Simple FFT and DCT algorithms with reduced number of operations

A simple algorithm for the evaluation of discrete Fourier transforms (DFT) and discrete cosine transforms (DCT) is presented. This approach, based on the divide and conquer technique, achieves a substantial decrease in the number of additions when compared to currently used FFT algorithms (30% for a DFT on real data, 15% for a DFT on complex data and 25% for a DCT) and keeps the same number of multiplications as the best known FFT algorithms. The simple structure of the algorithm and the fact that it is best suited for real data (one does not have to take a transform of two real sequences simultaneously anymore) should lead to efficient implementations and to a wide range of applications.     

Intensity-invariant nonlinear filtering for detection in camouflage

We introduce a method based on an orthonormal vector space basis representation to detect camouflaged targets in natural environments. The method is intensity invariant so that camouflaged targets are detected independently of the illumination conditions. The detection technique does not require one to know the exact camouflage pattern, but only the class of patterns (e.g., foliage, netting, woods). We use nonlinear filtering and the calculation of several correlations. The nonlinearity of the filtering process also allows high discrimination against false targets. Several experiments confirm the target detectability where strong camouflage might delude even human viewers.     

Suslin’s algorithms for reduction of unimodular rows

A well-known lemma of Suslin says that for a commutative ring $A$ if $(v_1\left(X\right),\dots ,v_n\left(X\right))\in {\left(A\left[X\right]\right)}^n$ is unimodular where $v_1$ is monic and $n\ge 3$, then there exist ${\gamma }_1,\dots ,{\gamma }_{\ell }\in E_{n-1}\left(A\left[X\right]\right)$ such that the ideal generated by $\mathrm{Res}(v_1,e_1.{\gamma }_1{}^t(v_2,\dots ,v_n)),\dots ,\mathrm{Res}(v_1,e_1.{\gamma }_{\ell }{}^t(v_2,\dots ,v_n))$ equals $A$. This lemma played a central role in the resolution of Serre’s Conjecture. In the case where $A$ contains a set $E$ of cardinality greater than $deg{v}_1+1$ such that $y-y^{\prime }$ is invertible for each $y\ne y^{\prime }$ in $E$, we prove that the ${\gamma }_i$ can simply correspond to the elementary operations $L_1\to L_1+y_i{\sum }_{j=2}^{n-1}{u}_{j+1}{L}_j$, $1\le i\le \ell =deg{v}_1+1$, where $u_1{v}_1+\cdots +u_n{v}_n=1$. These efficient elementary operations enable us to give new and simple algorithms for reducing unimodular rows with entries in $K[X_1,\dots ,X_k]$ to ${}^t(1,0,\dots ,0)$ using elementary operations in the case where $K$ is an infinite field. Another feature of this paper is that it shows that the concrete local–global principles can produce competitive complexity bounds.     

60]fullerene is a powerful antioxidant in vivo with no acute or subacute toxicity

In the present work, we report the effects of C(60)-pretreatments on acute carbon tetrachloride intoxication in rats, a classical model for studying free-radical-mediated liver injury. Our results show that aqueous C(60) suspensions prepared without using any polar organic solvent not only have no acute or subacute toxicity in rodents but they also protect their livers in a dose-dependent manner against free-radical damage. To be sure, according to histopathological examinations and biological tests, pristine C(60) can be considered as a powerful liver-protective agent.     

Segregation and conformational transitions in triblock copolymers in dilute solution: 3. Viscometric investigations in solvent mixtures

Viscometric measurements were carried out on a triblock copolymer PMMA/PS/PMMA at two temperatures in two binary solvent mixtures, in order to establish to what extent segregation between the two kinds of blocks is maintained as the composition of the solvent mixture i.e. its preferential affinity to one of the blocks, changes. From the variation of the limiting viscosity number of the polymer versus composition of the solvent mixture, taking into account the corresponding plots for the two homopolymers, it was established: that at relatively low temperature the molecular dimensions of the block copolymer are very close to those calculated neglecting the heterocontact interactions, i.e. assuming segregation, and that at higher temperatures the dimensions observed for the block copolymer are higher than the values calculated by assuming segregation, thus showing that the heterocontacts exert some influence, inducing the chain to expand. A comparison with a PS/PMMA random copolymer of the same composition showed, however, that in the same solvent mixtures the number of heterocontacts was far lower in the case of the block copolymer than in the case of the random copolymer, even at elevated temperatures.