Computer Simulations for a Fractional Calculus Derived Internet Traffic Model

In this work, two novel models have been proposed based on semi-empirical and factional calculus incorporating non-integer time derivatives in the Fick’s first law of anomalous diffusion. The experimental data has been collected from literature of 15 kinetics investigated in a convective dryer under the effect of temperatures ranging from 40 to 80 °C at 10 °C interval, and thickness of the slices of 2 to 6 mm at 2 mm interval. The collected experimental dataset was of apple slices (Golab variety). Results from this study were compared with a set of 64 thin-layer drying models previously published in the literature. The fitting capability of the models was compared using the mean of root mean square error MRMSE (%) of all kinetics and the global determination coefficient R2. All models’ constants and coefficients were optimised by dragonfly algorithm programmed in MATLAB software. Results show that the fractional model is highly capable of describing the drying curve of the apple slices with a determination coefficient (R2) of 0.99981, and average root mean square error (MRMSE) of 0.43 % in comparison to the best empirical models with R2 of 0.99968 and MRMSE of 0.61 %.

Welcome to the Second International Workshop on Intelligent Communication Networks (IntelNet 2011), which is being held in conjunction with the 10th IEEE International Conference on Ubiqutious Computing and Communications (IUCC 2011) on August 24-26, 2011, in Dalian, China. Modern communication networks have been becoming more and more large-scaled and complicated due to rapid development and interconnection among heterogeneous communication networks. Therefore, the management and maintenance of modern communication networks have posed many grand challenges to both industrial and academic communication communities. To overcome these challenges, it is very necessary to find new levels of autonomy and intelligence in designing, deploying, managing, and maintaining communication networks. This workshop aims to bring together scientists, researchers, professionals, and practitioners from both industry and academia to exchange ideas, discuss solutions, share experiences, and report state-of-the-art research results on various aspects of intelligent communication networks. In response to the Call-for-Papers of IntelNet 2011, twelve submissions were received from different countries. All submissions were reviewed by at least two referees from the technical program committee to ensure that papers published by IntelNet 2011 are of high quality. The submissions were then ranked according to their original contribution, technical strength, presentation, and relevance to the theme of the workshop. Finally, six papers were selected for presentation at the workshop and inclusion in the proceedings of IUCC 2011. We highly appreciate the IUCC Workshop Organizing Committee for giving us this opportunity to organize IntelNet 2011. We are very grateful to the Steering Committee for their valuable advice and continued support. We would also like to thank the authors for their great contributions and all Program Committee members for providing timely and in-depth reviews. Finally, we thank the attendees of this workshop and hope you will enjoy the program.

Deliberate destructive electromagnetic influences formed on the basis of existing technical means are an effective type of modern radio-electronic information and technical influences on information and communication networks. The radio-electronic material basis of information communication networks is potentially vulnerable to the influence of means of radio-electronic suppression. The need to ensure the high-quality functioning of modern information and communication networks under the conditions of intentional electromagnetic destructive effects requires correct and timely management decisions from the network management system to prevent undesirable consequences, which necessitates the creation of more advanced management methods. The purpose of the publication is to consider the vulnerabilities of modern information and communication networks from intentional destructive electromagnetic influences, which is understood as the deliberate creation of a powerful electromagnetic influence on electronic and electrical systems for criminal or terrorist purposes in order to disrupt their functioning. The effects manifested at different levels of information communication network functioning as a result of intentional destructive electromagnetic influences are considered. Based on the results of the research, the following conclusions can be drawn: intentional destructive electromagnetic influences are aimed at destroying information flows circulating between network elements; decrease in the speed of information exchange between elements of the control system, which significantly increases the duration of the control cycle and, as a result, reduces the efficiency of network management; ensuring sufficiently massive and long-term failure of network technical means; existing systems and methods of radio electronic suppression are focused on suppressing only individual channels of the network by disrupting the functioning of communication protocols at the physical and channel levels of the OSI model; in the future, there is a threat of transition to the use of individual elements of the radio segment of the information communication network as a kind of «entry points» for radio-electronic information and technical influences, which will disrupt the network processes of information transmission and spread their destabilizing influence on the entire network, including its wire segment. In the article presented to the readers, only some aspects of the researched topic are highlighted. Currently, the authors continue active research work in this subject area.

