Next Issue
Volume 27, June
Previous Issue
Volume 27, February
 
 

Math. Comput. Appl., Volume 27, Issue 2 (April 2022) – 15 articles

Cover Story (view full-size image): We implemented stochastic recurrent neural networks (Boltzmann machines) for automated cell tracking in image sequences of growing bacterial populations to minimize task-specific costs. These new non-linear functionals were inferred from data, with key parameters determined numerically with an innovative algorithm. This approach enables good identification of cell divisions and efficient cell tracking in tightly packed cell populations, reaching cell registration accuracies ranging from 90% to 100% per frame when applied to images of E. Coli populations in microfluidic traps, as well as image sequences of simulated bacterial colonies. View this paper
  • Issues are regarded as officially published after their release is announced to the table of contents alert mailing list.
  • You may sign up for e-mail alerts to receive table of contents of newly released issues.
  • PDF is the official format for papers published in both, html and pdf forms. To view the papers in pdf format, click on the "PDF Full-text" link, and use the free Adobe Reader to open them.
Order results
Result details
Section
Select all
Export citation of selected articles as:
14 pages, 2177 KiB  
Article
On the Prediction of Evaporation in Arid Climate Using Machine Learning Model
Math. Comput. Appl. 2022, 27(2), 32; https://doi.org/10.3390/mca27020032 - 05 Apr 2022
Cited by 5 | Viewed by 2054
Abstract
Evaporation calculations are important for the proper management of hydrological resources, such as reservoirs, lakes, and rivers. Data-driven approaches, such as adaptive neuro fuzzy inference, are getting popular in many hydrological fields. This paper investigates the effective implementation of artificial intelligence on the [...] Read more.
Evaporation calculations are important for the proper management of hydrological resources, such as reservoirs, lakes, and rivers. Data-driven approaches, such as adaptive neuro fuzzy inference, are getting popular in many hydrological fields. This paper investigates the effective implementation of artificial intelligence on the prediction of evaporation for agricultural area. In particular, it presents the adaptive neuro fuzzy inference system (ANFIS) and hybridization of ANFIS with three optimizers, which include the genetic algorithm (GA), firefly algorithm (FFA), and particle swarm optimizer (PSO). Six different measured weather variables are taken for the proposed modelling approach, including the maximum, minimum, and average air temperature, sunshine hours, wind speed, and relative humidity of a given location. Models are separately calibrated with a total of 86 data points over an eight-year period, from 2010 to 2017, at the specified station, located in Arizona, United States of America. Farming lands and humid climates are the reason for choosing this location. Ten statistical indices are calculated to find the best fit model. Comparisons shows that ANFIS and ANFIS–PSO are slightly better than ANFIS–FFA and ANFIS–GA. Though the hybrid ANFIS–PSO (R2= 0.99, VAF = 98.85, RMSE = 9.73, SI = 0.05) is very close to the ANFIS (R2 = 0.99, VAF = 99.04, RMSE = 8.92, SI = 0.05) model, preference can be given to ANFIS, due to its simplicity and easy operation. Full article
(This article belongs to the Special Issue Computational Mathematics and Applied Statistics)
Show Figures

Figure 1

26 pages, 11381 KiB  
Article
Benchmarking Regridding Libraries Used in Earth System Modelling
Math. Comput. Appl. 2022, 27(2), 31; https://doi.org/10.3390/mca27020031 - 01 Apr 2022
Cited by 3 | Viewed by 2530
Abstract
Components of Earth system models (ESMs) usually use different numerical grids because of the different environments they represent. Therefore, a coupling field sent by a source model has to be regridded to be used by a target model. The regridding has to be [...] Read more.
Components of Earth system models (ESMs) usually use different numerical grids because of the different environments they represent. Therefore, a coupling field sent by a source model has to be regridded to be used by a target model. The regridding has to be accurate and, in some cases, conservative, in order to ensure the consistency of the coupled model. Here, we present work done to benchmark the quality of four regridding libraries currently used in ESMs, i.e., SCRIP, YAC, ESMF and XIOS. We evaluated five regridding algorithms with four different analytical functions for different combinations of six grids used in real ocean or atmosphere models. Four analytical functions were used to define the coupling fields to be regridded. This benchmark calculated some of the metrics proposed by the CANGA project, including the mean, maximum, RMS misfit, and global conservation. The results show that, besides a few very specific cases that present anomalous values, the regridding functionality in YAC, ESMF and XIOS can be considered of high quality and do not present the specific problems observed for the conservative SCRIP remapping. The evaluation of the computing performance of those libraries is not included in the current work but is planned to be performed in the coming months. This exercise shows that benchmarking can be a great opportunity to favour interactions between users and developers of regridding libraries. Full article
(This article belongs to the Special Issue Computational Methods for Coupled Problems in Science and Engineering)
Show Figures

