Towards a relational theory of copyright law

This research provides a systematic and theoretical analysis of the digital challenges to the established exclusive regime of the economic rights enjoyed by authors (and related rightholders) under the law of copyright. Accordingly, this research has developed a relational theory of authorship and a relational approach to copyright, contending that the regulatory emphasis of copyright law should focus on the facilitation of the dynamic relations between the culture, the creators, the future creators, the users and the public, rather than the allocation of resources in a static world. In this networked digital world, the creative works and contents have become increasingly vital for people to engage in creativity and cultural innovation, and for the evolution of the economy. Hence, it is argued that today copyright owners, as content holders, have certain obligations to make their works accessible and available to the public under fair conditions. This research sets forward a number of recommendations for the reform of the current copyright system.

Numerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term

In this paper, we consider the variable-order Galilei advection diffusion equation with a nonlinear source term. A numerical scheme with first order temporal accuracy and second order spatial accuracy is developed to simulate the equation. The stability and convergence of the numerical scheme are analyzed. Besides, another numerical scheme for improving temporal accuracy is also developed. Finally, some numerical examples are given and the results demonstrate the effectiveness of theoretical analysis. Keywords: The variable-order Galilei invariant advection diffusion equation with a nonlinear source term; The variable-order Riemann–Liouville fractional partial derivative; Stability; Convergence; Numerical scheme improving temporal accuracy

Matrix regularization techniques for online multitask learning

In this paper we examine the problem of prediction with expert advice in a setup where the learner is presented with a sequence of examples coming from different tasks. In order for the learner to be able to benefit from performing multiple tasks simultaneously, we make assumptions of task relatedness by constraining the comparator to use a lesser number of best experts than the number of tasks. We show how this corresponds naturally to learning under spectral or structural matrix constraints, and propose regularization techniques to enforce the constraints. The regularization techniques proposed here are interesting in their own right and multitask learning is just one application for the ideas. A theoretical analysis of one such regularizer is performed, and a regret bound that shows benefits of this setup is reported.

On the robustness and security of digital image watermarking

In most of the digital image watermarking schemes, it becomes a common practice to address security in terms of robustness, which is basically a norm in cryptography. Such consideration in developing and evaluation of a watermarking scheme may severely affect the performance and render the scheme ultimately unusable. This paper provides an explicit theoretical analysis towards watermarking security and robustness in figuring out the exact problem status from the literature. With the necessary hypotheses and analyses from technical perspective, we demonstrate the fundamental realization of the problem. Finally, some necessary recommendations are made for complete assessment of watermarking security and robustness.

The uses of multilingualism in digital culture : the case of inter-language linking

Language-use has proven to be the most complex and complicating of all Internet features, yet people and institutions invest enormously in language and crosslanguage features because they are fundamental to the success of the Internet’s past, present and future. The thesis takes into focus the developments of the latter – features that facilitate and signify linking between or across languages – both in their historical and current contexts. In the theoretical analysis, the conceptual platform of inter-language linking is developed to both accommodate efforts towards a new social complexity model for the co-evolution of languages and language content, as well as to create an open analytical space for language and cross-language related features of the Internet and beyond. The practiced uses of inter-language linking have changed over the last decades. Before and during the first years of the WWW, mechanisms of inter-language linking were at best important elements used to create new institutional or content arrangements, but on a large scale they were just insignificant. This has changed with the emergence of the WWW and its development into a web in which content in different languages co-evolve. The thesis traces the inter-language linking mechanisms that facilitated these dynamic changes by analysing what these linking mechanisms are, how their historical as well as current contexts can be understood and what kinds of cultural-economic innovation they enable and impede. The study discusses this alongside four empirical cases of bilingual or multilingual media use, ranging from television and web services for languages of smaller populations, to large-scale, multiple languages involving web ventures by the British Broadcasting Corporation, the Special Broadcasting Service Australia, Wikipedia and Google. To sum up, the thesis introduces the concepts of ‘inter-language linking’ and the ‘lateral web’ to model the social complexity and co-evolution of languages online. The resulting model reconsiders existing social complexity models in that it is the first that can explain the emergence of large-scale, networked co-evolution of languages and language content facilitated by the Internet and the WWW. Finally, the thesis argues that the Internet enables an open space for language and crosslanguage related features and investigates how far this process is facilitated by (1) amateurs and (2) human-algorithmic interaction cultures.

