Memory is an imperfect record of past experiences that enables us to operate in the present and think about the future. Although various factors may give a chance to a false recollection of information that may not occur. These false memories are formed based on various neuro-cognitive processes the underlying mechanism still needs to be well understood. Considering the extended searching when no memory trace is found, we hypothesized that the self-similarities in the brain activations must be higher during false memory recalls. Therefore, a language-free task based on autobiographical brand images was designed using the Deese–Roediger–McDermott (DRM) paradigm. The task was then tested on 24 healthy participants while the brain activities during the test were recorded using a 32-channel EEG system. Subsequently, the self-similarities in the brain activity pattern were estimated by taking the fractal dimension (FD) of the cleaned EEG data. Statistical analysis showed a significant increase in complexity during false memory recalls as compared to true memory recalls prominent in the frontal regions. Interestingly, the EEG findings were consistent in both genders and significantly correlated with subjects’ accuracy rates and reaction times (RTs) to recall.
{"title":"Effect of autobiographical false memory on the complexity of neural oscillations","authors":"Mohsen Shabani, Masoumeh Sadeghi, Javad Salehi, Hamidreza Namazi, Reza Khosrowabadi","doi":"10.1142/s0218348x23501165","DOIUrl":"https://doi.org/10.1142/s0218348x23501165","url":null,"abstract":"Memory is an imperfect record of past experiences that enables us to operate in the present and think about the future. Although various factors may give a chance to a false recollection of information that may not occur. These false memories are formed based on various neuro-cognitive processes the underlying mechanism still needs to be well understood. Considering the extended searching when no memory trace is found, we hypothesized that the self-similarities in the brain activations must be higher during false memory recalls. Therefore, a language-free task based on autobiographical brand images was designed using the Deese–Roediger–McDermott (DRM) paradigm. The task was then tested on 24 healthy participants while the brain activities during the test were recorded using a 32-channel EEG system. Subsequently, the self-similarities in the brain activity pattern were estimated by taking the fractal dimension (FD) of the cleaned EEG data. Statistical analysis showed a significant increase in complexity during false memory recalls as compared to true memory recalls prominent in the frontal regions. Interestingly, the EEG findings were consistent in both genders and significantly correlated with subjects’ accuracy rates and reaction times (RTs) to recall.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135430954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-07DOI: 10.1142/s0218348x23401953
Humaira Kalsoom, Zareen A. Khan
The purpose of this paper is to introduce a more generalized class of convex stochastic processes and explore some of their algebraic properties. This new class of stochastic processes is called the [Formula: see text]-polynomial [Formula: see text]-type convex stochastic process. We demonstrate that this new class of stochastic processes leads to the discovery of novel Hermite–Hadamard type inequalities. These inequalities provide upper bounds on the integral of a convex function over an interval in terms of the moments of the stochastic process and the convexity parameter [Formula: see text]. To compare the effectiveness of the newly discovered Hermite–Hadamard type inequalities, we also consider other commonly used integral inequalities, such as Hölder, Hölder–Ïşcan, and power-mean, as well as improved power-mean integral inequalities. We show that the Hölder–Ïşcan and improved power-mean integral inequalities provide a better approach for the [Formula: see text]-polynomial [Formula: see text]-type convex stochastic process than the other integral inequalities. Finally, we provide some applications of the Hermite–Hadamard type inequalities to special means of real numbers. Our findings provide a useful tool for the analysis of stochastic processes in various fields, including finance, economics, and engineering.
{"title":"New Inequalities of Hermite-Hadamard Type for <i>n</i>-Polynomial <i>s</i>-Type Convex Stochastic Processes","authors":"Humaira Kalsoom, Zareen A. Khan","doi":"10.1142/s0218348x23401953","DOIUrl":"https://doi.org/10.1142/s0218348x23401953","url":null,"abstract":"The purpose of this paper is to introduce a more generalized class of convex stochastic processes and explore some of their algebraic properties. This new class of stochastic processes is called the [Formula: see text]-polynomial [Formula: see text]-type convex stochastic process. We demonstrate that this new class of stochastic processes leads to the discovery of novel Hermite–Hadamard type inequalities. These inequalities provide upper bounds on the integral of a convex function over an interval in terms of the moments of the stochastic process and the convexity parameter [Formula: see text]. To compare the effectiveness of the newly discovered Hermite–Hadamard type inequalities, we also consider other commonly used integral inequalities, such as Hölder, Hölder–Ïşcan, and power-mean, as well as improved power-mean integral inequalities. We show that the Hölder–Ïşcan and improved power-mean integral inequalities provide a better approach for the [Formula: see text]-polynomial [Formula: see text]-type convex stochastic process than the other integral inequalities. Finally, we provide some applications of the Hermite–Hadamard type inequalities to special means of real numbers. Our findings provide a useful tool for the analysis of stochastic processes in various fields, including finance, economics, and engineering.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135430955","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-03DOI: 10.1142/s0218348x24400127
