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.

Analysis of productive performance of crop production systems: an integrated analytical framework

Recent literature has argued that environmental efficiency (EE), which is built on the materials balance (MB) principle, is more suitable than other EE measures in situations where the law of mass conversation regulates production processes. In addition, the MB-based EE method is particularly useful in analysing possible trade-offs between cost and environmental performance. Identifying determinants of MB-based EE can provide useful information to decision makers but there are very few empirical investigations into this issue. This article proposes the use of data envelopment analysis and stochastic frontier analysis techniques to analyse variation in MB-based EE. Specifically, the article develops a stochastic nutrient frontier and nutrient inefficiency model to analyse determinants of MB-based EE. The empirical study applies both techniques to investigate MB-based EE of 96 rice farms in South Korea. The size of land, fertiliser consumption intensity, cost allocative efficiency, and the share of owned land out of total land are found to be correlated with MB-based EE. The results confirm the presence of a trade-off between MB-based EE and cost allocative efficiency and this finding, favouring policy interventions to help farms simultaneously achieve cost efficiency and MP-based EE.

Framework for evaluating collaborative intrusion detection systems

Securing IT infrastructures of our modern lives is a challenging task because of their increasing complexity, scale and agile nature. Monolithic approaches such as using stand-alone firewalls and IDS devices for protecting the perimeter cannot cope with complex malwares and multistep attacks. Collaborative security emerges as a promising approach. But, research results in collaborative security are not mature, yet, and they require continuous evaluation and testing. In this work, we present CIDE, a Collaborative Intrusion Detection Extension for the network security simulation platform ( NeSSi 2 ). Built-in functionalities include dynamic group formation based on node preferences, group-internal communication, group management and an approach for handling the infection process for malware-based attacks. The CIDE simulation environment provides functionalities for easy implementation of collaborating nodes in large-scale setups. We evaluate the group communication mechanism on the one hand and provide a case study and evaluate our collaborative security evaluation platform in a signature exchange scenario on the other.

Transmission system expansion planning considering combined operation of wind farms and energy storage systems

An energy storage system (ESS) can provide ancillary services such as frequency regulation and reserves, as well as smooth the fluctuations of wind power outputs, and hence improve the security and economics of the power system concerned. The combined operation of a wind farm and an ESS has become a widely accepted operating mode. Hence, it appears necessary to consider this operating mode in transmission system expansion planning, and this is an issue to be systematically addressed in this work. Firstly, the relationship between the cost of the NaS based ESS and its discharging cycle life is analyzed. A strategy for the combined operation of a wind farm and an ESS is next presented, so as to have a good compromise between the operating cost of the ESS and the smoothing effect of the fluctuation of wind power outputs. Then, a transmission system expansion planning model is developed with the sum of the transmission investment costs, the investment and operating costs of ESSs and the punishment cost of lost wind energy as the objective function to be minimized. An improved particle swarm optimization algorithm is employed to solve the developed planning model. Finally, the essential features of the developed model and adopted algorithm are demonstrated by 18-bus and 46-bus test systems.

Crowdsourcing information systems : definition, typology and design

Crowdsourcing has become a popular approach for capitalizing on the potential of large and open crowds of people external to the organization. While crowdsourcing as a phenomenon is studied in a variety of fields, research mostly focuses on isolated aspects and little is known about the integrated design of crowdsourcing efforts. We introduce a socio-technical systems perspective on crowdsourcing, which provides a deeper understanding of the components and relationships in crowdsourcing systems. By considering the function of crowdsourcing systems within their organizational context, we develop a typology of four distinct system archetypes. We analyze the characteristics of each type and derive a number of design requirements for the respective system components. The paper lays a foundation for IS-based crowdsourcing research, channels related academic work, and helps guiding the study and design of crowdsourcing information systems.

Process for forming alumino-silicate derivatives

A process for the preparation of an amorphous alumino-silicate derivative which involves reacting a solid corresponding starting material with MOH where M is alkali metal or ammonium cation. The solid corresponding starting material may be selected from montmorillonite, kaolin, natural zeolite (e.g., clinoliptolite/heulandite) as well as illite, palygorskite and saponite and additional reactant MX wherein X is halide may be utilized in conjunction with MOH. The invention also includes alumino-silicate derivatives of the general formula M.sub.p Al.sub.q Si.sub.2 O.sub.r (OH).sub.s X.sub.t.uH.sub.2 O as well as alumino-silicate derivatives of the general formula M.sub.p Al.sub.q Si.sub.2 O.sub.r (OH).sub.s.uH.sub.2 O.