International Journal of Mathematical Sciences and Computing @ijmsc
Journal articles - International Journal of Mathematical Sciences and Computing
All articles: 294
Revised Method for Sampling Coefficient Vector of GNR-enumeration Solution
Scientific article
For selecting security parameters in lattice-based cryptographic primitives, the exact manner of BKZ algorithm (as total cost and specification of output basis) should be estimated in high block sizes. The simulations of BKZ are used to predict (estimate) the exact manner of BKZ algorithm which cannot be studied by practical running of BKZ algorithm for higher block sizes. Sampling method of GNR (Gamma-Nguyen-Regev) enumeration solution vector v is one of the main components of designing BKZ-simulation and it includes two phases: sampling the norm of solution vector v and sampling corresponding coefficient vectors. Our work, by Moghissi and Payandeh in 2021, entitled as “Better Sampling Method of Enumeration Solution for BKZ-Simulation”, introduces a simple and efficient idea for sampling the norm and coefficient vectors of GNR enumeration solution v. This paper proposes much better analysis for approximating the expected value and variance of the entries of these coefficient vectors. By this analysis, our previous idea for sampling the coefficient vectors is revised, which means that the expected value and variance of every entry in these coefficient vectors sampled by our new sampling method, are more close to the expected value and variance of corresponding entries in original sampling method, while these new sampled coefficient vectors include no violation from main condition of GNR bounding function (i.e., our new sampling method is not a rejection sampling).
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Scientific article
Quantum cryptography is marches towards secure communication by using quantum protocols. Number of quantum protocols has been evolved based on an entanglement in three decades; similarly during this meanwhile non-entanglement based protocols have been evolved within the same period also. Among number of different protocols a torch bearer was BB84 protocol. Even though different quantum communication protocols exist, the BB84 protocol proved its application by initial experiments whereas most of the other protocols are theoretical which marches towards the practical application yet. But in quantum mechanics principle, cryptography based on an entanglement and superposition of entangled particle. Furthermore, challenges ahead are development and design high sensitive equipments for measurement of an entangled particle position at output end. Particle entanglements open a new door for computation worlds such as speedup, security. In this article, we discuss quantum protocols, their challenges, and applications based on above discussion.
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Roman Domination in Semi-Middle Graphs: Insights and Applications in Computer Network Design
Scientific article
Consider a G=(V,E) and the function f :V -{0,1,2}. . Unguarded with regard to is defined as a node u with f (u) = 0 that is not next to a node with 1 or 2 . The function f (V0 ,V1,V2 ) fulfilling the condition, in which each node u for which f (u)=0 is adjoint to at least one node v to which f (v) =2 , is referred to be a Roman dominant function, known as RDF of a graph G . Roman domination number (RDN) of graph represented by rR (G), is the bare lowest count of guards that must be employed in any RDF. In this paper, we introduce a new form for graph called Semi-Middle Graph for any given graph and we find the RDN for the Semi - Middle Graph of some specific graphs. In the field of networking, the concept of the Semi-Middle Graph can be applied to network topology optimization. Specifically, it can be used in the design of communication networks where each direct connection (edge) between two nodes (devices or routers) has an intermediary node that facilitates more efficient data routing or enhances fault tolerance. Usefulness of Roman Domination Number of a Semi-Middle Graph in Networking includes Network Coverage and Monitoring, Fault Tolerance and Redundancy, Optimal Placement of Relays and Routers, Load Balancing and Resource Allocation.
