Search results for: stochastic diffusion process

Authors: Tomoaki Hashimoto

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Recent technological advance has prompted significant interest in developing the control theory of quantum systems. Following the increasing interest in the control of quantum dynamics, this paper examines the control problem of Schrödinger equation because quantum dynamics is basically governed by Schrödinger equation. From the practical point of view, stochastic disturbances cannot be avoided in the implementation of control method for quantum systems. Thus, we consider here the robust stabilization problem of Schrödinger equation against stochastic disturbances. In this paper, we adopt model predictive control method in which control performance over a finite future is optimized with a performance index that has a moving initial and terminal time. The objective of this study is to derive the stability criterion for model predictive control of Schrödinger equation under stochastic disturbances.

Keywords: optimal control, stochastic systems, quantum systems, stabilization

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Authors: Nikolaos Simantiris, Markos Avlonitis

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This work builds a simulation platform, modeling the spatial diffusion of the invasive species Callinectes sapidus (blue crab) as a random walk, incorporating also generation, fatality, and fishing rates modeling the time evolution of its population. Antinioti lagoon in West Greece was used as a testbed for applying the simulation model. Field measurements from June 2020 to June 2021 on the lagoon’s setting, bathymetry, and blue crab juveniles provided the initial population simulation of blue crabs, as well as biological parameters from the current literature were used to calibrate simulation parameters. The scope of this study is to render the authors able to predict the evolution of the blue crab population in confined environments of the Ionian Islands region in West Greece. The first result of the simulation experiments shows the possibility for a robust prediction for blue crab population evolution in the Antinioti lagoon.

Keywords: antinioti lagoon, blue crab, stochastic simulation, random walk

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Authors: Fatemeh Torfi

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Estimation of stochastic demand in physical distribution in general and efficient transport routs management in particular is emerging as a crucial factor in urban planning domain. It is particularly important in some municipalities such as Tehran where a sound demand management calls for a realistic analysis of the routing system. The methodology involved critically investigating a fuzzy least-squares linear regression approach (FLLRs) to estimate the stochastic demands in the vehicle routing problem (VRP) bearing in mind the customer's preferences order. A FLLR method is proposed in solving the VRP with stochastic demands. Approximate-distance fuzzy least-squares (ADFL) estimator ADFL estimator is applied to original data taken from a case study. The SSR values of the ADFL estimator and real demand are obtained and then compared to SSR values of the nominal demand and real demand. Empirical results showed that the proposed methods can be viable in solving problems under circumstances of having vague and imprecise performance ratings. The results further proved that application of the ADFL was realistic and efficient estimator to face the stochastic demand challenges in vehicle routing system management and solve relevant problems.

Keywords: fuzzy least-squares, stochastic, location, routing problems

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Authors: Babak Kamrani, Nozar Kishi

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Stochastic catalog represents the events module of the earthquake loss estimation models. It includes series of events with different magnitudes and corresponding frequencies/probabilities. For the development of the stochastic catalog, random or uniform sampling methods are used to sample the events from the seismicity model. For covering all the Magnitude Frequency Distribution (MFD), a huge number of events should be generated for the above-mentioned methods. Characteristic Event (CE) method chooses the events based on the interest of the insurance industry. We divide the MFD of each source into bins. We have chosen the bins based on the probability of the interest by the insurance industry. First, we have collected the information for the available seismic sources. Sources are divided into Fault sources, subduction, and events without specific fault source. We have developed the MFD for each of the individual and areal source based on the seismicity of the sources. Afterward, we have calculated the CE magnitudes based on the desired probability. To develop the stochastic catalog, we have introduced uncertainty to the location of the events too.

Keywords: stochastic catalogue, earthquake loss, uncertainty, characteristic event

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Authors: Wilmer Osvaldo Martinez, Manuel Dario Hernandez, Juan Manuel Julio

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We propose to assess the performance of k forecast procedures by exploring the distributions of forecast errors and error losses. We argue that non systematic forecast errors minimize when their distributions are symmetric and unimodal, and that forecast accuracy should be assessed through stochastic loss order rather than expected loss order, which is the way it is customarily performed in previous work. Moreover, since forecast performance evaluation can be understood as a one way analysis of variance, we propose to explore loss distributions under two circumstances; when a strict (but unknown) joint stochastic order exists among the losses of all forecast alternatives, and when such order happens among subsets of alternative procedures. In spite of the fact that loss stochastic order is stronger than loss moment order, our proposals are at least as powerful as competing tests, and are robust to the correlation, autocorrelation and heteroskedasticity settings they consider. In addition, since our proposals do not require samples of the same size, their scope is also wider, and provided that they test the whole loss distribution instead of just loss moments, they can also be used to study forecast distributions as well. We illustrate the usefulness of our proposals by evaluating a set of real world forecasts.