Sequential fusion of decisions with favorable dependence for controlled verification errors

Statistical dependence between classifier decisions is often shown to improve performance over statistically independent decisions. Though the solution for favourable dependence between two classifier decisions has been derived, the theoretical analysis for the general case of 'n' client and impostor decision fusion has not been presented before. This paper presents the expressions developed for favourable dependence of multi-instance and multi-sample fusion schemes that employ 'AND' and 'OR' rules. The expressions are experimentally evaluated by considering the proposed architecture for text-dependent speaker verification using HMM based digit dependent speaker models. The improvement in fusion performance is found to be higher when digit combinations with favourable client and impostor decisions are used for speaker verification. The total error rate of 20% for fusion of independent decisions is reduced to 2.1% for fusion of decisions that are favourable for both client and impostors. The expressions developed here are also applicable to other biometric modalities, such as finger prints and handwriting samples, for reliable identity verification.

Alternating direction implicit numerical method for the space and time fractional Bloch-Torrey equation in 3-D

Recently, some authors have considered a new diffusion model–space and time fractional Bloch-Torrey equation (ST-FBTE). Magin et al. (2008) have derived analytical solutions with fractional order dynamics in space (i.e., _ = 1, β an arbitrary real number, 1 < β ≤ 2) and time (i.e., 0 < α < 1, and β = 2), respectively. Yu et al. (2011) have derived an analytical solution and an effective implicit numerical method for solving ST-FBTEs, and also discussed the stability and convergence of the implicit numerical method. However, due to the computational overheads necessary to perform the simulations for nuclear magnetic resonance (NMR) in three dimensions, they present a study based on a two-dimensional example to confirm their theoretical analysis. Alternating direction implicit (ADI) schemes have been proposed for the numerical simulations of classic differential equations. The ADI schemes will reduce a multidimensional problem to a series of independent one-dimensional problems and are thus computationally efficient. In this paper, we consider the numerical solution of a ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. A fractional alternating direction implicit scheme (FADIS) for the ST-FBTE in 3-D is proposed. Stability and convergence properties of the FADIS are discussed. Finally, some numerical results for ST-FBTE are given.

A new implicit numerical method for the space and time fractional Bloch-Torrey equation

In recent years, it has been found that many phenomena in engineering, physics, chemistry and other sciences can be described very successfully by models using mathematical tools from fractional calculus. Recently, noted a new space and time fractional Bloch-Torrey equation (ST-FBTE) has been proposed (see Magin et al. (2008)), and successfully applied to analyse diffusion images of human brain tissues to provide new insights for further investigations of tissue structures. In this paper, we consider the ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we propose a new effective implicit numerical method (INM) for the STFBTE whereby we discretize the Riesz fractional derivative using a fractional centered difference. Secondly, we prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent, and the order of convergence of the implicit numerical method is ( T2 - α + h2 x + h2 y + h2 z ). Finally, some numerical results are presented to support our theoretical analysis.

The Galerkin finite element approximation of the fractional cable equation

The cable equation is one of the most fundamental equations for modeling neuronal dynamics. Cable equations with a fractional order temporal derivative have been introduced to model electrotonic properties of spiny neuronal dendrites. In this paper, the fractional cable equation involving two integro-differential operators is considered. The Galerkin finite element approximations of the fractional cable equation are proposed. The main contribution of this work is outlined as follow: • A semi-discrete finite difference approximation in time is proposed. We prove that the scheme is unconditionally stable, and the numerical solution converges to the exact solution with order O(Δt). • A semi-discrete difference scheme for improving the order of convergence for solving the fractional cable equation is proposed, and the numerical solution converges to the exact solution with order O((Δt)2). • Based on the above semi-discrete difference approximations, Galerkin finite element approximations in space for a full discretization are also investigated. • Finally, some numerical results are given to demonstrate the theoretical analysis.

