Search results for: differential privacy

Authors: Mugabe Nzarama Gabriel

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In Rwanda, many healthcare organizations are still using a paper based patients’ data record system although it still present weaknesses to share health patients’ information across different services when necessary. In developed countries, the EHR has been put in place to revolutionize the paper based record system but still the EHR has some challenges related to privacy, security, or interoperability. The purpose of this research was to assess the existing patients’ data record system in healthcare sector in Rwanda, see what an EHR can improve to the system in place and assess the acceptance of EHR as system which is interoperable, very secure and interoperable and see whether stakeholders are ready to adopt the system. The case based methodology was used and TAM theoretical framework to design the questionnaire for the survey. A judgmental sample across two cases, CHUB and Hopital de Nemba, has been selected and SPSS has been used for descriptive statistics. After a qualitative analysis, the findings showed that the paper based record is useful, gives complete information about the patient, protects the privacy of patients but it is still less secure and less interoperable. The respondents shown that they are ready to use the proposed EHR System and want it secure, capable of enforcing the privacy but still they are not all ready for the interoperability. A conclusion has been formulated; recommendations and further research have been proposed.

Keywords: EHR system, healthcare service, TAM, privacy, interoperability

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Authors: Chao-Qing Dai

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In modern nonlinear science and textile engineering, nonlinear differential-difference equations are often used to describe some nonlinear phenomena. In this paper, we extend the variable coefficient Jacobian elliptic function method, which was used to find new exact travelling wave solutions of nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, we derive two series of Jacobian elliptic function solutions of the discrete sine-Gordon equation.

Keywords: discrete sine-Gordon equation, variable coefficient Jacobian elliptic function method, exact solutions, equation

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Authors: A. Dinelka Panagoda, Bathiya Bandara, Chamod Wijetunga, Chathura Malinda, Lakmal Rupasinghe, Chethana Liyanapathirana

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This research takes us forward with the concepts of Federated Learning and Software-Defined Networking (SDN) to introduce an efficient malware detection technique and provide a mitigation mechanism to give birth to a resilient and automated healthcare sector network system by also adding the feature of extended privacy preservation. Due to the daily transformation of new malware attacks on hospital Integrated Clinical Environment (ICEs), the healthcare industry is at an undefinable peak of never knowing its continuity direction. The state of blindness by the array of indispensable opportunities that new medical device inventions and their connected coordination offer daily, a factor that should be focused driven is not yet entirely understood by most healthcare operators and patients. This solution has the involvement of four clients in the form of hospital networks to build up the federated learning experimentation architectural structure with different geographical participation to reach the most reasonable accuracy rate with privacy preservation. While the logistic regression with cross-entropy conveys the detection, SDN comes in handy in the second half of the research to stack up the initial development phases of the system with malware mitigation based on policy implementation. The overall evaluation sums up with a system that proves the accuracy with the added privacy. It is no longer needed to continue with traditional centralized systems that offer almost everything but not privacy.

Keywords: software-defined network, federated learning, privacy, integrated clinical environment, decentralized learning, malware detection, malware mitigation

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Authors: Bhaumik Tyagi, Mandeep Kaur, Kanika Singla

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The advancement of blockchain has facilitated scholars to remodel e-voting systems for future generations. Server-side attacks like SQL injection attacks and DOS attacks are the most common attacks nowadays, where malicious codes are injected into the system through user input fields by illicit users, which leads to data leakage in the worst scenarios. Besides, quantum attacks are also there which manipulate the transactional data. In order to deal with all the above-mentioned attacks, integration of blockchain, convolutional neural network (CNN), and Quantum Key Distribution is done in this very research. The utilization of blockchain technology in e-voting applications is not a novel concept. But privacy and security issues are still there in a public and private blockchains. To solve this, the use of a hybrid blockchain is done in this research. This research proposed cryptographic signatures and blockchain algorithms to validate the origin and integrity of the votes. The convolutional neural network (CNN), a normalized version of the multilayer perceptron, is also applied in the system to analyze visual descriptions upon registration in a direction to enhance the privacy of voters and the e-voting system. Quantum Key Distribution is being implemented in order to secure a blockchain-based e-voting system from quantum attacks using quantum algorithms. Implementation of e-voting blockchain D-app and providing a proposed solution for the privacy of voters in e-voting using Blockchain, CNN, and Quantum Key Distribution is done.

