Context-Free Path Queries on RDF Graphs

Navigational graph queries are an important class of queries that canextract implicit binary relations over the nodes of input graphs. Most of the navigational query languages used in the RDF community, e.g. property paths in W3C SPARQL 1.1 and nested regular expressions in nSPARQL, are based on the regular expressions. It is known that regular expressions have limited expressivity; for instance, some natural queries, like same generation-queries, are not expressible with regular expressions. To overcome this limitation, in this paper, we present cfSPARQL, an extension of SPARQL query language equipped with context-free grammars. The cfSPARQL language is strictly more expressive than property paths and nested expressions. The additional expressivity can be used for modelling graph similarities, graph summarization and ontology alignment. Despite the increasing expressivity, we show that cfSPARQL still enjoys a low computational complexity and can be evaluated efficiently.Comment: 25 page

On large deviation properties of Erdos-Renyi random graphs

We show that large deviation properties of Erd\"os-R\'enyi random graphs can be derived from the free energy of the $q$-state Potts model of statistical mechanics. More precisely the Legendre transform of the Potts free energy with respect to $\ln q$ is related to the component generating function of the graph ensemble. This generalizes the well-known mapping between typical properties of random graphs and the $q\to 1$ limit of the Potts free energy. For exponentially rare graphs we explicitly calculate the number of components, the size of the giant component, the degree distributions inside and outside the giant component, and the distribution of small component sizes. We also perform numerical simulations which are in very good agreement with our analytical work. Finally we demonstrate how the same results can be derived by studying the evolution of random graphs under the insertion of new vertices and edges, without recourse to the thermodynamics of the Potts model.Comment: 38 pages, 9 figures, Latex2e, corrected and extended version including numerical simulation result

Disorder, Order, and Domain Wall Roughening in the 2d Random Field Ising Model

Ground states and domain walls are investigated with exact combinatorial optimization in two-dimensional random field Ising magnets. The ground states break into domains above a length scale that depends exponentially on the random field strength squared. For weak disorder, this paramagnetic structure has remnant long-range order of the percolation type. The domain walls are super-rough in ordered systems with a roughness exponent $\zeta$ close to 6/5. The interfaces exhibit rare fluctuations and multiscaling reminiscent of some models of kinetic roughening and hydrodynamic turbulence.Comment: to be published in Phys.Rev.E/Rapid.Com

Involvement of PrPC in kainate-induced excitotoxicity in several mouse strains

The cellular prion protein (PrPC) has been associated with a plethora of cellular functions ranging from cell cycle to neuroprotection. Mice lacking PrPC show an increased susceptibility to epileptic seizures; the protein, then, is neuroprotective. However, lack of experimental reproducibility has led to considering the possibility that other factors besides PrPC deletion, such as the genetic background of mice or the presence of so-called "Prnp flanking genes", might contribute to the reported susceptibility. Here, we performed a comparative analysis of seizure-susceptibility using characterized Prnp(+/+) and Prnp(0/0) mice of B6129, B6.129, 129/Ola or FVB/N genetic backgrounds. Our study indicates that PrPC plays a role in neuroprotection in KA-treated cells and mice. For this function, PrPC should contain the aa32-93 region and needs to be linked to the membrane. In addition, some unidentified "Prnp-flanking genes" play a role parallel to PrPC in the KA-mediated responses in B6129 and B6.129 Prnp(0/0) mice

Multifractals of Normalized First Passage Time in Sierpinski Gasket

The multifractal behavior of the normalized first passage time is investigated on the two dimensional Sierpinski gasket with both absorbing and reflecting barriers. The normalized first passage time for Sinai model and the logistic model to arrive at the absorbing barrier after starting from an arbitrary site, especially obtained by the calculation via the Monte Carlo simulation, is discussed numerically. The generalized dimension and the spectrum are also estimated from the distribution of the normalized first passage time, and compared with the results on the finitely square lattice.Comment: 10 pages, Latex, with 3 figures and 1 table. to be published in J. Phys. Soc. Jpn. Vol.67(1998

FORGE'd in FIRE: Resolving the End of Star Formation and Structure of AGN Accretion Disks from Cosmological Initial Conditions

It has recently become possible to zoom-in from cosmological to sub-pc scales in galaxy simulations to follow accretion onto supermassive black holes (SMBHs). However, at some point the approximations used on ISM scales (e.g. optically-thin cooling and stellar-population-integrated star formation [SF] and feedback [FB]) break down. We therefore present the first cosmological radiation-magnetohydrodynamic (RMHD) simulation which self-consistently combines the FIRE physics (relevant on galactic/ISM scales where SF/FB are ensemble-averaged) and STARFORGE physics (relevant on small scales where we track individual (proto)stellar formation and evolution), together with explicit RMHD (including non-ideal MHD and multi-band M1-RHD) which self-consistently treats both optically-thick and thin regimes. This allows us to span scales from ~100 Mpc down to <100 au (~300 Schwarzschild radii) around a SMBH at a time where it accretes as a bright quasar, in a single simulation. We show that accretion rates up to $\sim 10-100\,{\rm M_{\odot}\,yr^{-1}}$ can be sustained into the accretion disk at $\ll 10^{3}\,R_{\rm schw}$, with gravitational torques between stars and gas dominating on sub-kpc scales until star formation is shut down on sub-pc scales by a combination of optical depth to cooling and strong magnetic fields. There is an intermediate-scale, flux-frozen disk which is gravitoturbulent and stabilized by magnetic pressure sustaining strong turbulence and inflow with persistent spiral modes. In this paper we focus on how gas gets into the small-scale disk, and how star formation is efficiently suppressed.Comment: 37 pages, 18 figures. Submitted to The Open Journal of Astrophysics. Comments welcom

The Computational Complexity of Generating Random Fractals

In this paper we examine a number of models that generate random fractals. The models are studied using the tools of computational complexity theory from the perspective of parallel computation. Diffusion limited aggregation and several widely used algorithms for equilibrating the Ising model are shown to be highly sequential; it is unlikely they can be simulated efficiently in parallel. This is in contrast to Mandelbrot percolation that can be simulated in constant parallel time. Our research helps shed light on the intrinsic complexity of these models relative to each other and to different growth processes that have been recently studied using complexity theory. In addition, the results may serve as a guide to simulation physics.Comment: 28 pages, LATEX, 8 Postscript figures available from [email protected]