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Journal articles on the topic 'Fixed Exponential Kernel'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Jacob, Ashwin, Diptapriyo Majumdar, and Venkatesh Raman. "Expansion Lemma—Variations and Applications to Polynomial-Time Preprocessing." Algorithms 16, no. 3 (2023): 144. http://dx.doi.org/10.3390/a16030144.

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In parameterized complexity, it is well-known that a parameterized problem is fixed-parameter tractable if and only if it has a kernel—an instance equivalent to the input instance, whose size is just a function of the parameter. The size of the kernel can be exponential or worse, resulting in a quest for fixed-parameter tractable problems with polynomial-sized kernels. The developments in machinery (showing lower bounds for the sizes of the kernels) have led researchers to question what are the asymptotically optimum sizes for the kernels of fixed-parameter tractable problems. In this article,

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Tsuchida, Russell, Tim Pearce, Chris Van der Heide, Fred Roosta, and Marcus Gallagher. "Avoiding Kernel Fixed Points: Computing with ELU and GELU Infinite Networks." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 11 (2021): 9967–77. http://dx.doi.org/10.1609/aaai.v35i11.17197.

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Analysing and computing with Gaussian processes arising from infinitely wide neural networks has recently seen a resurgence in popularity. Despite this, many explicit covariance functions of networks with activation functions used in modern networks remain unknown. Furthermore, while the kernels of deep networks can be computed iteratively, theoretical understanding of deep kernels is lacking, particularly with respect to fixed-point dynamics. Firstly, we derive the covariance functions of multi-layer perceptrons (MLPs) with exponential linear units (ELU) and Gaussian error linear units (GELU)

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Nurpadilah, Winda, I. Made Sumertajaya, and Muhamad Nur Aidi. "Geographically Weighted Regression with Kernel Weighted Function on Poverty Cases in West Java Province." Indonesian Journal of Statistics and Its Applications 5, no. 1 (2021): 173–81. http://dx.doi.org/10.29244/ijsa.v5i1p173-181.

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Spatial regression analysis is a form of regression model that considers spatial effects. Geographically weighted regression (GWR) is the spatial regression methods that can be used to deal with the problem of spatial diversity. This method generates local model parameter estimates for each observation location. The application of spatial statistics can be done in all areas such as the problem of poverty. Poverty can be influenced by factors of proximity between regions, so that in determining the poverty factor, the proximity factor of the region cannot be ignored. West Java Province is a pro

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Rahmawati, Anis Dyah, Aji Hamim Wigena, and Muhammad Nur Aidi. "Influencing factors for the human development index in West Java using geographically and temporally weighted regression kernel functions." Jurnal Pendidikan Geografi: Kajian, Teori, dan Praktek dalam Bidang Pendidikan dan Ilmu Geografi 28, no. 2 (2023): 228. http://dx.doi.org/10.17977/um017v28i22023p228-241.

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Human Development Index (HDI) is a competitive index that serves as one of the crucial metrics for evaluating the effectiveness of enhancing the quality of human resources. HDI values from different areas can be compared. This study aims to spatially and temporally explore the HDI data from districts or cities in West Java and examine the factors that influence HDI in each of these districts or cities using the GTWR Great Circle Distance Fixed Kernels model. In this study, we used a combination of cross-sectional data from districts or cities in West Java and time series data with seven annual

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Azevedo, J. S., S. M. Afonso, and M. P. G. Silva. "Numerical Analysis of the Chebyshev Collocation Method for Functional Volterra Integral Equations." TEMA (São Carlos) 21, no. 3 (2020): 521. http://dx.doi.org/10.5540/tema.2020.021.03.521.

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The collocation method based on Chebyshev basis functions, coupled Picard iterative process, is proposed to solve a functional Volterra integral equation of the second kind. Using the Banach Fixed Point Theorem, we prove theorems on the existence and uniqueness solutions in the L2-norm. We also provide the convergence and stability analysis of the proposed method, which indicates that the numerical errors in the L2-norm decay exponentially, provided that the kernel function is sufficiently smooth. Numerical results are presented and they confirm the theoretical prediction of the exponential ra

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Azkiya, Azka Al, Yenni Angraini, and Rahma Anisa. "Penerapan Geographically Weighted Panel Regression dan Data Envelopment Analysis dalam Pemodelan Kemiskinan di Kalimantan Timur." Journal of Regional and Rural Development Planning 8, no. 1 (2024): 41–53. http://dx.doi.org/10.29244/jp2wd.2024.8.1.41-53.

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Indonesia currently still needs to focus on achieving sustainable development goals agreed by all countries in the world. Indonesia presently ranks 82nd out of 163 nations in terms of SDG accomplishment, indicating that there is still plenty of potential for improvement. One of the goals that hasn't been accomplished is ‘no poverty’. Regarding the poverty cases, among all province in Indonesia, East Kalimantan is important to be analyzed, because Penajam Paser Utara and Kutai Kartanegara in East Kalimantan are scheduled to become Indonesia's next capital, Nusantara. The goal of this research i

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Martha, Shantika, Yundari Yundari, Setyo Wira Rizki, and Ray Tamtama. "PENERAPAN METODE GEOGRAPHICALLY WEIGHTED PANEL REGRESSION (GWPR) PADA KASUS KEMISKINAN DI INDONESIA." BAREKENG: Jurnal Ilmu Matematika dan Terapan 15, no. 2 (2021): 241–48. http://dx.doi.org/10.30598/barekengvol15iss2pp241-248.

