Search results for: stochastic game

Authors: P. Jayashree, S. Rajkumar

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With the trend of virtual and augmented reality environments booming to provide a life like experience, gaming is a major tool in supporting such learning environments. In this work, a variant of Voronoi heuristics, employing supervised learning for the TRON game is proposed. The paper discusses the features that would be really useful when a machine learning bot is to be used as an opponent against a human player. Various game scenarios, nature of the bot and the experimental results are provided for the proposed variant to prove that the approach is better than those that are currently followed.

Keywords: artificial Intelligence, automation, machine learning, TRON game, Voronoi heuristics

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Authors: Hanmei Peng, Yiqun Wang, Mao Tan, Zhuocen Dai, Yongxin Su

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Efficient energy management in multi-microgrid distribution systems holds significant importance for enhancing the economic benefits of regional power grids. To better balance conflicts among various stakeholders, a two-stage game-based collaborative optimization approach is proposed in this paper, effectively addressing the realistic scenario involving both competition and collaboration among stakeholders. The first stage, aimed at maximizing individual benefits, involves constructing a non-cooperative tariff game model for the distribution network and surplus microgrid. In the second stage, considering power flow and physical line capacity constraints we establish a cooperative P2P game model for the multi-microgrid distribution system, and the optimization involves employing the Lagrange method of multipliers to handle complex constraints. Simulation results demonstrate that the proposed approach can effectively improve the system economics while harmonizing individual and collective rationality.

Keywords: cooperative game, collaborative optimization, multi-microgrid distribution system, non-cooperative game

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Authors: Yeliz Mert Kantar, İsmail Yeni̇lmez, Ibrahim Arik

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In this study, the efficiency measurement of the top fifty Turkish Universities has been conducted. The top fifty Turkish Universities are listed by The Scientific and Technological Research Council of Turkey (TÜBITAK) according to the Entrepreneur and Innovative University Index every year. The index is calculated based on four components since 2018. Four components are scientific and technological research competency, intellectual property pool, cooperation and interaction, and economic and social contribution. The four components consist of twenty-three sub-components. The 2021 list announced in January 2022 is discussed in this study. Efficiency analysis have been carried out using the Stochastic Frontier Model. Statistical significance of the sub-components that make up the index with certain weights has been examined in terms of the efficiency measurement calculated through the Stochastic Frontier Model. The relationship between the efficiency ranking estimated based on the Stochastic Frontier Model and the Entrepreneur and Innovative University Index ranking is discussed in detail.

Keywords: efficiency, entrepreneur and innovative universities, turkish universities, stochastic frontier model, tübi̇tak

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Authors: Naza Djafarova, Tony Bates, Margaret Verkuyl, Leonora Zefi, Ozgur Turetken, Alex Ferworn, Mastrilli Paula, Daria Romaniuk, Kosha Bramesfeld, Anastasia Dimitriadou, Cheryl To

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Designing serious games for education is a challenging and resource-intensive effort. If a well-designed process that balances pedagogical principles with game mechanics is in place, it can help to simplify the design process of serious games and increase efficiency. Multidisciplinary teams involved in designing serious games can benefit tremendously from such a process in their endeavours to develop and implement these games at undergraduate and graduate levels. This paper presentation will outline research results on identified gaps within existing processes and frameworks and present an adapted process that emerged from the research. The research methodology was based on a survey, semi-structured interviews and workshops for testing the adapted process for game design. Based on the findings, the authors propose a simple process for the pre-production stage of serious game design that may help guide multidisciplinary teams in their work. This process was used to facilitate team brainstorming, and is currently being tested to assess if multidisciplinary teams find value in using it in their process of designing serious games.