Figure 1

13 pages, 1670 KiB  
Article
Nadarajah–Haghighi Lomax Distribution and Its Applications
Math. Comput. Appl. 2022, 27(2), 30; https://doi.org/10.3390/mca27020030 - 01 Apr 2022
Cited by 4 | Viewed by 2719
Abstract
Over the years, several researchers have worked to model phenomena in which the distribution of data presents more or less heavy tails. With this aim, several generalizations or extensions of the Lomax distribution have been proposed. In this paper, an attempt is made [...] Read more.
Over the years, several researchers have worked to model phenomena in which the distribution of data presents more or less heavy tails. With this aim, several generalizations or extensions of the Lomax distribution have been proposed. In this paper, an attempt is made to create a hybrid distribution mixing the functionalities of the Nadarajah–Haghighi and Lomax distributions, namely the Nadarajah–Haghighi Lomax (NHLx) distribution. It can also be thought of as an extension of the exponential Lomax distribution. The NHLx distribution has the features of having four parameters, a lower bounded support, and very flexible distributional functions, including a decreasing or unimodal probability density function and an increasing, decreasing, or upside-down bathtub hazard rate function. In addition, it benefits from the treatable statistical properties of moments and quantiles. The statistical applicability of the NHLx model is highlighted, with simulations carried out. Four real data sets are also used to illustrate the practical applications. In particular, results are compared with Lomax-based models of importance, such as the Lomax, Weibull Lomax, and exponential Lomax models, and it is observed that the NHLx model fits better. Full article
(This article belongs to the Special Issue Computational Mathematics and Applied Statistics)
Show Figures

Figure 1

25 pages, 51555 KiB  
Article
Applications of ANFIS-Type Methods in Simulation of Systems in Marine Environments
Math. Comput. Appl. 2022, 27(2), 29; https://doi.org/10.3390/mca27020029 - 21 Mar 2022
Cited by 3 | Viewed by 1877
Abstract
ANFIS-type algorithms have been used in various modeling and simulation problems. With the help of algorithms with more accuracy and adaptability, it is possible to obtain better real-life emulating models. A critical environmental problem is the discharge of saline industrial effluents in the [...] Read more.
ANFIS-type algorithms have been used in various modeling and simulation problems. With the help of algorithms with more accuracy and adaptability, it is possible to obtain better real-life emulating models. A critical environmental problem is the discharge of saline industrial effluents in the form of buoyant jets into water bodies. Given the potentially harmful effects of the discharge effluents from desalination plants on the marine environment and the coastal ecosystem, minimizing such an effect is crucial. Hence, it is important to design the outfall system properly to reduce these impacts. To the best of the authors’ knowledge, a study that formulates the effluent discharge to find an optimum numerical model under the conditions considered here using AI methods has not been completed before. In this study, submerged discharges, specifically, negatively buoyant jets are modeled. The objective of this study is to compare various artificial intelligence algorithms along with multivariate regression models to find the best fit model emulating effluent discharge and determine the model with less computational time. This is achieved by training and testing the Adaptive Neuro-Fuzzy Inference System (ANFIS), ANFIS-Genetic Algorithm (GA), ANFIS-Particle Swarm Optimization (PSO) and ANFIS-Firefly Algorithm (FFA) models with input parameters, which are obtained by using the realizable k-ε turbulence model, and simulated parameters, which are obtained after modeling the turbulent jet using the OpenFOAM simulation platform. A comparison of the realizable k-ε turbulence model outputs and AI algorithms’ outputs is conducted in this study. Statistical parameters such as least error, coefficient of determination (R2), Mean Absolute Error (MAE), and Average Absolute Deviation (AED) are measured to evaluate the performance of the models. In this work, it is found that ANFIS-PSO performs better compared to the other four models and the multivariate regression model. It is shown that this model provides better R2, MAE, and AED, however, the non-hybrid ANFIS model provides reasonably acceptable results with lower computational costs. The results of the study demonstrate an error of 6.908% as the best-case scenario in the AI models. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2021)
Show Figures