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To analyze the factor affecting poverty during several periods by considering some geographical factors, we can use a geographically weighted panel regression (GWPR) method. GWPR is a combination of the geographically weighted regression (GWR) model and the panel regression model. The research conducts to identify the factors affecting the percentage of poor people in 34 provinces in Indonesia during 2015-2019. The results show that a suitable GWPR model is a fixed-effect model (FEM) with an exponential adaptive kernel function. Referring to the model, the province is divided into four groups

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Dokuyucu, Mustafa, and Hemen Dutta. "Analysis of a fractional tumor-immune interaction model with exponential kernel." Filomat 35, no. 6 (2021): 2023–42. http://dx.doi.org/10.2298/fil2106023d.

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In this paper, a tumor-immune interaction model has been analyzed via Caputo-Fabrizio fractional derivative operator with exponential kernel. Existence of solution of the model has been established with a fixed-point method and then it demonstrated the uniqueness of solution also. The stability of the model has been analyzed with the help of Hyers-Ulam stability approach and then numerical solution by using the Adam-Basford method. The results are further examined in detail with simulations for different fractional derivative values.

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Munteanu, Ionuţ. "Feedback exponential stabilization of the semilinear heat equation with nonlocal initial conditions." Nonlinear Analysis: Modelling and Control 26, no. 6 (2021): 1106–22. http://dx.doi.org/10.15388/namc.2021.26.24809.

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The present paper is devoted to the problem of stabilization of the one-dimensional semilinear heat equation with nonlocal initial conditions. The control is with boundary actuation. It is linear, of finite-dimensional structure, given in an explicit form. It allows to write the corresponding solution of the closed-loop equation in a mild formulation via a kernel, then to apply a fixed point argument in a convenient space.

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Swetha, Stanislaus Jasmin, Velusamy Kavitha, Mani Mallika Arjunan, and Dumitru Baleanu. "ON THE INITIAL VALUE PROBLEMS FOR NEUTRAL INTEGRO-DIFFERENTIAL SYSTEM WITHIN EXPONENTIAL KERNEL." Annals of the Academy of Romanian Scientists Series on Mathematics and Its Application 16, no. 1 (2024): 5–23. http://dx.doi.org/10.56082/annalsarscimath.2024.1.5.

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This paper deals with the existence results for neutral integro-differential system (NIDS) through Caputo-Fabrizio (CF) operator. The solution to our addressing system, which can be considered innovative, is explained and proven in preliminary section. Certain novel existence findings are shown using fixed point approaches. Finally, two numerical examples are provided in the work to demonstrate the application of our theoretical findings.

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Omaba, McSylvester Ejighikeme, Soh Edwin Mukiawa, and Eze R. Nwaeze. "On Implicit Time–Fractal–Fractional Differential Equation." Axioms 11, no. 7 (2022): 348. http://dx.doi.org/10.3390/axioms11070348.

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An implicit time–fractal–fractional differential equation involving the Atangana’s fractal–fractional derivative in the sense of Caputo with the Mittag–Leffler law type kernel is studied. Using the Banach fixed point theorem, the well-posedness of the solution is proved. We show that the solution exhibits an exponential growth bound, and, consequently, the long-time (asymptotic) property of the solution. We also give examples to illustrate our problem.

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Raad, Sameeha A., and Mohammed A. Abdou. "An Algorithm for the Solution of Integro-Fractional Differential Equations with a Generalized Symmetric Singular Kernel." Fractal and Fractional 8, no. 11 (2024): 644. http://dx.doi.org/10.3390/fractalfract8110644.

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This work studies an integro-fractional differential equation (I-FrDE) with a generalized symmetric singular kernel. The scientific approach in this study was to transform the integro-differential equation (I-DE) into a mixed integral equation (MIE) with an Able kernel in fractional time and a generalized symmetric singular kernel in position. Additionally, the authors first set conditions on the singular kernels, whether related to time or position, and then transform the integral equation into an integral operator. Secondly, the solution is unique, which is proven by means of fixed-point the

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Zhao, Kaihong. "Stability of a Nonlinear Fractional Langevin System with Nonsingular Exponential Kernel and Delay Control." Discrete Dynamics in Nature and Society 2022 (November 3, 2022): 1–16. http://dx.doi.org/10.1155/2022/9169185.

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Fractional Langevin system has great advantages in describing the random motion of Brownian particles in complex viscous fluid. This manuscript deals with a delayed nonlinear fractional Langevin system with nonsingular exponential kernel. Based on the fixed point theory, some sufficient criteria for the existence and uniqueness of solution are established. We also prove that this system is UH- and UHR-stable attributed to the nonlinear analysis and inequality techniques. As applications, we provide some examples and simulations to illustrate the availability of main findings.

