On the problem of algebraic completeness for the invariants of the Riemann Tensor: I

We present a new determining set, CZ, of Riemann invariants which possesses the minimum degree property. From an analysis on the possible independence of CZ, we are led to the division of all space-times into two distinct, invariantly characterized, classes: a general class M_G+, and a special, singular class M_S For each class, we provide an independent set of invariants (I_G+) ⊂ CZ and I_S ⊂ CZ, respectively) which, with the results of a sequel paper, will be shown to be algebraically complete.

On the problem of algebraic completeness for the invariants of the Riemann tensor. III.

We study the set CZ of invariants [Zakhary and Carminati, J. Math. Phys. 42, 1474 (2001)] for the class of space-times whose Ricci tensors possess a null eigenvector. We show that all cases are maximally backsolvable, in terms of sets of invariants from CZ, but that some cases are not completely backsolvable and these all possess an alignment between an eigenvector of the Ricci tensor with a repeated principal null vector of the Weyl tensor. We provide algebraically complete sets for each canonically different space-time and hence conclude with these results and those of a previous article [Carminati, Zakhary, and McLenaghan, J. Math. Phys. 43, 492 (2002)] that the CZ set is determining or maximal.

Algebraic attacks over GF(q)

Recent algebraic attacks on LFSR-based stream ciphers and S-boxes have generated much interest as they appear to be extremely powerful. Theoretical work has been developed focusing around the Boo- lean function case. In this paper, we generalize this theory to arbitrary finite fields and extend the theory of annihilators and ideals introduced at Eurocrypt 2004 by Meier, Pasalic and Carlet. In particular, we prove that for any function f in the multivariate polynomial ring over GF(q), f has a low degree multiple precisely when two low degree functions appear in the same coset of the annihilator of f ^{q – 1} – 1. In this case, many such low degree multiples exist.

Algebraic attacks on clock-controlled stream ciphers

We present an algebraic attack approach to a family of irregularly clock-controlled bit-based linear feedback shift register systems. In the general set-up, we assume that the output bit of one shift register controls the clocking of other registers in the system and produces a family of equations relating the output bits to the internal state bits. We then apply this general theory to four specific stream ciphers: the (strengthened) stop-and-go generator, the alternating step generator, the self-decimated generator and the step1/step2 generator. In the case of the strengthened stop-and-go generator and of the self-decimated generator, we obtain the initial state of the registers in a significantly faster time than any other known attack. In the other two situations, we do better than or as well as all attacks but the correlation attack. In all cases, we demonstrate that the degree of a functional relationship between the registers can be bounded by two. Finally, we determine the effective key length of all four systems.

Algebraic attacks on clock-controlled cascade ciphers

In this paper, we mount the first algebraic attacks against clock controlled cascade stream ciphers. We first show how to obtain relations between the internal state bits and the output bits of the Gollmann clock controlled cascade stream ciphers. We demonstrate that the initial states of the last two shift registers can be determined by the initial states of the others. An alternative attack on the Gollmann cascade is also described, which requires solving quadratic equations. We then present an algebraic analysis of Pomaranch, one of the phase two proposals to eSTREAM. A system of equations of maximum degree four that describes the full cipher is derived. We also present weaknesses in the filter functions of Pomaranch by successfully computing annihilators and low degree multiples of the functions.

An algebraic approach for delay-independent and delay-dependent stability of linear time-delay systems

This paper addresses the problem of asymptotic stability of a linear system with many delay units. A novel algebraic test is proposed for the delay-independent stability of the system, based on the root distribution of the system's characteristic equation. If the system is only stable dependent of delay, the whole stable regions of the system can be perfectly obtained. Two algorithms are derived to examine the delay-independent stability, and to compute the whole stable regions if the system is of delay-dependent stability. These algorithms are computationally efficient and applicable to both certain and uncertain systems. Some illustrative examples demonstrate the validity of the approach.