Keywords: forecast evaluation, stochastic order, multiple comparison, non parametric test

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Authors: Mei-Hsiu Chi, Jyh-Yang Wu, Sheng-Gwo Chen

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The diffusion-reaction equations are important Partial Differential Equations in mathematical biology, material science, physics, and so on. However, finding efficient numerical methods for diffusion-reaction systems on curved surfaces is still an important and difficult problem. The purpose of this paper is to present a convergent geometric method for solving the reaction-diffusion equations on closed surfaces by an O(r)-LTL configuration method. The O(r)-LTL configuration method combining the local tangential lifting technique and configuration equations is an effective method to estimate differential quantities on curved surfaces. Since estimating the Laplace-Beltrami operator is an important task for solving the reaction-diffusion equations on surfaces, we use the local tangential lifting method and a generalized finite difference method to approximate the Laplace-Beltrami operators and we solve this reaction-diffusion system on closed surfaces. Our method is not only conceptually simple, but also easy to implement.

Keywords: closed surfaces, high-order approachs, numerical solutions, reaction-diffusion systems

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Authors: Manlika Ratchagit

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This paper is concerned with robust mean square stability of uncertain stochastic switched discrete time-delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the robust mean square stability for the uncertain stochastic discrete time-delay system is designed via linear matrix inequalities. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.

Keywords: robust mean square stability, discrete-time stochastic systems, hybrid systems, interval time-varying delays, Lyapunov functional, linear matrix inequalities

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Authors: Manlika Rajchakit

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This paper is concerned with robust mean square stability of uncertain stochastic switched discrete time-delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the robust mean square stability for the uncertain stochastic discrete time-delay system is designed via linear matrix inequalities. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.

Keywords: robust mean square stability, discrete-time stochastic systems, hybrid systems, interval time-varying delays, lyapunov functional, linear matrix inequalities

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Authors: M. Mortada, A. Seleem, M. El-Morsi, M. Younan

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The present study introduces the folding technology to be utilized for the first time in vertical diffusion stills. This work represents a model of the distillation process by utilizing chevron pattern of folded structure. An experimental setup has been constructed, to investigate the performance of the folded sheets in the vertical effect diffusion still for a specific range of operating conditions. An experimental comparison between the folded type and the flat type sheets has been carried out. The folded pattern showed a higher performance and there is an increase in the condensate to feed ratio that ranges from 20-30 % through the operating hot plate temperature that ranges through 60-90°C. In addition, a parametric analysis of the system using Design of Experiments statistical technique, has been developed using the experimental results to determine the effect of operating conditions on the system's performance and the best operating conditions of the system has been evaluated.

Keywords: chevron pattern, fold structure, solar distillation, vertical diffusion still

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Authors: Md Al Masum Bhuiyan, Maria C. Mariani, Osei K. Tweneboah

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In the present work, we develop a technique for estimating the volatility of financial time series by using stochastic differential equation. Taking the daily closing prices from developed and emergent stock markets as the basis, we argue that the incorporation of stochastic volatility into the time-varying parameter estimation significantly improves the forecasting performance via Maximum Likelihood Estimation. While using the technique, we see the long-memory behavior of data sets and one-step-ahead-predicted log-volatility with ±2 standard errors despite the variation of the observed noise from a Normal mixture distribution, because the financial data studied is not fully Gaussian. Also, the Ornstein-Uhlenbeck process followed in this work simulates well the financial time series, which aligns our estimation algorithm with large data sets due to the fact that this algorithm has good convergence properties.

Keywords: financial time series, maximum likelihood estimation, Ornstein-Uhlenbeck type models, stochastic volatility model

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Authors: Faramarz Khosravi, Gokhan Izbirak

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A weighted statistical stochastic based Analytical Hierarchy Process (AHP) model for modeling the potential barriers and enablers of sustainability for measuring and assessing the sustainability level is proposed. For context-dependent potential barriers and enablers, the proposed model takes the basis of the properties of the variables describing the sustainability functions and was developed into a realistic analytical model for the sustainable behavior of an organization. This thus serves as a means for measuring the sustainability of the organization. The main focus of this paper was the application of the AHP tool in a statistically-based model for measuring sustainability. Hence a strong weighted stochastic AHP based procedure was achieved. A case study scenario of a widely reported major Canadian electric utility was adopted to demonstrate the applicability of the developed model and comparatively examined its results with those of an equal-weighted model method. Variations in the sustainability of a company, as fluctuations, were figured out during the time. In the results obtained, sustainability index for successive years changed form 73.12%, 79.02%, 74.31%, 76.65%, 80.49%, 79.81%, 79.83% to more exact values 73.32%, 77.72%, 76.76%, 79.41%, 81.93%, 79.72%, and 80,45% according to priorities of factors that have found by expert views, respectively. By obtaining relatively necessary informative measurement indicators, the model can practically and effectively evaluate the sustainability extent of any organization and also to determine fluctuations in the organization over time.