Keywords: hybrid blockchain, secure e-voting system, convolutional neural networks, quantum key distribution, one-time pad

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Authors: Deborah Garcia-Magna

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The use of new technologies has become widespread in the last decade, giving rise to various risks associated with the transfer of personal data and the publication of sensitive material on social media. There are already several supranational instruments that seek to protect the citizens involved in this growing traffic of personal information and, especially, the most vulnerable people, such as minors, who are also the ones who make the most intense use of these new means of communication. In this sense, the configuration of the concept of privacy as a legal right has necessarily been influenced by these new social uses and supranational instruments. The researcher considers correct the decision to introduce sexting as a new criminal behaviour in the Penal Code in 2015, but questions the concrete manner in which it has been made. To this end, an updated review of the various options that our legal system already offered is made, assessing whether these legal options adequately addressed the new social needs and guidelines from jurisprudence and other supranational instruments. Some important issues emerge as to whether the principles of fragmentarity and subsidiarity may be violated since the new article 197.7 of the Spanish Penal Code could refer to very varied behaviours and protect not only particularly vulnerable persons. In this sense, the research focuses on issues such as the concept of 'seriousness' of the infringement of privacy, the possible reckless conduct of the victim, who hang over its own private material to third parties, the affection to other legal rights such as freedom and sexual indemnity, the possible problems of concurrent offences, etc.

Keywords: criminal law reform, ECHR jurisprudence, right to privacy, sexting

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Authors: Andrei Bogdan Stanescu, Robert Stana

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Creating private and secure communication channels between employees has become a critical aspect in order to ensure organizational integrity and avoid leaks of sensitive information. With the widespread use of modern methods of disrupting communication between users, real use-cases of advanced encryption mechanisms have emerged to avoid cyber-attackers that are willing to intercept private conversations between critical employees in an organization. This paper aims to present a custom implementation of a messaging application named “Whisper” that uses end-to-end encryption (E2EE) mechanisms and blockchain-related components to protect sensitive conversations and mitigate the risks of information breaches inside organizations. The results of this research paper aim to expand the areas of applicability of E2EE algorithms and integrations with private blockchains in chat applications as a viable method of enhancing intra-organizational communication privacy.

Keywords: end-to-end encryption, mobile communication, cryptography, communication security, data privacy

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Authors: Mary Chriselda A

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This paper deals with the fact that the Hubble's parameter is not constant and tends to vary stochastically with time. This premise has been proven by converting it to a stochastic differential equation using the Ornstein-Uhlenbeck process. The formulated stochastic differential equation is further solved analytically using the Euler and the Kolmogorov Forward equations, thereby obtaining the probability density function using the Fourier transformation, thereby proving that the Hubble's parameter varies stochastically. This is further corroborated by simulating the observations using Python and R-software for validation of the premise postulated. We can further draw conclusion that the randomness in forces affecting the white noise can eventually affect the Hubble’s Parameter leading to scale invariance and thereby causing stochastic fluctuations in the density and the rate of expansion of the Universe.

Keywords: Chapman Kolmogorov forward differential equations, fourier transformation, hubble's parameter, ornstein-uhlenbeck process , stochastic differential equations

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Authors: Malika Elkyal

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We consider an iterative parallel multi-splitting method for differential algebraic equations. The main feature of the proposed idea is to use the asynchronous form. We prove that the multi-splitting technique can effectively accelerate the convergent performance of the iterative process. The main characteristic of an asynchronous mode is that the local algorithm does not have to wait at predetermined messages to become available. We allow some processors to communicate more frequently than others, and we allow the communication delays to be substantial and unpredictable. Accordingly, we note that synchronous algorithms in the computer science sense are particular cases of our formulation of asynchronous one.

Keywords: parallel methods, asynchronous mode, multisplitting, differential algebraic equations

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Authors: T. Vamsee Kiran, A. Gopi

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The undesired torque and flux ripple may occur in conventional direct torque control (DTC) induction motor drive. DTC can improve the system performance at low speeds by continuously tuning the regulator by adjusting the Kp, Ki values. In this differential evolution (DE) is proposed to adjust the parameters (Kp, Ki) of the speed controller in order to minimize torque ripple, flux ripple, and stator current distortion.The DE based PI controller has resulted is maintaining a constant speed of the motor irrespective of the load torque fluctuations.