Keywords: serious game-design, multidisciplinary team, game design framework, learning games, multidisciplinary game design process

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Authors: Teh Raihana Nazirah Roslan, Siti Zulaiha Ibrahim, Sharmila Karim

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A warrant is a financial contract that confers the right but not the obligation, to buy or sell a security at a certain price before expiration. The standard procedure to value equity warrants using call option pricing models such as the Black–Scholes model had been proven to contain many flaws, such as the assumption of constant interest rate and constant volatility. In fact, existing alternative models were found focusing more on demonstrating techniques for pricing, rather than empirical testing. Therefore, a mathematical model for pricing and analyzing equity warrants which comprises stochastic interest rate and stochastic volatility is essential to incorporate the dynamic relationships between the identified variables and illustrate the real market. Here, the aim is to develop dynamic pricing formulations for hybrid equity warrants by incorporating stochastic interest rates from the Cox-Ingersoll-Ross (CIR) model, along with stochastic volatility from the Heston model. The development of the model involves the derivations of stochastic differential equations that govern the model dynamics. The resulting equations which involve Cauchy problem and heat equations are then solved using partial differential equation approaches. The analytical pricing formulas obtained in this study comply with the form of analytical expressions embedded in the Black-Scholes model and other existing pricing models for equity warrants. This facilitates the practicality of this proposed formula for comparison purposes and further empirical study.

Keywords: Cox-Ingersoll-Ross model, equity warrants, Heston model, hybrid models, stochastic

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Authors: Bassam Shaikh, R. S. A. Jumain

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Game addiction has become an extremely important topic in psychology researchers, particularly in understanding and explaining why individuals become addicted (to video games). In previous studies, effect of online game addiction on social responsibilities, health problems, government action, and the behaviors of individuals to purchase and the causes of making individuals addicted on the video games has been discussed. Extending these concepts in marketing, it could be argued than the phenomenon could enlighten and extending our understanding on consumer loyalty. This study took the Grounded Theory approach, and found that motivation, satisfaction, fulfillments, exploration and achievements to be part of the important elements that builds consumer loyalty.

Keywords: grounded theory, consumer loyalty, video games, video game addiction

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Authors: Fawad Zaidi

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This paper discusses a variety of challenges and solutions involved with creating computer games and the issues faced by the software engineers working in this field. This review further investigates the articles coverage of project scope and the problem of feature creep that appears to be inherent with game development. The paper tries to answer the following question: Is this a problem caused by a shortage, or bad software engineering practices, or is this outside the control of the software engineering component of the game production process?

Keywords: software engineering, computer games, software applications, development

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Authors: S. B. Kumbalavati, J. D. Mallapur, K. Y. Bendigeri

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A mobile Ad-hoc network (MANET) is a multihop wireless network where nodes communicate each other without any pre-deployed infrastructure. There is no central administrating unit. Hence, MANET is generally prone to many of the attacks. These attacks may alter, release or deny data. These attacks are nothing but intrusions. Intrusion is a set of actions that attempts to compromise integrity, confidentiality and availability of resources. A major issue in the design and operation of ad-hoc network is sharing the common spectrum or common channel bandwidth among all the nodes. We are performing intrusion detection using game theory approach. Game theory is a mathematical tool for analysing problems of competition and negotiation among the players in any field like marketing, e-commerce and networking. In this paper mathematical model is developed using game theory approach and intruders are detected and removed. Bandwidth utilization is estimated and comparison is made between bandwidth utilization with intrusion detection technique and without intrusion detection technique. Percentage of intruders and efficiency of the network is analysed.

Keywords: ad-hoc network, IDS, game theory, sensor networks

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Authors: Brando Vagenende, Marie-Anne Guerry

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For stochastic matrices of any order, the geometric description of the convex set of eigenvalues is completely known. The purpose of this study is to investigate the subset of the monotone matrices. This type of matrix appears in contexts such as intergenerational occupational mobility, equal-input modeling, and credit ratings-based systems. Monotone matrices are stochastic matrices in which each row stochastically dominates the previous row. The monotonicity property of a stochastic matrix can be expressed by a nonnegative lower-order matrix with the same eigenvalues as the original monotone matrix (except for the eigenvalue 1). Specifically, the aim of this research is to focus on the properties of eigenvalues of monotone matrices. For those matrices up to order 3, there already exists a complete description of the convex set of eigenvalues. For monotone matrices of order at least 4, this study gives, through simulations, more insight into the geometric description of their eigenvalues. Furthermore, this research treats in a geometric and algebraic way the properties of eigenvalues of monotone matrices of order at least 4.

