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Partial Differential Equations (PDE) appear in multiple Physic and Engineering applications. Normally, when modeling an application, the use of well-known and already solved PDE is considered. But what happens if a new PDE is used? Solving a new PDE is not an easy task. In this paper, we use a Computer Algebra System (Cas) in order to find the solution of PDE of first order. Specifically, we deal with Pfaff Equations , Quasilinear PDE and general first order PDE (using Lagrange–Charpit Method). To solve these PDE, we combine the power of a Cas with the flexibility of programming with it. Furthermore, the developed programs do not only provide the final result but also display all the intermediate steps which lead to find the solution of the PDE. This way, we introduce SFOPDES, a new Stepwise First Order PDE Solver which serves as a tutorial showing, step by step, the way to deal with PDE. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the utilization of chaos pseudorandom number generators based on three different chaotic maps to alter the behavior and overall performance of PSO algorithm is proposed. This paper presents results of testing the performance and behavior of the proposed algorithm on typical benchmark functions that represent unimodal and multimodal problems. The promising results are analyzed and discussed. [Copyright &y& Elsevier]

Abstract: The paper deals with symbolic regression of deterministic chaos systems using a GPA-ES system. A Lorenz attractor, Rössler attractor, Rabinovich–Fabrikant equations and a van der Pol oscillator are used as examples of deterministic chaos systems to demonstrate significant differences in the efficiency of the symbolic regression of systems described by equations of similar complexity. Within the paper, the source of this behavior is identified in presence of structures which are hard to be discovered during the evolutionary process due to the low probability of their occurrence in the initial population and by the low chance to produce them by standard evolutionary operators given by small probability to form them in a single step and low fitness function magnitudes of inter-steps when GPA tries to form them in more steps. This low magnitude of fitness function for particular solutions tends to eliminate them, thus increasing the number of needed evolutionary steps. As the solution of identified problems, modification of terminals and related crossover and mutation operators are suggested. [Copyright &y& Elsevier]

Abstract: A quantitative measure for the fairness of network resource distribution was proposed in [1]. This fairness function is widely adopted in network design and management. This paper proposes a new distribution fairness score function. Compared to the fairness function proposed by Jain, Chiu and Hawe, the fairness function proposed in this paper keeps all the nice properties that Jain, Chiu and Hawe''s fairness function possesses. In addition, the proposed fairness score function has better performance in dealing with completely unfair cases. [Copyright &y& Elsevier]

Abstract: This paper deals with the observer design for nonlinear systems in Takagi–Sugeno fuzzy representation. Based on the Lyapunov method and Linear Matrix Inequalities (LMI) formulation, sufficient conditions have been derived for observers design. Unknown inputs can result either from model uncertainty, faults or due to the presence of unknown external excitation. These different results have been widely applied in the field of fault diagnosis and fault tolerance. Based on unknown inputs observer design, secure communication and chaotic system reconstruction problems have been also studied. Examples are given to illustrate a chaotic cryptosystem procedure where the plaintext (message) is encrypted using chaotic signals at the drive system side and the plaintext is retrieved via the designed unknown input observer. [Copyright &y& Elsevier]

Abstract: Solving systems of nonlinear equations is a relatively complicated problem in which arise a diverse range of sciences. There are a number of different approaches that have been proposed. In this paper, we employ the imperialist competitive algorithm (ICA) for solving systems of nonlinear equations. Some well-known problems are presented to demonstrate the efficiency of this new robust optimization method in comparison to other known methods. [Copyright &y& Elsevier]

Abstract: In this paper, a novel active contour model (R-DRLSE model) based on level set method is proposed for image segmentation. The R-DRLSE model is a variational level set approach that utilizes the region information to find image contours by minimizing the presented energy functional. To avoid the time-consuming re-initialization step, the distance regularization term is used to penalize the deviation of the level set function from a signed distance function. The numerical implementation scheme of the model can significantly reduce the iteration number and computation time. The results of experiments performed on some synthetic and real images show that the R-DRLSE model is effective and efficient. In particular, our method has been applied to MR kidney image segmentation with desirable results. [Copyright &y& Elsevier]

Abstract: Adaptive networks are a novel class of dynamical networks whose topologies and states coevolve. Many real-world complex systems can be modeled as adaptive networks, including social networks, transportation networks, neural networks and biological networks. In this paper, we introduce fundamental concepts and unique properties of adaptive networks through a brief, non-comprehensive review of recent literature on mathematical/computational modeling and analysis of such networks. We also report our recent work on several applications of computational adaptive network modeling and analysis to real-world problems, including temporal development of search and rescue operational networks, automated rule discovery from empirical network evolution data, and cultural integration in corporate merger. [Copyright &y& Elsevier]

Abstract: In recent years, various computers have been compromised through several paths. In particular, the attack patterns and paths are becoming more various than in the past. Furthermore, systems damaged by hackers are used as zombie systems to attack other web servers or personal computers, so there is a high probability to spread secondary damage such as DDoS. Also, previously, hacking and malicious code were carried out for self-display or simple curiosity, but recently they are related to monetary extortion. In order to respond to incidents correctly, it is important to measure the damage to a system rapidly and determine the attack paths. This paper will discuss an on-site investigation methodology for incident response and also describe the limitations of this methodology. [Copyright &y& Elsevier]

