Comment on ‘Persistent inputs and the standard H2-multivariable control problem’ by K. Park and J.J. Bongiorno Jr

It is necessary to welcome the publication of the paper by Park and Bongiorno Jr (Park, K. and Bongiorno Jr, J.J. (2009 Park, K and Bongiorno Jr, JJ. 2009. Persistent Inputs and the Standard H₂-multivariable Control Problem. International Journal of Control, 82: 2002–2012. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), ‘Persistent Inputs and the Standard H₂-multivariable Control Problem’, International Journal of Control, 82, 2002–2012) in which the special cases in H₂-optimisation problems are considered. However, for correct orientation of readers we would like to note some publications which, in our opinion, are connected to a problem given by Park and Bongiorno Jr (2009 Park, K and Bongiorno Jr, JJ. 2009. Persistent Inputs and the Standard H₂-multivariable Control Problem. International Journal of Control, 82: 2002–2012. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), but are absent there.     

A parallel time-memory tradeoff attack on the Hill cipher

Leap et al. (2016 Leap, T., T. McDevitt, K. Novak, and N. Siermine. 2016. Further improvements to the Bauer-Millward attack on the Hill cipher. Cryptologia 40:1–16.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) reduced the time complexity of the Bauer-Millward (2007 Bauer, C., and K. Millward. 2007. Cracking matrix encryption row by row. Cryptologia 31(1):76–83.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) ciphertext-only attack on the Hill cipher from 𝒪(Lⁿ) to 𝒪(L^n?1), where L is the length of the alphabet, and n is the block size. This article presents an attack that reduces the complexity to 𝒪(L^n?1?s), 0?≤?s?≤?n???1. The practical limitation on the size of s is the memory available on the computer being used for the attack. Specifically, the computer must be able to hold L^s integer arrays of length N, where N is the number of blocks of ciphertext. The key idea is not to iterate over potential rows of the decryption matrix, but to iterate over randomly chosen characters in the plaintext. This attack also admits a straightforward parallel implementation on multiple processors to further decrease the run time of the attack.     

A continuous review inventory model with controllable backorder rate and investments

In this study, we investigate a continuous review inventory model to reduce lead time, yield variability and setup cost simultaneously through capital investments. We assume that the backorder rate is depending on the length of the lead time through the amount of shortages. We also assume that lead time demand's distribution is not known but its first and second moments are known. We apply minimax distribution free procedure to minimise the expected total annual cost. By using logarithmic investment function we describe the relationship between the reduction in lead time, yield variability and setup cost with capital investment. This function was used in many existing models. Our main aim is to determine the optimal capital investment and ordering policies that minimises the expected total annual cost. To find out the optimal solution, an algorithm is given. With the help of this algorithm, optimal capital investment and ordering policies are wrought out. Numerical examples are given to elucidate the model. Our proposed model greatly differs from the model existing in the literature (the model by Lin and Hou (2005 Lin, LC and Hou, KL. 2005. An Inventory System with Investment to Reduce Yield Variability and Setup Cost. Journal of the Operational Research Society, 56: 67–74. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar])) viz: (1) In the above model, yield variability and setup cost were reduced through capital investment. In our model we reduce yield variability setup cost and also the lead time, which plays a vital role in any business. By reducing lead time we can improve the service level to the customer so as to increase the competitive edge in business. (2) In the model (the model by Lin and Hou (2005 Lin, LC and Hou, KL. 2005. An Inventory System with Investment to Reduce Yield Variability and Setup Cost. Journal of the Operational Research Society, 56: 67–74. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar])), it was assumed that lead time demand follows normal distribution. But in our model we take the distribution of lead time demand as distribution free. That is, it can follow any distribution which is more general. (3) In the above model (the model by Lin and Hou (2005 Lin, LC and Hou, KL. 2005. An Inventory System with Investment to Reduce Yield Variability and Setup Cost. Journal of the Operational Research Society, 56: 67–74. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar])), shortages are completely backlogged. But we consider partial backlogging and take the backlogging rate as 0 ≤ B ≤ 1. If we set backlogging rate B = 1 we get the above model. That is, the above model is particular case of our model. (4) We also assume that the backorder rate depends on the length of the lead time through the amount of shortages. If the lead time is longer then shortage accumulation is higher. The patience of customers will result in failure in business since some customers may turn to some other supplier. Hence, the backorder rate will be reduced. This assumption is very realistic.     