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SIP Model and Bifurcation Analysis for Spread of Misinformation in Online Social Networks
Scientific article
The spreading of misinformation in Online Social Networks (OSNs) is quite similar to the spreading of infection in biological diseases. As the biological virus spreads and makes one infected as well as those who come into contact with the infected person, the nature and behavior of the spread of misinformation in an online social network is similar. So in order to understand the functioning of misinformation and to control over epidemic outbreak of misinformation in OSNs, epidemic models can be quite handy. The introduction of Bifurcation theory in the epidemic model explains the qualitative behavior of the system with changes in parameters. In this paper, we have introduced the Susceptible, Infectious, and Protected (SIP) model with Bifurcation for the propagation of misinformation in OSNs. Here Bifurcation is due to the limited number of users who are ready to adopt the Security and Privacy Policies of Social Network Sites. We define the threshold number for the system of equations and explain the stability of an Infection Free Equilibrium (IFE), representing the absence of misinformation. We have discussed about the endemic equilibrium point and bifurcation conditions along with its nature and stability at those points. Also, we have shown global stability at the endemic Equilibrium of the system. Finally, numerical simulation has been used to show the existence of bifurcation in the system with a change in the value of parameters.
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Scientific article
How to manage patient's service time has been a burden in view of the condition of patients who have to wait for required service from doctors in many hospitals in developing countries. This paper deals with the management of service time of doctor's consultation using parallel service time. Though, the theoretical underlying distribution of service time is exponential, but this research showed service time to be non-exponential but, normal. This unusual distribution of service time was attributed to non-identical services required by patients from doctors in the considered sample space. Secondly, the mean service time from each service point as researched was found the same. This showed that no line could be preferred to other.
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Signature-based malware detection using approximate boyer moore string matching algorithm
Scientific article
Adversaries to any system restlessly continues to sought effective, non-detectable means to aid them successful penetrate secure systems, either for fun or commercial gains. They achieve these feats easily through the use of malware, which keeps on the rise, an ever-growing and corresponding overpopulated malware zoo. As such, information technology industry will continue to encounter via these escapades, both monetary and prestigious losses. Malware by design aims to alter the behaviour of its host by self-replicating its genome or codes unto it. They are quite fascinating in that on execution, some malware change their own structure so that its copies have same functionality but differ in signature and syntax from the original or parent virus. This makes signature detection quite unreliable. Study investigates detection of metamorphic malware attacks using the Boyer Moore algorithm for string-based signature detection scheme.
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Simulation of CPU Scheduling Algorithms using Poisson Distribution
Scientific article
Numerous scheduling algorithms have been developed and implemented in a bid to optimized CPU utilization. However, selecting a scheduling algorithm for real system is still very challenging as most of these algorithms have their peculiarities. In this paper, a comparative analysis of three CPU scheduling algorithms Shortest Job First Non-Preemptive, Dynamic Round-Robin even-odd number quantum Scheduling algorithm and Highest Response-Ratio-Next (HRRN) was carried out using dataset generated using Poisson Distribution. The performance of these algorithms was evaluated in the context of Average Waiting Time (AWT), Average Turnaround Time (ATT). Experimental results showed that Shortest Job First Non-Pre-emptive resulted in minimal AWT and ATT when compared with two other algorithms.
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Slow Invariant Manifold Analysis in a Mitotic Model of Frog Eggs via Flow Curvature Method
Scientific article
A slow-fast dynamical systems can be investigated qualitatively and quantitatively in the study of nonlinear chaotic dynamical systems. Slow-fast autonomous dynamical systems exhibit a dichotomy of motion, which is alternately slow and quick, according to experiments. Some investigations show that slow-fast dynamical systems have slow manifolds, which is supported by theory. The goal of the proposed study is to show how differential geometry may be used to examine the slow manifold of the dynamical system known as the mitotic model of frog eggs. The algebraic equation of the flow curvature manifold is obtained using the flow curvature technique applied to the dynamical mitosis model. Using the Darboux invariance theorem, we then argue that this slow manifold equation is invariant with regard to the flow.
