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.

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.

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.

General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systems

In many modeling situations in which parameter values can only be estimated or are subject to noise, the appropriate mathematical representation is a stochastic ordinary differential equation (SODE). However, unlike the deterministic case in which there are suites of sophisticated numerical methods, numerical methods for SODEs are much less sophisticated. Until a recent paper by K. Burrage and P.M. Burrage (1996), the highest strong order of a stochastic Runge-Kutta method was one. But K. Burrage and P.M. Burrage (1996) showed that by including additional random variable terms representing approximations to the higher order Stratonovich (or Ito) integrals, higher order methods could be constructed. However, this analysis applied only to the one Wiener process case. In this paper, it will be shown that in the multiple Wiener process case all known stochastic Runge-Kutta methods can suffer a severe order reduction if there is non-commutativity between the functions associated with the Wiener processes. Importantly, however, it is also suggested how this order can be repaired if certain commutator operators are included in the Runge-Kutta formulation. (C) 1998 Elsevier Science B.V. and IMACS. 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.

Exponential asymptotics of free surface flow due to a line source

The steady problem of free surface flow due to a submerged line source is revisited for the case in which the fluid depth is finite and there is a stagnation point on the free surface directly above the source. Both the strength of the source and the fluid speed in the far field are measured by a dimensionless parameter, the Froude number. By applying techniques in exponential asymptotics, it is shown that there is a train of periodic waves on the surface of the fluid with an amplitude which is exponentially small in the limit that the Froude number vanishes. This study clarifies that periodic waves do form for flows due to a source, contrary to a suggestion by Chapman & Vanden-Broeck (2006, J. Fluid Mech., 567, 299--326). The exponentially small nature of the waves means they appear beyond all orders of the original power series expansion; this result explains why attempts at describing these flows using a finite number of terms in an algebraic power series incorrectly predict a flat free surface in the far field.

Smartphone malware evolution revisited : Android next target?

Smartphones started being targets for malware in June 2004 while malware count increased steadily until the introduction of a mandatory application signing mechanism for Symbian OS in 2006. From this point on, only few news could be read on this topic. Even despite of new emerging smartphone platforms, e.g. android and iPhone, malware writers seemed to lose interest in writing malware for smartphones giving users an unappropriate feeling of safety. In this paper, we revisit smartphone malware evolution for completing the appearance list until end of 2008. For contributing to smartphone malware research, we continue this list by adding descriptions on possible techniques for creating the first malware(s) for Android platform. Our approach involves usage of undocumented Android functions enabling us to execute native Linux application even on retail Android devices. This can be exploited to create malicious Linux applications and daemons using various methods to attack a device. In this manner, we also show that it is possible to bypass the Android permission system by using native Linux applications.

Collaborative intrusion detection framework : characteristics, adversarial opportunities and countermeasures

Complex Internet attacks may come from multiple sources, and target multiple networks and technologies. Nevertheless, Collaborative Intrusion Detection Systems (CIDS) emerges as a promising solution by using information from multiple sources to gain a better understanding of objective and impact of complex Internet attacks. CIDS also help to cope with classical problems of Intrusion Detection Systems (IDS) such as zero-day attacks, high false alarm rates and architectural challenges, e. g., centralized designs exposing the Single-Point-of-Failure. Improved complexity on the other hand gives raise to new exploitation opportunities for adversaries. The contribution of this paper is twofold. We first investigate related research on CIDS to identify the common building blocks and to understand vulnerabilities of the Collaborative Intrusion Detection Framework (CIDF). Second, we focus on the problem of anonymity preservation in a decentralized intrusion detection related message exchange scheme. We use techniques from design theory to provide multi-path peer-to-peer communication scheme where the adversary can not perform better than guessing randomly the originator of an alert message.

Assessing eco-environmental performance of agricultural production in OECD countries : combination of soil surface, soil system and farm gate methods of nutrient auditing

Nitrogen balance is increasingly used as an indicator of the environmental performance of agricultural sector in national, international, and global contexts. There are three main methods of accounting the national nitrogen balance: farm gate, soil surface, and soil system. OECD (2008) recently reported the nitrogen and phosphorus balances for member countries for the 1985 - 2004 period using the soil surface method. The farm gate and soil system methods were also used in some international projects. Some studies have provided the comparison among these methods and the conclusion is mixed. The motivation of this present paper was to combine these three methods to provide a more detailed auditing of the nitrogen balance and flows for national agricultural production. In addition, the present paper also provided a new strategy of using reliable international and national data sources to calculate nitrogen balance using the farm gate method. The empirical study focused on the nitrogen balance of OECD countries for the period from 1985 to 2003. The N surplus sent to the total environment of OECD surged dramatically in early 1980s, gradually decreased during 1990s but exhibited an increasing trends in early 2000s. The overall N efficiency however fluctuated without a clear increasing trend. The eco-environmental ranking shows that Australia and Ireland were the worst while Korea and Greece were the best.

