Waiting time dynamics of priority-queue networks

We study the dynamics of priority-queue networks, generalizations of the binary interacting priority queue model introduced by Oliveira and Vazquez [Physica A {\bf 388}, 187 (2009)]. We found that the original AND-type protocol for interacting tasks is not scalable for the queue networks with loops because the dynamics becomes frozen due to the priority conflicts. We then consider a scalable interaction protocol, an OR-type one, and examine the effects of the network topology and the number of queues on the waiting time distributions of the priority-queue networks, finding that they exhibit power-law tails in all cases considered, yet with model-dependent power-law exponents. We also show that the synchronicity in task executions, giving rise to priority conflicts in the priority-queue networks, is a relevant factor in the queue dynamics that can change the power-law exponent of the waiting time distribution.Comment: 5 pages, 3 figures, minor changes, final published versio

Lensing of Fast Radio Bursts by Plasma Structures in Host Galaxies

Plasma lenses in the host galaxies of fast radio bursts (FRBs) can strongly modulate FRB amplitudes for a wide range of distances, including the $\sim$ Gpc distance of the repeater FRB121102. To produce caustics, the lens' dispersion-measure depth (${\rm DM}_{\ell}$), scale size ($a$), and distance from the source ($d_{\rm sl}$) must satisfy ${\rm DM}_{\ell} d_{\rm sl} / a^2 \gtrsim 0.65~ {\rm pc^2 \ AU^{-2} \ cm^{-3}}$. Caustics produce strong magnifications ($\lesssim 10^2$) on short time scales ($\sim$ hours to days and perhaps shorter) along with narrow, epoch dependent spectral peaks (0.1 to 1~GHz). However, strong suppression also occurs in long-duration ($\sim$ months) troughs. For geometries that produce multiple images, the resulting burst components will arrive differentially by $< 1~\mu$s to tens of ms and they will show different apparent dispersion measures, $\delta{\rm DM}_{\rm apparent} \sim 1$ pc cm$^{-3}$. Arrival time perturbations may mask any underlying periodicity with period $\lesssim 1$ s. When arrival times differ by less than the burst width, interference effects in dynamic spectra are expected. Strong lensing requires source sizes smaller than $({\rm Fresnel~scale)^2} / a$, which can be satisfied by compact objects such as neutron star magnetospheres but not by AGNs. Much of the phenomenology of the repeating fast radio burst source FRB121102 is similar to lensing effects. The overall picture can be tested by obtaining wideband spectra of bursts (from $<1$ to 10 GHz and possibly higher), which can also be used to characterize the plasma environment near FRB sources. A rich variety of phenomena is expected from an ensemble of lenses near the FRB source. We discuss constraints on densities, magnetic fields, and locations of plasma lenses related to requirements for lensing to occur.Comment: 11 pages, 7 figures, submitted to the Astrophysical Journa

Patterns of link reciprocity in directed networks

We address the problem of link reciprocity, the non-random presence of two mutual links between pairs of vertices. We propose a new measure of reciprocity that allows the ordering of networks according to their actual degree of correlation between mutual links. We find that real networks are always either correlated or anticorrelated, and that networks of the same type (economic, social, cellular, financial, ecological, etc.) display similar values of the reciprocity. The observed patterns are not reproduced by current models. This leads us to introduce a more general framework where mutual links occur with a conditional connection probability. In some of the studied networks we discuss the form of the conditional connection probability and the size dependence of the reciprocity.Comment: Final version accepted for publication on Physical Review Letter