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Raihani, Risti, Sifriyani Sifriyani, and Surya Prangga. "Geographically Weighted Panel Regression Modelling of Dengue Hemorrhagic Fever Data Using Exponential Kernel Function." JTAM (Jurnal Teori dan Aplikasi Matematika) 7, no. 4 (2023): 961. http://dx.doi.org/10.31764/jtam.v7i4.16235.

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Geographically Weighted Panel Regression (GWPR) model is a panel regression model applied to spatial data. This research takes the Fixed Effect Model (FEM) panel regression as the global model and GWPR as the local model for dengue hemorrhagic fever (DHF) in East Kalimantan Province data over the years 2018-2020. DHF is a disease that has the potential to become an extraordinary event which is accompanied by death. In comparison to Indonesia, East Kalimantan Province's DHF Incident Rate (IR) was high in 2020. East Kalimantan's IR is 60.6 per 100,000 population, compared to Indonesia's IR of 40

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15

Hoang, Van Ha. "Estimating the division kernel of a size-structured population." ESAIM: Probability and Statistics 21 (2017): 275–302. http://dx.doi.org/10.1051/ps/2017011.

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We consider a size-structured model describing a population of cells proliferating by division. Each cell contain a quantity of toxicity which grows linearly according to a constant growth rate α. At division, the cells divide at a constant rate R and share their content between the two daughter cells into fractions Γ and 1 − Γ where Γ has a symmetric density h on [ 0,1 ], since the daughter cells are exchangeable. We describe the cell population by a random measure and observe the cells on the time interval [ 0,T ] with fixed T. We address here the problem of estimating the division kernel h

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Aljoudi, Shorog. "Existence and uniqueness results for coupled system of fractional differential equations with exponential kernel derivatives." AIMS Mathematics 8, no. 1 (2022): 590–606. http://dx.doi.org/10.3934/math.2023027.

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<abstract><p>In the framework of Caputo–Fabrizio derivatives, we study a new coupled system of fractional differential equations of higher orders supplemented with coupled nonlocal boundary conditions. The existence and uniqueness results of the solutions are proved. We consider the classical fixed–point theories due to Banach and Krasnoselskii for the main results. An example illustrating the main results is introduced.</p></abstract>

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Supianti, Filo. "Poverty Modeling in Indonesia using Geographically and Temporally Weighted Regression (GTWR)." Journal of Statistics and Data Science 2, no. 2 (2024): 62–69. https://doi.org/10.33369/jsds.v2i2.32644.

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Poverty is a big problem that must be resolved by the government and the people of Indonesia. Various programs are designed and implemented to alleviate poverty in Indonesia. Research is needed to find out what factors influence the problem of poverty. One statistical method that can be used to analyze this effect is the geographically and temporally weighted regression (GTWR) method. This method combines the effects of spatial and time simultaneously. The formation of the model begins with determining the weighting matrix. In determining the weighting matrix, a fixed kernel function is used w

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Suryani, Indah, Hasbi Yasin, and Puspita Kartikasari. "PEMODELAN JUMLAH KASUS DEMAM BERDARAH DENGUE (DBD) DI JAWA TENGAH DENGAN GEOGRAPHICALLY WEIGHTED NEGATIVE BINOMIAL REGRESSION (GWNBR)." Jurnal Gaussian 10, no. 1 (2021): 136–48. http://dx.doi.org/10.14710/j.gauss.v10i1.29400.

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Dengue Hemorrhagic Fever (DHF) is one of the diseases with unsual occurrence in Central Java and spread throughout the regency/city. The number sufferers of this disease is still high because the mortality rate is still above the national target. Regarding the less handling of DHF spread, it is necessary to make a plan by identify the factors that allegedly affect that case. Characteristics of data the DHF cases is count data, so this research is carried out using poisson regression. If in poisson regression there is overdispersion, it can be overcome using negative binomial regression. Meanwh

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Warsito, Budi, Hasbi Yasin, Dwi Ispriyanti, and Arief Rachman Hakim. "The Step Construction of Geographically Weighted Panel Regression in Air Polluter Standard Index (APSI) Data." E3S Web of Conferences 73 (2018): 12006. http://dx.doi.org/10.1051/e3sconf/20187312006.

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Geographically Weighted Panel Regression or GWPR is a local linear regression model that combines GWR model and panel data regression model with considering spatial effect, especially spatial heterogeneity problem. This article is focused on the soft computation of GWPR model using Fixed Effect Model (FEM). Parameter estimation in GWPR is obtain by Weighted Least Squares (WLS) methods and the resulting model for each location will be different from one to another. This study will compare the fixed-effect GWPR model with several weighting functions. The best model is determined based on the big

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Rahayu, Latifah, Elvitra Mutia Ulfa, Novi Reandy Sasmita, et al. "Unraveling Geospatial Determinants: Robust Geographically Weighted Regression Analysis of Maternal Mortality in Indonesia." Infolitika Journal of Data Science 1, no. 2 (2023): 73–81. http://dx.doi.org/10.60084/ijds.v1i2.133.

