Comment on "Effective of the q-deformed pseudoscalar magnetic field on the charge carriers in graphene"

We point out a misleading treatment in a recent paper published in this Journal [J. Math. Phys. (2016) 57, 082105] concerning solutions for the two-dimensional Dirac-Weyl equation with a q-deformed pseudoscalar magnetic barrier. The authors misunderstood the full meaning of the potential and made erroneous calculations, this fact jeopardizes the main results in this system.Comment: 7 pages, 2 figure

A sharp threshold for minimum bounded-depth and bounded-diameter spanning trees and Steiner trees in random networks

In the complete graph on n vertices, when each edge has a weight which is an exponential random variable, Frieze proved that the minimum spanning tree has weight tending to zeta(3)=1/1^3+1/2^3+1/3^3+... as n goes to infinity. We consider spanning trees constrained to have depth bounded by k from a specified root. We prove that if k > log_2 log n+omega(1), where omega(1) is any function going to infinity with n, then the minimum bounded-depth spanning tree still has weight tending to zeta(3) as n -> infinity, and that if k < log_2 log n, then the weight is doubly-exponentially large in log_2 log n - k. It is NP-hard to find the minimum bounded-depth spanning tree, but when k < log_2 log n - omega(1), a simple greedy algorithm is asymptotically optimal, and when k > log_2 log n+omega(1), an algorithm which makes small changes to the minimum (unbounded depth) spanning tree is asymptotically optimal. We prove similar results for minimum bounded-depth Steiner trees, where the tree must connect a specified set of m vertices, and may or may not include other vertices. In particular, when m = const * n, if k > log_2 log n+omega(1), the minimum bounded-depth Steiner tree on the complete graph has asymptotically the same weight as the minimum Steiner tree, and if 1 <= k <= log_2 log n-omega(1), the weight tends to (1-2^{-k}) sqrt{8m/n} [sqrt{2mn}/2^k]^{1/(2^k-1)} in both expectation and probability. The same results hold for minimum bounded-diameter Steiner trees when the diameter bound is 2k; when the diameter bound is increased from 2k to 2k+1, the minimum Steiner tree weight is reduced by a factor of 2^{1/(2^k-1)}.Comment: 30 pages, v2 has minor revision

Card shuffling and diophantine approximation

The ``overlapping-cycles shuffle'' mixes a deck of $n$ cards by moving either the $n$th card or the $(n-k)$th card to the top of the deck, with probability half each. We determine the spectral gap for the location of a single card, which, as a function of $k$ and $n$, has surprising behavior. For example, suppose $k$ is the closest integer to $\alpha n$ for a fixed real $\alpha\in(0,1)$. Then for rational $\alpha$ the spectral gap is $\Theta(n^{-2})$, while for poorly approximable irrational numbers $\alpha$, such as the reciprocal of the golden ratio, the spectral gap is $\Theta(n^{-3/2})$.Comment: Published in at http://dx.doi.org/10.1214/07-AAP484 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Scanning tunneling microscopy simulations of poly(3-dodecylthiophene) chains adsorbed on highly oriented pyrolytic graphite

We report on a novel scheme to perform efficient simulations of Scanning Tunneling Microscopy (STM) of molecules weakly bonded to surfaces. Calculations are based on a tight binding (TB) technique including self-consistency for the molecule to predict STM imaging and spectroscopy. To palliate the lack of self-consistency in the tunneling current calculation, we performed first principles density-functional calculations to extract the geometrical and electronic properties of the system. In this way, we can include, in the TB scheme, the effects of structural relaxation upon adsorption on the electronic structure of the molecule. This approach is applied to the study of regioregular poly(3-dodecylthiophene) (P3DDT) polymer chains adsorbed on highly oriented pyrolytic graphite (HOPG). Results of spectroscopic calculations are discussed and compared with recently obtained experimental datComment: 15 pages plus 5 figures in a tar fil

Detecting series periodicity with horizontal visibility graphs

The horizontal visibility algorithm has been recently introduced as a mapping between time series and networks. The challenge lies in characterizing the structure of time series (and the processes that generated those series) using the powerful tools of graph theory. Recent works have shown that the visibility graphs inherit several degrees of correlations from their associated series, and therefore such graph theoretical characterization is in principle possible. However, both the mathematical grounding of this promising theory and its applications are on its infancy. Following this line, here we address the question of detecting hidden periodicity in series polluted with a certain amount of noise. We first put forward some generic properties of horizontal visibility graphs which allow us to define a (graph theoretical) noise reduction filter. Accordingly, we evaluate its performance for the task of calculating the period of noisy periodic signals, and compare our results with standard time domain (autocorrelation) methods. Finally, potentials, limitations and applications are discussed.Comment: To be published in International Journal of Bifurcation and Chao

Power Spectra in a Zero-Range Process on a Ring: Total Occupation Number in a Segment

We study the dynamics of density fluctuations in the steady state of a non-equilibrium system, the Zero-Range Process on a ring lattice. Measuring the time series of the total number of particles in a \emph{segment} of the lattice, we find remarkable structures in the associated power spectra, namely, two distinct components of damped-oscillations. The essential origin of both components is shown in a simple pedagogical model. Using a more sophisticated theory, with an effective drift-diffusion equation governing the stochastic evolution of the local particle density, we provide reasonably good fits to the simulation results. The effects of altering various parameters are explored in detail. Avenues for improving this theory and deeper understanding of the role of particle interactions are indicated.Comment: 21 pages, 15 figure

Dark-ages Reionization & Galaxy Formation Simulation VIII. Suppressed growth of dark matter halos during the Epoch of Reionization

We investigate how the hydrostatic suppression of baryonic accretion affects the growth rate of dark matter halos during the Epoch of Reionization. By comparing halo properties in a simplistic hydrodynamic simulation in which gas only cools adiabatically, with its collisionless equivalent, we find that halo growth is slowed as hydrostatic forces prevent gas from collapsing. In our simulations, at the high redshifts relevant for reionization (between ${\sim}6$ and ${\sim}11$), halos that host dwarf galaxies ($\lesssim 10^{9} \mathrm{M_\odot}$) can be reduced by up to a factor of 2 in mass due to the hydrostatic pressure of baryons. Consequently, the inclusion of baryonic effects reduces the amplitude of the low mass tail of the halo mass function by factors of 2 to 4. In addition, we find that the fraction of baryons in dark matter halos hosting dwarf galaxies at high redshift never exceeds ${\sim}90\%$ of the cosmic baryon fraction. When implementing baryonic processes, including cooling, star formation, supernova feedback and reionization, the suppression effects become more significant with further reductions of ${\sim}30\%$ to 60\%. Although convergence tests suggest that the suppression may become weaker in higher resolution simulations, this suppressed growth will be important for semi-analytic models of galaxy formation, in which the halo mass inherited from an underlying N-body simulation directly determines galaxy properties. Based on the adiabatic simulation, we provide tables to account for these effects in N-body simulations, and present a modification of the halo mass function along with explanatory analytic calculations.Comment: 17 pages, 11 figures; Updated to match the published version. Two changes in Figures 1 and 3 in order to 1) correct bin sizes of the 10^8 and 10^8.5 Msol bins for NOSN_NOZCOOL_NoRe (was 0.5, should be 0.25); 2) include stellar mass in baryon fraction (was missed in Fig. 3). Quantitative description of Fig. 3 changed slightly in Section 2.2. All other results and conclusions remain unchange