Figure 1

14 pages, 2635 KiB  
Article
In Vivo Validation of a Cardiovascular Simulation Model in Pigs
Math. Comput. Appl. 2022, 27(2), 28; https://doi.org/10.3390/mca27020028 - 18 Mar 2022
Cited by 2 | Viewed by 2019
Abstract
Many computer simulation models of the cardiovascular system, of varying complexity and objectives, have been proposed in physiological science. Every model needs to be parameterized and evaluated individually. We conducted a porcine animal model to parameterize and evaluate a computer simulation model, recently [...] Read more.
Many computer simulation models of the cardiovascular system, of varying complexity and objectives, have been proposed in physiological science. Every model needs to be parameterized and evaluated individually. We conducted a porcine animal model to parameterize and evaluate a computer simulation model, recently proposed by our group. The results of an animal model, on thirteen healthy pigs, were used to generate consistent parameterization data for the full heart computer simulation model. To evaluate the simulation model, differences between the resulting simulation output and original animal data were analysed. The input parameters of the animal model, used to individualize the computer simulation, showed high interindividual variability (range of coefficient of variation: 10.1–84.5%), which was well-reflected by the resulting haemodynamic output parameters of the simulation (range of coefficient of variation: 12.6–45.7%). The overall bias between the animal and simulation model was low (mean: −3.24%, range: from −26.5 to 20.1%). The simulation model used in this study was able to adapt to the high physiological variability in the animal model. Possible reasons for the remaining differences between the animal and simulation model might be a static measurement error, unconsidered inaccuracies within the model, or unconsidered physiological interactions. Full article
(This article belongs to the Collection Feature Papers in Mathematical and Computational Applications)
Show Figures

Figure 1

17 pages, 691 KiB  
Article
Theoretical and Computational Results of a Memory-Type Swelling Porous-Elastic System
Math. Comput. Appl. 2022, 27(2), 27; https://doi.org/10.3390/mca27020027 - 11 Mar 2022
Cited by 5 | Viewed by 1911
Abstract
In this paper, we consider a memory-type swelling porous-elastic system. First, we use the multiplier method to prove explicit and general decay results to solutions of the system with sufficient regularities. These decay results are established under a very general assumption on the [...] Read more.
In this paper, we consider a memory-type swelling porous-elastic system. First, we use the multiplier method to prove explicit and general decay results to solutions of the system with sufficient regularities. These decay results are established under a very general assumption on the relaxation function and for suitable given data. We also perform several numerical tests to illustrate our theoretical decay results. Our results generalize and improve many earlier results in the literature. Full article
Show Figures

Figure 1

16 pages, 3150 KiB  
Article
Image Segmentation with a Priori Conditions: Applications to Medical and Geophysical Imaging
Math. Comput. Appl. 2022, 27(2), 26; https://doi.org/10.3390/mca27020026 - 11 Mar 2022
Cited by 3 | Viewed by 2090
Abstract
In this paper, we propose a method for semi-supervised image segmentation based on geometric active contours. The main novelty of the proposed method is the initialization of the segmentation process, which is performed with a polynomial approximation of a user defined initialization (for [...] Read more.
In this paper, we propose a method for semi-supervised image segmentation based on geometric active contours. The main novelty of the proposed method is the initialization of the segmentation process, which is performed with a polynomial approximation of a user defined initialization (for instance, a set of points or a curve to be interpolated). This work is related to many potential applications: the geometric conditions can be useful to improve the quality the segmentation process in medicine and geophysics when it is required (weak contrast of the image, missing parts in the image, non-continuous contour…). We compare our method to other segmentation algorithms, and we give experimental results related to several medical and geophysical applications. Full article
(This article belongs to the Collection Feature Papers in Mathematical and Computational Applications)
Show Figures