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Maternal Mortality Rate (MMR) in Indonesia has experienced a concerning annual increase, reaching 4,627 deaths in 2020 compared to 4,221 in 2019. This upward trajectory underscores the urgency of investigating the factors contributing to MMR. Recognizing the spatial heterogeneity and outliers in the data, our study employs the Robust Geographically Weighted Regression (RGWR) method with the Least Absolute Deviation approach. Using secondary data from the 2020 Indonesian Health Profile publication, the research seeks to establish province-specific models for MMR in 2020 and identify the key inf

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Primasari, Riszki Bella, Agus Rusgiyono, and Dwi Ispriyanti. "PEMODELAN MIXED GEOGRAPHICALLY WEIGHTED REGRESSION (MGWR) DENGAN JARAK EUCLIDEAN DAN JARAK MANHATTAN (STUDI KASUS : KEMATIAN BAYI NEONATAL DI JAWA TENGAH TAHUN 2018-2020)." Jurnal Gaussian 11, no. 4 (2023): 478–87. http://dx.doi.org/10.14710/j.gauss.11.4.478-487.

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Neonatal is a condition of babies from birth to 28 days. Data on Indonesia's health profile in 2020 showed that 72% of the number of deaths of toddlers occurred during the neonatal period and Central Java became the highest province of cases. Factors that are suspected to influence are the number of low birth weight babies (X1), the number of obstetric complications (X2), the number of Puskesmas (X3), the number of Posyandu (X4), the number of exclusive breastfeeding babies 0-6 months (X5), the number of pediatricians (X6), the number of ambulance cars (X7). Linear regression modeling on the n

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Khan, Asif, Tayyaba Akram, Arshad Khan, Shabir Ahmad, and Kamsing Nonlaopon. "Investigation of time fractional nonlinear KdV-Burgers equation under fractional operators with nonsingular kernels." AIMS Mathematics 8, no. 1 (2022): 1251–68. http://dx.doi.org/10.3934/math.2023063.

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<abstract><p>In this manuscript, the Korteweg-de Vries-Burgers (KdV-Burgers) partial differential equation (PDE) is investigated under nonlocal operators with the Mittag-Leffler kernel and the exponential decay kernel. For both fractional operators, the existence of the solution of the KdV-Burgers PDE is demonstrated through fixed point theorems of $ \alpha $-type $ \digamma $ contraction. The modified double Laplace transform is utilized to compute a series solution that leads to the exact values when fractional order equals unity. The effectiveness and reliability of the suggeste

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Zhang, Chang, Yuchen Zhang, and Fulin Li. "Feature Extraction of Sequence of Keystrokes in Fixed Text Using the Multivariate Hawkes Process." Mathematical Problems in Engineering 2021 (May 24, 2021): 1–16. http://dx.doi.org/10.1155/2021/6648726.

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In this paper, we propose a new method of extracting the features of keystrokes. The Hawkes process based on exponential excitation kernel was used to model the sequence of keystrokes in fixed text, and the intensity function vector and adjacency matrix of the model obtained through training were regarded as the characteristics of the keystrokes. A visual analysis was carried out on the CMU keystroke raw data and the feature data extracted using the proposed method. We used one-class classifier to compare the classification effect of CMU keystroke raw data and the feature data extracted by the

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Meutuah, Yasin, and Maruddani. "PEMODELAN FIXED EFFECT GEOGRAPHICALLY WEIGHTED PANEL REGRESSION UNTUK INDEKS PEMBANGUNAN MANUSIA DI JAWA TENGAH." Jurnal Gaussian 6, no. 2 (2017): 241–50. https://doi.org/10.5281/zenodo.1065051.

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Human development index is an indicator for assessing the quality of human resources and  measure the results of human development. The achievements of the human development index is not enough if conducting observations in each cities in just one particular time, but the observations  need to be made in some period of time. The distribution in each cities is also a concern, because the conditions are so diverse that led to their spatial effects. Therefore, it is necessary to study these variables in some time periods that affect human development index taking into acc

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Saber, Sayed, Brahim Dridi, Abdullah Alahmari, and Mohammed Messaoudi. "Hyers-Ulam Stability and Control of Fractional Glucose-Insulin Systems." European Journal of Pure and Applied Mathematics 18, no. 2 (2025): 6152. https://doi.org/10.29020/nybg.ejpam.v18i2.6152.

