The application of GMOs in agriculture and in food production for a better nutrition: two different scientific points of view

This commentary is a face-to-face debate between two almost opposite positions regarding the application of genetic engineering in agriculture and food production. Seven questions on the potential benefits of the application of genetic engineering in agriculture and on the potentially adverse impacts on the environment and human health were posed to two scientists: one who is sceptical about the use of GMOs in Agriculture, and one who views GMOs as an important tool for quantitatively and qualitatively improving food production.Research at the Universitat de Lleida is supported by MICINN, Spain (BFU2007-61413); European Union Framework 7 Program-SmartCell Integrated Project 222716; European Union Framework 7 European Research Council IDEAS Advanced Grant Program-BIOFORCE; COST Action FA0804: Molecular farming: plants as a production platform for high value proteins; Centre CONSOLIDER on Agrigenomics funded by MICINN, Spain

Universal renormalization-group dynamics at the onset of chaos in logistic maps and nonextensive statistical mechanics

We uncover the dynamics at the chaos threshold $\mu_{\infty}$ of the logistic map and find it consists of trajectories made of intertwined power laws that reproduce the entire period-doubling cascade that occurs for $\mu <\mu_{\infty}$. We corroborate this structure analytically via the Feigenbaum renormalization group (RG) transformation and find that the sensitivity to initial conditions has precisely the form of a $q$-exponential, of which we determine the $q$-index and the $q$-generalized Lyapunov coefficient $\lambda _{q}$. Our results are an unequivocal validation of the applicability of the non-extensive generalization of Boltzmann-Gibbs (BG) statistical mechanics to critical points of nonlinear maps.Comment: Revtex, 3 figures. Updated references and some general presentation improvements. To appear published as a Rapid communication of PR

Screen-detected vs clinical breast cancer: the advantage in the relative risk of lymph node metastases decreases with increasing tumour size

Screen-detected (SD) breast cancers are smaller and biologically more indolent than clinically presenting cancers. An often debated question is: if left undiagnosed during their preclinical phase, would they become more aggressive or would they only increase in size? This study considered a registry-based series (1988–1999) of 3329 unifocal, pT1a-pT3 breast cancer cases aged 50–70 years, of which 994 were SD cases and 2335 clinical cases. The rationale was that (1) the average risk of lymph node involvement (N+) is lower for SD cases, (2) nodal status is the product of biological aggressiveness and chronological age of the disease, (3) for any breast cancer, tumour size is an indicator of chronological age, and (4) for SD cases, tumour size is specifically an indicator of the duration of the preclinical phase, that is, an inverse indicator of lead time. The hypothesis was that the relative protection of SD cases from the risk of N+ and, thus, their relative biological indolence decrease with increasing tumour size. The odds ratio (OR) estimate of the risk of N+ was obtained from a multiple logistic regression model that included terms for detection modality, tumour size category, patient age, histological type, and number of lymph nodes recovered. A term for the detection modality-by-tumour size category interaction was entered, and the OR for the main effect of detection by screening vs clinical diagnosis was calculated. This increased linearly from 0.05 (95% confidence interval: 0.01–0.39) in the 2–7 mm size category to 0.95 (0.64–1.40) in the 18–22 mm category. This trend is compatible with the view that biological aggressiveness of breast cancer increases during the preclinical phase

L\'{e}vy scaling: the Diffusion Entropy Analysis applied to DNA sequences

We address the problem of the statistical analysis of a time series generated by complex dynamics with a new method: the Diffusion Entropy Analysis (DEA) (Fractals, {\bf 9}, 193 (2001)). This method is based on the evaluation of the Shannon entropy of the diffusion process generated by the time series imagined as a physical source of fluctuations, rather than on the measurement of the variance of this diffusion process, as done with the traditional methods. We compare the DEA to the traditional methods of scaling detection and we prove that the DEA is the only method that always yields the correct scaling value, if the scaling condition applies. Furthermore, DEA detects the real scaling of a time series without requiring any form of de-trending. We show that the joint use of DEA and variance method allows to assess whether a time series is characterized by L\'{e}vy or Gauss statistics. We apply the DEA to the study of DNA sequences, and we prove that their large-time scales are characterized by L\'{e}vy statistics, regardless of whether they are coding or non-coding sequences. We show that the DEA is a reliable technique and, at the same time, we use it to confirm the validity of the dynamic approach to the DNA sequences, proposed in earlier work.Comment: 24 pages, 9 figure

Anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation: Exact time-dependent solutions

We consider the $d=1$ nonlinear Fokker-Planck-like equation with fractional derivatives $\frac{\partial}{\partial t}P(x,t)=D \frac{\partial^{\gamma}}{\partial x^{\gamma}}[P(x,t) ]^{\nu}$. Exact time-dependent solutions are found for $\nu = \frac{2-\gamma}{1+ \gamma}$ ($-\infty<\gamma \leq 2$). By considering the long-distance {\it asymptotic} behavior of these solutions, a connection is established, namely $q=\frac{\gamma+3}{\gamma+1}$ ($0<\gamma \le 2$), with the solutions optimizing the nonextensive entropy characterized by index $q$ . Interestingly enough, this relation coincides with the one already known for L\'evy-like superdiffusion (i.e., $\nu=1$ and $0<\gamma \le 2$). Finally, for $(\gamma,\nu)=(2, 0)$ we obtain $q=5/3$ which differs from the value $q=2$ corresponding to the $\gamma=2$ solutions available in the literature ($\nu<1$ porous medium equation), thus exhibiting nonuniform convergence.Comment: 3 figure

A Dynamic Approach to the Thermodynamics of Superdiffusion

We address the problem of relating thermodynamics to mechanics in the case of microscopic dynamics without a finite time scale. The solution is obtained by expressing the Tsallis entropic index q as a function of the Levy index alpha, and using dynamical rather than probabilistic arguments.Comment: 4 pages, new revised version resubmitted to Phys. Rev. Let

Nonextensive Thermostatistics and the H-Theorem

The kinetic foundations of Tsallis' nonextensive thermostatistics are investigated through Boltzmann's transport equation approach. Our analysis follows from a nonextensive generalization of the ``molecular chaos hypothesis". For $q>0$, the $q$-transport equation satisfies an $H$-theorem based on Tsallis entropy. It is also proved that the collisional equilibrium is given by Tsallis' $q$-nonextensive velocity distribution.Comment: 4 pages, no figures, corrected some typo

Average Entropy of a Subsystem from its Average Tsallis Entropy

In the nonextensive Tsallis scenario, Page's conjecture for the average entropy of a subsystem[Phys. Rev. Lett. {\bf 71}, 1291(1993)] as well as its demonstration are generalized, i.e., when a pure quantum system, whose Hilbert space dimension is $mn$, is considered, the average Tsallis entropy of an $m$-dimensional subsystem is obtained. This demonstration is expected to be useful to study systems where the usual entropy does not give satisfactory results.Comment: Revtex, 6 pages, 2 figures. To appear in Phys. Rev.

Reply: An inverse association between tumour size and overdiagnosis may explain the results by Bucchi et al

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