Figure 1

15 pages, 1031 KiB  
Article
Soret & Dufour and Triple Stratification Effect on MHD Flow with Velocity Slip towards a Stretching Cylinder
Math. Comput. Appl. 2022, 27(2), 25; https://doi.org/10.3390/mca27020025 - 09 Mar 2022
Cited by 10 | Viewed by 1850
Abstract
The phenomenon of convective flow with heat and mass transfer has been studied extensively due to its applications in various fields. The effects of nonlinear thermal radiation (NLTR), slip, thermal-diffusion (Soret) and diffusion-thermo (Dufour) on magenoto-hydrodynamic (MHD) flow towards a stretching cylinder in [...] Read more.
The phenomenon of convective flow with heat and mass transfer has been studied extensively due to its applications in various fields. The effects of nonlinear thermal radiation (NLTR), slip, thermal-diffusion (Soret) and diffusion-thermo (Dufour) on magenoto-hydrodynamic (MHD) flow towards a stretching cylinder in the presence of triple stratification (TSF) are investigated in this paper. The governing equations are transformed into an ODE by suitable transformations. The homotopy analysis method (HAM) is used to solve the ODE. The revamping of fluid flow, and heat transfer due to the presence of the Soret and Dufour effect, concentration slip and concentration stratification are analyzed. The temperature and local Sherwood number increases as the Dufour number rises, whereas the local Nusselt number decreases. While elevating the Soret number, the Sherwood number diminishes, whereas the concentration profile rises. The thermal boundary layer thickness enhances when thermal radiation increases. The rate of solute transport reduces while the concentration slip increases. Full article
(This article belongs to the Special Issue Advances in Computational Fluid Dynamics and Heat & Mass Transfer)
Show Figures

Figure 1

18 pages, 1136 KiB  
Article
Evaluation of Machine Learning Algorithms for Early Diagnosis of Deep Venous Thrombosis
Math. Comput. Appl. 2022, 27(2), 24; https://doi.org/10.3390/mca27020024 - 04 Mar 2022
Cited by 4 | Viewed by 3879
Abstract
Deep venous thrombosis (DVT) is a disease that must be diagnosed quickly, as it can trigger the death of patients. Nowadays, one can find different ways to determine it, including clinical scoring, D-dimer, ultrasonography, etc. Recently, scientists have focused efforts on using machine [...] Read more.
Deep venous thrombosis (DVT) is a disease that must be diagnosed quickly, as it can trigger the death of patients. Nowadays, one can find different ways to determine it, including clinical scoring, D-dimer, ultrasonography, etc. Recently, scientists have focused efforts on using machine learning (ML) and neural networks for disease diagnosis, progressively increasing the accuracy and efficacy. Patients with suspected DVT have no apparent symptoms. Using pattern recognition techniques, aiding good timely diagnosis, as well as well-trained ML models help to make good decisions and validation. The aim of this paper is to propose several ML models for a more efficient and reliable DVT diagnosis through its implementation on an edge device for the development of instruments that are smart, portable, reliable, and cost-effective. The dataset was obtained from a state-of-the-art article. It is divided into 85% for training and cross-validation and 15% for testing. The input data in this study are the Wells criteria, the patient’s age, and the patient’s gender. The output data correspond to the patient’s diagnosis. This study includes the evaluation of several classifiers such as Decision Trees (DT), Extra Trees (ET), K-Nearest Neighbor (KNN), Multi-Layer Perceptron Neural Network (MLP-NN), Random Forest (RF), and Support Vector Machine (SVM). Finally, the implementation of these ML models on a high-performance embedded system is proposed to develop an intelligent system for early DVT diagnosis. It is reliable, portable, open source, and low cost. The performance of different ML algorithms was evaluated, where KNN achieved the highest accuracy of 90.4% and specificity of 80.66% implemented on personal computer (PC) and Raspberry Pi 4 (RPi4). The accuracy of all trained models on PC and Raspberry Pi 4 is greater than 85%, while the area under the curve (AUC) values are between 0.81 and 0.86. In conclusion, as compared to traditional methods, the best ML classifiers are effective at predicting DVT in an early and efficient manner. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2021)
Show Figures