Keywords: eigenvalues of matrices, finite Markov chains, monotone matrices, nonnegative matrices, stochastic matrices

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Authors: Ogar Ofut Tumenayu, Olga Shabalina

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This paper describes the application of two types of pedagogical agents’ technology with different functions in an adaptive educational game with the sole aim of improving learning and enhancing interactivities in Digital Educational Games (DEG). This idea could promote the elimination of some problems of DEG, like isolation in game-based learning, by introducing a tutor and tutee pedagogical agents. We present an analysis of a learning companion interacting in a peer tutoring environment as a step toward improving social interactions in the educational game environment. We show that tutor and tutee agents use different interventions and interactive approaches: the tutor agent is engaged in tracking the learner’s activities and inferring the learning state, while the tutee agent initiates interactions with the learner at the appropriate times and in appropriate manners. In order to provide motivation to prevent mistakes and clarity a game task, the tutor agent uses the help dialog tool to provide assistance, while the tutee agent provides collaboration assistance by using the hind tool. We presented our idea on a prototype game called “Pyramid Programming Game,” a 2D game that was developed using Libgdx. The game's Pyramid component symbolizes a programming task that is presented to the player in the form of a puzzle. During gameplay, the Agents can instruct, direct, inspire, and communicate emotions. They can also rapidly alter the instructional pattern in response to the learner's performance and knowledge. The pyramid must be effectively destroyed in order to win the game. The game also teaches and illustrates the advantages of utilizing educational agents such as TrA and TeA to assist and motivate students. Our findings support the idea that the functionality of a pedagogical agent should be dualized into an instructional and learner’s companion agent in order to enhance interactivity in a game-based environment.

Keywords: tutor agent, tutee agent, learner’s companion interaction, agent collaboration

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Authors: Hiba El Assibi

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This study aims to weakly solve Kalah, a two-player board game, by developing a start-to-finish winning strategy using an optimized Minimax algorithm with Alpha-Beta Pruning. In weakly solving Kalah, our focus is on creating an optimal strategy from the game's beginning rather than analyzing every possible position. The project will explore additional enhancements like symmetry checking and code optimizations to speed up the decision-making process. This approach is expected to give insights into efficient strategy formulation in board games and potentially help create games with a fair distribution of outcomes. Furthermore, this research provides a unique perspective on human versus Artificial Intelligence decision-making in strategic games. By comparing the AI-generated optimal moves with human choices, we can explore how seemingly advantageous moves can, in the long run, be harmful, thereby offering a deeper understanding of strategic thinking and foresight in games. Moreover, this paper discusses the evaluation of our strategy against existing methods, providing insights on performance and computational efficiency. We also discuss the scalability of our approach to the game, considering different board sizes (number of pits and stones) and rules (different variations) and studying how that affects performance and complexity. The findings have potential implications for the development of AI applications in strategic game planning, enhancing our understanding of human cognitive processes in game settings, and offer insights into creating balanced and engaging game experiences.

Keywords: minimax, alpha beta pruning, transposition tables, weakly solving, game theory

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Authors: Aarthy Anandan, Anitha Narasimhan, Madhan Karky

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Word-based games are popular in helping people to improve their vocabulary skills. Games like ‘word search’ and crosswords provide a smart way of increasing vocabulary skills. Word search games are fun to play, but also educational which actually helps to learn a language. Finding the words from word search puzzle helps the player to remember words in an easier way, and it also helps to learn the spellings of words. In this paper, we present a tile distribution algorithm for a Maze-Based Treasure Hunt Game 'Pudhaiyal’ for Tamil words, which describes how words can be distributed horizontally, vertically or diagonally in a 10 x 10 grid. Along with the tile distribution algorithm, we also present an algorithm for the scoring model of the game. The proposed game has been tested with 20,000 Tamil words.