Mutually clock-controlled feedback shift registers provide resistance to algebraic attacks

Algebraic attacks have been applied to several types of clock-controlled stream ciphers. However, to date there are no such attacks in the literature on mutually clock-controlled ciphers. In this paper, we present a preliminary step in this direction by giving the first algebraic analysis of mutually clock-controlled feedback shift register stream ciphers: the bilateral stop-and-go generator, A5/1, Alpha 1 and the MICKEY cipher. We show that, if there are no regularly clocked shift registers included in the system, mutually clock-controlled feedback shift register ciphers appear to be highly resistant to algebraic attacks. As a demonstration of the weakness inherent in the presence of a regularly clocked shift register, we present a simple algebraic attack on Alpha 1 based on only 29 keystream bits.

On the problem of algebraic completeness for the invariants of the Riemann tensor. II

We study the set of invariants CZ [E. Zakhary and J. Carminati, J. Math. Phys. 42, 1474 (2001)] for the class of space-times whose Ricci tensors do not possess a null eigenvector. We show that all cases are completely backsolvable in terms of sets of invariants from CZ. We provide algebraically complete sets for each canonically different space-time.

An algebraic framework for multimodal image fusion

This thesis presents an algebraic framework for multimodal image fusion. The framework derives algebraic constructs and equations that govern the fusion process. The derived equations serve as objective functions according to which image fusion algorithms and metrics can be tuned. The equations also prove the duality between image fusion algorithms and metrics.

Sui generis protection for plant varieties and traditional agricultural knowledge : the example of India

Explores the sui generis protection of intellectual property, particularly patents, in biotechnology and traditional agricultural knowledge under Indian law. Focuses on the impact of amendments to the Patents Act 1970 and of the Plant Variety Protection and Farmers' Rights Act 2001 and Biological Diversity Act 2002.

Sui Generis protection for plant varieties and traditional knowledge in biodiversity and agriculture : the international framework and national approaches in the Philippines and India

The so-called ‘biotechnology clause’ of Article 27.3(b) of the WTO-TRIPS Agreement requires from member states protection for plant varieties either via the patent system or via an ‘effective sui generis system’ or by a combination of the two. Many developing countries prefer forms of sui generis protection, which allow them to include exceptions and protection measures for traditional agricultural practices and the traditional knowledge of farmers and local communities. However, ‘traditional knowledge’ remains a vaguely defined term. Its extension to biodiversity has brought a diffusion of the previously clearer link between protected subject matter, intellectual property and potential beneficiaries. The Philippine legislation attempts a ‘bottom-up’ approach focusing on the holistic perceptions of indigenous communities, whereas national economic interests thus far receive priority in India’s more centralist approach. Administrative decentralisation, recognition of customary rights, disclosure requirements, registers of landraces and geographical indications are discussed as additional measures, but their implementation is equally challenging. The article concludes that many of the concepts remain contested and that governments have to balance the new commercial incentives with the biodiversity considerations that led to their introduction, so that the system can be made sufficiently attractive for both knowledge holders and potential users of the knowledge.

The manifestation of varieties of blended learning pedagogy (BLP) : interplay between academic, institutional and global pedagogy

Despite the increased recognition of the potential use of online technologies to deliver flexible and student-centered learning environments in higher education, there are numerous critiques that its usage does not transform the daily practices of teaching and learning. This paper draws on some of the findings from three case studies that explored the manifestation of blended learning pedagogies (BLP). Six academics teaching at three different higher education contexts at two different countries, namely Australia and Malaysia were interviewed. The study aimed to interrogate the different manifestation of BLP at the different contexts of higher education, highlighting the complex interplay between the users (academics), technology and the specific socio-cultural contexts. Focusing on the academic identities that are shaped and reshaped within its socio-cultural context, this study demonstrated the complexity and fluidity of the manifestation of the different varieties of BLP. It contributes to further understanding the ways in which online technologies are used in teaching and learning within context of global knowledge economy that emphasizes flexibility and active co-production of knowledge.