On the validity of the arithmetic–geometric mean method to locate the optimal solution in a supply chain system

Cardenas-Barron [Cardenas-Barron, L.E. (2010) ‘A Simple Method to Compute Economic order Quantities: Some Observations’, Applied Mathematical Modelling, 34, 1684–1688] indicates that there are several functions in which the arithmetic–geometric mean method (AGM) does not give the minimum. This article presents another situation to reveal that the AGM inequality to locate the optimal solution may be invalid for Teng, Chen, and Goyal [Teng, J.T., Chen, J., and Goyal S.K. (2009), ‘A Comprehensive Note on: An Inventory Model under Two Levels of Trade Credit and Limited Storage Space Derived without Derivatives’, Applied Mathematical Modelling, 33, 4388–4396], Teng and Goyal [Teng, J.T., and Goyal S.K. (2009), ‘Comment on ‘Optimal Inventory Replenishment Policy for the EPQ Model under Trade Credit Derived without Derivatives’, International Journal of Systems Science, 40, 1095–1098] and Hsieh, Chang, Weng, and Dye [Hsieh, T.P., Chang, H.J., Weng, M.W., and Dye, C.Y. (2008), ‘A Simple Approach to an Integrated Single-vendor Single-buyer Inventory System with Shortage’, Production Planning and Control, 19, 601–604]. So, the main purpose of this article is to adopt the calculus approach not only to overcome shortcomings of the arithmetic–geometric mean method of Teng et al. (2009), Teng and Goyal (2009 Teng, JT, Chen, J and Goyal, SK. 2009. A Comprehensive Note on: An Inventory Model under Two Levels of Trade Credit and Limited Storage Space Derived without Derivatives. Applied Mathematical Modelling, 33: 4388–4396. [Crossref], [Web of Science ®] , [Google Scholar]) and Hsieh et al. (2008), but also to develop the complete solution procedures for them.     

Adaptive learning control design for robotic manipulators driven by permanent magnet synchronous motors

On the basis of the ideas recently presented in Tomei and Verrelli (Tomei, P., and Verrelli, C.M. (2010 Tomei, P and Verrelli, CM. 2010. Learning Control for Induction Motor Servo Drives with Uncertain Rotor Resistance. International Journal of Control, 83: 1515–1528. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), ‘Learning Control for Induction Motor Servo Drives with Uncertain Rotor Resistance’, International Journal of Control, 83, 1515–1528) and Marino et al. (Marino, R., Tomei, P., and Verrelli, C.M. (2011 Marino, R, Tomei, P and Verrelli, CM. 2011. Robust Adaptive Learning Control for Nonlinear Systems with Extended Matching Unstructured Uncertainties. International Journal of Robust and Nonlinear Control, Early View, doi: 10.1002/rnc.1720 [Google Scholar]), ‘Robust Adaptive Learning Control for Nonlinear Systems with Extended Matching Unstructured Uncertainties’, International Journal of Robust and Nonlinear Control, Early View, doi: 10.1002/rnc.1720), we briefly show how the adaptive learning control design proposed in Liuzzo and Tomei (Liuzzo, S., and Tomei, P. (2009 Liuzzo, S and Tomei, P. 2009. Global Adaptive Learning Control of Robotic Manipulators by Output Error Feedback. International Journal of Adaptive Control and Signal Processing, 23: 97–109.  [Google Scholar]), Global Adaptive Learning Control of Robotic Manipulators by Output Error Feedback, International Journal of Adaptive Control and Signal Processing, 23, 97–109) can be extended to robotic manipulators driven by nonsalient-pole (surface) permanent magnet synchronous motors. Unstructured uncertain dynamics (that is no parameterisation is available for the uncertainties) of the rigid robot with rotational joints are considered as well as uncertainties in stator resistances of the synchronous motors are taken into account. Two solutions with clear stability proofs are presented: a global decentralised control via state feedback and a semi-global control via output feedback. Output tracking of known periodic reference signals and learning of corresponding uncertain input reference signals are achieved. Available results in the literature are thus improved since no simplification concerning negligible electrical motor dynamics is used.     

