Order conditions of stochastic Runge-Kutta methods by B-series

In this paper, general order conditions and a global convergence proof are given for stochastic Runge Kutta methods applied to stochastic ordinary differential equations ( SODEs) of Stratonovich type. This work generalizes the ideas of B-series as applied to deterministic ordinary differential equations (ODEs) to the stochastic case and allows a completely general formalism for constructing high order stochastic methods, either explicit or implicit. Some numerical results will be given to illustrate this theory.

Modeling and detection of complex attacks

A complex attack is a sequence of temporally and spatially separated legal and illegal actions each of which can be detected by various IDS but as a whole they constitute a powerful attack. IDS fall short of detecting and modeling complex attacks therefore new methods are required. This paper presents a formal methodology for modeling and detection of complex attacks in three phases: (1) we extend basic attack tree (AT) approach to capture temporal dependencies between components and expiration of an attack, (2) using enhanced AT we build a tree automaton which accepts a sequence of actions from input message streams from various sources if there is a traversal of an AT from leaves to root, and (3) we show how to construct an enhanced parallel automaton that has each tree automaton as a subroutine. We use simulation to test our methods, and provide a case study of representing attacks in WLANs.

Numerical solutions of stochastic differential equations – implementation and stability issues

Stochastic differential equations (SDEs) arise fi om physical systems where the parameters describing the system can only be estimated or are subject to noise. There has been much work done recently on developing numerical methods for solving SDEs. This paper will focus on stability issues and variable stepsize implementation techniques for numerically solving SDEs effectively.

A variable stepsize implementation for stochastic differential equations

Stochastic differential equations (SDEs) arise from physical systems where the parameters describing the system can only be estimated or are subject to noise. Much work has been done recently on developing higher order Runge-Kutta methods for solving SDEs numerically. Fixed stepsize implementations of numerical methods have limitations when, for example, the SDE being solved is stiff as this forces the stepsize to be very small. This paper presents a completely general variable stepsize implementation of an embedded Runge Kutta pair for solving SDEs numerically; in this implementation, there is no restriction on the value used for the stepsize, and it is demonstrated that the integration remains on the correct Brownian path.

Adams-Type Methods for the Numerical Solution of Stochastic Ordinary Differential Equations

Stochastic differential equations (SDEs) arise fi om physical systems where the parameters describing the system can only be estimated or are subject to noise. There has been much work done recently on developing numerical methods for solving SDEs. This paper will focus on stability issues and variable stepsize implementation techniques for numerically solving SDEs effectively. (C) 2000 Elsevier Science B.V. All rights reserved.

Porohyperelastic analysis to explore mechanical properties of chondrocytes using numerical modeling and experiments : a finite element study

There are many continuum mechanical models have been developed such as liquid drop models, solid models, and so on for single living cell biomechanics studies. However, these models do not give a fully approach to exhibit a clear understanding of the behaviour of single living cells such as swelling behaviour, drag effect, etc. Hence, the porohyperelastic (PHE) model which can capture those aspects would be a good candidature to study cells behaviour (e.g. chondrocytes in this study). In this research, an FEM model of single chondrocyte cell will be developed by using this PHE model to simulate Atomic Force Microscopy (AFM) experimental results with the variation of strain rate. This material model will be compared with viscoelastic model to demonstrate the advantages of PHE model. The results have shown that the maximum value of force applied of PHE model is lower at lower strain rates. This is because the mobile fluid does not have enough time to exude in case of very high strain rate and also due to the lower permeability of the membrane than that of the protoplasm of chondrocyte. This behavior is barely observed in viscoelastic model. Thus, PHE model is the better model for cell biomechanics studies.

