Stability and convergence of an implicit numerical method for the non-linear fractional reaction-subdiffusion process

In this paper, we consider the following non-linear fractional reaction–subdiffusion process (NFR-SubDP): Formula where f(u, x, t) is a linear function of u, the function g(u, x, t) satisfies the Lipschitz condition and 0Dt1–{gamma} is the Riemann–Liouville time fractional partial derivative of order 1 – {gamma}. We propose a new computationally efficient numerical technique to simulate the process. Firstly, the NFR-SubDP is decoupled, which is equivalent to solving a non-linear fractional reaction–subdiffusion equation (NFR-SubDE). Secondly, we propose an implicit numerical method to approximate the NFR-SubDE. Thirdly, the stability and convergence of the method are discussed using a new energy method. Finally, some numerical examples are presented to show the application of the present technique. This method and supporting theoretical results can also be applied to fractional integrodifferential equations.

Marx as critical discourse analyst : the genesis of a critical method and its relevance to the critique of global capital.

In this paper we identify elements in Marx´s economic and political writings that are relevant to contemporary critical discourse analysis (CDA). We argue that Marx can be seen to be engaging in a form of discourse analysis. We identify the elements in Marx´s historical materialist method that support such a perspective, and exemplify these in a longitudinal comparison of Marx´s texts.

Biometric template security using higher order spectra

A method of improving the security of biometric templates which satisfies desirable properties such as (a) irreversibility of the template, (b) revocability and assignment of a new template to the same biometric input, (c) matching in the secure transformed domain is presented. It makes use of an iterative procedure based on the bispectrum that serves as an irreversible transformation for biometric features because signal phase is discarded each iteration. Unlike the usual hash function, this transformation preserves closeness in the transformed domain for similar biometric inputs. A number of such templates can be generated from the same input. These properties are illustrated using synthetic data and applied to images from the FRGC 3D database with Gabor features. Verification can be successfully performed using these secure templates with an EER of 5.85%

Generation in context : an exploratory method for musical enquiry

This paper discusses a method, Generation in Context, for interrogating theories of music analysis and music perception. Given an analytic theory, the method consists of creating a generative process that implements the theory in reverse. Instead of using the theory to create analyses from scores, the theory is used to generate scores from analyses. Subjective evaluation of the quality of the musical output provides a mechanism for testing the theory in a contextually robust fashion. The method is exploratory, meaning that in addition to testing extant theories it provides a general mechanism for generating new theoretical insights. We outline our initial explorations in the use of generative processes for music research, and we discuss how generative processes provide evidence as to the veracity of theories about how music is experienced, with insights into how these theories may be improved and, concurrently, provide new techniques for music creation. We conclude that Generation in Context will help reveal new perspectives on our understanding of music.

Eco-structure data forms : classification of data analysis using perceived design affordances for musical outcomes

This paper explores a method of comparative analysis and classification of data through perceived design affordances. Included is discussion about the musical potential of data forms that are derived through eco-structural analysis of musical features inherent in audio recordings of natural sounds. A system of classification of these forms is proposed based on their structural contours. The classifications include four primitive types; steady, iterative, unstable and impulse. The classification extends previous taxonomies used to describe the gestural morphology of sound. The methods presented are used to provide compositional support for eco-structuralism.