A Novel High Quality High Capacity Image Hiding Scheme Based on Image Compression and an Optical Pixel Adjustment Process

ABSTRACT

Image hiding methods embed a secret image into a host image. The resultant stego-image does not attract the interceptors that would not detect the differences between the host image and the stego-image. To exploit the great developments in the area of image compression and to improve the quality of stego-image, this paper proposes a new method to embed the secret image into the host image. Basically, the secret image is compressed and then embedded into host image. The embedding method is based on the Optimal Pixel Adjustment Process (OPAP) and genetic algorithm. In the paper we addressed the important issues to build such systems. The experimental results showed that the proposed method can improve the quality from 60% to 80% when compared with the simple Least Significant Bit (LSB) replacement methods. Adding to that, the mean square error of the stego-image is much lower compared with other methods (Chan & Cheng, 2004 Chan, C.K. and Cheng, L.M. 2004. Hiding data in images by simple LSB substitution. Pattern Recognition, 37(3): 469–474. [Crossref], [Web of Science ®] , [Google Scholar]; Chang, Hsiao, & Chan, 2003 Chang, C.C., Hsiao, J.Y. and Chan, C.S. 2003. Finding optimal least-significant-bit substitution in image hiding by dynamic programming strategy. Pattern Recognition, 36(7): 1583–1595. [Crossref], [Web of Science ®] , [Google Scholar]; Thien & Lin, 2003 Thien, C.C. and Lin, J.C. 2003. A simple and high-hiding capacity method for hiding digit-by-digit data in images based on modulus function. Pattern Recognition, 36(12): 2875–2881. [Crossref], [Web of Science ®] , [Google Scholar]; Tseng, Chan, Ho, & Chu, 208; Wang, Lin, & Lin, 2001 Wang, R.Z., Lin, C.F. and Lin, J.C. 2001. Image hiding by optimal LSB substitution and genetic algorithm. Pattern Recognition, 34(3): 671–683. [Crossref], [Web of Science ®] , [Google Scholar]). Also, the proposed technique improves capacity. In other words, we can embed a secret image with size 450?×?450 inside a hosting image with size 512?×?512.     

Continuous-time non-linear flatness-based predictive control: an exact feedforward linearisation setting with an induction drive example

A general flatness-based framework for non-linear continuous-time predictive control is presented. It extends the results of Fliess and Marquez (2000 Fliess, M and Marquez, R. 2000. Continuous-time Linear Predictive Control and Flatness: A Module-theoretic Setting with Examples. International Journal of Control, 73: 606–623. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) to the non-linear case. The mathematical setting, which is valid for multivariable systems, is provided by the theory of flatness-based exact feedforward linearisation introduced by the authors (Hagenmeyer and Delaleau 2003b Hagenmeyer, V and Delaleau, E. 2003b. Exact Feedforward Linearization Based on Differential Flatness. International Journal of Control, 76: 537–556. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). Thereby differential flatness does not only yield an easy calculation of the predicted trajectories considering the respective system constraints, but allows to use simple linear feedback parts in a two-degree-of-freedom control structure. Moreover, this formalism permits one to handle non-minimum phase systems, and furthermore to deal with parameter uncertainties and exogenous perturbations. Respective robustness analysis tools are available. Finally, an induction drive example is discussed in detail and experimental results for this fast electro-mechanical system are presented.     

Comment on ‘Optimal inventory replenishment policy for the EPQ model under trade credit derived without derivatives’

In this article, we complement the shortcoming of the inventory economic production quantity (EPQ) model developed by Huang and Huang (2008 Huang, YF and Huang, HF. 2008. Optimal Inventory Replenishment Policy for the EPQ Model Under Trade Credit Derived Without Derivatives. International Journal of Systems Science, 39: 539–546. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), ‘Optimal Inventory Replenishment Policy for the EPQ Model Under Trade Credit Derived Without Derivatives’, International Journal of Systems Science, 39, 539–546), and propose an arithmetic–geometric inequality method to obtain the global optimal solution without taking complex differential calculus or using tedious algebraic manipulations. Finally, we provide an economical interpretation of the theoretical result so that the reader can understand the insight of the result.     