Keywords: AHP, sustainability fluctuation, environmental indicators, performance measurement

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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: Mok-Tan Ahn, Joon-Hong Park, Yeon-Jong Jeong

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Diffusion bonding has been continuously studied. Temperature and pressure are the most important factors to increase the strength between diffusion bonded interfaces. Diffusion bonding is an important factor affecting the bonding strength of the lined pipe. The increase of the diffusion bonding force results in a high formability clad pipe. However, in the case of drawing, it is difficult to obtain a high pressure between materials due to a relatively small reduction in cross-section, and it is difficult to prevent elongation or to tear of material in heat drawing even if the reduction in section is increased. In this paper, to increase the diffusion bonding force, we derive optimal temperature and pressure to suppress material stretching and realize precise thickness precision.

Keywords: drawing speed, FEM (Finite Element Method), diffusion bonding, temperature, heat drawing, lined pipe

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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: 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: Gkolfo I. Smani, Vasileios Megalooikonomou

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Social influence and influence diffusion have been studied in social networks. However, most existing tasks on this subject focus on static networks. In this paper, the problem of maximizing influence diffusion in dynamic social networks, i.e., the case of networks that change over time, is studied. The DM algorithm is an extension of the MATI algorithm and solves the influence maximization (IM) problem in dynamic networks and is proposed under the linear threshold (LT) and independent cascade (IC) models. Experimental results show that our proposed algorithm achieves a diffusion performance better by 1.5 times than several state-of-the-art algorithms and comparable results in diffusion scale with the Greedy algorithm. Also, the proposed algorithm is 2.4 times faster than previous methods.

Keywords: influence maximization, dynamic social networks, diffusion, social influence, graphs

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Authors: Sheldon Liu, Gordon Wang, Lei Liu, Xuefeng Liu

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Anomaly detection, also referred to as one-class classification, plays a crucial role in identifying product images that deviate from the expected distribution. This study introduces Data-centric Anomaly Detection with Diffusion Models (DCADDM), presenting a systematic strategy for data collection and further diversifying the data with image generation via diffusion models. The algorithm addresses data collection challenges in real-world scenarios and points toward data augmentation with the integration of generative AI capabilities. The paper explores the generation of normal images using diffusion models. The experiments demonstrate that with 30% of the original normal image size, modeling in an unsupervised setting with state-of-the-art approaches can achieve equivalent performances. With the addition of generated images via diffusion models (10% equivalence of the original dataset size), the proposed algorithm achieves better or equivalent anomaly localization performance.

Keywords: diffusion models, anomaly detection, data-centric, generative AI

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Authors: Tan Zhang, Zhongjian Wang, Jack Xin, Zhiwen Zhang

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We aim to efficiently compute the spreading speeds of reaction-diffusion-advection (RDA) fronts in divergence-free random flows under the Kolmogorov-Petrovsky-Piskunov (KPP) nonlinearity. We study a stochastic interacting particle method (IPM) for the reduced principal eigenvalue (Lyapunov exponent) problem of an associated linear advection-diffusion operator with spatially random coefficients. The Fourier representation of the random advection field and the Feynman-Kac (FK) formula of the principal eigenvalue (Lyapunov exponent) form the foundation of our method implemented as a genetic evolution algorithm. The particles undergo advection-diffusion and mutation/selection through a fitness function originated in the FK semigroup. We analyze the convergence of the algorithm based on operator splitting and present numerical results on representative flows such as 2D cellular flow and 3D Arnold-Beltrami-Childress (ABC) flow under random perturbations. The 2D examples serve as a consistency check with semi-Lagrangian computation. The 3D results demonstrate that IPM, being mesh-free and self-adaptive, is simple to implement and efficient for computing front spreading speeds in the advection-dominated regime for high-dimensional random flows on unbounded domains where no truncation is needed.