Abstract: Parallel key-insulated encryption (PKIE) usually allows two independent helper keys to be alternately used in temporary secret key update operations. At least half of temporary secret keys would be exposed and at least half of ciphertexts could be decrypted if one of the helper keys is exposed. In this paper, we propose a new PKIE scheme with helper keys, where . If one of the helper keys is exposed, only temporary secret keys would be exposed and ciphertexts could be decrypted, so the new PKIE scheme can greatly decrease loss due to key-exposure. The scheme is provably secure without random oracles based on a bilinear group of composite order. Most important, the scheme is practical and much more efficient than the extended ones from the previous PKIE schemes. [Copyright &y& Elsevier]

Abstract: As online games become popular and the boundary between virtual and real economies blurs, cheating in games has proliferated in volume and method. In this paper, we propose a framework for user behavior analysis for bot detection in online games. Specifically, we focus on party play which reflects the social activities among gamers: in a Massively Multi-user Online Role Playing Game (MMORPG), party play is a major activity that game bots exploit to keep their characters safe and facilitate the acquisition of cyber assets in a fashion very different from that of normal humans. Through a comprehensive statistical analysis of user behaviors in game activity logs, we establish threshold levels for the activities that allow us to identify game bots. Based on this, we also build a knowledge base of detection rules, which are generic. We apply our rule reasoner to AION, a popular online game serviced by NCsoft, Inc., a leading online game company based in Korea. [Copyright &y& Elsevier]

Abstract: In MBarka and Stern (2011) [3], we proposed a new algorithm to validate certificates in the past with the goals of it being simple to present, simple to implement and to fall back on standard algorithms with current time settings. This paper improves our algorithm through a much cleaner handling of time issues by defining a new notion, called revocation freshness, yielding a better fall-back on the standard algorithm. It also takes into account a practical “caution period” to lessen some of our previous hypothesis. [Copyright &y& Elsevier]

Abstract: The main purpose of this paper is to compute the weights of Clenshaw–Curtis and Fejér type quadrature rules via DCT and DST, for general weight functions . The approach is different from that used by Waldvogel (2006) in [10], where the author considered the computation of these sets only for the Legendre weight using DFT arguments. [Copyright &y& Elsevier]

Abstract: This paper surveys recent research on the use of sensor networks, communications and computer systems to enhance the human outcome of emergency situations. Areas covered include sensing, communication with evacuees and emergency personnel, path finding algorithms for safe evacuation, simulation and prediction, and decision tools. The systems being considered are a special instance of real-time cyber-physical-human systems that have become a crucial component of all large scale physical infrastructures such as buildings, campuses, sports and entertainment venues, and transportation hubs. [Copyright &y& Elsevier]

Abstract: A -container of a graph is a set of -disjoint paths joining to . A -container of is a -container if it contains all the vertices of . A graph is -connected if there exists a -container between any two distinct vertices in . Let be the connectivity of . A graph is superconnected if is -connected for all . The pyramid network is one of the important networks applied in parallel and distributed computer systems. The connectivity of a pyramid network is three. In this paper, we prove that the pyramid network is -connected and superconnected for . [Copyright &y& Elsevier]

Abstract: The Laplace–Beltrami system of nonlinear, elliptic, partial differential equations has utility in the generation of computational grids on complex and highly curved geometry. Discretization of this system using the finite-element method accommodates unstructured grids, but generates a large, sparse, ill-conditioned system of nonlinear discrete equations. The use of the Laplace–Beltrami approach, particularly in large-scale applications, has been limited by the scalability and efficiency of solvers. This paper addresses this limitation by developing two nonlinear solvers based on the Jacobian-Free Newton–Krylov (JFNK) methodology. A key feature of these methods is that the Jacobian is not formed explicitly for use by the underlying linear solver. Iterative linear solvers such as the Generalized Minimal RESidual (GMRES) method do not technically require the stand-alone Jacobian; instead its action on a vector is approximated through two nonlinear function evaluations. The preconditioning required by GMRES is also discussed. Two different preconditioners are developed, both of which employ existing Algebraic Multigrid (AMG) methods. Further, the most efficient preconditioner, overall, for the problems considered is based on a Picard linearization. Numerical examples demonstrate that these solvers are significantly faster than a standard Newton–Krylov approach; a speedup factor of approximately 26 was obtained for the Picard preconditioner on the largest grids studied here. In addition, these JFNK solvers exhibit good algorithmic scaling with increasing grid size. [Copyright &y& Elsevier]

This paper deals with the construction of discrete numerical solutions of mixed problems for the telegraph equation. After discretization, the two-variables partial difference mixed problem is solved by means of a discrete eigenfunctions method that mimics the advantages of the continuous eigenfunction method while eliminating its computational disadvantages. The solution is based on a closed form solution of the inhomogeneous second order difference equation without increasing the problem’s dimension. [Copyright &y& Elsevier]

