Hardness of Exact Distance Queries in Sparse Graphs Through Hub Labeling

A distance labeling scheme is an assignment of bit-labels to the vertices of an undirected, unweighted graph such that the distance between any pair of vertices can be decoded solely from their labels. An important class of distance labeling schemes is that of hub labelings, where a node $v \in G$ stores its distance to the so-called hubs $S_v \subseteq V$, chosen so that for any $u,v \in V$ there is $w \in S_u \cap S_v$ belonging to some shortest $uv$ path. Notice that for most existing graph classes, the best distance labelling constructions existing use at some point a hub labeling scheme at least as a key building block. Our interest lies in hub labelings of sparse graphs, i.e., those with $|E(G)| = O(n)$, for which we show a lowerbound of $\frac{n}{2^{O(\sqrt{\log n})}}$ for the average size of the hubsets. Additionally, we show a hub-labeling construction for sparse graphs of average size $O(\frac{n}{RS(n)^{c}})$ for some $0 < c < 1$, where $RS(n)$ is the so-called Ruzsa-Szemer{\'e}di function, linked to structure of induced matchings in dense graphs. This implies that further improving the lower bound on hub labeling size to $\frac{n}{2^{(\log n)^{o(1)}}}$ would require a breakthrough in the study of lower bounds on $RS(n)$, which have resisted substantial improvement in the last 70 years. For general distance labeling of sparse graphs, we show a lowerbound of $\frac{1}{2^{O(\sqrt{\log n})}} SumIndex(n)$, where $SumIndex(n)$ is the communication complexity of the Sum-Index problem over $Z_n$. Our results suggest that the best achievable hub-label size and distance-label size in sparse graphs may be $\Theta(\frac{n}{2^{(\log n)^c}})$ for some $0<c < 1$

Shortest Path Computation with No Information Leakage

Shortest path computation is one of the most common queries in location-based services (LBSs). Although particularly useful, such queries raise serious privacy concerns. Exposing to a (potentially untrusted) LBS the client's position and her destination may reveal personal information, such as social habits, health condition, shopping preferences, lifestyle choices, etc. The only existing method for privacy-preserving shortest path computation follows the obfuscation paradigm; it prevents the LBS from inferring the source and destination of the query with a probability higher than a threshold. This implies, however, that the LBS still deduces some information (albeit not exact) about the client's location and her destination. In this paper we aim at strong privacy, where the adversary learns nothing about the shortest path query. We achieve this via established private information retrieval techniques, which we treat as black-box building blocks. Experiments on real, large-scale road networks assess the practicality of our schemes.Comment: VLDB201

HerschelHerschel SPIRE-FTS observations of RCW 120

The expansion of Galactic HII regions can trigger the formation of a new generation of stars. However, little is know about the physical conditions that prevail in these regions. We study the physical conditions that prevail in specific zones towards expanding HII regions that trace representative media such as the photodissociation region, the ionized region, and condensations with and without ongoing star formation. We use the SPIRE Fourier Transform Spectrometer (FTS) on board $Herschel$ to observe the HII region RCW 120. Continuum and lines are observed in the $190-670\,\mu$m range. Line intensities and line ratios are obtained and used as physical diagnostics of the gas. We used the Meudon PDR code and the RADEX code to derive the gas density and the radiation field at nine distinct positions including the PDR surface and regions with and without star-formation activity. For the different regions we detect the atomic lines [NII] at $205\,\mu$m and [CI] at $370$ and $609\,\mu$m, the $^{12}{\rm CO}$ ladder between the $J=4$ and $J=13$ levels and the $^{13}{\rm CO}$ ladder between the $J=5$ and $J=14$ levels, as well as CH$^{+}$ in absorption. We find gas temperatures in the range $45-250\,$K for densities of $10^4-10^6\,{\rm cm}^{-3}$, and a high column density on the order of $N_{{\rm H}}\sim10^{22}\,{\rm cm}^{-2}$ that is in agreement with dust analysis. The ubiquitousness of the atomic and CH$^{+}$ emission suggests the presence of a low-density PDR throughout RCW 120. High-excitation lines of CO indicate the presence of irradiated dense structures or small dense clumps containing young stellar objects, while we also find a less dense medium ($N_{{\rm H}}\sim10^{20}\,{\rm cm}^{-2}$) with high temperatures ($80-200\,$K).Comment: 11 pages, 11 figures, accepted by A&