Keywords: KPP front speeds, random flows, Feynman-Kac semigroups, interacting particle method, convergence analysis

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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: Josip Vasilj, Petar Sarajcev, Damir Jakus

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One of the major difficulties introduced with wind power penetration is the inherent uncertainty in production originating from uncertain wind conditions. This uncertainty impacts many different aspects of power system operation, especially the balancing power requirements. For this reason, in power system development planing, it is necessary to evaluate the potential uncertainty in future wind power generation. For this purpose, simulation models are required, reproducing the performance of wind power forecasts. This paper presents a wind power forecast error simulation models which are based on the stochastic process simulation. Proposed models capture the most important statistical parameters recognized in wind power forecast error time series. Furthermore, two distinct models are presented based on data availability. First model uses wind speed measurements on potential or existing wind power plant locations, while the seconds model uses statistical distribution of wind speeds.

Keywords: wind power, uncertainty, stochastic process, Monte Carlo simulation

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Authors: Douglas Yeboah, Jai Singh

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It has been experimentally demonstrated that exciton diffusion length in organic solids can be improved by fine-tuning the material parameters that govern exciton transfer. Here, a theoretical study is carried out to support this finding. We have therefore derived expressions for the exciton diffusion length and diffusion coefficient of singlet and triplet excitons using Förster resonance energy transfer and Dexter carrier transfer mechanisms and are plotted as a function of photoluminescence (PL) quantum yield, spectral overlap integral, refractive index and dipole moment of the photoactive material. We found that singlet exciton diffusion length increases with PL quantum yield and spectral overlap integral, and decreases with increase in refractive index. Likewise, the triplet exciton diffusion length increases when PL quantum yield increases and dipole moment decreases. The calculated diffusion lengths in different organic materials are compared with existing experimental values and found to be in reasonable agreement. The results are expected to provide insight in developing new organic materials for fabricating bulk heterojunction (BHJ) organic solar cells (OSCs) with better photoconversion efficiency.

Keywords: Dexter carrier transfer, diffusion coefficient, exciton diffusion length, Föster resonance energy transfer, photoactive materials, photophysical parameters

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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: Nassim Bessaad, Qilian Bao, Zhao Jiangkang

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The fiber optics gyroscope in the strap-down inertial navigation system (FOG-SINS) suffers from precision degradation due to the influence of random errors. In this work, an enhanced Allan variance (AV) stochastic modeling method combined with discrete wavelet transform (DWT) for signal denoising is implemented to estimate the random process in the FOG signal. Furthermore, we devise a measurement-based iterative adaptive Sage-Husa nonlinear filter with augmented states to integrate a star tracker sensor with SINS. The proposed filter adapts the measurement noise covariance matrix based on the available data. Moreover, the enhanced stochastic modeling scheme is invested in tuning the process noise covariance matrix and the augmented state Gauss-Markov process parameters. Finally, the effectiveness of the proposed filter is investigated by employing the collected data in laboratory conditions. The result shows the filter's improved accuracy in comparison with the conventional Kalman filter (CKF).

Keywords: inertial navigation, adaptive filtering, star tracker, FOG

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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: Pavlo Selyshchev, Samuel Akintunde

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A theoretical approach to consider formation of chemical compound layer at the interface between initial substances A and B due to the interfacial interaction and diffusion is developed. It is considered situation when speed of interfacial interaction is large enough and diffusion of A-atoms through AB-layer is much more then diffusion of B-atoms. Atoms from A-layer diffuse toward B-atoms and form AB-atoms on the surface of B-layer. B-atoms are assumed to be immobile. The growth kinetics of the AB-layer is described by two differential equations with non-linear coupling, producing a good fit to the experimental data. It is shown that growth of the thickness of the AB-layer determines by dependence of chemical reaction rate on reactants concentration. In special case the thickness of the AB-layer can grow linearly or parabolically depending on that which of processes (interaction or the diffusion) controls the growth. The thickness of AB-layer as function of time is obtained. The moment of time (transition point) at which the linear growth are changed by parabolic is found.

Keywords: phase formation, binary systems, interfacial reaction, diffusion, compound layers, growth kinetics

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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: Sachin Kumar

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Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy.

Keywords: fractional PDE, fuzzy valued function, diffusion equation, Legendre polynomial, spectral method

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Authors: Md. Abud Darda

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Different options for natural gas production in wide geographic areas may be described through diffusion of innovation models. This type of modeling approach provides an indirect estimate of an ultimately recoverable resource, URR, capture the quantitative effects of observed strategic interventions, and allow ex-ante assessments of future scenarios over time. In order to ensure a sustainable energy policy, it is important to forecast the availability of this natural resource. Considering a finite life cycle, in this paper we try to investigate the natural gas production of Myanmar and Algeria, two important natural gas provider in the world energy market. A number of homogeneous and heterogeneous diffusion models, with convenient extensions, have been used. Models validation has also been performed in terms of prediction capability.

Keywords: diffusion models, energy forecast, natural gas, nonlinear production

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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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