Keywords: Pudhaiyal, Tamil word game, word search, scoring, maze, algorithm

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Authors: Lori L. Scarlatos, Ryan Courtney

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This paper explores the impact that playing a casual game can have on a player's learning and subsequent behavior. A casual mobile game, Container Chaos, was created to teach undergraduate students about the carbon footprint of various disposable beverage containers. Learning was tested with a short quiz, and behavior was tested by observing which beverage containers players choose when offered a drink and a snack. The game was tested multiple times, under a variety of different circumstances. Findings of these tests indicate that, with extended play over time, players can learn new information and sometimes even change their behavior as a result. This has implications for how other casual games can be used to teach concepts and possibly modify behavior.

Keywords: behavior, carbon footprint, casual games, environmental impact, material sciences

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Authors: Mane Varosyan, Diana Tumanyan, Agnesa Martirosyan

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There are many catastrophic events that end with dire consequences, and to avoid them, people should be well-armed with the necessary information about these situations. During the last years, Serious Games have increasingly gained popularity for training people for different types of emergencies. The major discussed problem is the usage of gamification in education. Moreover, it is mandatory to understand how and what kind of gamified e-learning modules promote engagement. As the theme is emergency, we also find out people’s behavior for creating the final approach. Our proposed solution is an educational video game, “EZZRA”.

Keywords: gamification, education, emergency, serious games, game design, virtual reality, digitalisation

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Authors: Desiderio S. Camitan IV

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The standard view of lay people in the Philippine society is that young children do not lie and that if they do, their lies are easily detectable. The present study investigated the deceptive behaviors of 373 children aged 2-8 using the temptation resistance paradigm. Children were instructed that they will participate in a game where they are to guess the color of a candy placed inside a downward facing cup. After the instruction was given to them, they are left alone in a room with the cup on top of a table for 15 minutes. The researcher observed the number of children who peeked at the card as well as number of those who confessed to the said act. Age, gender, IQ, and having autism seem to influence the frequency of peeking and confession of the participants.

Keywords: cheating, lying, dishonesty, young children, guessing game, autism

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Authors: Olfa Kaabia, Ilyes Abid, Khaled Guesmi

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This pioneer paper studies whether and how Bitcoin shocks are transmitted to the U.S economy. We employ a new methodology: TVP FAVAR model with stochastic volatility. We use a large dataset of 111 major U.S variables from 1959:m1 to 2016:m12. The results show that Bitcoin shocks significantly impact the U.S. economy. This significant impact is pronounced in a volatile and increasing U.S economy. The Bitcoin has a positive relationship on the U.S real activity, and a negative one on U.S prices and interest rates. Effects on the Monetary Policy exist via the inter-est rates and the Money, Credit and Finance transmission channels.

Keywords: bitcoin, US economy, FAVAR models, stochastic volatility

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Authors: Ramazan Kadiev, Arkadi Ponossov

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Semidiscrete systems contain both continuous and discrete components. This means that the dynamics is mostly continuous, but at certain instants, it is exposed to abrupt influences. Such systems naturally appear in applications, for example, in biological and ecological models as well as in the control theory. Therefore, the study of semidiscrete systems has recently attracted the attention of many specialists. Stochastic effects are an important part of any realistic approach to modeling. For example, stochasticity arises in the population dynamics, demographic and ecological due to a change in time of factors external to the system affecting the survival of the population. In control theory, random coefficients can simulate inaccuracies in measurements. It will be shown in the presentation how to incorporate such effects into semidiscrete systems. Stability analysis is an essential part of modeling real-world problems. In the presentation, it will be explained how sufficient conditions for the moment stability of solutions in terms of the coefficients for linear semidiscrete stochastic equations can be derived using non-Lyapunov technique.