High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula

In recent years considerable attention has been paid to the numerical solution of stochastic ordinary differential equations (SODEs), as SODEs are often more appropriate than their deterministic counterparts in many modelling situations. However, unlike the deterministic case numerical methods for SODEs are considerably less sophisticated due to the difficulty in representing the (possibly large number of) random variable approximations to the stochastic integrals. Although Burrage and Burrage [High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations, Applied Numerical Mathematics 22 (1996) 81-101] were able to construct strong local order 1.5 stochastic Runge-Kutta methods for certain cases, it is known that all extant stochastic Runge-Kutta methods suffer an order reduction down to strong order 0.5 if there is non-commutativity between the functions associated with the multiple Wiener processes. This order reduction down to that of the Euler-Maruyama method imposes severe difficulties in obtaining meaningful solutions in a reasonable time frame and this paper attempts to circumvent these difficulties by some new techniques. An additional difficulty in solving SODEs arises even in the Linear case since it is not possible to write the solution analytically in terms of matrix exponentials unless there is a commutativity property between the functions associated with the multiple Wiener processes. Thus in this present paper first the work of Magnus [On the exponential solution of differential equations for a linear operator, Communications on Pure and Applied Mathematics 7 (1954) 649-673] (applied to deterministic non-commutative Linear problems) will be applied to non-commutative linear SODEs and methods of strong order 1.5 for arbitrary, linear, non-commutative SODE systems will be constructed - hence giving an accurate approximation to the general linear problem. Secondly, for general nonlinear non-commutative systems with an arbitrary number (d) of Wiener processes it is shown that strong local order I Runge-Kutta methods with d + 1 stages can be constructed by evaluated a set of Lie brackets as well as the standard function evaluations. A method is then constructed which can be efficiently implemented in a parallel environment for this arbitrary number of Wiener processes. Finally some numerical results are presented which illustrate the efficacy of these approaches. (C) 1999 Elsevier Science B.V. All rights reserved.

A bound on the maximum strong order of stochastic Runge-Kutta methods for stochastic ordinary differential equations

In Burrage and Burrage [1] it was shown that by introducing a very general formulation for stochastic Runge-Kutta methods, the previous strong order barrier of order one could be broken without having to use higher derivative terms. In particular, methods of strong order 1.5 were developed in which a Stratonovich integral of order one and one of order two were present in the formulation. In this present paper, general order results are proven about the maximum attainable strong order of these stochastic Runge-Kutta methods (SRKs) in terms of the order of the Stratonovich integrals appearing in the Runge-Kutta formulation. In particular, it will be shown that if an s-stage SRK contains Stratonovich integrals up to order p then the strong order of the SRK cannot exceed min{(p + 1)/2, (s - 1)/2), p greater than or equal to 2, s greater than or equal to 3 or 1 if p = 1.

Design and modeling of collaboration architecture for security

Threats against computer networks evolve very fast and require more and more complex measures. We argue that teams respectively groups with a common purpose for intrusion detection and prevention improve the measures against rapid propagating attacks similar to the concept of teams solving complex tasks known from field of work sociology. Collaboration in this sense is not easy task especially for heterarchical environments. We propose CIMD (collaborative intrusion and malware detection) as a security overlay framework to enable cooperative intrusion detection approaches. Objectives and associated interests are used to create detection groups for exchange of security-related data. In this work, we contribute a tree-oriented data model for device representation in the scope of security. We introduce an algorithm for the formation of detection groups, show realization strategies for the system and conduct vulnerability analysis. We evaluate the benefit of CIMD by simulation and probabilistic analysis.

Modeling destination brand equity in an emerging long haul market

The destination branding literature emerged as recently as 1998, and there remains a dearth of empirical data that tests the effectiveness of brand campaigns over time. This paper reports the results of an investigation into consumer-based brand equity for Australia as a long haul destination in an emerging South American market. In spite of the high level of academic interest in the measurement of perceptions of destinations since the 1970s, few previous studies have examined perceptions held by South American consumers. Findings suggest that destination brand awareness, brand image, and brand value are positively related to brand loyalty for a long-haul destination. The results also indicate that Australia is a more compelling destination brand for previous visitors compared to non-visitors.

Ontology-based feature modeling for construction information extraction from a building information model

A building information model (BIM) provides a rich representation of a building's design. However, there are many challenges in getting construction-specific information from a BIM, limiting the usability of BIM for construction and other downstream processes. This paper describes a novel approach that utilizes ontology-based feature modeling, automatic feature extraction based on ifcXML, and query processing to extract information relevant to construction practitioners from a given BIM. The feature ontology generically represents construction-specific information that is useful for a broad range of construction management functions. The software prototype uses the ontology to transform the designer-focused BIM into a construction-specific feature-based model (FBM). The formal query methods operate on the FBM to further help construction users to quickly extract the necessary information from a BIM. Our tests demonstrate that this approach provides a richer representation of construction-specific information compared to existing BIM tools.