Figure 1

18 pages, 580 KiB  
Article
Variable Decomposition for Large-Scale Constrained Optimization Problems Using a Grouping Genetic Algorithm
Math. Comput. Appl. 2022, 27(2), 23; https://doi.org/10.3390/mca27020023 - 03 Mar 2022
Cited by 2 | Viewed by 2083
Abstract
Several real optimization problems are very difficult, and their optimal solutions cannot be found with a traditional method. Moreover, for some of these problems, the large number of decision variables is a major contributing factor to their complexity; they are known as Large-Scale [...] Read more.
Several real optimization problems are very difficult, and their optimal solutions cannot be found with a traditional method. Moreover, for some of these problems, the large number of decision variables is a major contributing factor to their complexity; they are known as Large-Scale Optimization Problems, and various strategies have been proposed to deal with them. One of the most popular tools is called Cooperative Co-Evolution, which works through a decomposition of the decision variables into smaller subproblems or variables subgroups, which are optimized separately and cooperate to finally create a complete solution of the original problem. This kind of decomposition can be handled as a combinatorial optimization problem where we want to group variables that interact with each other. In this work, we propose a Grouping Genetic Algorithm to optimize the variable decomposition by reducing their interaction. Although the Cooperative Co-Evolution approach is widely used to deal with unconstrained optimization problems, there are few works related to constrained problems. Therefore, our experiments were performed on a test benchmark of 18 constrained functions under 100, 500, and 1000 variables. The results obtained indicate that a Grouping Genetic Algorithm is an appropriate tool to optimize the variable decomposition for Large-Scale Constrained Optimization Problems, outperforming the decomposition obtained by a state-of-the-art genetic algorithm. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2021)
Show Figures

Figure 1

35 pages, 2658 KiB  
Article
Stochastic Neural Networks for Automatic Cell Tracking in Microscopy Image Sequences of Bacterial Colonies
Math. Comput. Appl. 2022, 27(2), 22; https://doi.org/10.3390/mca27020022 - 02 Mar 2022
Cited by 2 | Viewed by 2827
Abstract
Our work targets automated analysis to quantify the growth dynamics of a population of bacilliform bacteria. We propose an innovative approach to frame-sequence tracking of deformable-cell motion by the automated minimization of a new, specific cost functional. This minimization is implemented by dedicated [...] Read more.
Our work targets automated analysis to quantify the growth dynamics of a population of bacilliform bacteria. We propose an innovative approach to frame-sequence tracking of deformable-cell motion by the automated minimization of a new, specific cost functional. This minimization is implemented by dedicated Boltzmann machines (stochastic recurrent neural networks). Automated detection of cell divisions is handled similarly by successive minimizations of two cost functions, alternating the identification of children pairs and parent identification. We validate the proposed automatic cell tracking algorithm using (i) recordings of simulated cell colonies that closely mimic the growth dynamics of E. coli in microfluidic traps and (ii) real data. On a batch of 1100 simulated image frames, cell registration accuracies per frame ranged from 94.5% to 100%, with a high average. Our initial tests using experimental image sequences (i.e., real data) of E. coli colonies also yield convincing results, with a registration accuracy ranging from 90% to 100%. Full article
(This article belongs to the Collection Feature Papers in Mathematical and Computational Applications)
Show Figures

Figure 1

20 pages, 28880 KiB  
Article
Attention Measurement of an Autism Spectrum Disorder User Using EEG Signals: A Case Study
Math. Comput. Appl. 2022, 27(2), 21; https://doi.org/10.3390/mca27020021 - 02 Mar 2022
Cited by 9 | Viewed by 5085
Abstract
Autism Spectrum Disorder (ASD) is a neurodevelopmental life condition characterized by problems with social interaction, low verbal and non-verbal communication skills, and repetitive and restricted behavior. People with ASD usually have variable attention levels because they have hypersensitivity and large amounts of environmental [...] Read more.
Autism Spectrum Disorder (ASD) is a neurodevelopmental life condition characterized by problems with social interaction, low verbal and non-verbal communication skills, and repetitive and restricted behavior. People with ASD usually have variable attention levels because they have hypersensitivity and large amounts of environmental information are a problem for them. Attention is a process that occurs at the cognitive level and allows us to orient ourselves towards relevant stimuli, ignoring those that are not, and act accordingly. This paper presents a methodology based on electroencephalographic (EEG) signals for attention measurement in a 13-year-old boy diagnosed with ASD. The EEG signals are acquired with an Epoc+ Brain–Computer Interface (BCI) via the Emotiv Pro platform while developing several learning activities and using Matlab 2019a for signal processing. For this article, we propose to use electrodes F3, F4, P7, and P8. Then, we calculate the band power spectrum density to detect the Theta Relative Power (TRP), Alpha Relative Power (ARP), Beta Relative Power (BRP), Theta–Beta Ratio (TBR), Theta–Alpha Ratio (TAR), and Theta/(Alpha+Beta), which are features related to attention detection and neurofeedback. We train and evaluate several machine learning (ML) models with these features. In this study, the multi-layer perceptron neural network model (MLP-NN) has the best performance, with an AUC of 0.9299, Cohen’s Kappa coefficient of 0.8597, Matthews correlation coefficient of 0.8602, and Hamming loss of 0.0701. These findings make it possible to develop better learning scenarios according to the person’s needs with ASD. Moreover, it makes it possible to obtain quantifiable information on their progress to reinforce the perception of the teacher or therapist. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2021)
Show Figures

