item solid fractional transport model (FIF-MMSFTM). It is to be anticipated that the parameters of the conveyance model will be imprecise by virtue of numerous uncontrollable factors. The model under consideration incorporates intuitionistic fuzzy (IF) quantities of shipments, costs and profit coefficients, supplies, demands, and transport. The FIF-MMSFTM that has been devised is transformed into a linear form through a series of operations. The accuracy function and ordering relations of IF sets are then used to reduce the linearized model to a concise multi-objective multi-item solid transportation model (MMSTM). Furthermore, an examination is conducted on several theorems that illustrate the correlation between the FIF-MMSFTM and its corresponding crisp model, which is founded upon linear, hyperbolic, and parabolic membership functions. A numerical example was furnished to showcase the efficacy and feasibility of the suggested methodology. The numerical data acquired indicates that the linear, hyperbolic, and parabolic models require fewer computational resources to achieve the optimal solution. The parabolic model has the greatest number of iterations, in contrast to the hyperbolic model which has the fewest. Additionally, the elapsed run time for the three models is a negligible amount of time: 0.2, 0.15, and 1.37 s, respectively. In conclusion, suggestions for future research are provided.
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Heredia, Nathaly S., Karla Vizuete, Marco Flores-Calero, et al. "Comparative statistical analysis of the release kinetics models for nanoprecipitated drug delivery systems based on poly(lactic-co-glycolic acid)." PLOS ONE 17, no. 3 (2022): e0264825. http://dx.doi.org/10.1371/journal.pone.0264825.
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Poly(lactic-co-glycolic acid) is one of the most used polymers for drug delivery systems (DDSs). It shows excellent biocompatibility, biodegradability, and allows spatio-temporal control of the release of a drug by altering its chemistry. In spite of this, few formulations have reached the market. To characterize and optimize the drug release process, mathematical models offer a good alternative as they allow interpreting and predicting experimental findings, saving time and money. However, there is no general model that describes all types of drug release of polymeric DDSs. This study aims to perform a statistical comparison of several mathematical models commonly used in order to find which of them best describes the drug release profile from PLGA particles synthesized by nanoprecipitation method. For this purpose, 40 datasets extracted from scientific articles published since 2016 were collected. Each set was fitted by the models: order zero to fifth order polynomials, Korsmeyer-Peppas, Weibull and Hyperbolic Tangent Function. Some data sets had few observations that do not allow to apply statistic test, thus bootstrap resampling technique was performed. Statistic evidence showed that Hyperbolic Tangent Function model is the one that best fit most of the data.
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Asjad, Muhammad Imran, Naeem Ullah, Asma Taskeen, and Fahd Jarad. "Study of power law non-linearity in solitonic solutions using extended hyperbolic function method." AIMS Mathematics 7, no. 10 (2022): 18603–15. http://dx.doi.org/10.3934/math.20221023.
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<abstract><p>This paper retrieves the optical solitons to the Biswas-Arshed equation (BAE), which is examined with the lack of self-phase modulation by applying the extended hyperbolic function (EHF) method. Novel constructed solutions have the shape of bright, singular, periodic singular, and dark solitons. The achieved solutions have key applications in engineering and physics. These solutions define the wave performance of the governing models. The outcomes show that our scheme is very active and reliable. The acquired results are illustrated by 3-D and 2-D graphs to understand the real phenomena for such sort of non-linear models.</p></abstract>
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Nagasawa, Takumi, Kaito Iuchi, Ryo Takahashi, et al. "Blood Pressure Estimation by Photoplethysmogram Decomposition into Hyperbolic Secant Waves." Applied Sciences 12, no. 4 (2022): 1798. http://dx.doi.org/10.3390/app12041798.
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Photoplethysmographic (PPG) pulses contain information about cardiovascular parameters. In particular, blood pressure can be estimated using PPG pulse decomposition analysis, which assumes that a PPG pulse is composed of the original heart ejection blood wave and its reflections in arterial branchings. Among pulse decomposition wave functions that have been studied in the literature, Gaussian waves are the most successful ones. However, a more adequate pulse decomposition function could be found to improve blood pressure estimates. In this paper, we propose pulse decomposition analysis using hyperbolic secant (sech) waves and compare results with corresponding Gaussian wave decomposition. We analyze how the parameters of each of the two types of decomposition waves correlate with blood pressure. For this analysis, continuous blood pressure data and PPG data were acquired from ten healthy volunteers. The blood pressure of volunteers was varied by asking them to hold their breath for up to 60 s. The results suggested sech wave decomposition had higher accuracy in estimating blood pressure than the Gaussian function. Thus, sech wave decomposition should be considered as a more robust alternative to Gaussian wave pulse decomposition for blood pressure estimation models.