Modeling as a means for making powerful ideas accessible to children at an early age

The SimCalc Vision and Contributions Advances in Mathematics Education 2013, pp 419-436 Modeling as a Means for Making Powerful Ideas Accessible to Children at an Early Age Richard Lesh, Lyn English, Serife Sevis, Chanda Riggs … show all 4 hide » Look Inside » Get Access Abstract In modern societies in the 21st century, significant changes have been occurring in the kinds of “mathematical thinking” that are needed outside of school. Even in the case of primary school children (grades K-2), children not only encounter situations where numbers refer to sets of discrete objects that can be counted. Numbers also are used to describe situations that involve continuous quantities (inches, feet, pounds, etc.), signed quantities, quantities that have both magnitude and direction, locations (coordinates, or ordinal quantities), transformations (actions), accumulating quantities, continually changing quantities, and other kinds of mathematical objects. Furthermore, if we ask, what kind of situations can children use numbers to describe? rather than restricting attention to situations where children should be able to calculate correctly, then this study shows that average ability children in grades K-2 are (and need to be) able to productively mathematize situations that involve far more than simple counts. Similarly, whereas nearly the entire K-16 mathematics curriculum is restricted to situations that can be mathematized using a single input-output rule going in one direction, even the lives of primary school children are filled with situations that involve several interacting actions—and which involve feedback loops, second-order effects, and issues such as maximization, minimization, or stabilizations (which, many years ago, needed to be postponed until students had been introduced to calculus). …This brief paper demonstrates that, if children’s stories are used to introduce simulations of “real life” problem solving situations, then average ability primary school children are quite capable of dealing productively with 60-minute problems that involve (a) many kinds of quantities in addition to “counts,” (b) integrated collections of concepts associated with a variety of textbook topic areas, (c) interactions among several different actors, and (d) issues such as maximization, minimization, and stabilization.

Modeling and multiway analysis of chatroom tensors

This work identifies the limitations of n-way data analysis techniques in multidimensional stream data, such as Internet chat room communications data, and establishes a link between data collection and performance of these techniques. Its contributions are twofold. First, it extends data analysis to multiple dimensions by constructing n-way data arrays known as high order tensors. Chat room tensors are generated by a simulator which collects and models actual communication data. The accuracy of the model is determined by the Kolmogorov-Smirnov goodness-of-fit test which compares the simulation data with the observed (real) data. Second, a detailed computational comparison is performed to test several data analysis techniques including svd [1], and multi-way techniques including Tucker1, Tucker3 [2], and Parafac [3].

Dynamic modeling for construction innovation

Previous research on construction innovation has commonly recognized the importance of the organizational climate and key individuals, often called “champions,” for the success of innovation. However, it rarely focuses on the role of participants at the project level and addresses the dynamics of construction innovation. This paper therefore presents a dynamic innovation model that has been developed using the concept of system dynamics. The model incorporates the influence of several individual and situational factors and highlights two critical elements that drive construction innovations: (1) normative pressure created by project managers through their championing behavior, and (2) instrumental motivation of team members facilitated by a supportive organizational climate. The model is qualified empirically, using the results of a survey of project managers and their project team members working for general contractors in Singapore, by assessing casual relationships for key model variables. Finally, the paper discusses the implications of the model structure for fostering construction innovations.

Designing a new robust on-line secondary path modeling technique for feedforward active noise control systems

Several approaches have been introduced in the literature for active noise control (ANC) systems. Since the filtered-x least-mean-square (FxLMS) algorithm appears to be the best choice as a controller filter, researchers tend to improve performance of ANC systems by enhancing and modifying this algorithm. This paper proposes a new version of the FxLMS algorithm, as a first novelty. In many ANC applications, an on-line secondary path modeling method using white noise as a training signal is required to ensure convergence of the system. As a second novelty, this paper proposes a new approach for on-line secondary path modeling on the basis of a new variable-step-size (VSS) LMS algorithm in feed forward ANC systems. The proposed algorithm is designed so that the noise injection is stopped at the optimum point when the modeling accuracy is sufficient. In this approach, a sudden change in the secondary path during operation makes the algorithm reactivate injection of the white noise to re-adjust the secondary path estimate. Comparative simulation results shown in this paper indicate the effectiveness of the proposed approach in reducing both narrow-band and broad-band noise. In addition, the proposed ANC system is robust against sudden changes of the secondary path model.