Optimal control of the production–inventory system with deteriorating items and tradable emission permits

Using the well-known Arrow and Karlin (1958) Arrow, K.J., and Karlin, S. (1958), ‘Production over Time with Increasing Marginal Costs’, in Studies in the Mathematical Theory of Inventory and Production, eds. K.J. Arrow and S. Karlin, Stanford: Stanford University Press, pp. 61–69. [Google Scholar] dynamic production–inventory model and the model with tradable emission permits which was presented by Dobos (2005 Dobos, I. (2005), ‘The Effects of Emission Trading on Production and Inventories in the Arrow–Karlin Model’, International Journal of Production Economics, 93–94, 301–308.[Crossref], [Web of Science ®] , [Google Scholar], 2007) Dobos I. (2007), ‘Tradable Emission Permits and Production-inventory Strategies of the Firm’, International Journal of Production Economics, 108, 329–333.[Crossref], [Web of Science ®] , [Google Scholar], we develop a model of the production–inventory system with deteriorating items and tradable emission permits. The objective of this paper is to apply the optimal control theory to solve the production–inventory problem with deteriorating items and tradable emission permits, and derive the optimal inventory level and the optimal production rate that minimise the total cost. The results are discussed with a numerical example and a sensitivity analysis of the optimal solution with respect to the parameters of the production–inventory system is carried out.     

A new predicto-corrector method for pseudomonotone nonlinear complementarity problems

Based on the Logarithmic-Quadratic Proximal (LQP) method 2 Auslender, A., Teboulle, M. and Ben-Tiba, S. 1999. A logarithmic-quadratic proximal method for variational inequalities. Comput. Optim. Appl., 12: 31–40. [Crossref], [Web of Science ®] , [Google Scholar], we propose a new prediction-correction method for nonlinear complementarity problem (NCP). We obtain the predictor through a simplified inexact logarithmic-quadratic proximal method under a relaxed inexact criterion. The corrector is obtained by the improved extragradient method. Under certain conditions, the global convergence of the proposed method is proved. Preliminary numerical results indicate the efficiency of the proposed method.     

A numerical algorithm to find soft-constrained Nash equilibria in scalar LQ-games

This paper provides a numerical algorithm to calculate all soft-constrained Nash equilibria in a regular scalar indefinite linear-quadratic game. The algorithm is based on the calculation of the eigenstructure of a certain matrix. The analysis follows the lines of the approach taken by Engwerda (2003 Engwerda, JC. 2003. Solving the scalar feedback Nash algebraic Riccati equations: an eigenvector approach. IEEE Trans. Automat. Contr., 48: 847–853. [Crossref] , [Google Scholar]) to calculate the solutions of a set of scalar coupled feedback Nash algebraic Riccati equations.     

Further results on sampled-data design for robust control of a single qubit

This paper presents further results on the robust control method for qubit systems in Dong et al. (2013) Dong, D., Petersen, I.R., &; Rabitz, H. (2013). Sampled-data design for robust control of a single qubit. IEEE Transactions on Automatic Control, 58, 2654–2659.[Crossref], [Web of Science ®] , [Google Scholar]. Based on the properties of an antisymmetric system, an alternative method is presented to analyse and exclude singularity intervals in the proof of partial original results. For the case of amplitude damping decoherence, a larger sampling period is presented when the upper bound of the probability of failure is small enough. For the case of phase damping decoherence, a larger sampling period is given when the lower bound of the target coherence is large enough. Furthermore, we provide improved sampling periods for amplitude damping decoherence and phase damping decoherence without the above prior constraints.     

Mean-square stability and error analysis of implicit time-stepping schemes for linear parabolic SPDEs with multiplicative Wiener noise in the first derivative