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Latuamury, Bokiraiya, Gun Mardiatmoko, and Agustinus Kastanya. "MASTER RECESSION CURVE VISUALIZATION USING SEVEN BASEFLOW RECESSION MODELS IN PAIRED WATERSHEDS." Jurnal Teknosains 14, no. 1 (2024): 1. https://doi.org/10.22146/teknosains.90705.
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River flow recession analysis plays a crucial role in understanding how watersheds release water during dry periods. Consequently, modeling baseflow recession is closely related to the characteristics of unconfined aquifers, storage behavior, and the discharge properties of the watershed. While several theories exist on modeling recession curves, limited research has compared different approaches regarding baseflow recession characteristics. This study aims to model seven baseflow recession equations in paired watersheds in Ambon City. The research methodology involves calibrating seven baseflow recession models using the Recession Curve (RC) 4.0 Hydro Office software. The tested models include Linear Reservoir, Exponential Reservoir, Double Exponential Horton, Dupuit-Boussinesq Aquifer Storage, Depression Storage, Turbulent Flow Model, and Hyperbolic Function Model. The calibration results yield optimal combinations of recession parameters. The parameterization order from highest to lowest is as follows: Depression Storage, followed by the Hyperbolic Function, Exponential Reservoir, Turbulent Flow Model, Double Exponential Horton, Linear Reservoir, and Dupuit-Boussinesq Aquifer Storage. Quantifying baseflow recession constants and coefficients is essential for understanding baseflow behavior. Visualizing the slope of the Recession Curve (MRC) reveals that models with high recession constants tend to have gradual MRCs, while low recession constants result in steep MRCs. The MRC slope further describes the relationship between storage conditions and discharge from the watershed. The advantage of creating MRCs from discontinuous recession segments lies in their ability to appropriately describe the MRC process and provide quantitative parameters relevant to drainage mechanisms. MRCs also serve as an optimal automated computational tool.
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Shakeel, Muhammad, Attaullah, Nehad Ali Shah, and Jae Dong Chung. "Modified Exp-Function Method to Find Exact Solutions of Microtubules Nonlinear Dynamics Models." Symmetry 15, no. 2 (2023): 360. http://dx.doi.org/10.3390/sym15020360.
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In this paper, we use the modified exp−ψθ-function method to observe some of the solitary wave solutions for the microtubules (MTs). By treating the issues as nonlinear model partial differential equations describing microtubules, we were able to solve the problem. We then found specific solutions to the nonlinear evolution equation (NLEE) covering various parameters that are particularly significant in biophysics and nanobiosciences. In addition to the soliton-like pulse solutions, we also find the rational, trigonometric, hyperbolic, and exponential function characteristic solutions for this equation. The validity of the method we developed and the fact that it provides more solutions are demonstrated by comparison to other methods. We next use the software Mathematica 10 to generate 2D, 3D, and contour plots of the precise findings we observed using the suggested technique and the proper parameter values.
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Korkmaz, Mustafa Ç., Christophe Chesneau, and Zehra Sedef Korkmaz. "On the Arcsecant Hyperbolic Normal Distribution. Properties, Quantile Regression Modeling and Applications." Symmetry 13, no. 1 (2021): 117. http://dx.doi.org/10.3390/sym13010117.
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This work proposes a new distribution defined on the unit interval. It is obtained by a novel transformation of a normal random variable involving the hyperbolic secant function and its inverse. The use of such a function in distribution theory has not received much attention in the literature, and may be of interest for theoretical and practical purposes. Basic statistical properties of the newly defined distribution are derived, including moments, skewness, kurtosis and order statistics. For the related model, the parametric estimation is examined through different methods. We assess the performance of the obtained estimates by two complementary simulation studies. Also, the quantile regression model based on the proposed distribution is introduced. Applications to three real datasets show that the proposed models are quite competitive in comparison to well-established models.
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ISAH, Muhammad Abubakar, and Asıf YOKUŞ. "Optical solitons of the complex Ginzburg-Landau equation having dual power nonlinear form using $\varphi^{6}$-model expansion approach." Mathematical Modelling and Numerical Simulation with Applications 3, no. 3 (2023): 188–215. http://dx.doi.org/10.53391/mmnsa.1337648.