Keywords: differential evolution, direct torque control, PI controller

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Authors: Rizwan Rizwan

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Secure Multiparty Computation is an emerging area of research within the cryptographic community, enabling secure collaboration among multiple parties while safeguarding their sensitive data. Secure Multiparty Computation has been extensively studied in the context of plane geometry, its application to complex solid geometry shapes remains relatively unexplored. This research paper aims to bridge this gap by proposing a solution for the secure multiparty computation of intersecting tetrahedra. We present an approach to calculate the volume of intersecting tetrahedra securely while preserving the privacy of the input data provided by each participating party. The proposed solution leverages accepted simulation paradigms to prove the privacy of the computation. We thoroughly analyze the computational and communication complexities of our approach, demonstrating that they closely align with the minimum theoretical complexity for the problems at hand. This optimal nature of our solution ensures efficient and secure collaborative geometric computations.

Keywords: cryptography, secure multiparty computation, solid geometry, protocol, simulation paradigm

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Authors: Jiya Mohammed, Ibrahim Ismail Giwa

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Unsteady squeezing flow of a viscous fluid between parallel plates is considered. The two plates are considered to be approaching each other symmetrically, causing the squeezing flow. Two-dimensional rectangular Cartesian coordinate is considered. The Navier-Stokes equation was reduced using similarity transformation to a single fourth order non-linear ordinary differential equation. The energy equation was transformed to a second order coupled differential equation. We obtained solution to the resulting ordinary differential equations via Homotopy Perturbation Method (HPM). HPM deforms a differential problem into a set of problem that are easier to solve and it produces analytic approximate expression in the form of an infinite power series by using only sixth and fifth terms for the velocity and temperature respectively. The results reveal that the proposed method is very effective and simple. Comparisons among present and existing solutions were provided and it is shown that the proposed method is in good agreement with Variation of Parameter Method (VPM). The effects of appropriate dimensionless parameters on the velocity profiles and temperature field are demonstrated with the aid of comprehensive graphs and tables.

Keywords: coupled differential equation, Homotopy Perturbation Method, plates, squeezing flow

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Authors: Maryam Mosleh, Mahmood Otadi

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The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: Fuzzy number, parametric form of a fuzzy number, fuzzy integrodifferential equation, homotopy analysis method

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Authors: O. Iyare, A. H. Afolayan, O. T. Oluwadare, B. K. Alese

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Access to advanced medical services has been one of the medical challenges faced by our present society especially in distant geographical locations which may be inaccessible. Then the need for telemedicine arises through which live videos of a doctor can be streamed to a patient located anywhere in the world at any time. Patients’ medical records contain very sensitive information which should not be made accessible to unauthorized people in order to protect privacy, integrity and confidentiality. This research work focuses on a more robust security measure which is biometric (fingerprint) as a form of access control to data of patients by the medical specialist/practitioner.

Keywords: biometrics, telemedicine, privacy, patient information

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Authors: Sarthak Mishra, Astha Sinha

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There’s no doubt about the convenience of making commercial and business transactions over the Internet under the new business model known as the e-Commerce. The term 'Electronic commerce' or e-Commerce refers to the use of an electronic medium to carry out commercial transactions. E-Commerce is one of the parts of Information Science framework and its uses are gradually becoming popular. Thus, the threat of security issues in Information Science has now become an important subject of discussion amongst the concerned users. These two issues i.e. security and privacy are required to be looked into through social, organizational, technical and economic perspectives. The current paper analyses the effect of these two issues in the arena of e-commerce. Here, no specification has been discussed rather an attempt has been made to provide a general overview. Further, attempts have been made to discuss the security and privacy issues in relation to the E-Commerce financial transactions. We shall also discuss in particular different steps required to be taken before online shopping and also shall discuss the purpose of security and privacy in E-Commerce and why it has currently become the need of the present hour. Lastly, an attempt has been made to discuss the plausible future course of development of this practice and its impact upon the global economy and if any changes should be bought about to ensure a smooth evolution of the practice. This paper has adopted a descriptive methodology to undertake its major area of study, wherein the major source of information has been via the secondary resources. Also, the study is of a comparative nature wherein the position of the various national regimes have compared with regards to the research question.