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This paper presents a novel fractional-order model for glucose-insulin dynamics using the Caputo-Fabrizio (CF) derivative, which accounts for memory effects through its nonsingular exponential kernel. Existence and uniqueness of the solution are established via fixed point theory, and infinite series solutions are obtained using the Sumudu transform. Hyers-Ulam stability is analyzed to assess the system’s robustness against perturbations. A linear control strategy is introduced to regulate glucose levels, demonstrating potential for integration with real-time insulin delivery systems. Compared

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CAMPOLIETI, G., R. MAKAROV, and K. WOUTERLOOT. "PRICING STEP OPTIONS UNDER THE CEV AND OTHER SOLVABLE DIFFUSION MODELS." International Journal of Theoretical and Applied Finance 16, no. 05 (2013): 1350027. http://dx.doi.org/10.1142/s0219024913500271.

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We consider a special family of occupation-time derivatives, namely proportional step options introduced by [18]. We develop new closed-form spectral expansions for pricing such options under a class of nonlinear volatility diffusion processes which includes the constant-elasticity-of-variance (CEV) model as an example. In particular, we derive a general analytically exact expression for the resolvent kernel (i.e. Green's function) of such processes with killing at an exponential stopping time (independent of the process) of occupation above or below a fixed level. Moreover, we succeed in Lapl

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Amelia Fadila Rahman, Syafriandi Syafriandi, Nonong Amalita, and Zilrahmi. "Geographically Weighted Panel Regression Modeling on Human Development Index in West Sumatra." UNP Journal of Statistics and Data Science 1, no. 3 (2023): 232–39. http://dx.doi.org/10.24036/ujsds/vol1-iss3/63.

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The Human Development Index (HDI) is an important issue that has a negative impact on the field of human development and people's welfare in West Sumatra Province. An effort to overcome the problem of the HDI is to identify the influencing factors. A method that can be used to identify influencing factors and explain the influence of characteristic areas of observation is Geographically Weighted Panel Regression (GWPR). GWPR is a combination of panel data regression method with GWR which is used when the data has the influence of spatial heterogeneity. The purpose of this study is to form a GW

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Aychluh, Mulualem. "Application of a fast Fibonacci wavelet method for the fractional cryosphere model." Mathematical Modelling and Numerical Simulation with Applications 5, no. 2 (2025): 257–79. https://doi.org/10.53391/mmnsa.1529457.

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This paper presents an efficient numerical approach for approximating the fractional-order cryosphere model using a Caputo-Fabrizio derivative with a non-singular exponential decay kernel. We develop a Fibonacci wavelet-based collocation method to solve the system, transforming the governing equations into nonlinear algebraic equations via operational matrix integration. The resulting system is solved using the Newton-Raphson method. We establish the existence and uniqueness of solutions through the Banach fixed-point theorem and Picard operator theory, and provide a comprehensive convergence

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Yu, Yajuan, Zhenhua Gu, Min Shi, and Feng Wang. "Fractional-Order Tabu Learning Neuron Models and Their Dynamics." Fractal and Fractional 8, no. 7 (2024): 428. http://dx.doi.org/10.3390/fractalfract8070428.

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In this paper, by replacing the exponential memory kernel function of a tabu learning single-neuron model with the power-law memory kernel function, a novel Caputo’s fractional-order tabu learning single-neuron model and a network of two interacting fractional-order tabu learning neurons are constructed firstly. Different from the integer-order tabu learning model, the order of the fractional-order derivative is used to measure the neuron’s memory decay rate and then the stabilities of the models are evaluated by the eigenvalues of the Jacobian matrix at the equilibrium point of the fractional

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Gupta, Hoshin V., Mohammad Reza Ehsani, Tirthankar Roy, Maria A. Sans-Fuentes, Uwe Ehret, and Ali Behrangi. "Computing Accurate Probabilistic Estimates of One-D Entropy from Equiprobable Random Samples." Entropy 23, no. 6 (2021): 740. http://dx.doi.org/10.3390/e23060740.

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We develop a simple Quantile Spacing (QS) method for accurate probabilistic estimation of one-dimensional entropy from equiprobable random samples, and compare it with the popular Bin-Counting (BC) and Kernel Density (KD) methods. In contrast to BC, which uses equal-width bins with varying probability mass, the QS method uses estimates of the quantiles that divide the support of the data generating probability density function (pdf) into equal-probability-mass intervals. And, whereas BC and KD each require optimal tuning of a hyper-parameter whose value varies with sample size and shape of the

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Sihombing, Pardomuan Robinson. "Pendekatan Model Nonparametrik untuk Memodelkan Hubungan Antara Jumlah Uang Beredar dan Indeks Harga Konsumen di Indonesia Tahun 1969-2017." Indonesian Journal of Applied Statistics 3, no. 1 (2020): 24. http://dx.doi.org/10.13057/ijas.v3i1.41093.

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<p class="Abstract-Title">Inflation is one of the macroeconomic variables of concern to the government in addition to economic growth, unemployment and poverty. Inflation is measured by the Consumer Price Index (CPI). According to the quantity theory of the classics, argues that the price level is determined by the amount of money in circulation, prices will rise if there is an increase in the money supply, assuming the amount of goods offered is fixed, while the amount of money is doubled, sooner or later the price will doubled. Often the relationship between macroeconomic variables is

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Razi, Nausheen, Ambreen Bano, Umar Ishtiaq, Tayyab Kamran, Mubariz Garayev, and Ioan-Lucian Popa. "Probing Malware Propagation Model with Variable Infection Rates Under Integer, Fractional, and Fractal–Fractional Orders." Fractal and Fractional 9, no. 2 (2025): 90. https://doi.org/10.3390/fractalfract9020090.