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This paper employs a novel $\varphi ^{6}$-model expansion approach to get dark, bright, periodic, dark-bright, and singular soliton solutions to the complex Ginzburg-Landau equation with dual power-law non-linearity. The dual-power law found in photovoltaic materials is used to explain nonlinearity in the refractive index. The results of this paper may assist in comprehending some of the physical effects of various nonlinear physics models. For example, the hyperbolic sine arises in the calculation of the Roche limit and the gravitational potential of a cylinder, the hyperbolic tangent arises in the calculation of the magnetic moment and the rapidity of special relativity, and the hyperbolic cotangent arises in the Langevin function for magnetic polarization. Frequency values, one of the soliton's internal dynamics, are used to examine the behavior of the traveling wave. Finally, some of the obtained solitons' three-, two-dimensional, and contour graphs are plotted.
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Shi, Junzhe. "Hyperbolic-Tangent-Function-Modeled Transit Light Curve and Planet Radius Calculation." Theoretical and Natural Science 34, no. 1 (2024): 134–40. http://dx.doi.org/10.54254/2753-8818/34/20240704.
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This report presents a novel model that utilizes the transit method to calculate the ratios between stars and exoplanets. The WASP-12 system data, obtained from the Transiting Exoplanet Survey Satellite (TESS), is employed for analysis. The model, implemented in Python, incorporates the hyperbolic tangent function to process data, generate graphs, and determine the best-fit line. By leveraging the TESS Mission data, this model offers a potentially more precise approach to understanding exoplanets. The results reveal a radius ratio of 0.124 between the star and its companion exoplanet in the WASP-12 system, with a maximum uncertainty of 0.0965. To assess accuracy, comparisons are made with existing methodologies, and the report discusses the models limitations and potential for further development. Through these comparisons, the model demonstrates its efficacy in accurately estimating star-exoplanet ratios using the transit method. The findings open avenues for refining the model and expanding its applications within the field of exoplanet research. By improving our understanding of these ratios, we can deepen our knowledge of exoplanetary systems and their characteristics.
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Ogundunmade, Tayo P., and Adedayo A. Adepoju. "The Performance of Artificial Neural Network Using Heterogeneous Transfer Functions." International Journal of Data Science 2, no. 2 (2021): 92–103. http://dx.doi.org/10.18517/ijods.2.2.92-103.2021.
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Neural networks have been very important models across computer vision, natural language processing, speech and image recognition, aircraft safety and many more. It uses a variety of architectures that centres on the Multi-Layer Perceptron (MLP) which is the most commonly used type of Artificial Neural Network. MLP has been found to be good in terms of model precision in the usage of Homogenous Transfer/activation Functions (HTFs), especially with large data set. Based on the preliminary investigations of ranking of transfer functions by error variance (Udomboso, 2014), three HTFs are considered to perform better than other HTFs in prediction. These HTFs are the Hyperbolic Tangent Transfer functions (TANH), Hyperbolic Tangent Sigmoid Transfer function (TANSIG) and the Symmetric Saturating Linear Transfer Function (SSLTF). In this work, the performance of two Heterogeneous Transfer Functions (HETFs), which came as a result of the convolution of the three best HTFs, were compared with the performance of the three above listed HTFs. The hidden neurons used are 2, 5 and 10, while the sample sizes include 50, 100, 200, 500 and 1000. The data were divided into training sets of 90, 80 and 70 respectively.
 The results showed that the HETFs performed better in terms of the forecast using Mean Square Error (MSE), Mean Absolute Error (MAE) and Test Error as the forecast prediction criteria.
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Chesneau, Christophe. "A Collection of New Trigonometric- and Hyperbolic-FGM-Type Copulas." AppliedMath 3, no. 1 (2023): 147–74. http://dx.doi.org/10.3390/appliedmath3010010.