Keywords: business-business transaction (B2B), business-consumer transaction (B2C), e-commerce, online transaction, privacy and security threats

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Authors: Derick M. Rakgoale, Topside E. Mathonsi, Vusumuzi Malele

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Cloud computing offers distributed online and on-demand computational services from anywhere in the world. Cloud computing services have grown immensely over the past years, especially in the past year due to the Coronavirus pandemic. Cloud computing has changed the working environment and introduced work from work phenomenon, which enabled the adoption of technologies to fulfill the new workings, including cloud services offerings. The increased cloud computing adoption has come with new challenges regarding data privacy and its integrity in the cloud environment. Previously advanced encryption algorithms failed to reduce the memory space required for cloud computing performance, thus increasing the computational cost. This paper reviews the existing encryption algorithms used in cloud computing. In the future, artificial neural networks (ANN) algorithm design will be presented as a security solution to ensure data integrity, confidentiality, privacy, and availability of user data in cloud computing. Moreover, MATLAB will be used to evaluate the proposed solution, and simulation results will be presented.

Keywords: cloud computing, data integrity, confidentiality, privacy, availability

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Authors: Davood Yazdani Cherati, Hussein Hashemi Senejani

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In this paper, a convenient analytical solution for a system of coupled differential equations, derived from thermo-hydro-mechanical analysis of three-phase porous media such as unsaturated soils is developed. This kind of analysis can be used in various fields such as geothermal energy systems and seepage of leachate from buried municipal and domestic waste in geomaterials. Initially, a system of coupled differential equations, including energy, mass, and momentum conservation equations is considered, and an analytical method called AGM is employed to solve the problem. The method is straightforward and comprehensible and can be used to solve various nonlinear partial differential equations (PDEs). Results indicate the accuracy of the applied method for solving nonlinear partial differential equations.

Keywords: AGM, analytical solution, porous media, thermo-hydro-mechanical, unsaturated soils

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Authors: Pantaleon Lutta, Mohamed Sedky, Mohamed Hassan

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The inability of organizations to put in place management control measures for Internet of Things (IoT) complexities persists to be a risk concern. Policy makers have been left to scamper in finding measures to combat these security and privacy concerns. IoT forensics is a cumbersome process as there is no standardization of the IoT products, no or limited historical data are stored on the devices. This paper highlights why IoT forensics is a unique adventure and brought out the legal challenges encountered in the investigation process. A quadrant model is presented to study the conflicting aspects in IoT forensics. The model analyses the effectiveness of forensic investigation process versus the admissibility of the evidence integrity; taking into account the user privacy and the providers’ compliance with the laws and regulations. Our analysis concludes that a semi-automated forensic process using machine learning, could eliminate the human factor from the profiling and surveillance processes, and hence resolves the issues of data protection (privacy and confidentiality).

Keywords: cloud forensics, data protection Laws, GDPR, IoT forensics, machine Learning

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Authors: João Filipe Papel, Tatsuji Munaka

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With society's aging and the number of elderly with dementia rising, researchers have been actively studying how to support the elderly in the early stages of dementia with the objective of allowing them to have a better life quality and as much as possible independence. To make this possible, most researchers in this field are using the Internet Of Things to monitor the elderly activities and assist them in performing them. The most common sensor used to monitor the elderly activities is the Camera sensor due to its easy installation and configuration. The other commonly used sensor is the sound sensor. However, we need to consider privacy when using these sensors. This research aims to develop a system capable of predicting the early stages of dementia based on monitoring and controlling the elderly activities of daily living. To make this system possible, some issues need to be addressed. First, the issue related to elderly privacy when trying to detect their Activities of Daily Living. Privacy when performing detection and monitoring Activities of Daily Living it's a serious concern. One of the purposes of this research is to achieve this detection and monitoring without putting the privacy of the elderly at risk. To make this possible, the study focuses on using an approach based on using Magnet Sensors to collect binary data. The second is to use the data collected by monitoring Activities of Daily Living to predict the early stages of Dementia. To make this possible, the research team suggests developing a proprietary ontology combined with both data-driven and knowledge-driven.