Keywords: abrupt changes, exponential stability, regularization, stochastic noises

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Authors: Min Wei

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The green hotel provides the products/services consistent with the full utilization of resources, protecting the ecological environment conducive to customers’ requirements and health. In order to better develop the green hospitality industry, this paper applies the game theory to analyze the intrinsic relationship and balanced interests among the stakeholders including government, hotels, and tourists during green hospitality development. Based on the hypothesis in game theory, this paper tries to construct a linkage mechanism in stakeholders, by which a theoretical basis for the interests’ balance can be realized. By using game theory and constructing a game model including tourists, hotels and government, this paper analyzes the relationship of the various stakeholders involved in the green hospitality development, and subsequently proposes the development model of green hospitality industry. On the one hand, this paper applies game theory to construct a green hotel development model and provides a theoretical basis for the interest balance of stakeholders based on theoretical perspective. On the other hand, the current development of green hospitality industry is still in initial phase, and the outcome of this research tries to guide tourists to form a green awareness and to establish the concept of green consumption for hotel development, so that green hotel products/services are provided. In addition, this paper provides a basis for decision making in the relevant government departments so that the interests of all stakeholders are promoted and cooperative game between stakeholders is established, for which the sustainable development of green hotels is achieved. The findings indicate that the process of achieving green hospitality industry development is to maximize the whole interests of stakeholders.

Keywords: green hospitality, game theory, stakeholders, development model

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Authors: Marina Tsetseli, Eleni Zetou, Maria Michalopoulou, Nikos Vernadakis

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Game performance, besides the accuracy and the quality skills execution, depends heavily on where the athletes will focus their attention while performing a skill. The purpose of the present study was to examine and compare the effect of internal and external focus of attention instructions on the decision making in tennis at players 8-9 years old (M=8.4, SD=0.49). The participants (N=40) were divided into two groups and followed an intervention training program that lasted 4 weeks; first group (N=20) under internal focus of attention instructions and the second group (N=20) under external focus of attention instructions. Three measurements took place (pre-test, post-test, and retention test) in which the participants were video recorded while playing matches in real scoring conditions. GPAI (Game Performance Assessment Instrument) was used to evaluate decision making in three game situations; service, return of the service, baseline game. ANOVA repeated measures (2 groups x 3 measurements) revealed a significant interaction between groups and measurements. Specifically, the data analysis showed superiority of the group that was instructed to focus externally. The high scores of the external attention group were maintained at the same level at the third measurement as well, which indicates that the impact was concerning not only performance but also learning. Thus, cues that lead to an external focus of attention enhance the decision-making skill and therefore the game performance of the young tennis players.

Keywords: decision making, evaluation, focus of attention, game performance, tennis

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Authors: Yael Deutsch, Arieh Gavious

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The threat of aviation terrorism and its potential damage became significant after the 9/11 terror attacks. These attacks have led authorities and leaders to suggest that security personnel should overcome politically correct scruples about profiling and use it openly. However, there is a lack of knowledge about the smart usage of profiling and its advantages. We analyze game models that are suitable to specific real-world scenarios, focusing on profiling as a tool to detect potential violators, such as terrorists and smugglers. We provide analytical and clear answers to difficult questions, and by that help fighting against harmful violation acts.