The premise of this work is that fractional (non-integer order) calculus can provide the basis for a greater understanding of the dynamic processes that occur in biological tissues. Such an understanding is fundamental in bioengineering where engineers seek a simpler description of the underlying multi-scale processes that occur, for example, when tissues are mechanically stressed or strained. Fractional order models work well in physics, electrochemistry and rheology, particularly in describing dielectric, magnetic and viscoelastic materials over extended ranges of time and frequency. In heat transfer and electrochemistry, for example, the half-order fractional integral is the natural integral operator connecting applied gradients (thermal or material) with the resultant diffusion of ions or heat. Can fractional calculus be applied in bioengineering to uncover similar relatively simple links between stress and strain in load-bearing tissues, such as cartilage, the electrical impedance of implanted cardiac pacemaker electrodes, or in predicting changes in the shear modulus of tumors developing in breast tissue? Since the constitutive properties of tissue depend on the micro-scale architecture of the cellular and extracellular networks, the challenge for the bioengineer is to develop new modeling, visualization and assessment tools that better predict the macro-scale mechanical performance from measurements observations at the micro- and nano-scale. In this paper I describe some of the characteristics of fractional calculus that I believe make it well suited for this application, and outline three areas of bioengineering research where fractional calculus is being applied.

Differentiating Cytokeratin 19 expression of hepatocellular carcinoma by using multi-b-value diffusion-weighted MR imaging with mono-exponential, stretched exponential, intravoxel incoherent motion, diffusion kurtosis imaging and fractional order calculus models

Recently, the numerical modelling and simulation for anomalous subdiffusion equation (ASDE), which is a type of fractional partial differential equation( FPDE) and has been found with widely applications in modern engineering and sciences, are attracting more and more attentions. The current dominant numerical method for modelling ASDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of the non-linear ASDE. The discrete system of equations is obtained by using the meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formulations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the ASDE. Therefore, the meshless technique should have good potential in development of a robust simulation tool for problems in engineering and science which are governed by the various types of fractional differential equations.

Fractional calculus constitutive models are of wide applicability. They have been used, for example, for: xanthan gum, bread dough, synthetic polymers (e.g. nylon), single collagen fibrils, semi-hard zero-fat cheese, pure ice at −35∘C, asphalt sealants, epithelial cells, gels, polymers, concrete, asphalt, rock mass, waxy crude oil, breast tissue cells, lung parenchyma, and red blood cell membranes (e.g. Bonfanti et al. (2020)). In this note we are motivated by applications to dispersive media such as lossy dielectrics and viscoelastic polymers, both of which involve constitutive laws with fading memory convolution Volterra integrals, and both of which have been modelled by fractional calculus — which implies a weakly singular Volterra kernel. To step forward in time with such a model the entire hereditary Volterra integral needs to be numerically re-computed at each time step. Done naïvely with standard quadrature this involves O(N2) operations and O(N) storage to compute over N time steps, and this severely limits the usefulness of such simple methods in large scale computations. Several alternatives addressing these shortcomings of this naïve approach have been offered in the literature, all of which can provide remedies. Here we propose another method, but ours is rather different in that we use a Fourier series proxy over much of the integration range. This allows for a recursive update to the ‘history integral’, with a much smaller effort expended in standard quadrature near the singularity. The recursive update is basically the same as that used when the Volterra kernel comprises decaying exponentials, a method which is already employed in some commercial codes. Given that this partial implementation is already in use, we intend that our method therefore has a lower ‘barrier to entry’ for incorporating fractional calculus models into commercial codes: it requires only minor surgery on the weakly singular kernel in order to apply the Fourier series proxy. This study is presented in the spirit of a discussion piece — there are several directions one could take from the basic observations presented here. We have aimed for simplicity and economy of presentation, and included just enough numerical results to give evidence that the method works. In summary, our method mitigates the O(N) storage and O(N2) storage issues using an easily implemented proxy. It can also be implemented for variable time steps. The code is available from https://github.com/variationalform/fouvol and https://hub.docker.com/u/variationalform.

