Clustering data by inhomogeneous chaotic map lattices

A new approach to clustering, based on the physical properties of inhomogeneous coupled chaotic maps, is presented. A chaotic map is assigned to each data-point and short range couplings are introduced. The stationary regime of the system corresponds to a macroscopic attractor independent of the initial conditions. The mutual information between couples of maps serves to partition the data set in clusters, without prior assumptions about the structure of the underlying distribution of the data. Experiments on simulated and real data sets show the effectiveness of the proposed algorithm.Comment: 8 pages, 6 figures. Revised version accepted for publication on Physical Review Letter

Scale-Free model for governing universe dynamics

We investigate the effects of scale-free model on cosmology, providing, in this way, a statistical background in the framework of general relativity. In order to discuss properties and time evolution of some relevant universe dynamical parameters (cosmographic parameters), such as $H(t)$ (Hubble parameter), $q(t)$ (deceleration parameter), $j(t)$ (jerk parameter) and $s(t)$ (snap parameter), which are well re-defined in the framework of scale-free model, we analyze a comparison between WMAP data. Hence the basic purpose of the work is to consider this statistical interpretation of mass distribution of universe, in order to have a mass density $\rho$ dynamics, not inferred from Friedmann equations, via scale factor $a(t)$. This model, indeed, has been used also to explain a possible origin and a viable explanation of cosmological constant, which assumes a statistical interpretation without the presence of extended theories of gravity; hence the problem of dark energy could be revisited in the context of a classical probability distribution of mass, which is, in particular, for the scale-free model, $P(k)\sim k^{-\gamma}$, with $2<\gamma<3$. The $\Lambda$CDM model becomes, with these considerations, a consequence of the particular statistics together with the use of general relativity.Comment: 7 pages, 4 figure

Spatial organization in cyclic Lotka-Volterra systems

We study the evolution of a system of $N$ interacting species which mimics the dynamics of a cyclic food chain. On a one-dimensional lattice with N<5 species, spatial inhomogeneities develop spontaneously in initially homogeneous systems. The arising spatial patterns form a mosaic of single-species domains with algebraically growing size, $\ell(t)\sim t^\alpha$, where $\alpha=3/4$ (1/2) and 1/3 for N=3 with sequential (parallel) dynamics and N=4, respectively. The domain distribution also exhibits a self-similar spatial structure which is characterized by an additional length scale, ${\cal L}(t)\sim t^\beta$, with $\beta=1$ and 2/3 for N=3 and 4, respectively. For $N\geq 5$, the system quickly reaches a frozen state with non interacting neighboring species. We investigate the time distribution of the number of mutations of a site using scaling arguments as well as an exact solution for N=3. Some possible extensions of the system are analyzed.Comment: 18 pages, 10 figures, revtex, also available from http://arnold.uchicago.edu/~ebn

Dihydropyrimidine dehydrogenase pharmacogenetics for predicting fluoropyrimidine-related toxicity in the randomised, phase III adjuvant TOSCA trial in high-risk colon cancer patients

Background: Dihydropyrimidine dehydrogenase (DPD) catabolizes approximately 85% of the administered dose of fluoropyrimidines. Functional DPYD gene variants cause reduced/abrogated DPD activity. DPYD variants analysis may help for defining individual patients' risk of fluoropyrimidine-related severe toxicity. Methods: The TOSCA Italian randomized trial enrolled colon cancer patients for 3 or 6 months of either FOLFOX-4 or XELOX adjuvant chemotherapy. In an ancillary pharmacogenetic study, ten 49 DPYD variants (*2A rs3918290 G>A, *13 rs55886062 T>G, rs67376798 A>T, *4 rs1801158 G>A, *5 rs1801159 A>G, *6 rs1801160 G>A, *9A rs1801265 T>C, rs2297595 A>G, rs17376848 T>C, rs75017182 C>G), were retrospectively tested for associations with > grade 3 fluoropyrimidine-related adverse events (FAEs). An association analysis and a time-to-toxicity (TTT) analysis were planned. To adjust for multiple testing, the Benjamini and Hochberg's False Discovery Rate (FDR) procedure was used. 55 Results: FAEs occurred in 194/508 assessable patients (38.2%). In the association analysis, FAEs 56 occurred more frequently in *6 rs1801160 A allele carriers (FDR=0.0083). At multivariate TTT 57 analysis, significant associations were found for *6 rs1801160 A allele carriers (FDR<0.0001), 58 *2A rs3918290 A allele carriers (FDR <0.0001), rs2297595 GG genotype carriers (FDR=0.0014). 59 Neutropenia was the commonest FAEs (28.5%). *6 rs1801160 (FDR <.0001), and *2A 60 rs3918290 (FDR =0.0004) variant alleles were significantly associated with time to neutropenia. 61 Conclusions: This study adds evidence on the role of DPYD pharmacogenetics for safety of 62 patients undergoing fluoropyrimidine-based chemotherapy