Timed Up and Go Tests in cardiac rehabilitation : reliability and comparison with the 6-minute walk test

PURPOSE: To test the reliability of Timed Up and Go Tests (TUGTs) in cardiac rehabilitation (CR) and compare TUGTs to the 6-Minute Walk Test (6MWT) for outcome measurement. METHODS: Sixty-one of 154 consecutive community-based CR patients were prospectively recruited. Subjects undertook repeated TUGTs and 6MWTs at the start of CR (start-CR), postdischarge from CR (post-CR), and 6 months postdischarge from CR (6 months post-CR). The main outcome measurements were TUGT time (TUGTT) and 6MWT distance (6MWD). RESULTS: Mean (SD) TUGTT1 and TUGTT2 at the 3 assessments were 6.29 (1.30) and 5.94 (1.20); 5.81 (1.22) and 5.53 (1.09); and 5.39 (1.60) and 5.01 (1.28) seconds, respectively. A reduction in TUGTT occurred between each outcome point (P ≤ .002). Repeated TUGTTs were strongly correlated at each assessment, intraclass correlation (95% CI) = 0.85 (0.76–0.91), 0.84 (0.73–0.91), and 0.90 (0.83–0.94), despite a reduction between TUGTT1 and TUGTT2 of 5%, 5%, and 7%, respectively (P ≤ .006). Relative decreases in TUGTT1 (TUGTT2) occurred from start-CR to post-CR and from start-CR to 6 months post-CR of −7.5% (−6.9%) and −14.2% (−15.5%), respectively, while relative increases in 6MWD1 (6MWD2) occurred, 5.1% (7.2%) and 8.4% (10.2%), respectively (P < .001 in all cases). Pearson correlation coefficients for 6MWD1 to TUGTT1 and TUGTT2 across all times were −0.60 and −0.68 (P < .001) and the intraclass correlations (95% CI) for the speeds derived from averaged 6MWDs and TUGTTs were 0.65 (0.54, 0.73) (P < .001). CONCLUSIONS: Similar relative changes occurred for the TUGT and the 6MWT in CR. A significant correlation between the TUGTT and 6MWD was demonstrated, and we suggest that the TUGT may provide a related or a supplementary measurement of functional capacity in CR.

Video-based training combined with flotation tank recovery does not improve three-point shooting in basketball

Video-based training combined with flotation tank recovery may provide an additional stimulus for improving shooting in basketball. A pre-post controlled trial was conducted to assess the effectiveness of a 3 wk intervention combining video-based training and flotation tank recovery on three-point shooting performance in elite female basketball players. Players were assigned to an experimental (n=10) and control group (n=9). A 3 wk intervention consisted of 2 x 30 min float sessions a week which included 10 min of video-based training footage, followed by a 3 wk retention phase. A total of 100 three-point shots were taken from 5 designated positions on the court at each week to assess three-point shooting performance. There was no clear difference in the mean change in the number of successful three-point shots between the groups (-3%; ±18%, mean; ±90% confidence limits). Video-based training combined with flotation recovery had little effect on three-point shooting performance.

Application of multi-criteria decision making methods to compression ignition engine efficiency and gaseous, particulate and greenhouse gas emissions

Compression ignition (CI) engine design is subject to many constraints which presents a multi-criteria optimisation problem that the engine researcher must solve. In particular, the modern CI engine must not only be efficient, but must also deliver low gaseous, particulate and life cycle greenhouse gas emissions so that its impact on urban air quality, human health, and global warming are minimised. Consequently, this study undertakes a multi-criteria analysis which seeks to identify alternative fuels, injection technologies and combustion strategies that could potentially satisfy these CI engine design constraints. Three datasets are analysed with the Preference Ranking Organization Method for Enrichment Evaluations and Geometrical Analysis for Interactive Aid (PROMETHEE-GAIA) algorithm to explore the impact of 1): an ethanol fumigation system, 2): alternative fuels (20 % biodiesel and synthetic diesel) and alternative injection technologies (mechanical direct injection and common rail injection), and 3): various biodiesel fuels made from 3 feedstocks (i.e. soy, tallow, and canola) tested at several blend percentages (20-100 %) on the resulting emissions and efficiency profile of the various test engines. The results show that moderate ethanol substitutions (~20 % by energy) at moderate load, high percentage soy blends (60-100 %), and alternative fuels (biodiesel and synthetic diesel) provide an efficiency and emissions profile that yields the most “preferred” solutions to this multi-criteria engine design problem. Further research is, however, required to reduce Reactive Oxygen Species (ROS) emissions with alternative fuels, and to deliver technologies that do not significantly reduce the median diameter of particle emissions.

The adoption of e-learning 2.0 in higher education by teachers and students : an investigation using mixed methods approach

This paper describes an approach to investigate the adoption of Web 2.0 in the classroom using a mixed methods study. By using a combination of qualitative or quantitative data collection and analysis techniques, we attempt to synergize the results and provide a more valid understanding of Web 2.0 adoption for learning by both teachers and students. This approach is expected to yield a better holistic view on the adoption issues associated with the e-learning 2.0 concept in current higher education as opposed to single method studies done previously. This paper also presents some early findings of e-learning 2.0 adoption using this research method

Methods to estimate the size and shape of the unaccommodated crystalline lens in vivo

Purpose. The purpose of this article was to present methods capable of estimating the size and shape of the human eye lens without resorting to phakometry or magnetic resonance imaging (MRI). Methods. Previously published biometry and phakometry data of 66 emmetropic eyes of 66 subjects (age range [18, 63] years, spherical equivalent range [−0.75, +0.75] D) were used to define multiple linear regressions for the radii of curvature and thickness of the lens, from which the lens refractive index could be derived. MRI biometry was also available for a subset of 30 subjects, from which regressions could be determined for the vertex radii of curvature, conic constants, equatorial diameter, volume, and surface area. All regressions were compared with the phakometry and MRI data; the radii of curvature regressions were also compared with a method proposed by Bennett and Royston et al. Results. The regressions were in good agreement with the original measurements. This was especially the case for the regressions of lens thickness, volume, and surface area, which each had an R2 > 0.6. The regression for the posterior radius of curvature had an R2 < 0.2, making this regression unreliable. For all other regressions we found 0.25 < R2 < 0.6. The Bennett-Royston method also produced a good estimation of the radii of curvature, provided its parameters were adjusted appropriately. Conclusions. The regressions presented in this article offer a valuable alternative in case no measured lens biometry values are available; however care must be taken for possible outliers.