Koszul Calculus

We present a new calculus which is well-adapted to quadratic algebras. This calculus consists in Koszul (co)homology, together with Koszul cup and cap products. Some applications are given. Koszul duality for Koszul (co)homology is proved for any quadratic algebra.Comment: 40 pages; minor changes; to be published in Glasgow Mathematical Journa

Revisiting LFSMs

Linear Finite State Machines (LFSMs) are particular primitives widely used in information theory, coding theory and cryptography. Among those linear automata, a particular case of study is Linear Feedback Shift Registers (LFSRs) used in many cryptographic applications such as design of stream ciphers or pseudo-random generation. LFSRs could be seen as particular LFSMs without inputs. In this paper, we first recall the description of LFSMs using traditional matrices representation. Then, we introduce a new matrices representation with polynomial fractional coefficients. This new representation leads to sparse representations and implementations. As direct applications, we focus our work on the Windmill LFSRs case, used for example in the E0 stream cipher and on other general applications that use this new representation. In a second part, a new design criterion called diffusion delay for LFSRs is introduced and well compared with existing related notions. This criterion represents the diffusion capacity of an LFSR. Thus, using the matrices representation, we present a new algorithm to randomly pick LFSRs with good properties (including the new one) and sparse descriptions dedicated to hardware and software designs. We present some examples of LFSRs generated using our algorithm to show the relevance of our approach.Comment: Submitted to IEEE-I

Improving the Watermarking Process with Usage of Block Error-Correcting Codes

The emergence of digital imaging and of digital networks has made duplication of original artwork easier. Watermarking techniques, also referred to as digital signature, sign images by introducing changes that are imperceptible to the human eye but easily recoverable by a computer program. Usage of error correcting codes is one of the good choices in order to correct possible errors when extracting the signature. In this paper, we present a scheme of error correction based on a combination of Reed-Solomon codes and another optimal linear code as inner code. We have investigated the strength of the noise that this scheme is steady to for a fixed capacity of the image and various lengths of the signature. Finally, we compare our results with other error correcting techniques that are used in watermarking. We have also created a computer program for image watermarking that uses the newly presented scheme for error correction

Interlaced spin grating for optical wave filtering

Interlaced Spin Grating is a scheme for the preparation of spectro-spatial periodic absorption gratings in a inhomogeneously broadened absorption profile. It relies on the optical pumping of atoms in a nearby long-lived ground state sublevel. The scheme takes advantage of the sublevel proximity to build large contrast gratings with unlimited bandwidth and preserved average optical depth. It is particularly suited to Tm-doped crystals in the context of classical and quantum signal processing. In this paper, we study the optical pumping dynamics at play in an Interlaced Spin Grating and describe the corresponding absorption profile shape in an optically thick atomic ensemble. We show that, in Tm:YAG, the diffraction efficiency of such a grating can reach 18.3% in the small angle, and 11.6% in the large angle configuration when the excitation is made of simple pulse pairs, considerably outperforming conventional gratings.Comment: 11 pages, 13 figures in Physical Review A, 201

Agricultural Investments under International Investment Law

International investment law, based primarily on international investment treaties, plays an important role in the governance of investment in agriculture, forestry, and fishing. The obligations established by these treaties, and enforced by means of investor–state arbitration, can present challenges for policy-makers and others seeking to ensure that investments are sustainable, including by affecting the ways in which the costs and benefits of investments are distributed among different actors. CCSI partnered with the International Institute for Environment and Development (IIED) and the International Institute for Sustainable Development (IISD) to produce a briefing note on agricultural investments under international investment law. The briefing note provides an overview of the following issues: Who and what do international investment treaties protect, and how are they enforced? Why does international investment law matter for the governance of sustainable, responsible investment in agriculture? How can investment treaties and investor-state arbitration impact laws, policies, and other actions or measures taken by states concerning investment in agriculture? What impact does international investment law have on local perspectives, responsible governance of tenure, and responsible business conduct? And how can policy-makers address challenges posed by investment treaties and investor-state arbitration

Groupe d'automorphismes des codes de Reed-Muller P-aires

Nous demontrons que le groupe d'automorphismes des codes de Reed-Muller p-aires est le groupe general affine. Les codes de Reed-Muller generalises ont ete definis par Kasami, Lin et Peterson, puis etudies en detail par Delsarte, Goethals et Mac William. Les codes de Reed-Muller p-aires sont les puissances du radical d'une algebre modulaire et sous cette forme, P. Charpin a donne une description de l'ensemble des mots de poids minimum de ces codes. Nous utilisons cette description pour caracteriser geometriquement le groupe d'automorphismes de ces codes

Advanced approach for the public transportation regulation system based on cybercars

International audienceIn the last decade, the authorities require the use of safe, comfortable vehicles to assure a door to door aspect with respect of environment in the urban context. In this paper, we propose an advanced approach of transport regulation where we integrate cybercars into a regulation process as an alternative in disruption cases. For that, we propose an ITS architecture including public transportation and cybercars into the same framework. We will show that collaboration between these two systems provides better results than managing them separably

Almost Perfect Nonlinear functions

We investigate some open problems on Almost Perfect Nonlinear (APN) functions over a finite field of characteristic $2$. We provide new characterizations of APN functions and of APN permutations by means of their component functions. We generalize some results of Nyberg (1994) and strengthen a conjecture on the upper bound of nonlinearity of APN functions. We also focus on the case of quadratic functions. We contribute to the current works on APN quadratic functions, by proving that a large class of quadratic functions cannot be APN