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Slow Invariant Manifold of Brusselator Model
Scientific article
The slow invariant manifold is a unique trajectory of the dynamical system that describes the long-time dynamics of the system’s evolution efficiently. Determining such manifolds is of obvious importance. On one hand they provide a basic insight into the dynamics of the system, on the other hand they allow a reduction of dimension of the system occurs on the invariant manifold only. If the dimension of the invariant manifold is sufficiently low, this reduction may result in substantial savings in computational costs. In this paper, differential geometry based new developed approach called the flow curvature method is considered to analyse the Brusselator model. According to this method, the trajectory curve or flow of any dynamical system of dimension considers as a curve in Euclidean space of dimension . Then the flow curvature or the curvature of the trajectory curve may be computed analytically. The set of points where the flow curvature is null or empty defines the flow curvature manifold. This manifold connected with the dynamical system of any dimension directly describes the analytical equation of the slow invariant manifold incorporated with the same dynamical system. In this article, we apply the flow curvature method for the first time on the two-dimensional Brusselator model to compute the analytical equation of the slow invariant manifold where we use the Darboux theorem to prove the invariance property of the slow manifold.
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Smart Contract Obfuscation Technique to Enhance Code Security and Prevent Code Reusability
Scientific article
Along with the advancements in blockchain technology, many blockchain-based successful projects have been done mainly on the ethereum platform, most of which deal with transactions. Still, it also carries various risks when it comes to security, as evident from past attacks. Most big projects like uniswap, decentraland, and others use smart contracts, deployed on the ethereum platform, leading to similar projects via code reuse. Code reuse practice is quite frequent as a survey suggests 26% of contract code deployed is via code reuse. Smart contract code obfuscation techniques can be used on solidity code that is publicly verified, published (in the case of Ethereum), and on the deployment address. All the above techniques work by replacing characters with their random counterpart, known as statistical substitution. A statistical substitution is a process of transforming an input string into a new string where each character has been replaced by a random character drawn from a stock of all possible 'random' characters. Therefore, we proposed numerous methods in this paper to solve the above problems using various smart contract code obfuscation techniques. These techniques can be really useful in blockchain projects and can save millions of dollars to investors & companies by enhancing code security and preventing code reusability. Techniques mentioned in this paper when compared with other techniques. Our methods are not expensive to implement, very easy to use, and provide a developer-friendly selective increment in code complexity.
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Scientific article
Combining Near Field Communication (NFC) technology with Secure Hash Algorithm (SHA) 256-bit encryption into smart homes may offer new opportunities to improve the security and usability of today’s homes. The goal of this paper is to explore a new way to automate home functions using NFC to authenticate users and share information seamlessly, while also using SHA 256-bit for secure encryption of sensitive information. By using this combined technology, homeowners will be able to securely operate their smart home devices through NFC-enabled Smartphone’s or wearable devices rather than having to remember complicated passwords or use complicated authentication methods. Because all communications between each user’s device and the smart home hub will be securely encrypted with SHA 256, protected from unauthorized access or tampering, the transferred data will be both confidential and have its integrity preserved. Additionally, because of the flexibility of the described system, it will be possible to easily integrate existing smart homes into a single platform and support users in many different applications, such as home security, energy management, remote monitoring, etc. Performance testing and validation will continue throughout this process. Then we demonstrate the way technology presented in this paper has improved both security and user experience in a smart home environment. The research presented will advance the technology used in smart homes through the use of NFC with SHA-256-based hashing for integrity and authentication to create a stable and user friendly method for providing security, as well as efficiency, in home automation.
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Software Reliability Allocation using FAHP and Trapezoidal Fuzzy Set Theory
Scientific article
Reliability of a software system is an important attribute of software quality, and its importance has increased significantly due to the growing demand for high-quality software systems. Evaluating reliability during the design phase is essential for improving system performance and ensuring effective planning. At this stage, an important challenge is to identify suitable methods for achieving the desired reliability of the software system. Reliability allocation methods can be applied to assign reliability targets to individual components prior to the actual system design. To address this, a new hierarchical model is proposed that integrates the perspectives of users, software programmers, and software managers. The system is decomposed into multiple levels, including functions, programs, modules, and submodules, to enable systematic analysis. To handle uncertainty and vagueness in human judgments, the fuzzy analytic hierarchy process (FAHP) is employed, incorporating the geometric mean method with trapezoidal fuzzy numbers. The proposed approach determines reliable weights and effectively allocates reliability targets at each level. A comparison with the classical AHP method demonstrates that FAHP provides a more flexible and realistic representation by capturing uncertainty, making it more suitable for reliability allocation in complex software systems.
