Extremal circular permutations with concave functions

Let {a(1), a(2), ..., a(n)} be a set of n distinct real numbers and let alpha(1), alpha(2), ..., alpha(n) an be a permutation of the numbers. We construct the permutation to maximise L-f = Sigma(i=1)(n) f(\alpha(i+1) - alpha(i)\), for any increasing concave function f, where we denote alpha(n+1) equivalent to alpha(1). The optimal permutation depends on the particular numbers {a(1), a(2), ..., a(n)} and the function f, contrary to a postulate by Chao and Liang (European J. Combin. 13 (1992) 325). (C) 2004 Elsevier Ltd. All rights reserved.

Structure and folding of potato type II proteinase inhibitors: Circular permutation and intramolecular domain swapping

Potato type II serine proteinase inhibitors are proteins that consist of multiple sequence repeats, and exhibit a multidomain structure. The structural domains are circular permutations of the repeat sequence.. as a result or intramolecular domain swapping. Structural studies give indications for the origins of this folding behaviour, and the evolution of the inhibitor family.

Continuous-variable quantum-state sharing via quantum disentanglement

Quantum-state sharing is a protocol where perfect reconstruction of quantum states is achieved with incomplete or partial information in a multipartite quantum network. Quantum-state sharing allows for secure communication in a quantum network where partial information is lost or acquired by malicious parties. This protocol utilizes entanglement for the secret-state distribution and a class of quantum disentangling protocols for the state reconstruction. We demonstrate a quantum-state sharing protocol in which a tripartite entangled state is used to encode and distribute a secret state to three players. Any two of these players can collaborate to reconstruct the secret state, while individual players obtain no information. We investigate a number of quantum disentangling processes and experimentally demonstrate quantum-state reconstruction using two of these protocols. We experimentally measure a fidelity, averaged over all reconstruction permutations, of F=0.73 +/- 0.02. A result achievable only by using quantum resources.

Dynamic response: Real-time adaptation for music emotion

Music plays an enormous role in today's computer games; it serves to elicit emotion, generate interest and convey important information. Traditional gaming music is fixed at the event level, where tracks loop until a state change is triggered. This behaviour however does not reflect musically the in-game state between these events. We propose a dynamic music environment, where music tracks adjust in real-time to the emotion of the in-game state. We are looking to improve the affective response to symbolic music through the modification of structural and performative characteristics through the application of rule-based techniques. In this paper we undertake a multidiscipline approach, and present a series of primary music-emotion structural rules for implementation. The validity of these rules was tested in small study involving eleven participants, each listening to six permutations from two musical works. Preliminary results indicate that the environment was generally successful in influencing the emotion of the musical works for three of the intended four directions (happier, sadder & content/dreamier). Our secondary aim of establishing that the use of music-emotion rules, sourced predominantly from Western classical music, could be applied with comparable results to modern computer gaming music was also largely successfully.