Keywords: game theory, profiling, security, nash equilibrium

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Authors: Marylene S. Eder, Dorothy M. Jao, Paolo Marc Nicolas S. Laspiñas, Pukilan A. Malim, Sarah Jean D. Raterta

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Trash Dash is an android game application developed to serve as an alternative tool to practice proper waste segregation for children ages 3 years old and above. The researchers designed the application using Unity 3D and developed the text file that served as the database of the game application. An observation of a pre-school teacher shows that children know how to throw their garbage but they do not know yet how to segregate wastes. After launching the mobile application to K-2 pupils 4 – 5 years of age, the researchers have noticed that children within this age are active and motivated to learn the difference between biodegradable and non-biodegradable. Based on the result of usability test conducted, it was concluded that the game is easy to use and children will most likely use this application frequently. Furthermore, the children may need assistance from their parents and teachers when playing the game. An actual testing of the application has been conducted to different devices as well as functionality test by Thwack Application and it can be concluded that the mobile application can be launched and installed on a device with a minimum API requirement of Gingerbread (2.3.1).

Keywords: waste segregation, android application, biodegradable, non-biodegradable

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Authors: Yutae Lee

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In this paper, we consider the performance and availability of a redundancy model. The redundancy model is a form of resilience that ensures service availability in the event of component failure. This paper considers a 2N redundancy model. In the model there are at most one active service unit and at most one standby service unit. The active one is providing the service while the standby is prepared to take over the active role when the active fails. We design our analysis model using Stochastic Reward Nets, and then evaluate the performance and availability of 2N redundancy model using Stochastic Petri Net Package (SPNP).

Keywords: availability, performance, stochastic reward net, 2N redundancy

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Authors: Homa Ghave, Parmis Shahmaleki

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This paper presents a new multi-criteria stochastic mathematical model for a single machine scheduling with outsourcing allowed. There are multiple jobs processing in batch. For each batch, all of job or a quantity of it can be outsourced. The jobs have stochastic processing time and lead time and deterministic due dates arrive randomly. Because of the stochastic inherent of processing time and lead time, we use the chance constrained programming for modeling the problem. First, the problem is formulated in form of stochastic programming and then prepared in a form of deterministic mixed integer linear programming. The objectives are considered in the model to minimize the maximum tardiness and outsourcing cost simultaneously. Several procedures have been developed to deal with the multi-criteria problem. In this paper, we utilize the concept of satisfaction functions to increases the manager’s preference. The proposed approach is tested on instances where the random variables are normally distributed.

Keywords: single machine scheduling, multi-criteria mathematical model, outsourcing strategy, uncertain lead times and processing times, chance constrained programming, satisfaction function

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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: Haif Alharthy, Samar Altarteer

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Blind and sighted teenagers might find it challenging to communicate and have fun interaction with each other. The previous studies emphasize the importance of the interactive communication of the blind with the sighted people in developing the interpersonal and social skills of the blind people . Playing games is one of the effective ways used to engage the blind with the sighted people and help in enhancing their social skills. However, it is difficult to find a fun game that is designed to encourage interaction between blind and sighted teenagers in which the blind can play it independently without help and that the sighted find its design attractive and satisfying. The aim of this paper is to examine how challenging is to have fun interaction between blind and sighted people and offer interactive tabletop game solution in which both of them can independently participate and enjoy. The paper discusses the importance and the impact of the interactive fun communication between blind and sighted people and how to get them involved with each other through games. The paper investigates several approaches to design a universal game. A survey was conducted for blind teenager’s family members to discover what difficulties they face while playing and communicating with their blind family member and to identify the blind’s needs and interests in games. The study reveals that although families like to play tabletop games with their blind member, they find difficulties in finding universal games that is interesting and adequate for both. Also, qualitative interviews were conducted with blind teenager shows the sufficiency in tabletop games that do not require help from another family member to play the game. The results suggested that an effective approach is to develop an interactive tabletop game embedded with audio and tactile techniques. The findings of the pilot study highlighted the necessary information such as tools, visuals, and game concepts that should be considered in developing interactive card game for blind and sighted teenagers.