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Solutions of Black-Scholes Equation by Some Numerical Approaches
Scientific article
The Black-Scholes equation plays an important role in financial mathematics for the evaluation of European options. It is a fundamental PDE in financial mathematics, models the price dynamics of options and derivatives. While a closed-form of analytical solution exists for European options, numerical methods remain essential for validating computational approaches and extending solutions to more complex derivatives. This study explores and compares various numerical techniques for solving the Black-Scholes partial differential equation, including the finite difference method (explicit, implicit, and Crank-Nicolson schemes), and Monte Carlo simulation. Each method is implemented and tested against the analytical Black-Scholes formula to assess accuracy, convergence, and computational efficiency. The results demonstrate the strengths and limitations of each numerical approach, providing insights into their suitability for different option pricing scenarios. This comparative analysis highlights the importance of method selection in practical financial modeling applications.
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Solving Bi-matrix Games in Tourism Planning Management under Rough Interval Approach
Scientific article
The aim of this article is to propose a novel and simple technique for solving bi-matrix games with rough intervals payoffs. Since the payoffs of the rough bi-matrix games are rough intervals, then its value is also a rough interval. In this technique, we derived four bilinear programming problems, which are used to obtain the upper lower bound, lower lower bound, lower upper bound and upper upper bound of the rough interval values of the players in rough bi-matrix games which we called in this article as 'solution space'. Moreover, the expected value operator and trust measure of rough interval have been used to find the α-trust equilibrium strategies and the expected equilibrium strategies of rough interval bi-matrix games. Finally, numerical example of tourism planning management model is presented to illustrate the methodologies adopted and solution procedure.
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Some Properties of Anti Imprecise Subgroup and its Application
Scientific article
Various authors from around the world have extended the fuzzy concept to study the uncertainty condition and define its degree of certainty in various real-life experiments. At the same time, many authors have discussed the shortcomings of the definition of fuzzy sets that currently exist. However, no author has properly highlighted the problem of not following the two main classical set theories logically. To address this issue, an imprecise set definition is introduced as an extended definition of fuzzy sets, where the new concept applies two parameters, namely the functions of membership and reference, instead of one, and is helpful in defining the uncertainty problem in a more convenient manner than the existing one. In our previous work, we have studied imprecise subgroup using this new concept addressed by Baruah. In this paper, using the concept of complement of imprecise subgroup, we have introduced anti imprecise subgroup and some properties of anti imprecise subgroup with examples. Imprecise subgroup is an extended version of fuzzy group theory developed using the definition of imprecise set defined by Baruah. In addition, we expected an application developed from an anti imprecise subgroup that can be used to resolve various networking problems.
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Some measures of picture fuzzy sets and their application in multi-attribute decision making
Scientific article
To measure the difference of two fuzzy sets / intuitionistic sets, we can use the distance measure and dissimilarity measure between fuzzy sets. Characterization of distance/dissimilarity measure between fuzzy sets/intuitionistic fuzzy set is important as it has application in different areas: pattern recognition, image segmentation, and decision making. Picture fuzzy set (PFS) is a generalization of fuzzy set and intuitionistic set, so that it have many application. In this paper, we introduce concepts: difference between PFS-sets, distance measure and dissimilarity measure between picture fuzzy sets, and also provide the formulas for determining these values. We also present an application of dissimilarity measures in multi-attribute decision making.
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Sorting using a combination of bubble sort, selection sort & counting sort
Scientific article
One of the most important problems in computer science is the ordering of the data. Although sorting is a very old computer science problem, it still attracts a great deal of research. Usually, when we face a problem, we’re concerned with finding the solution, then getting it out of our heads and into a text editor, white-board, or down on a piece of paper. Eventually, we start transforming that idea into code, and the code is pretty terrible the first time around. But at some point, once we’ve made it work and made it right, we find ourselves asking: Can I make it fast? Can I make it better? This paper presents an enhanced sorting algorithm which comprises of a combination of Bubble Sort, Selection Sort, and Counting Sort. The new algorithm is analyzed, implemented, tested, compared and the results were promising.