Figure 1

19 pages, 1567 KiB  
Article
On Appearance of Fast or Late Self-Synchronization between Non-Ideal Sources Mounted on a Rectangular Plate Due to Time Delay
Math. Comput. Appl. 2022, 27(2), 20; https://doi.org/10.3390/mca27020020 - 24 Feb 2022
Cited by 1 | Viewed by 1874
Abstract
The present paper aims to present the effects of late switching on (time delay) between two or three DC electrical machines characterized by limited power supplies on their fast or late self-synchronization when mounted on a rectangular plate with simply supported edges. The [...] Read more.
The present paper aims to present the effects of late switching on (time delay) between two or three DC electrical machines characterized by limited power supplies on their fast or late self-synchronization when mounted on a rectangular plate with simply supported edges. The DC electrical machines are considered here as non-ideal oscillators, rotating in the same direction and acting as an external excitation on a specific surface of the plate. The stability analysis of the whole studied system (with two machines) around the obtained fixed point is done through analytical and numerical approaches by using the generalized Lyapunov and Routh-Hurwitz criterion. The existence conditions of the fixed point and the stability conditions are derived and presented. Great attention is put on the incidence of such study on the vibrations amplitude of the plate, which are considerably reduced in some cases. It appears that the time delay induces a rapid or late synchronization observed between the DC sources. This has been observed by numerically exploring the dynamics of the system for various possibilities that could occur. Moreover, in the modelling of the system, the positions on the plate occupied by DC electrical machines are taken into account by using the Heaviside function. It is shown that, in the case of three DC electrical machines, these positions influence the time to obtain a synchronous state between the DC electrical machines. Full article
Show Figures

Figure 1

15 pages, 896 KiB  
Article
Meshless Computational Strategy for Higher Order Strain Gradient Plate Models
Math. Comput. Appl. 2022, 27(2), 19; https://doi.org/10.3390/mca27020019 - 22 Feb 2022
Cited by 3 | Viewed by 2215
Abstract
The present research focuses on the use of a meshless method for the solution of nanoplates by considering strain gradient thin plate theory. Unlike the most common finite element method, meshless methods do not rely on a domain decomposition. In the present approach [...] Read more.
The present research focuses on the use of a meshless method for the solution of nanoplates by considering strain gradient thin plate theory. Unlike the most common finite element method, meshless methods do not rely on a domain decomposition. In the present approach approximating functions at collocation nodes are obtained by using radial basis functions which depend on shape parameters. The selection of such parameters can strongly influences the accuracy of the numerical technique. Therefore the authors are presenting some numerical benchmarks which involve the solution of nanoplates by employing an optimization approach for the evaluation of the undetermined shape parameters. Stability is discussed as well as numerical reliability against solutions taken for the existing literature. Full article
Show Figures

Figure 1

8 pages, 239 KiB  
Article
Equity Warrants Pricing Formula for Uncertain Financial Market
Math. Comput. Appl. 2022, 27(2), 18; https://doi.org/10.3390/mca27020018 - 22 Feb 2022
Viewed by 2303
Abstract
In this paper, inside the system of uncertainty theory, the valuation of equity warrants is explored. Different from the strategies of probability theory, the valuation problem of equity warrants is unraveled by utilizing the strategy of uncertain calculus. Based on the suspicion that [...] Read more.
In this paper, inside the system of uncertainty theory, the valuation of equity warrants is explored. Different from the strategies of probability theory, the valuation problem of equity warrants is unraveled by utilizing the strategy of uncertain calculus. Based on the suspicion that the firm price follows an uncertain differential equation, a valuation formula of equity warrants is proposed for an uncertain stock model. Full article
(This article belongs to the Topic Fractional Calculus: Theory and Applications)
Show Figures

Figure 1

Previous Issue
Next Issue
Back to TopTop