In this article, we extend a Milstein finite difference scheme introduced in 8 Giles, M. B. and Reisinger, C. 2012. Stochastic finite differences and multilevel Monte Carlo for a class of SPDEs in finance. SIAM Financ. Math., 3(1): 572–592. (doi:10.1137/110841916)[Crossref] , [Google Scholar] for a certain linear stochastic partial differential equation (SPDE) to semi-implicit and fully implicit time-stepping as introduced by Szpruch 32 Szpruch, L. 2010. Numerical approximations of nonlinear stochastic systems PhD Thesis, University of Strathclyde [Google Scholar] for stochastic differential equations (SDEs). We combine standard finite difference Fourier analysis for partial differential equations with the linear stability analysis in 3 Buckwar, E. and Sickenberger, T. 2011. A comparative linear mean-square stability analysis of Maruyama- and Milstein-type methods. Math. Comput. Simulation, 81: 1110–1127. (doi:10.1016/j.matcom.2010.09.015)[Crossref], [Web of Science ®] , [Google Scholar] for SDEs to analyse the stability and accuracy. The results show that Crank–Nicolson time-stepping for the principal part of the drift with a partially implicit but negatively weighted double Itô integral gives unconditional stability over all parameter values and converges with the expected order in the mean-square sense. This opens up the possibility of local mesh refinement in the spatial domain, and we show experimentally that this can be beneficial in the presence of reduced regularity at boundaries.     

The effects of individual differences,prior experience and cognitive load on the transfer of dynamic decision-making performance

Situational awareness is recognised as an important factor in the performance of individuals and teams in dynamic decision-making (DDM) environments (Salmon et al. 2014 Salmon, P. M., N. A.Stanton, G. H.Walker, D.Jenkins, D.Ladva, L.Rafferty, and M.Young. 2014. “Measuring SA in Complex Systems: Comparison of Measurement Study.” International Journal of Industrial Ergonomics39: 490–500.[Crossref], [Web of Science ®] , [Google Scholar]). The present study was designed to investigate whether the scores on the WOMBAT? Situational Awareness and Stress Tolerance Test (Roscoe and North 1980 Roscoe, S. N., and R.North. 1980. “Prediction of Pilot Performance.” In Aviation Psychology, edited by S. N.Roscoe, 123–127. Ames: The Iowa State University Press. [Google Scholar]) would predict the transfer of DDM performance from training under different levels of cognitive load to a novel situation. Participants practised a simulated firefighting task under either low or high conditions of cognitive load and then performed a (transfer) test in an alternative firefighting environment under an intermediate level of cognitive load. WOMBAT? test scores were a better predictor of DDM performance than scores on the Raven Matrices. Participants with high WOMBAT? scores performed better regardless of their training condition. Participants with recent gaming experience who practised under low cognitive load showed better practice phase performance but worse transfer performance than those who practised under high cognitive load.

Practitioner Summary: The relationship between task experience, situational awareness ability, cognitive load and the transfer of dynamic decision-making (DDM) performance was investigated. Results showed that the WOMBAT? test predicted transfer of DDM performance regardless of task cognitive load. The effects of cognitive load on performance varied according to previous task-relevant experience.     

Knowledge processes in virtual teams: consolidating the evidence

This article takes stock of the current state of research on knowledge processes in virtual teams (VTs) and consolidates the extent research findings. Virtual teams, on the one hand, constitute important organisational entities that facilitate the integration of diverse and distributed knowledge resources. On the other hand, collaborating in a virtual environment creates particular challenges for the knowledge processes. The article seeks to consolidate the diverse evidence on knowledge processes in VTs with a specific focus on identifying the factors that influence the effectiveness of these knowledge processes. The article draws on the four basic knowledge processes outlined by Alavi and Leidner (2001 Alavi, M.Leidner, D.E., 2001. Review: knowledge management and knowledge management systems: conceptual foundations and research issues. MIS Quarterly, 25 (1), 107–136. doi: 10.2307/3250961[Crossref], [Web of Science ®] , [Google Scholar]) (i.e. creation, transferring, storage/retrieval and application) to frame the investigation and discuss the extent research. The consolidation of the existing research findings allows us to recognise the gaps in the understanding of knowledge processes in VTs and identify the important avenues for future research.     