Rotational Broadening of Atomic Spectral Features from Neutron Stars

The discovery of the first gravitationally redshifted spectral line from a neutron star (NS) by Cottam, Paerels and Mendez has triggered theoretical studies of the physics of atomic line formation in NS atmospheres. Chang, Bildsten and Wasserman showed that the hydrogenic Fe H$\alpha$ line formed above the photosphere of a bursting NS is intrinsically broad. We now include rotational broadening within general relativity and compare the resulting profile to that observed during Type I bursts from EXO 0748-676. We show that the fine structure splitting of the line precludes a meaningful constraint on the radius. Our fitting of the data show that the line forming Fe column is ${\rm log}_{10} (N_{\rm Fe, n=2}/{\rm cm^{-2}})=17.9_{-0.42}^{+0.27}$ and gravitational redshift $1+z =1.345_{-0.008}^{+0.005}$ with 95% confidence. We calculate the detectability of this spectral feature for a large range of spins and inclinations assuming that the emission comes from the entire surface. We find that at 300 (600) Hz only 10-20% (5-10%) of NSs would have spectral features as deep as that seen in EXO 0748-676.Comment: 4 pages, 4 figures, to appear in ApJ Letter

Magnetoelastic coupling in iron

Exchange interactions in {\alpha}- and {\gamma}-Fe are investigated within an ab-initio spin spiral approach. We have performed total energy calculations for different magnetic structures as a function of lattice distortions, related with various cell volumes and the Bain tetragonal deformations. The effective exchange parameters in {\gamma}-Fe are very sensitive to the lattice distortions, leading to the ferromagnetic ground state for the tetragonal deformation or increase of the volume cell. At the same time, the magnetic-structure-independent part of the total energy changes very slowly with the tetragonal deformations. The computational results demonstrate a strong mutual dependence of crystal and magnetic structures in Fe and explain the observable "anti-Invar" behavior of thermal expansion coefficient in {\gamma}-Fe.Comment: Submitted to Phys. Rev.

Statistical Mechanics of Community Detection

Starting from a general \textit{ansatz}, we show how community detection can be interpreted as finding the ground state of an infinite range spin glass. Our approach applies to weighted and directed networks alike. It contains the \textit{at hoc} introduced quality function from \cite{ReichardtPRL} and the modularity $Q$ as defined by Newman and Girvan \cite{Girvan03} as special cases. The community structure of the network is interpreted as the spin configuration that minimizes the energy of the spin glass with the spin states being the community indices. We elucidate the properties of the ground state configuration to give a concise definition of communities as cohesive subgroups in networks that is adaptive to the specific class of network under study. Further we show, how hierarchies and overlap in the community structure can be detected. Computationally effective local update rules for optimization procedures to find the ground state are given. We show how the \textit{ansatz} may be used to discover the community around a given node without detecting all communities in the full network and we give benchmarks for the performance of this extension. Finally, we give expectation values for the modularity of random graphs, which can be used in the assessment of statistical significance of community structure

Anderson lattice with explicit Kondo coupling: general features and the field-induced suppression of heavy-fermion state in ferromagnetic phase

We apply the extended (statistically-consistent, SGA) Gutzwiller-type approach to the periodic Anderson model (PAM) in an applied magnetic field and in the strong correlation limit. The finite-U corrections are included systematically by transforming PAM into the form with Kondo-type interaction and residual hybridization, appearing both at the same time. This effective Hamiltonian represents the essence of \textit{Anderson-Kondo lattice model}. We show that in ferromagnetic phases the low-energy single-particle states are strongly affected by the presence of the applied magnetic field. We also find that for large values of hybridization strength the system enters the so-called \textit{locked heavy fermion state}. In this state the chemical potential lies in the majority-spin hybridization gap and as a consequence, the system evolution is insensitive to further increase of the applied field. However, for a sufficiently strong magnetic field, the system transforms from the locked state to the fully spin-polarized phase. This is accompanied by a metamagnetic transition, as well as by drastic reduction of the effective mass of quasiparticles. In particular, we observe a reduction of effective mass enhancement in the majority-spin subband by as much as 20% in the fully polarized state. The findings are consistent with experimental results for Ce$_x$La$_{1-x}$B$_6$ compounds. The mass enhancement for the spin-minority electrons may also diminish with the increasing field, unlike for the quasiparticles states in a single narrow band in the same limit of strong correlations