Rashid Jan, Normy Norfiza Abdul Razak, Sultan Alyobi, Zaryab Khan, Kamyar Hosseini, Choonkil Park, Soheil Salahshour, Siriluk Paokanta
{"title":"Fractional Dynamics of Chronic Lymphocytic Leukemia with the Effect of Chemoimmunotherapy Treatment","authors":"Rashid Jan, Normy Norfiza Abdul Razak, Sultan Alyobi, Zaryab Khan, Kamyar Hosseini, Choonkil Park, Soheil Salahshour, Siriluk Paokanta","doi":"10.1142/s0218348x24400127","DOIUrl":"https://doi.org/10.1142/s0218348x24400127","url":null,"abstract":"","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135875289","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-02DOI: 10.1142/s0218348x23402004
Mostafa M. A. Khater, Raghda A. M. Attia
In recent years, there has been growing interest in fractional differential equations, which extend the concept of ordinary differential equations by including fractional-order derivatives. The fractional Chaffee–Infante ([Formula: see text]) equation, a nonlinear partial differential equation that describes physical systems with fractional-order dynamics, has received particular attention. Previous studies have explored analytical solutions for this equation using the method of solitary wave solutions, which seeks traveling wave solutions that are localized in space and time. To construct these solutions, the extended Khater II ([Formula: see text]) method was used in conjunction with the properties of the truncated Mittag-Leffler ([Formula: see text]) function. The resulting soliton wave solutions demonstrate how solitary waves propagate through the system and can be used to investigate the system’s response to different stimuli. The accuracy of the solutions is verified using the variational iteration [Formula: see text] technique. This study demonstrates the effectiveness of analytical and numerical methods for finding accurate solitary wave solutions to the [Formula: see text] equation, and how these methods can be used to gain insights into the behavior of physical systems with fractional-order dynamics.
{"title":"Simulating the behavior of the population dynamics using the non-local fractional Chaffee-Infante equation","authors":"Mostafa M. A. Khater, Raghda A. M. Attia","doi":"10.1142/s0218348x23402004","DOIUrl":"https://doi.org/10.1142/s0218348x23402004","url":null,"abstract":"In recent years, there has been growing interest in fractional differential equations, which extend the concept of ordinary differential equations by including fractional-order derivatives. The fractional Chaffee–Infante ([Formula: see text]) equation, a nonlinear partial differential equation that describes physical systems with fractional-order dynamics, has received particular attention. Previous studies have explored analytical solutions for this equation using the method of solitary wave solutions, which seeks traveling wave solutions that are localized in space and time. To construct these solutions, the extended Khater II ([Formula: see text]) method was used in conjunction with the properties of the truncated Mittag-Leffler ([Formula: see text]) function. The resulting soliton wave solutions demonstrate how solitary waves propagate through the system and can be used to investigate the system’s response to different stimuli. The accuracy of the solutions is verified using the variational iteration [Formula: see text] technique. This study demonstrates the effectiveness of analytical and numerical methods for finding accurate solitary wave solutions to the [Formula: see text] equation, and how these methods can be used to gain insights into the behavior of physical systems with fractional-order dynamics.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135874613","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-01DOI: 10.1142/s0218348x24400061
Binyan Yu, Yongshun Liang
{"title":"Construction of Monotonous Approximation by Fractal Interpolation Functions and Fractal Dimensions","authors":"Binyan Yu, Yongshun Liang","doi":"10.1142/s0218348x24400061","DOIUrl":"https://doi.org/10.1142/s0218348x24400061","url":null,"abstract":"","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135372198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Fermat problem is a crucial topological issue corresponding to fractal networks. In this paper, we discuss the average Fermat distance (AFD) of the Vicsek polygon network and analyze structural properties. We construct the Vicsek polygon network based on Vicsek fractal in an iterative way. Given the structure of network, we present an elaborate analysis of the Fermat point under various situations. The special network structure allows a way to calculate the AFD based on average geodesic distance (AGD). Moreover, we introduce the Vicsek polygon fractal and calculate its AGD and AFD. Its relationship with the network enables us to deduce the above two indices of the network directly. The results show that both in network and fractal, the ratio of AFD and AGD tends to 3/2, which demonstrates that both of them can serve as indicators of small-world property of complex networks. In fact, in Vicsek polygon network, the AFD grows linearly with network order, implying that our evolving network does not possess the small-world property.