Particle production in quantum transport theories

The particle production in the intermediate energy heavy ion collisions is discussed in the framework of the nonequilibrium Green's functions formalism. The evolution equations of the Green's functions for fermions allows for the discussion of the off-shell fermion propagator and of the large momentum component in the initial state. For the case of a homogeneous system numerical calculations of the meson production rate are performed and compared with the semiclassical production rate.Comment: 45 pages, figures included, uses FEYNMAN macro

Binaries in star clusters and the origin of the field stellar population

Many, possibly most, stars form in binary and higher-order multiple systems. Therefore, the properties and frequency of binary systems provide strong clues to the star-formation process, and constraints on star-formation models. However, the majority of stars also form in star clusters in which the birth binary properties and frequency can be altered rapidly by dynamical processing. Thus, we almost never see the birth population, which makes it very difficult to know if star formation (as traced by binaries, at least) is universal, or if it depends on environment. In addition, the field population consists of a mixture of systems from different clusters which have all been processed in different ways.Comment: 16 pages, no figures. To appear as invited review article in a special issue of the Phil. Trans. Royal Soc. A: Ch. 8 "Star clusters as tracers of galactic star-formation histories" (ed. R. de Grijs). Fully peer reviewed. LaTeX, requires rspublic.cls style fil

Towards a fully self-consistent spectral function of the nucleon in nuclear matter

We present a calculation of nuclear matter which goes beyond the usual quasi-particle approximation in that it includes part of the off-shell dependence of the self-energy in the self-consistent solution of the single-particle spectrum. The spectral function is separated in contributions for energies above and below the chemical potential. For holes we approximate the spectral function for energies below the chemical potential by a $\delta$-function at the quasi-particle peak and retain the standard form for energies above the chemical potential. For particles a similar procedure is followed. The approximated spectral function is consistently used at all levels of the calculation. Results for a model calculation are presented, the main conclusion is that although several observables are affected by the inclusion of the continuum contributions the physical consistency of the model does not improve with the improved self-consistency of the solution method. This in contrast to expectations based on the crucial role of self-consistency in the proofs of conservation laws.Comment: 26 pages Revtex with 4 figures, submitted to Phys. Rev.

A Self-Consistent Solution to the Nuclear Many-Body Problem at Finite Temperature

The properties of symmetric nuclear matter are investigated within the Green's functions approach. We have implemented an iterative procedure allowing for a self-consistent evaluation of the single-particle and two-particle propagators. The in-medium scattering equation is solved for a realistic (non-separable) nucleon-nucleon interaction including both particle-particle and hole-hole propagation. The corresponding two-particle propagator is constructed explicitely from the single-particle spectral functions. Results are obtained for finite temperatures and an extrapolation to T=0 is presented.Comment: 11 pages 5 figure

Electric-Field Tuning of Spin-Dependent Exciton-Exciton Interactions in Coupled Quantum Wells

We have shown experimentally that an electric field decreases the energy separation between the two components of a dense spin-polarized exciton gas in a coupled double quantum well, from a maximum splitting of $\sim 4$ meV to zero, at a field of $\sim$35 kV/cm. This decrease, due to the field-induced deformation of the exciton wavefunction, is explained by an existing calculation of the change in the spin-dependent exciton-exciton interaction with the electron-hole separation. However, a new theory that considers the modification of screening with that separation is needed to account for the observed dependence on excitation power of the individual energies of the two exciton components.Comment: 5 pages, 4 eps figures, RevTeX, Physical Review Letters (in press