A percolation system with extremely long range connections and node dilution

We study the very long-range bond-percolation problem on a linear chain with both sites and bonds dilution. Very long range means that the probability $p_{ij}$ for a connection between two occupied sites $i,j$ at a distance $r_{ij}$ decays as a power law, i.e. $p_{ij} = \rho/[r_{ij}^\alpha N^{1-\alpha}]$ when $0 \le \alpha < 1$, and $p_{ij} = \rho/[r_{ij} \ln(N)]$ when $\alpha = 1$. Site dilution means that the occupancy probability of a site is $0 < p_s \le 1$. The behavior of this model results from the competition between long-range connectivity, which enhances the percolation, and site dilution, which weakens percolation. The case $\alpha=0$ with $p_s =1$ is well-known, being the exactly solvable mean-field model. The percolation order parameter $P_\infty$ is investigated numerically for different values of $\alpha$, $p_s$ and $\rho$. We show that in the ranges $0 \le \alpha \le 1$ and $0 < p_s \le 1$ the percolation order parameter $P_\infty$ depends only on the average connectivity $\gamma$ of sites, which can be explicitly computed in terms of the three parameters $\alpha$, $p_s$ and $\rho$

Majority-Vote Model on a Random Lattice

The stationary critical properties of the isotropic majority vote model on random lattices with quenched connectivity disorder are calculated by using Monte Carlo simulations and finite size analysis. The critical exponents $\gamma$ and $\beta$ are found to be different from those of the Ising and majority vote on the square lattice model and the critical noise parameter is found to be $q_{c}=0.117\pm0.005$.Comment: 4 pages, 6 figure

Delocalization and wave-packet dynamics in one-dimensional diluted Anderson models

We study the nature of one-electron eigen-states in a one-dimensional diluted Anderson model where every Anderson impurity is diluted by a periodic function $f(l)$ . Using renormalization group and transfer matrix techniques, we provide accurate estimates of the extended states which appear in this model, whose number depends on the symmetry of the diluting function $f(l)$. The density of states (DOS) for this model is also numerically obtained and its main features are related to the symmetries of the diluting function $f(l)$. Further, we show that the emergence of extended states promotes a sub-diffusive spread of an initially localized wave-packet.Comment: 6 pages, 6 figures, to appear in EPJ

Pair contact process with diffusion of pairs

The pair contact process (PCP) is a nonequilibrium stochastic model which, like the basic contact process (CP), exhibits a phase transition to an absorbing state. The two models belong to the directed percolation (DP) universality class, despite the fact that the PCP possesses infinitely many absorbing configurations whereas the CP has but one. The critical behavior of the PCP with hopping by particles (PCPD) is as yet unclear. Here we study a version of the PCP in which nearest-neighbor particle {\it pairs} can hop but individual particles cannot. Using quasistationary simulations for three values of the diffusion probability ($D=0.1$, 0.5 and 0.9), we find convincing evidence of DP-like critical behavior.Comment: 9 pages, 3 figure

Black hole thermodynamical entropy

As early as 1902, Gibbs pointed out that systems whose partition function diverges, e.g. gravitation, lie outside the validity of the Boltzmann-Gibbs (BG) theory. Consistently, since the pioneering Bekenstein-Hawking results, physically meaningful evidence (e.g., the holographic principle) has accumulated that the BG entropy $S_{BG}$ of a $(3+1)$ black hole is proportional to its area $L^2$ ($L$ being a characteristic linear length), and not to its volume $L^3$. Similarly it exists the \emph{area law}, so named because, for a wide class of strongly quantum-entangled $d$-dimensional systems, $S_{BG}$ is proportional to $\ln L$ if $d=1$, and to $L^{d-1}$ if $d>1$, instead of being proportional to $L^d$ ($d \ge 1$). These results violate the extensivity of the thermodynamical entropy of a $d$-dimensional system. This thermodynamical inconsistency disappears if we realize that the thermodynamical entropy of such nonstandard systems is \emph{not} to be identified with the BG {\it additive} entropy but with appropriately generalized {\it nonadditive} entropies. Indeed, the celebrated usefulness of the BG entropy is founded on hypothesis such as relatively weak probabilistic correlations (and their connections to ergodicity, which by no means can be assumed as a general rule of nature). Here we introduce a generalized entropy which, for the Schwarzschild black hole and the area law, can solve the thermodynamic puzzle.Comment: 7 pages, 2 figures. Accepted for publication in EPJ

Efficient CRISPR/Cas9 genome editing in a salmonid fish cell line using a lentivirus delivery system

The present study was funded by were funded by the Biotechnology and Biological Sciences Research Council (BB/R008612/1, BB/S004343/1 to RH and RG; grant BB/R008973/1 to SM and CD) and the Institute Strategic Programme Grants (BBS/E/D/20002172, BBS/E/D/30002275 and BBS/E/D/10002070, to RH and RG). The funders had no roles in the study design, data collection and analysis, decision to publish or preparation of the manuscript.Peer reviewedPublisher PD

AMPK Regulates Circadian Rhythms in a Tissue- and Isoform-Specific Manner

AMP protein kinase (AMPK) plays an important role in food intake and energy metabolism, which are synchronized to the light-dark cycle. In vitro, AMPK affects the circadian rhythm by regulating at least two clock components, CKIα and CRY1, via direct phosphorylation. However, it is not known whether the catalytic activity of AMPK actually regulates circadian rhythm in vivo.THE CATALYTIC SUBUNIT OF AMPK HAS TWO ISOFORMS: α1 and α2. We investigate the circadian rhythm of behavior, physiology and gene expression in AMPKα1-/- and AMPKα2-/- mice. We found that both α1-/- and α2-/- mice are able to maintain a circadian rhythm of activity in dark-dark (DD) cycle, but α1-/- mice have a shorter circadian period whereas α2-/- mice showed a tendency toward a slightly longer circadian period. Furthermore, the circadian rhythm of body temperature was dampened in α1-/- mice, but not in α2-/- mice. The circadian pattern of core clock gene expression was severely disrupted in fat in α1-/- mice, but it was severely disrupted in the heart and skeletal muscle of α2-/- mice. Interestingly, other genes that showed circadian pattern of expression were dysreguated in both α1-/- and α2-/- mice. The circadian rhythm of nicotinamide phosphoryl-transferase (NAMPT) activity, which converts nicotinamide (NAM) to NAD+, is an important regulator of the circadian clock. We found that the NAMPT rhythm was absent in AMPK-deficient tissues and cells.This study demonstrates that the catalytic activity of AMPK regulates circadian rhythm of behavior, energy metabolism and gene expression in isoform- and tissue-specific manners