{"title":"Average Fermat distance on Vicsek polygon network","authors":"Zixuan Zhao, Yumei Xue, Cheng Zeng, Daohua Wang, Zhiqiang Wu","doi":"10.1142/s0218348x23501177","DOIUrl":"https://doi.org/10.1142/s0218348x23501177","url":null,"abstract":"The Fermat problem is a crucial topological issue corresponding to fractal networks. In this paper, we discuss the average Fermat distance (AFD) of the Vicsek polygon network and analyze structural properties. We construct the Vicsek polygon network based on Vicsek fractal in an iterative way. Given the structure of network, we present an elaborate analysis of the Fermat point under various situations. The special network structure allows a way to calculate the AFD based on average geodesic distance (AGD). Moreover, we introduce the Vicsek polygon fractal and calculate its AGD and AFD. Its relationship with the network enables us to deduce the above two indices of the network directly. The results show that both in network and fractal, the ratio of AFD and AGD tends to 3/2, which demonstrates that both of them can serve as indicators of small-world property of complex networks. In fact, in Vicsek polygon network, the AFD grows linearly with network order, implying that our evolving network does not possess the small-world property.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134957780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-01DOI: 10.1142/s0218348x24400164
Thanin Sitthiwirattham, Miguel Vivas-Cortez, Muhammad Aamir Ali, Huseyin Budak, Ibrahim Avci
{"title":"A Study of Fractional Hermite-Hadamard-Mercer Inequalities for Differentiable Functions","authors":"Thanin Sitthiwirattham, Miguel Vivas-Cortez, Muhammad Aamir Ali, Huseyin Budak, Ibrahim Avci","doi":"10.1142/s0218348x24400164","DOIUrl":"https://doi.org/10.1142/s0218348x24400164","url":null,"abstract":"","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135372029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-01DOI: 10.1142/s0218348x24400103
Kamal Shah, Bahaaeldin Abdalla, Thabet Abdeljawad, Manar A. Alqudah
{"title":"A Fractal-Fractional Order Model to Study Multiple Sclerosis: A Chronic Disease","authors":"Kamal Shah, Bahaaeldin Abdalla, Thabet Abdeljawad, Manar A. Alqudah","doi":"10.1142/s0218348x24400103","DOIUrl":"https://doi.org/10.1142/s0218348x24400103","url":null,"abstract":"","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135371905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-31DOI: 10.1142/s0218348x23501220
GUANG-QING FENG, LI ZHANG, WEI TANG
The dynamic pull-in instability of a microstructure is a vast research field and its analysis is of great significance for ensuring the effective operation and reliability of micro-electromechanical systems (MEMS). A fractal modification for the traditional MEMS system is suggested to be closer to the real state as a practical application in the air with impurities or humidity. In this paper, we establish a fractal model for a class of electrostatically driven microstructure resonant sensors and find the phenomenon of pull-in instability caused by DC bias voltage and AC excitation voltage. The variational iteration method has been extended to obtain approximate analytical solutions and the pull-in threshold value for the fractal MEMS system. The result obtained from this method shows good agreement with the numerical solution. The simple and efficient operability is demonstrated through theoretical analysis and results comparisons.
{"title":"FRACTAL PULL-IN MOTION OF ELECTROSTATIC MEMS RESONATORS BY THE VARIATIONAL ITERATION METHOD","authors":"GUANG-QING FENG, LI ZHANG, WEI TANG","doi":"10.1142/s0218348x23501220","DOIUrl":"https://doi.org/10.1142/s0218348x23501220","url":null,"abstract":"The dynamic pull-in instability of a microstructure is a vast research field and its analysis is of great significance for ensuring the effective operation and reliability of micro-electromechanical systems (MEMS). A fractal modification for the traditional MEMS system is suggested to be closer to the real state as a practical application in the air with impurities or humidity. In this paper, we establish a fractal model for a class of electrostatically driven microstructure resonant sensors and find the phenomenon of pull-in instability caused by DC bias voltage and AC excitation voltage. The variational iteration method has been extended to obtain approximate analytical solutions and the pull-in threshold value for the fractal MEMS system. The result obtained from this method shows good agreement with the numerical solution. The simple and efficient operability is demonstrated through theoretical analysis and results comparisons.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135871291","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-27DOI: 10.1142/s0218348x23401904
M. Abdelhakem
Shifted Legendre polynomials (SLPs) with the Riemann–Liouville fractional integral operator have been used to create a novel fractional integration tool. This tool will be called the fractional shifted Legendre integration matrix (FSL B-matrix). Two algorithms depending on this matrix are designed to solve two different types of integral equations. The first algorithm is to solve fractional Volterra integro-differential equations (VIDEs) with a non-singular kernel. The second algorithm is for Abel’s integral equations. In addition, error analysis for the spectral expansion has been proven to ensure the expansion’s convergence. Finally, several examples have been illustrated, including an application for the population model.
{"title":"Shifted Legendre Fractional Pseudo-spectral Integration Matrices for Solving Fractional Volterra Integro-Differential Equations and Abel's Integral Equations","authors":"M. Abdelhakem","doi":"10.1142/s0218348x23401904","DOIUrl":"https://doi.org/10.1142/s0218348x23401904","url":null,"abstract":"Shifted Legendre polynomials (SLPs) with the Riemann–Liouville fractional integral operator have been used to create a novel fractional integration tool. This tool will be called the fractional shifted Legendre integration matrix (FSL B-matrix). Two algorithms depending on this matrix are designed to solve two different types of integral equations. The first algorithm is to solve fractional Volterra integro-differential equations (VIDEs) with a non-singular kernel. The second algorithm is for Abel’s integral equations. In addition, error analysis for the spectral expansion has been proven to ensure the expansion’s convergence. Finally, several examples have been illustrated, including an application for the population model.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136233159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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