Non-extensive Trends in the Size Distribution of Coding and Non-coding DNA Sequences in the Human Genome

We study the primary DNA structure of four of the most completely sequenced human chromosomes (including chromosome 19 which is the most dense in coding), using Non-extensive Statistics. We show that the exponents governing the decay of the coding size distributions vary between $5.2 \le r \le 5.7$ for the short scales and $1.45 \le q \le 1.50$ for the large scales. On the contrary, the exponents governing the decay of the non-coding size distributions in these four chromosomes, take the values $2.4 \le r \le 3.2$ for the short scales and $1.50 \le q \le 1.72$ for the large scales. This quantitative difference, in particular in the tail exponent $q$, indicates that the non-coding (coding) size distributions have long (short) range correlations. This non-trivial difference in the DNA statistics is attributed to the non-conservative (conservative) evolution dynamics acting on the non-coding (coding) DNA sequences.Comment: 13 pages, 10 figures, 2 table

DNA viewed as an out-of-equilibrium structure

The complexity of the primary structure of human DNA is explored using methods from nonequilibrium statistical mechanics, dynamical systems theory and information theory. The use of chi-square tests shows that DNA cannot be described as a low order Markov chain of order up to $r=6$. Although detailed balance seems to hold at the level of purine-pyrimidine notation it fails when all four basepairs are considered, suggesting spatial asymmetry and irreversibility. Furthermore, the block entropy does not increase linearly with the block size, reflecting the long range nature of the correlations in the human genomic sequences. To probe locally the spatial structure of the chain we study the exit distances from a specific symbol, the distribution of recurrence distances and the Hurst exponent, all of which show power law tails and long range characteristics. These results suggest that human DNA can be viewed as a non-equilibrium structure maintained in its state through interactions with a constantly changing environment. Based solely on the exit distance distribution accounting for the nonequilibrium statistics and using the Monte Carlo rejection sampling method we construct a model DNA sequence. This method allows to keep all long range and short range statistical characteristics of the original sequence. The model sequence presents the same characteristic exponents as the natural DNA but fails to capture point-to-point details

Effective Mean Field Approach to Kinetic Monte Carlo Simulations in Limit Cycle Dynamics with Reactive and Diffusive Rewiring

The dynamics of complex reactive schemes is known to deviate from the Mean Field (MF) theory when restricted on low dimensional spatial supports. This failure has been attributed to the limited number of species-neighbours which are available for interactions. In the current study, we introduce effective reactive parameters, which depend on the type of the spatial support and which allow for an effective MF description. As working example the Lattice Limit Cycle dynamics is used, restricted on a 2D square lattice with nearest neighbour interactions. We show that the MF steady state results are recovered when the kinetic rates are replaced with their effective values. The same conclusion holds when reactive stochastic rewiring is introduced in the system via long distance reactive coupling. Instead, when the stochastic coupling becomes diffusive the effective parameters no longer predict the steady state. This is attributed to the diffusion process which is an additional factor introduced into the dynamics and is not accounted for, in the kinetic MF scheme.Comment: 8 pages, 6 figure

Reactive dynamics on fractal sets: anomalous fluctuations and memory effects

We study the effect of fractal initial conditions in closed reactive systems in the cases of both mobile and immobile reactants. For the reaction $A+A\to A$, in the absence of diffusion, the mean number of particles $A$ is shown to decay exponentially to a steady state which depends on the details of the initial conditions. The nature of this dependence is demonstrated both analytically and numerically. In contrast, when diffusion is incorporated, it is shown that the mean number of particles $$ decays asymptotically as $t^{-d_f/2}$, the memory of the initial conditions being now carried by the dynamical power law exponent. The latter is fully determined by the fractal dimension $d_f$ of the initial conditions.Comment: 7 pages, 2 figures, uses epl.cl

Amplitude chimeras and bump states with and without frequency entanglement: a toy model

When chaotic oscillators are coupled in complex networks a number of interesting synchronization phenomena emerge. Notable examples are the frequency and amplitude chimeras, chimera death states, solitary states as well as combinations of these. In a previous study [Journal of Physics: Complexity, 2020, 1(2), 025006], a toy model was introduced addressing possible mechanisms behind the formation of frequency chimera states. In the present study a variation of the toy model is proposed to address the formation of amplitude chimeras. The proposed oscillatory model is now equipped with an additional 3rd order equation modulating the amplitude of the network oscillators. This way, the single oscillators are constructed as bistable in amplitude and depending on the initial conditions their amplitude may result in one of the two stable fixed points. Numerical simulations demonstrate that when these oscillators are nonlocally coupled in networks, they organize in domains with alternating amplitudes (related to the two fixed points), naturally forming amplitude chimeras. A second extension of this model incorporates nonlinear terms merging amplitude together with frequency, and this extension allows for the spontaneous production of composite amplitude-and-frequency chimeras occurring simultaneously in the network. Moreover the extended model allows to understand the emergence of bump states via the continuous passage from chimera states, when both fixed point amplitudes are positive, to bump states when one of the two fixed points vanishes. The proposed mechanisms of creating domains with variable amplitudes and/or frequencies provide a generic scenario for understanding the formation of the complex synchronization phenomena observed in networks of coupled nonlinear and chaotic oscillators.Comment: 16 pages, 12 figures: Fig.1 (4 panels); Fig.2 (3 panels); Fig.3 (3 panels); Fig.4 (3 panels); Fig.5 (3 panels); Fig.6 (1 panel); Fig.7 (2 panels); Fig.8 (3 panels); Fig.9 (3 panels); Fig.10 (1 panel); Fig.11 (3 panels); Fig.12 (3 panels

Regards Saint-simoniens sur la Grèce insurgée: l’éphémère Producteur (1825–1826)

La parution du Producteur (1825–1826), publié par les disciples de Saint-Simon au lendemain de la mort du maître, commence dans un climat hautement philhellene marqué par la fondation du Comité Grec de Paris. Bien qu’il fût un journal de doctrine, Le Producteur n’est pas resté à l’écart du mouvement qui s’était emparé de la presse française. Il consacre à la Grèce une série d’articles entre 1825 et 1826 dans lesquels sont évoqués les aspects économiques et intellectuels du pays assujetti qui intéressent particulièrement les saint-simoniens et sont présentées des manifestations philhellènes, comme des représentations théâtrales inspirées par la grèce ou les souscriptions en faveur des Grecs. C’est enfin le témoignage personnel d’un des fondateurs du journal, Etienne-Marin Bailly, parti en Grèce dans une mission du Comité de Paris qui apporte aux lecteurs du Producteur des informations plus concrètes sur la situation réelle du pays insurgé