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Malware software has become a pervasive threat in computer and mobile technology attacks. Attackers use this software to obtain information about users of the digital world to obtain benefits by hijacking their data. Antivirus software has been developed to prevent the propagation of malware, but this problem is not yet under control. To develop this software, we have to check the propagation of malware. In this paper, we explore an advanced malware propagation model with a time-delay factor and a variable infection rate. To better understand this model, we use fractal–fractional theory. We us

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Sun, Zhenglong, Chuanlin Liu, and Siyuan Peng. "Maximum Correntropy with Variable Center Unscented Kalman Filter for Robust Power System State Estimation." Entropy 24, no. 4 (2022): 516. http://dx.doi.org/10.3390/e24040516.

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The robust Kalman filter with correntropy loss has received much attention in recent years for forecasting-aided state estimation in power systems, since it efficiently reduces the negative influence of various abnormal situations, such as non-Gaussian communication, changing environment, and instrument failures, and obviously improves the stability of power systems. However, the existing correntropy-based robust Kalman filters usually use the Gaussian function with a fixed center as the kernel function in correntropy, which may not be a suitable choice in practical applications of power syste

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Chini, Peter, Roland Meyer, and Prakash Saivasan. "Fine-Grained Complexity of Safety Verification." Journal of Automated Reasoning 64, no. 7 (2020): 1419–44. http://dx.doi.org/10.1007/s10817-020-09572-x.

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Abstract We study the fine-grained complexity of Leader Contributor Reachability ($${\textsf {LCR}} $$ LCR ) and Bounded-Stage Reachability ($${\textsf {BSR}} $$ BSR ), two variants of the safety verification problem for shared memory concurrent programs. For both problems, the memory is a single variable over a finite data domain. Our contributions are new verification algorithms and lower bounds. The latter are based on the Exponential Time Hypothesis ($${\textsf {ETH}} $$ ETH ), the problem $${\textsf {Set~Cover}} $$ Set Cover , and cross-compositions. $${\textsf {LCR}} $$ LCR is the questi

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Gutin, Gregory, Magnus Wahlström, and Meirav Zehavi. "r -Simple k -Path and Related Problems Parameterized by k / r." ACM Transactions on Algorithms 17, no. 1 (2021): 1–64. http://dx.doi.org/10.1145/3439721.

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Abasi et al. (2014) introduced the following two problems. In the r -S imple k -P ath problem, given a digraph G on n vertices and positive integers r , k , decide whether G has an r -simple k -path, which is a walk where every vertex occurs at most r times and the total number of vertex occurrences is k . In the ( r , k )-M onomial D etection problem, given an arithmetic circuit that succinctly encodes some polynomial P on n variables and positive integers k , r , decide whether P has a monomial of total degree k where the degree of each variable is at most r . Abasi et al. obtained randomize

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Haq, Ihtisham Ul, Nigar Ali, and Hijaz Ahmad. "Analysis of a chaotic system using fractal-fractional derivatives with exponential decay type kernels." Mathematical Modelling and Control 2, no. 4 (2022): 185–99. http://dx.doi.org/10.3934/mmc.2022019.

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<abstract><p>In this article, we introduce and analyze a novel fractal-fractional chaotic system. We extended the memristor-based chaotic system to the fractal-fractional mathematical model using Atangana-Baleanu–Caputo and Caputo-Fabrizio types of derivatives with exponential decay type kernels. We established the uniqueness and existence of the solution through Banach's fixed theory and Schauder's fixed point. We used some new numerical methods to derive the solution of the considered model and study the dynamical behavior using these operators. The numerical simulation results p

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Durdiev, Durdimurod Kalandarovich, Hilola B. Elmuradova, and Askar Akhmadovich Rakhmonov. "Inverse kernel determination problem for a class of pseudo-parabolic integro-differential equations." Вестник Самарского государственного технического университета. Серия «Физико-математические науки» 29, no. 1 (2025): 7–20. https://doi.org/10.14498/vsgtu2095.

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This study investigates an inverse problem involving the determination of the kernel function in a multidimensional integrodifferential pseudo-parabolic equation of the third order. The study begins with an analysis of the direct problem, where we examine an initial-boundary value problem with homogeneous boundary conditions for a known kernel. Employing the Fourier method, we construct the solution as a series expansion in terms of eigenfunctions of the Laplace operator with Dirichlet boundary conditions. A crucial component of our analysis involves deriving a priori estimates for the series

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Lovalenti, Phillip M., and John F. Brady. "The force on a sphere in a uniform flow with small-amplitude oscillations at finite Reynolds number." Journal of Fluid Mechanics 256 (November 1993): 607–14. http://dx.doi.org/10.1017/s0022112093002897.