Numerical methods for solving the multi-term time-fractional wave-diffusion equations

In this paper, the multi-term time-fractional wave diffusion equations are considered. The multiterm time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

A second-order accurate numerical approximation for the Riesz space fractional advection-dispersion equation

In this paper, we consider a space Riesz fractional advection-dispersion equation. The equation is obtained from the standard advection-diffusion equation by replacing the ¯rst-order and second-order space derivatives by the Riesz fractional derivatives of order β 1 Є (0; 1) and β2 Є(1; 2], respectively. Riesz fractional advection and dispersion terms are approximated by using two fractional centered difference schemes, respectively. A new weighted Riesz fractional ¯nite difference approximation scheme is proposed. When the weighting factor Ѳ = 1/2, a second- order accurate numerical approximation scheme for the Riesz fractional advection-dispersion equation is obtained. Stability, consistency and convergence of the numerical approximation scheme are discussed. A numerical example is given to show that the numerical results are in good agreement with our theoretical analysis.

Numerical simulation of a fractional mathematical model for epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider numerical simulation of fractional model based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in advection and diffusion terms belong to the intervals (0; 1) or (1; 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of the Riemann-Liouville and Gr¨unwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.

Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation

Anomalous subdiffusion equations have in recent years received much attention. In this paper, we consider a two-dimensional variable-order anomalous subdiffusion equation. Two numerical methods (the implicit and explicit methods) are developed to solve the equation. Their stability, convergence and solvability are investigated by the Fourier method. Moreover, the effectiveness of our theoretical analysis is demonstrated by some numerical examples. © 2011 American Mathematical Society.

The competing-complementarity engagement of news media with online social media

The rapid growth of online social media networks like Facebook and Twitter is strongly influencing news media to engage with such networks for generating newsworthy content, accessing mass audiences for news consumption and using the platforms for news distribution. While both media’s complement each other as sources of news and information, they also compete against each other as news repositories and are observed vying for the same audiences. We call this phenomenon the competing-complementarity (C-C) engagement. To investigate the C-C relationship we use Fidler’s “mediamorphosis” concept to explain the metamorphosis of news media in the online domain. We make two contributions to Fidler’s concept by offering an additional principle “mass user migration” to address the characteristics of metamorphosis and an additional driver “transcended social engagement” to show the force that propels it. Besides, we also propose four accelerators that influence metamorphosis. Theoretical analysis of news media’s metamorphosis indicates its affinity to online social media. We apply niche and gratification theories to explain complementarity, and displacement effects on media consumption habits to trace competition between both media’s.

Analytical and numerical solutions of the space and time fractional bloch-torrey equation

Fractional order dynamics in physics, particularly when applied to diffusion, leads to an extension of the concept of Brown-ian motion through a generalization of the Gaussian probability function to what is termed anomalous diffusion. As MRI is applied with increasing temporal and spatial resolution, the spin dynamics are being examined more closely; such examinations extend our knowledge of biological materials through a detailed analysis of relaxation time distribution and water diffusion heterogeneity. Here the dynamic models become more complex as they attempt to correlate new data with a multiplicity of tissue compartments where processes are often anisotropic. Anomalous diffusion in the human brain using fractional order calculus has been investigated. Recently, a new diffusion model was proposed by solving the Bloch-Torrey equation using fractional order calculus with respect to time and space (see R.L. Magin et al., J. Magnetic Resonance, 190 (2008) 255-270). However effective numerical methods and supporting error analyses for the fractional Bloch-Torrey equation are still limited. In this paper, the space and time fractional Bloch-Torrey equation (ST-FBTE) is considered. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we derive an analytical solution for the ST-FBTE with initial and boundary conditions on a finite domain. Secondly, we propose an implicit numerical method (INM) for the ST-FBTE, and the stability and convergence of the INM are investigated. We prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent. Finally, we present some numerical results that support our theoretical analysis.