Corner contribution to percolation cluster numbers in three dimensions

In three-dimensional critical percolation we study numerically the number of clusters, $N_{\Gamma}$, which intersect a given subset of bonds, $\Gamma$. If $\Gamma$ represents the interface between a subsystem and the environment, then $N_{\Gamma}$ is related to the entanglement entropy of the critical diluted quantum Ising model. Due to corners in $\Gamma$ there are singular corrections to $N_{\Gamma}$, which scale as $b_{\Gamma} \ln L_{\Gamma}$, $L_{\Gamma}$ being the linear size of $\Gamma$ and the prefactor, $b_{\Gamma}$, is found to be universal. This result indicates that logarithmic finite-size corrections exist in the free-energy of three-dimensional critical systems.Comment: 6 pages, 7 figures. arXiv admin note: text overlap with arXiv:1210.467

Critical behavior and entanglement of the random transverse-field Ising model between one and two dimensions

We consider disordered ladders of the transverse-field Ising model and study their critical properties and entanglement entropy for varying width, $w \le 20$, by numerical application of the strong disorder renormalization group method. We demonstrate that the critical properties of the ladders for any finite $w$ are controlled by the infinite disorder fixed point of the random chain and the correction to scaling exponents contain information about the two-dimensional model. We calculate sample dependent pseudo-critical points and study the shift of the mean values as well as scaling of the width of the distributions and show that both are characterized by the same exponent, $\nu(2d)$. We also study scaling of the critical magnetization, investigate critical dynamical scaling as well as the behavior of the critical entanglement entropy. Analyzing the $w$-dependence of the results we have obtained accurate estimates for the critical exponents of the two-dimensional model: $\nu(2d)=1.25(3)$, $x(2d)=0.996(10)$ and $\psi(2d)=0.51(2)$.Comment: 10 pages, 9 figure

Drug-therapy networks and the predictions of novel drug targets

Recently, a number of drug-therapy, disease, drug, and drug-target networks have been introduced. Here we suggest novel methods for network-based prediction of novel drug targets and for improvement of drug efficiency by analysing the effects of drugs on the robustness of cellular networks.Comment: This is an extended version of the Journal of Biology paper containing 2 Figures, 1 Table and 44 reference

Supervoids in the WISE-2MASS catalogue imprinting Cold Spots in the Cosmic Microwave Background

The Cold Spot (CS) is a clear feature in the Cosmic Microwave Background (CMB); it could be of primordial origin, or caused by a intervening structure along the line of sight. We identified a large projected underdensity in the recently constructed WISE-2MASS all-sky infrared galaxy catalogue aligned with the Cold Spot direction at $(l,b)\approx(209^\circ,-57^\circ)$. It has an angular size of tens of degrees, and shows a $\sim20\%$ galaxy underdensity in the center. Moreover, we find another large underdensity in the projected WISE-2MASS galaxy map at $(l,b)\approx(101^\circ,46^\circ)$ (hereafter Draco Supervoid), also aligned with a CMB decrement, although less significant than that of the CS direction. Motivated by these findings, we develop spherically symmetric Lemaitre-Tolman-Bondi (LTB) compensated void models to explain the observed CMB decrements with these two underdensities, or "supervoids". Within our perturbative treatment of the LTB voids, we find that the Integrated Sachs-Wolfe and Riess-Sciama effects due to the Draco Supervoid can account for the CMB decrement observed in the same direction. On the contrary, the extremely deep CMB decrement in the CS direction is more difficult to explain by the presence of the CS supervoid only. Nevertheless, the probability of a random alignment between the CS and the corresponding supervoid is disfavored, and thus its contribution as a secondary anisotropy cannot be neglected. We comment on how the approximations used in this paper, in particular the assumption of spherical symmetry, could change quantitatively our conclusions and might provide a better explanation for the CMB CS.Comment: 12 pages, 11 figures, major revision, new results, resubmitted to MNRA

Cosmology with Gamma-Ray Bursts Using k-correction

In the case of Gamma-Ray Bursts with measured redshift, we can calculate the k-correction to get the fluence and energy that were actually produced in the comoving system of the GRB. To achieve this we have to use well-fitted parameters of a GRB spectrum, available in the GCN database. The output of the calculations is the comoving isotropic energy E_iso, but this is not the endpoint: this data can be useful for estimating the {\Omega}M parameter of the Universe and for making a GRB Hubble diagram using Amati's relation.Comment: 4 pages, 6 figures. Presented as a talk on the conference '7th INTEGRAL/BART Workshop 14 -18 April 2010, Karlovy Vary, Czech Republic'. Published in Acta Polytechnic

Invertibility-preserving maps of C

In 1996, Harris and Kadison posed the following problem: show that a linear bijection between C∗-algebras that preserves the identity and the set of invertible elements is a Jordan isomorphism. In this paper, we show that if A and B are semisimple Banach algebras and Φ:A→B is a linear map onto B that preserves the spectrum of elements, then Φ is a Jordan isomorphism if either A or B is a C∗-algebra of real rank zero. We also generalize a theorem of Russo