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The unsteady force acting on a sphere that is held fixed in a steady uniform flow with small-amplitude oscillations is evaluated to O(Re) for small Reynolds number Re. Good agreement is shown with the numerical results of Mei, Lawrence & Adrian (1991) up to Re ≈ 0.5. The analytical result is transformed by Fourier inversion to allow for an arbitrary time-dependent motion which is small relative to the steady uniform flow. This yields a history-dependent force which has an integration kernel that decays exponentially for large time.

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Rashid, Saima, Saad Ihsan Butt, Zakia Hammouch, and Ebenezer Bonyah. "An Efficient Method for Solving Fractional Black-Scholes Model with Index and Exponential Decay Kernels." Journal of Function Spaces 2022 (September 21, 2022): 1–21. http://dx.doi.org/10.1155/2022/2613133.

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The Black-Scholes equation (BSe) is fascinating in the business world for predicting the performance of financial investment valuation systems. The Caputo fractional derivative (CFD) and Caputo-Fabrizio fractional derivative operators are used in this research to analyze the BSe. The Adomian decomposition method (ADM) and the new iterative transform (NIM) approach are combined alongside the Yang transform. In addition, the convergence and uniqueness results for the aforementioned framework have been calculated. The existence and uniqueness results have been established and frequently accompani

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Alsulami, Amer, Rasmiyah Alharb, Tahani Albogami, Nidal Eljaneid, Haroon Adam, and Sayed Saber. "Controlled chaos of a fractal-fractional Newton-Leipnik system." Thermal Science 28, no. 6 Part B (2024): 5153–60. https://doi.org/10.2298/tsci2406153a.

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In this study, fractal-fractional derivatives (FFD) with exponential decay laws kernels are applied to explain the chaotic behavior of a Newton-Leipnik system (NLS) with constant and time-varying derivatives. By using Caputo-Fabrizio fractal-fractional derivatives, fixed point theory verifies their existence and uniqueness. Using the implicit finite difference method, the Caputo-Fabrizio (CF) FF NLS is numerically solved. There are several numerical examples presented to illustrate the method?s applicability and efficiency. The CF fractal-fractional solutions are more general as compared to cl

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Jiang, Shidong, Jiwei Zhang, Qian Zhang, and Zhimin Zhang. "Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations." Communications in Computational Physics 21, no. 3 (2017): 650–78. http://dx.doi.org/10.4208/cicp.oa-2016-0136.

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AbstractThe computational work and storage of numerically solving the time fractional PDEs are generally huge for the traditional direct methods since they require totalmemory andwork, whereNTandNSrepresent the total number of time steps and grid points in space, respectively. To overcome this difficulty, we present an efficient algorithm for the evaluation of the Caputo fractional derivativeof orderα∈(0,1). The algorithm is based on an efficient sum-of-exponentials (SOE) approximation for the kernelt–1–αon the interval [Δt,T] with a uniform absolute errorε. We give the theoretical analysis to

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Abouelregal, Ahmed E., Hijaz Ahmad, and Shao-Wen Yao. "Functionally Graded Piezoelectric Medium Exposed to a Movable Heat Flow Based on a Heat Equation with a Memory-Dependent Derivative." Materials 13, no. 18 (2020): 3953. http://dx.doi.org/10.3390/ma13183953.

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The current work deals with the study of a thermo-piezoelectric modified model in the context of generalized heat conduction with a memory-dependent derivative. The investigations of the limited-length piezoelectric functionally graded (FGPM) rod have been considered based on the presented model. It is assumed that the specific heat and density are constant for simplicity while the other physical properties of the FGPM rod are assumed to vary exponentially through the length. The FGPM rod is subject to a moving heat source along the axial direction and is fixed to zero voltage at both ends. Us

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DeWitt, Jessica D., Peter G. Chirico, Marissa A. Alessi, and Kathleen M. Boston. "Remote Sensing Inventory and Geospatial Analysis of Brick Kilns and Clay Quarrying in Kabul, Afghanistan." Minerals 11, no. 3 (2021): 296. http://dx.doi.org/10.3390/min11030296.

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Reconstruction and urban development in Kabul, Afghanistan, has prompted vast expansion of the clay quarrying and brick making industry. This study identified the extent and distribution of clay quarrying and brick kilns in the greater Kabul area between 1965 and 2018. Very high-resolution satellite imagery was interpreted to quantify and characterize the type, number, and location of brick kilns for 1965, 2004, 2011, and 2018. Geospatial analysis of kilns together with geologic data and the results of hyperspectral image analysis yielded information regarding the extent of relevant mineral re

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Chernov, A. V. "On application of Gaussian kernels and Laplace functions combined with Kolmogorov's theorem for approximation of functions of several variables." Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta 63 (May 2024): 114–31. http://dx.doi.org/10.35634/2226-3594-2024-63-08.