Keywords: dementia, activity recognition, magnet sensors, ontology, data driven and knowledge driven, IoT, activities of daily living

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Authors: Tolga Yazıcı

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As a matter of the fact that online social networks like Twitter, Facebook and MySpace have experienced an extensive growth in recent years. Social media offers individuals with a tool for communicating and interacting with one another. These social networks enable people to stay in touch with other people and express themselves. This process makes the users of online social networks active creators of content rather than being only consumers of traditional media. That’s why millions of people show strong desire to learn the methods and tools of digital content production and necessary communication skills. However, the booming interest in communication and interaction through online social networks and high level of eagerness to invent and implement the ways to participate in content production raise some privacy and security concerns. This presentation aims to open the assumed revolutionary, democratic and liberating nature of the online social media up for discussion by reviewing some recent political developments in Turkey. Firstly, the role of Internet and online social networks in mobilizing collective movements through social interactions and communications will be questioned. Secondly, some cases from Gezi and Okmeydanı Protests and also December 17-25 period will be presented in order to illustrate misinformation and manipulation in social media and violation of individual privacy through online social networks in order to damage social unity and stability contradictory to democratic nature of online social networking.

Keywords: online social media networks, democratic participation, social movements, social polarization, privacy of individuals, Turkey

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Authors: Somveer Singh, Vineet Kumar Singh

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We present a new model based on viscoelasticity for the Non-Newtonian fluids.We use a matrix formulated algorithm to approximate solutions of a class of partial integro-differential equations with the given initial and boundary conditions. Some numerical results are presented to simplify application of operational matrix formulation and reduce the computational cost. Convergence analysis, error estimation and numerical stability of the method are also investigated. Finally, some test examples are given to demonstrate accuracy and efficiency of the proposed method.

Keywords: Legendre Wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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Authors: Abdullah M. Almeshal, Mohammad R. Alenezi, Muhammad Moaz

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In this paper, we discuss the performance of applying hybrid spiral dynamic bacterial chemotaxis (HSDBC) optimisation algorithm on an intelligent controller for a differential drive robot. A unicycle class of differential drive robot is utilised to serve as a basis application to evaluate the performance of the HSDBC algorithm. A hybrid fuzzy logic controller is developed and implemented for the unicycle robot to follow a predefined trajectory. Trajectories of various frictional profiles and levels were simulated to evaluate the performance of the robot at different operating conditions. Controller gains and scaling factors were optimised using HSDBC and the performance is evaluated in comparison to previously adopted optimisation algorithms. The HSDBC has proven its feasibility in achieving a faster convergence toward the optimal gains and resulted in a superior performance.

Keywords: differential drive robot, hybrid fuzzy controller, optimization, path tracking, unicycle robot

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Authors: Ramdas Sonawane, Mahaveer Gadiya

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The control problem associated with nuclear dynamics is represented by nonlinear integro-differential equation with additive controls. To control chain reaction, certain amount of neutrons is added into (or withdrawn out of) chamber as and when required. It is not realistic. So, we can think of controlling the reactor dynamics by bilinear control, which enters the system as coefficient of state. In this paper, we study the approximate and exact controllability of parabolic integro-differential equation controlled by bilinear control with non-homogeneous boundary conditions in bounded domain. We prove the existence of control and propose an explicit control strategy.

Keywords: approximate control, exact control, bilinear control, nuclear dynamics, integro-differential equations

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Authors: Hassan Manouzi, Taous-Meriem Laleg-Kirati

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In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Ito chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm alternative. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.

Keywords: eigenvalue problem, Wick product, SPDEs, finite element, Wiener-Ito chaos expansion

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Authors: Eugenio Ferrer Santiago

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The growing complexities of the modern world on high-end gadgets, software applications, scams, identity theft, and Artificial Intelligence (AI) make the “uninformed” the weak and vulnerable to be victims of cybercrimes. Artificial Intelligence is not a new thing in our daily lives; the principles of database management, logical programming, and garbage in and garbage out are all connected to AI. The Philippines had in place legal safeguards against the abuse of cyberspace, but self-regulation of key industry players and self-protection by individuals are primordial to attain the success of these initiatives. Data protection, Data Privacy, and Research Ethics must work hand in hand during the policy process in the course of urban planning practice in different environments. This paper focuses on the interconnection of data protection, data privacy, and research ethics in coming up with clear-cut policies against perpetrators in the urban planning professional practice relevant in sustainable communities and smart cities. This paper shall use expository methodology under qualitative research using secondary data from related literature, interviews/blogs, and the World Wide Web resources. The claims and recommendations of this paper will help policymakers and implementers in the policy cycle. This paper shall contribute to the body of knowledge as a simple treatise and communication channel to the reading community and future researchers to validate the claims and start an intellectual discourse for better knowledge generation for the good of all in the near future.