Traditional queueing models for traffic flows in communications networks are based on Markovian assumptions. However, recent studies within Bellcore of large sets of real-time network traffic measurements have revealed that traffic in computer and emerging high-speed networks has features that are more accurately and more efficiently described in terms of fractal models, rather than traditional Markovian models. This paper briefly reviews these measurement studies, and motivates the application of fractals to describe and analyze traffic flows in modern communications networks.

Modern communication networks are expected to have hundreds or thousands of network nodes to which thousands of users are connected. Neural networks can contribute to this emerging new telecommunication infrastructure by providing fast, flexible, adaptive, and intelligent control. This article discusses the neural networks used for solving various control problems in high-speed communication networks.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The new 5G network is to come very soon. Still many challenges have to be overcome, severe problems to be solved. One of these challenges is to reduce the power consumption drastically compared to existing networks. With a short literature review, a few examples of how power consumption in modern communication networks could be decreased, while data through-put and the quality of service could be increased, are discussed briefly in the following sections.

The paper is devoted to the application of fractional calculus concepts to modeling, identification and control of discrete-time systems. Fractional difference equations (FAE) models are presented and their use in identification, state estimation and control context is discussed. The fractional difference state-space model is proposed for that purpose. For such a model stability conditions are given. A fractional Kalman filter (FKF) for this model is recalled. The proposed state-space model and fractional order difference equation are used in an identification procedure which produces very accurate results. Finally, the state-space model is used in closed-loop state feedback control form together with FKF as a state estimator. The latter is also given in an adaptive form together with FKF and a modification of recursive least squares (RLS) algorithm as a parameters identification procedure. All the algorithms presented were tested in simulations and the example results are given in the paper

Analysis of inhomogeneous anisotropic viscoelastic bodies described by multi-parameter fractional differential constitutive models

The functioning of modern information and communication networks is impossible without data processing. With the emergence of new network services, the amount of information that needs to be processed increases, while the requirements to the data processing quality become more and more stringent. Therefore, the problem of designing and maintaining a scalable data processing system with a flexible quality of service management is becoming more and more important for a network operator. Such data processing systems have a complex internal structure with many interrelated parameters, which makes them difficult to analyze, manage, and expand. This study proposes to use an ontological model to store, represent, and manipulate the information in the operator’s data processing system. The ontological model allows to structure and systematize the data of an information processing system, and transparently reflects the relationships between the parameters of the system to simplify its analysis and scaling. The proposed ontology of a data processing system consists of three related subsystems. The paper describes the proposed ontological model and additionally analyzes the sources of information that needs to be processed in the information and communication network.

In order to solve some shortcomings, such as the traditional integer order calculus theoretical model is in good agreement with the numerical experimental results, the fractional order calculus model in many fields such as modern engineering calculation is proposed, which has been paid more attention and applied than the integer order calculus model. In such problems, nonlinear fractional differential equations sometimes bring us many unexpected surprises, so as to get unexpected conclusions about the description of the problem. The experiment shows that when the time t = 0.5 , the error between them is 0.0305, and the error is slightly larger. In this case, we can reduce the overall error by adding a new term of the decomposition sequence, and the approximate analytical solution can be closer to the exact solution, which verifies the effectiveness of the experiment.

The major aim of this article is to obtain the numerical solution of a fractional mathematical model with a nonsingular kernel for thrombin receptor activation in calcium signals using two numerical schemes based on the collocation techniques. We present the computational solution of the considered fractional model using the Laguerre collocation method (LCM) and Jacobi collocation method (JCM). An operational matrix of the fractional order derivative in the Caputo sense is needed for the recommended approach. The computational scheme converts fractional differential equations (FDEs) into an algebraic set of equations using the collocation method. The technique is used more quickly and successfully than in other existing schemes. A comparison between LCM and JCM is also presented in the form of figures. We obtained very good results with a great agreement between both the schemes. Additionally, an error analysis of the suggested procedures is provided.