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A special class of approximations of measurable functions of several variables on the unit coordinate cube is investigated. The class is constructed on the base of Kolmogorov's theorem (in version by Sprecher–Golubkov) stating that a continuous function $f$ of several variables can be represented as a finite superposition of continuous single-variable functions — so called outer functions (which depend of $f$) and inner one $\Psi$ (which is independent of $f$ and is monotone). In the case of continuous functions $f$ the class under study is obtained with outer functions approximated by linear

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Menge, Enock O., and Michael J. Lawes. "Influence of Landscape Characteristics on Wind Dispersal Efficiency of Calotropis procera." Land 12, no. 3 (2023): 549. http://dx.doi.org/10.3390/land12030549.

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Rubber bush (Calotropis procera), a perennial invasive milkweed, infests large swathes of pastoral land in northern Australia and Queensland, diminishing pasture productivity. The seeds of rubber are small with fluffy pappi that confer buoyancy during wind dispersal. Long-distance seed dispersal (LDD) by wind is dependent in part on seed terminal velocity, the height of release above the ground, the surrounding vegetation, and wind parameters such as speed and vertical turbulence. Using empirical dispersal data, spatial population distribution, and historical knowledge of three experimental si

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Thanasilp, Supanut, Samson Wang, M. Cerezo, and Zoë Holmes. "Exponential concentration in quantum kernel methods." Nature Communications 15, no. 1 (2024). http://dx.doi.org/10.1038/s41467-024-49287-w.

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AbstractKernel methods in Quantum Machine Learning (QML) have recently gained significant attention as a potential candidate for achieving a quantum advantage in data analysis. Among other attractive properties, when training a kernel-based model one is guaranteed to find the optimal model’s parameters due to the convexity of the training landscape. However, this is based on the assumption that the quantum kernel can be efficiently obtained from quantum hardware. In this work we study the performance of quantum kernel models from the perspective of the resources needed to accurately estimate k

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Khoshkalam, Zahra, Hadi Zayyani, and Mehdi Korki. "Secure multiple adaptive kernel diffusion LMS algorithm for distributed estimation over sensor networks." IET Wireless Sensor Systems, September 20, 2024. http://dx.doi.org/10.1049/wss2.12096.

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AbstractThis paper introduces a kernel‐based approach to enhance the security of distributed estimation in the presence of adversary links. Adversary links often degrade distributed recovery algorithm performance in distributed estimation. The authors propose secure distributed estimation algorithms employing an adaptive kernel and adaptive combination coefficients derived from it. The authors’ method includes a multiple kernel approach with varied widths and a heuristic formula for combination coefficients, improving performance in the presence of adversary links. Additionally, the approach i

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Kalpavruksha, Rohan, Roshan Kalpavruksha, Teryn Cha, and Sung-Hyuk Cha. "Kernel Density Based Spatial Clustering of Applications with Noise." International FLAIRS Conference Proceedings 38 (May 14, 2025). https://doi.org/10.32473/flairs.38.1.138998.

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Density-Based Spatial Clustering of Applications with Noise (DBSCAN) is a widely used clustering algorithm renowned for its ability to identify clusters of arbitrary shapes and detect noise. However, its reliance on fixed parameters, such as the minimum number of points (MinPts) and the epsilon radius (epsilon), makes it sensitive to variations in sample density. This paper reinterprets DBSCAN as a specific case of kernel density estimation (KDE)-based clustering, where the kernel shape corresponds to a hyper-rectangular pillar or cylindrical kernel, depending on the distance metric. Building

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Ahmad, Saeed, Rafi Ullah, and Dumitru Baleanu. "Mathematical analysis of tuberculosis control model using nonsingular kernel type Caputo derivative." Advances in Difference Equations 2021, no. 1 (2021). http://dx.doi.org/10.1186/s13662-020-03191-x.

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AbstractThis research work investigates some theoretical and semi-analytical results for the mathematical model of tuberculosis disease via derivative due to Caputo and Fabrizio. The concerned derivative involves exponential kernel and very recently it has been adapted for various applied problems. The required results are established by using some fixed point approach of Krasnoselskii and Banach. Further, by the use of iterative tools of Adomian decomposition and Laplace, the semi-analytical results are studied. Some graphical results are given with discussion.

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Akyildiz, F. Talay, and Fehaid Salem Alshammari. "Complex mathematical SIR model for spreading of COVID-19 virus with Mittag-Leffler kernel." Advances in Difference Equations 2021, no. 1 (2021). http://dx.doi.org/10.1186/s13662-021-03470-1.

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AbstractThis paper investigates a new model on coronavirus-19 disease (COVID-19), that is complex fractional SIR epidemic model with a nonstandard nonlinear incidence rate and a recovery, where derivative operator with Mittag-Leffler kernel in the Caputo sense (ABC). The model has two equilibrium points when the basic reproduction number $R_{0} > 1$ R 0 > 1 ; a disease-free equilibrium $E_{0}$ E 0 and a disease endemic equilibrium $E_{1}$ E 1 . The disease-free equilibrium stage is locally and globally asymptotically stable when the basic reproduction number $R_{0} <1$ R 0 < 1 , we

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