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Copula analysis was created to explain the dependence of two or more quantitative variables. Due to the need for in-depth data analysis involving complex variable relationships, there is always a need for new copula models with original features. As a modern example, for the analysis of circular or periodic data types, trigonometric copulas are particularly attractive and recommended. This is, however, an underexploited topic. In this article, we propose a new collection of eight trigonometric and hyperbolic copulas, four based on the sine function and the others on the tangent function, all derived from the construction of the famous Farlie–Gumbel–Morgenstern copula. In addition to their original trigonometric and hyperbolic functionalities, the proposed copulas have the feature of depending on three parameters with complementary roles: one is a dependence parameter; one is a shape parameter; and the last can be viewed as an angle parameter. In our main findings, for each of the eight copulas, we determine a wide range of admissible values for these parameters. Subsequently, the capabilities, features, and functions of the new copulas are thoroughly examined. The shapes of the main functions of some copulas are illustrated graphically. Theoretically, symmetry in general, stochastic dominance, quadrant dependence, tail dependence, Archimedean nature, correlation measures, and inference on the parameters are investigated. Some copula shapes are illustrated with the help of figures. On the other hand, some two-dimensional inequalities are established and may be of separate interest.
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Lu, Dianchen, and Jie Liu. "Application of the Homotopy Analysis Method for Solving the Variable Coefficient KdV-Burgers Equation." Abstract and Applied Analysis 2014 (2014): 1–4. http://dx.doi.org/10.1155/2014/309420.
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The homotopy analysis method is applied to solve the variable coefficient KdV-Burgers equation. With the aid of generalized elliptic method and Fourier’s transform method, the approximate solutions of double periodic form are obtained. These solutions may be degenerated into the approximate solutions of hyperbolic function form and the approximate solutions of trigonometric function form in the limit cases. The results indicate that this method is efficient for the nonlinear models with the dissipative terms and variable coefficients.
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Miah, Md Musa, Ali AlArjani, Abdur Rashid, Aminur Rahman Khan, Md Sharif Uddin, and El-Awady Attia. "Multi-objective optimization to the transportation problem considering non-linear fuzzy membership functions." AIMS Mathematics 8, no. 5 (2023): 10397–419. http://dx.doi.org/10.3934/math.2023527.
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<abstract> <p>Considering the uncertainty of transporting goods from numerous origins to diverse destinations is a critical task for the decision-maker (DM). The ultimate goal of the DM is to make the right decisions that optimize the profit or loss of the organization under the vagueness of the uncontrollable effects. In this paper, mathematical models are proposed using fuzzy non-linear membership functions for the transportation problem considering the parameters' uncertainty that can help the DM to optimize the multi-objective transportation problems (MOTP) and to achieve the desired goals by choosing a confidence level of the uncertain parameters. Based on DM's selection of the confidence level, a compromise solution of the uncertain multi-objective transportation (UMOTP) is obtained along with the satisfaction level in percent for the DM. Two non-linear fuzzy membership functions are considered: the exponential and the hyperbolic functions. Using both membership functions, the sensitivity analysis was implemented by considering different confidence levels. According to the experimental results, the hyperbolic membership function gives 100% DM's satisfaction in many instances. Moreover, it shows stability against the exponential and linear functions.</p> </abstract>
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Fu, Shuai, and Nicolas P. Avdelidis. "Novel Prognostic Methodology of Bootstrap Forest and Hyperbolic Tangent Boosted Neural Network for Aircraft System." Applied Sciences 14, no. 12 (2024): 5057. http://dx.doi.org/10.3390/app14125057.
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Complex aviation systems’ integrity deteriorates over time due to operational factors; hence, the ability to forecast component remaining useful life (RUL) is vital to their optimal operation. Data-driven prognostic models are essential for system RUL prediction. These models benefit run-to-failure datasets the most. Thus, significant factors that could affect systematic integrity must be examined to quantify the operational component of RUL. To expand predictive approaches, the authors of this research developed a novel method for calculating the RUL of a group of aircraft engines using the N-CMAPSS dataset, which provides simulated degradation trajectories under real flight conditions. They offered bootstrap trees and hyperbolic tangent NtanH(3)Boost(20) neural networks as prognostic alternatives. The hyperbolic tangent boosted neural network uses damage propagation modelling based on earlier research and adds two accuracy levels. The suggested neural network architecture activates with the hyperbolic tangent function. This extension links the deterioration process to its operating history, improving degradation modelling. During validation, models accurately predicted observed flight cycles with 95–97% accuracy. We can use this work to combine prognostic approaches to extend the lifespan of critical aircraft systems and assist maintenance approaches in reducing operational and environmental hazards, all while maintaining normal operation. The proposed methodology yields promising results, making it suitable for adoption due to its relevance to prognostic difficulties.