Keywords: data privacy, data protection, urban planning, research ethics

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Authors: Qinghua Zhang, Yanhe Zhu, Xiang Zhao, Yeqin Yang, Hongwei Jing, Guoan Zhang, Jie Zhao

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This paper presents a wearable reconfigurable supernumerary robotic limb with differential actuated joints, which is lightweight, compact and comfortable for the wearers. Compared to the existing supernumerary robotic limbs which mostly adopted series structure with large movement space but poor carrying capacity, a prototype with the series-parallel configuration to better adapt to different task requirements has been developed in this design. To achieve a compact structure, two kinds of cable-driven mechanical structures based on guide pulleys and differential actuated joints were designed. Moreover, two different tension devices were also designed to ensure the reliability and accuracy of the cable-driven transmission. The proposed device also employed self-designed bearings which greatly simplified the structure and reduced the cost.

Keywords: cable-driven, differential actuated joints, reconfigurable, supernumerary robotic limb

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Authors: Haniye Dehestani, Yadollah Ordokhani

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In this work, we present an efficient approach for solving variable-order time-fractional partial differential equations, which are based on Legendre and Laguerre polynomials. First, we introduced the pseudo-operational matrices of integer and variable fractional order of integration by use of some properties of Riemann-Liouville fractional integral. Then, applied together with collocation method and Legendre-Laguerre functions for solving variable-order time-fractional partial differential equations. Also, an estimation of the error is presented. At last, we investigate numerical examples which arise in physics to demonstrate the accuracy of the present method. In comparison results obtained by the present method with the exact solution and the other methods reveals that the method is very effective.

Keywords: collocation method, fractional partial differential equations, legendre-laguerre functions, pseudo-operational matrix of integration

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Authors: Khosrow Maleknejad, Asyieh Ebrahimzadeh

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In this paper, the numerical solution of optimal control problem (OCP) for systems governed by Volterra integro-differential (VID) equation is considered. The method is developed by means of the Legendre wavelet approximation and collocation method. The properties of Legendre wavelet accompany with Gaussian integration method are utilized to reduce the problem to the solution of nonlinear programming one. Some numerical examples are given to confirm the accuracy and ease of implementation of the method.

Keywords: collocation method, Legendre wavelet, optimal control, Volterra integro-differential equation

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Authors: Daniil Karzanov

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This paper studies the effect of quarterly earnings reports on the stock price. The profitability of the stock is modeled by geometric Brownian diffusion and the Constant Elasticity of Variance model. We fit several variations of stochastic differential equations to the pre-and after-report period using the Maximum Likelihood Estimation and Grid Search of parameters method. By examining the change in the model parameters after reports’ publication, the study reveals that the reports have enough evidence to be a structural breakpoint, meaning that all the forecast models exploited are not applicable for forecasting and should be refitted shortly.

Keywords: stock market, earnings reports, financial time series, structural breaks, stochastic differential equations

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Authors: Somveer Singh, Vineet Kumar Singh

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This work contributes a numerical method based on Legendre wavelet approximation for the treatment of partial integro-differential equation (PIDE). Operational matrices of Legendre wavelets reduce the solution of PIDE into the system of algebraic equations. Some useful results concerning the computational order of convergence and error estimates associated to the suggested scheme are presented. Illustrative examples are provided to show the effectiveness and accuracy of proposed numerical method.

Keywords: legendre wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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Authors: A. Guezane-Lakoud, S. Bensebaa

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In this paper, we study a boundary value problem of nonlinear fractional differential equation. Existence and positivity results of solutions are obtained.

Keywords: positive solution, fractional caputo derivative, Banach contraction principle, Avery and Peterson fixed point theorem

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