Keywords: Blind, card game, communication, interaction, play, tabletop game, teenager

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Authors: Yasith Nayana, Janani Manamperuma, Lalindi Amarasinghe, Sasanka Kodithuwakku

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Educational games are popular among current e-learning systems. The approach to education through interactive media is expected to motivate students and encourage participation and engagement. ‘Kalayathra’ is an adaptive, player centered e-learning 3D game. The game identifies the player’s personality and adapt the gaming environment according to the player’s preference. Our platform measures the student’s performance and support learning through player assessment. Player experience is a good measure of the level of fun and education presented to players. To assess the level of playability we introduce an educational playability model. ‘Kalayathra’ is developed according to the GCE O/L syllabus and teaching guide in Sri Lankan education system. The game is capable of guiding players into the environment and aid them in tasks and activities depending on how much the player requires help.

Keywords: e-learning, games, adaptive, personality, gamification, player experience

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Authors: Jaime E. Fernandez, Pablo J. Valverde

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This paper presents a methodological approach that aims to contrast/validate theoretical results from a corruption network game through probabilistic analysis of simulated microdata using Bayesian Networks (BNs). The research develops a public corruption model in a game theory framework. Theoretical results suggest a series of 'optimal settings' of model's exogenous parameters that boost the emergence of corruption. The paper contrasts these outcomes with probabilistic inference results based on BNs adjusted over simulated microdata. Principal findings indicate that probabilistic reasoning based on BNs significantly improves parameter specification and causal analysis in a public corruption game.

Keywords: Bayesian networks, probabilistic reasoning, public corruption, theoretical games

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Authors: Liliana O. Martínez, Juan E González, Manuel Ramírez-Aranda, Ana Cervantes-Herrera

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A serious game category mobile application called Math Dominoes is presented. The main objective of this applications is to strengthen the teaching-learning process of solving algebraic equations and is based on the board game "Double 6" dominoes. Math Dominoes allows the practice of solving first, second-, and third-degree algebraic equations. This application is aimed to students who seek to strengthen their skills in solving algebraic equations in a dynamic, interactive, and fun way, to reduce the risk of failure in subsequent courses that require mastery of this algebraic tool.

Keywords: algebra, equations, dominoes, serious games

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Authors: Raphael Naryongo, Philip Ngare, Anthony Waititu

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This paper deals with numerical simulation of Wishart processes for a single asset risky pricing model whose volatility is described by Wishart affine diffusion processes. The multi-factor specification of volatility will make the model more flexible enough to fit the stock market data for short or long maturities for better returns. The Wishart process is a stochastic process which is a positive semi-definite matrix-valued generalization of the square root process. The aim of the study is to model the log asset stock returns under the double Wishart stochastic volatility model. The solution of the log-asset return dynamics for Bi-Wishart processes will be obtained through Euler-Maruyama discretization schemes. The numerical results on the asset returns are compared to the existing models returns such as Heston stochastic volatility model and double Heston stochastic volatility model

Keywords: euler schemes, log-asset return, infinitesimal generator, wishart diffusion affine processes

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Authors: Michael Fundator

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Groundbreaking application of biomathematical and biochemical research in neural networks processes to formation of non-canonical bases, islands, and analog bases in DNA and mRNA at or near the transcription that contradicts the long anticipated statistical assumptions for the distribution of bases and analog bases compounds is implemented through statistical and stochastic methods apparatus with addition of quantum principles, where the usual transience of Poisson spike train becomes very instrumental tool for finding even almost periodical type of solutions to Fokker-Plank stochastic differential equation. Present article develops new multidimensional methods of finding solutions to stochastic differential equations based on more rigorous approach to mathematical apparatus through Kolmogorov-Chentsov continuity theorem that allows the stochastic processes with jumps under certain conditions to have γ-Holder continuous modification that is used as basis for finding analogous parallels in dynamics of neutral networks and formation of analog bases and transcription in DNA.

Keywords: Fokker-Plank stochastic differential equation, Kolmogorov-Chentsov continuity theorem, neural networks, translation and transcription

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