Hohenberg-Kohn theorem for the lowest-energy resonance of unbound systems

We show that under well-defined conditions the Hohenberg-Kohn theorem (HKT) can be extended to the lowest-energy resonance of unbound systems. Using the Gel'fand Levitan theorem, the extended version of the HKT can also be applied to systems that support a finite number of bound states. The extended version of the HKT provides an adequate framework to carry out DFT calculations of negative electron affinities.Comment: 4 pages, 3 figure

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

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

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