Extending Query-Subquery Nets for Deductive Databases under the Well-Founded Semantics

ABSTRACT

We propose a method, called QSQN-WF, for evaluating queries to Datalog^¬ databases under the well-founded semantics. It is the first one that is set-at-a-time and strictly goal-directed w.r.t. SLS-resolution defined by Przymusinski. These properties are important for reducing accesses to the secondary storage and redundant computations. The first property distinguishes our method from the one based on SLG-resolution by Chen, Swift, and Warren (1995 Chen, W., T. Swift, and D. S. Warren. 1995. Efficient top-down computation of queries under the well-founded semantics. Journal of Logic Programming 24 (3):161–99. doi:10.1016/0743-1066(94)00028-5[Crossref] , [Google Scholar]) (which is tuple-at-a-time). The second property distinguishes our method from the ones based on the magic-sets transformation by Kemp, Srivastava, and Stuckey (1995 Kemp, D. B., D. Srivastava, and P. J. Stuckey. 1995. Bottom-up evaluation and query optimization of well-founded models. Theoretical Computer Science 146 (1 & 2):145–84. doi:10.1016/0304-3975(94)00153-a[Crossref], [Web of Science ®] , [Google Scholar]) and Morishita (1996 Morishita, S. 1996. An extension of Van Gelder's alternating fixpoint to magic programs. Journal of Computer and System Sciences 52 (3):506–21. doi:10.1006/jcss.1996.0038[Crossref], [Web of Science ®] , [Google Scholar]), which use magic atoms not in the most appropriate way and are not strictly goal-directed w.r.t. SLS-resolution. Our method follows SLS-resolution, with Van Gelder’s alternating fixpoint semantics on the background, but uses a query-subquery net to implement tabulation and the set-at-a-time technique, reduce redundant computations, and allow any control strategy within each iteration of the main loop. It is sound and complete w.r.t. the well-founded semantics and has PTIME data complexity.     

Majorizing sequences for Newton's method under centred conditions for the derivative

We present semi-local and local convergence results for Newton's method in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our technique is more flexible than in earlier studies such that [J.A. Ezquerro, D. González, and M.A. Hernández, Majorizing sequences for Newton's method from initial value problems, J. Comput. Appl. Math. 236 (2012), pp. 2246–2258; J.A. Ezquerro, D. González, and M.A. Hernández, A general semi-local convergence result for Newton's method under centred conditions for the second derivative, ESAIM: Math. Model. Numer. Anal. 47 (2013), pp. 149–167]. The operator involved is twice Fréchet-differentiable. We also assume certain centred Lipschitz-type conditions for the derivative which are more precise than the Lipschitz conditions used in earlier works. Numerical examples are used to show that our results apply to solve equations but earlier ones do not in the semi-local case. In the local case we obtain a larger convergence ball. These advantages are obtained under the same computational cost as before [17 J.A. Ezquerro, D. González, and M.A. Hernández, Majorizing sequences for Newton's method from initial value problems, J. Comput. Appl. Math. 236 (2012), pp. 2246–2258. doi: 10.1016/j.cam.2011.11.012[Crossref], [Web of Science ®] , [Google Scholar],18 J.A. Ezquerro, D. González, and M.A. Hernández, A general semilocal convergence result for Newton's method under centered conditions for the second derivative, ESAIM: Math. Model. Numer. Anal. 47 (2013), pp. 149–167. doi: 10.1051/m2an/2012026[Crossref], [Web of Science ®] , [Google Scholar]].     

Mapping the image

The Brainstorm feature introduced in Adobe After Effects CS3 (2007) allows users to automate parts of the process of generating design variations for the purposes of comparison and selection. The paper begins with a brief discussion of current discursive formations around software and software-based practice among digital design practitioners and educators. Next, the paper draws upon critical concepts drawn from multimodal discourse analysis, media theory and sociology to analyse Brainstorm in terms of the interplay of software structure and design agency. The key concepts used are modality, articulation and interpretation (Kress and van Leeuwen 1996 Kress, G. and van Leeuwen, T. 1996. Reading images: the grammar of visual design, London: Routledge.  [Google Scholar], 2001), the database as cultural form and the logic of selection (Manovich 2001 Manovich, L. 2001. The language of new media, Cambridge, MA: MIT Press.  [Google Scholar]), habitus and practical logic (Bourdieu 1977 Bourdieu, P. 1977. Outline of a theory of practice, New York: Cambridge University Press. [Crossref] , [Google Scholar]) and the radius of creativity (Toynbee 2000 Toynbee, J. 2000. Making popular music: musicians, creativity and institutions, London: Arnold.  [Google Scholar]). Throughout, the paper addresses specific structural features of the software, thus developing an overview of the affordances and constraints of Brainstorm as a creative tool.