Abstract: As computer systems have been widely used, Internet, which is a network-of-network, has been greatly developed and rapidly spread all over the world. In addition to unicast transmissions of point-to-point, multicast transmissions of one-to-many and many-to-many have been recently used. This paper considers a stochastic model where data are transmitted through multicast. The data are divided into n packets at a transmission server, and their packets are transmitted successively to each receiver of multicast group. Positive (ACK) or negative (NAK) acknowledgements are returned from each receiver, by depending on whether he or she has received all packets, correctly or not. When the server has received NAK, retransmissions only for receivers with NAK are made. The mean time until the data transmission succeeds is analytically derived and an optimal policy which maximizes the throughput is discussed. Finally, numerical examples are given under suitable conditions. [Copyright &y& Elsevier]

Abstract: It is important to design computer systems to tolerate some failures. This paper proposes two-level recovery schemes, soft checkpoint (SC) and hard checkpoint (HC), which are useful to recover from failures. Soft checkpoint is less reliable and less overhead than those of HC, and is set up between HCs to reduce the overhead of the process. The total expected overhead of one cycle from HC to HC is obtained, using Markov renewal processes, and an optimal interval which minimizes it is computed. It is shown in a numerical example that a two-level recovery scheme can achieve a good performance. [Copyright &y& Elsevier]

Abstract: This paper considers periodic testing policies for a system with self-testing. The system can detect its failure by either self-testing or periodic inspection. If the system fails then its failure is detected by self-testing while it is on-line, or otherwise, it is detected at the next periodic test. Introducing the loss cost elapsed between a failure and its detection, the expected costs are obtained. Optimal intervals of periodic testing which minimize the expected costs are analytically derived. Numerical examples are given when both times of failure and its detection by self-testing are exponential distributions. [Copyright &y& Elsevier]

Abstract: In general, a newly purchased item or system is warranted for a specific period. When the system fails during the warranty period, it is repaired free of charge. Even if the system is repairable, there exist some warranty services under which the manufacturer replaces the failed system during the warranty period. This study considers a case where a manufacturer offers an additional warranty service under which the failed system is replaced by a new one for its first failure, but minimal repairs are carried out to the system for its succeeding failures before the warranty expires. In this paper, we propose a mathematical model for setting a suitable charge of such an additional warranty service. Numerical examples assuming a personal computer are also presented. [Copyright &y& Elsevier]

Abstract: This paper concentrates on a limited-flow network in which each node and branch has a designated capacity, which will have different lower levels due to various partial and complete failures. We try to evaluate the system unreliability that the maximum flow of the network is less than or equal to the demand d without exceeding the budget B. First, a simple algorithm in terms of minimal cuts is proposed to generate all (d, B)-MCs in order to evaluate the system unreliability. A computer example is shown to illustrate the solution procedure. [Copyright &y& Elsevier]

In this paper, we propose a software availability model considering the number of restoration actions. We correlate the failure and restoration characteristics of the software system with the cumulative number of corrected faults. Furthermore, we consider an imperfect debugging environment where the detected faults are not always corrected and removed from the system. The time-dependent behavior of the system alternating between up and down states is described by a Markov process. From this model, we can derive quantitative measures for software availability assessment based on the number of restoration actions. Finally, we show numerical examples of software availability analysis. [Copyright &y& Elsevier]

This paper considers replacement and minimal repair polices for an extended cumulative damage model with maintenance at each shock: shocks occur at a nonhomogeneous Poisson process. A system undergoes maintenance at each shock when the total damage does not exceed a failure level K, undergoes minimal repair at each shock when the total damage exceeds a failure level K, and is replaced at time T* or at failure N* whichever occurs first. The expected cost rate is obtained and the optimal T* and N* minimizing the expected cost are analytically discussed. It is shown that this model would be applied to the backup of secondary storage files in a database system as an example. [Copyright &y& Elsevier]

This paper addresses a problem of energy reduction on computer systems, namely the problem of determining the optimal auto-sleep schedule on which the system is changed into a low-power state. For this problem, we provide a stochastic model for a computer system with autosleep function. In our modeling framework, user requests arrive at the system in accordance with a general renewal process and are served by generally distributed service times. To obtain the optimal auto-sleep schedule minimizing the expected power consumption per unit time in the steady state, the phase-type approximation is applied to the renewal arrival process. In numerical examples, we investigate accuracy of the phase-type approximation through a simulation study. [Copyright &y& Elsevier]

With growing emphasis on reuse, the software development process moves toward component-based software design. As a result, there is a need for modeling approaches that are capable of considering the architecture of the software made out of components. This paper presents an overview of the state of the research and practice in the architecture-based approach to quantitative assessment of software systems. First, the common requirements of the architecture-based models are identified and the classification is proposed. Then, the key models in each class are described in detail with a focus on their relation and unification. Finally, a critical analysis of the underlying assumptions, limitations, and applicability of these models is provided, which should be helpful in determining the directions for future research. [Copyright &y& Elsevier]