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Stability Analysis of COVID-19 Model with Quarantine
Scientific article
In this paper, A 6 (six) compartmental (S, IU, IS, IA, Q, R) model was presented to examine the dynamical behavior of disease transmission in the system with quarantine effect on the symptomatic infected, asymptomatic infected and Reproduction number R0 within a given population. The parameters model was analyzed and estimated experimentally using the real data of COVID-19 confirmed cases for Ethiopia via MATLAB 2021a. Reproduction number R0 which is a key indicator to whether a disease outbreak spread force will persist or die out within population. R0 was found using the next generation matrix with Gaussian elimination method to obtain the inverse of the transitive matrix. The model also aims at reducing R0 owning to the fact that when the basic reproduction number is less than 1 infected person, disease dies out and when the reproduction number is greater than 1 infected person, the disease persists. The facts about R0 geared us to mathematically check for the Routh-Hurwitz stability criteria and Lyapunov Functions to concisely establish the necessary and sufficient conditions for the Local and Global stability of model. results show that, when R0 - 1 and R0 > 1 the diseases free equilibrium and endemic equilibrium points are locally and globally asymptotically stable respectively. In order to interpret results and recommend possible control measure of disease, The dynamics of the Quarantine compartment in model was tested via sensitivity analysis to experimentally investigate transition/ transmission pattern. The effect of quarantine analysis on the model shows that preventive measures such as increase in quarantine with treatments during disease outbreak will significantly decrease the Reproduction number. Hence, increase in Quarantine compartment will flatten the curve of (S, IU, IS, IA, Q, R) dynamic model correspondingly.
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Scientific article
Newcastle is a viral disease of chicken and other avian species. In this paper, the stability analysis of the disease free and endemic equilibrium points of the Newcastle disease model of the village chicken in the absence of any control are studied. The Hurwitz matrix criterion is applied to study the stability of the Newcastle disease free equilibrium point,Q0. The result shows that the disease free equilibrium point is locally asymptotically stable iff the principle leading minors of the Hurwitz Matrix, (for n∈ℝ+) are all positive. Using the Castillo Chavez Theorem we showed that, the disease free equilibrium point is globally asymptotically when R0-1. Furthermore, using the logarithmic function and the LaSalle’s Theorem, the endemic equilibrium point is found globally asymptotically stable for R0-1. Finally the numerical simulations confirm the existence and stability of the equilibrium points of the model. This reveals that, proper interventions are needed so as to decrease the frequently occurrence of the Newcastle disease in the village chicken population.
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Stochastic Model Including Refining Stage to Improve Water Supply System in Bangladesh
Scientific article
People around the world use fresh water daily for drinking, sanitation, and washing. At the same time, they discharge wastewater into canals, which can be harmful to both human health and the ecosystem of surface water sources. A significant amount of water is consumed for washing purposes. However, it is possible to disinfect and purify this large volume of wastewater for reuse. The process of treating used wastewater is known as refinement. This study aims to develop a two-stage stochastic recourse model that refines wastewater before it is released into the environment. The goal is to ensure that the refined wastewater does not harm the ecosystem. The treated water can then be repurposed for various secondary uses. The proposed model will account for uncertainties related to the availability of water from the supplying authority. To evaluate the effectiveness of this model, we will compare the costs of the water supply system both with and without refinement. The advantages of the proposed model will be assessed through calculations of the expected value of perfect information (EVPI), the value of the stochastic solution (VSS), the recourse solution (RS), the wait-and-see solution (WS), and the expected solution based on first-stage decisions (EEV). Additionally, a risk-averse (RA) optimization model will be used to analyze the sensitivity of system costs.
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