We present a new model for self-organizing networks such as the web graph, and analyze its limit behaviour. In the model, new vertices are introduced over time that copy the neighbourhood structure of existing vertices, and a certain number of extra edges may be added to the new vertex that randomly join to any of the existing vertices. A function ρ parameterizes the number of extra edges. We s...

Limit theorems are established and relatively simple closed-form approximations are developed for the busy-period distribution in single-server queues. For the M/G/1 queue, the complementary busy-period cdf is shown to be asymptotically equivalent as t → ∞ to a scaled version of the heavy-traffic limit (obtained as ρ → 1), where the scaling parameters are based on the asymptotics as t → ∞. We c...

We study the statistical limits of both detecting and estimating a rank-one deformation of a symmetric random Gaussian tensor. We establish upper and lower bounds on the critical signal-to-noise ratio, under a variety of priors for the planted vector: (i) a uniformly sampled unit vector, (ii) i.i.d. ±1 entries, and (iii) a sparse vector where a constant fraction ρ of entries are i.i.d. ±1 and t...

Let FBC(λ, k; t) be the Heckman-Opdam hypergeometric function of type BC with multiplicities k = (k1, k2, k3) and weighted half sum ρ(k) of positive roots. We prove that FBC(λ + ρ(k), k; t) converges for k1 + k2 → ∞ and k1/k2 → ∞ to a function of type A for t ∈ R and λ ∈ C. This limit is obtained from a corresponding result for Jacobi polynomials of type BC, which is proven for a slightly more ...

Surfur-bearing molecules have been found at the surface of Mars by the Viking lander, the Spirit and Opportunity rovers, and the OMEGA infrared spectrometer aboard Mars Express. However, no gaseous sulfur-bearing species have ever been detected in the Martian atmosphere. We search for SO2 signatures in the thermal spectrum of Mars at 7.4 μm using the Texas Echelon Cross Echelle Spectrograph (TE...

Using polarized neutron reflectometry we measured the neutron spin-dependent reflectivity from four LaAlO(3)/SrTiO(3) superlattices. Our results imply that the upper limit for the magnetization averaged over the lateral dimensions of the sample induced by an 11 T magnetic field at 1.7 K is less than 2 G. SQUID magnetometry of the neutron superlattice samples sporadically finds an enhanced momen...

It is important to know the spatial extent over which the binocular visual system searches for "matches" or image correspondence. Most models of stereopsis define fixed neighbourhoods in one monocular image in which a search is conducted for a match to some element in the other image. We were unable to experimentally determine fixed values for the extent of these neighbourhoods. We were, howeve...

The uncommonly high rf absorption efficiency of helicon discharges has been thought to be caused by Landau damping of helicon waves and the concomitant acceleration of primary electrons. By constructing an energy analyzer that accounts for rf fluctuations in plasma potential, it is shown that Landau-accelerated electrons are too sparse to explain the ionization efficiency. Instead, rf absorptio...

For a finite abelian group G and positive integers m and h, we let ρ(G,m, h) = min{|hA| : A ⊆ G, |A| = m} and ρ±(G,m, h) = min{|h±A| : A ⊆ G, |A| = m}, where hA and h±A denote the h-fold sumset and the h-fold signed sumset of A, respectively. The study of ρ(G,m, h) has a 200-year-old history and is now known for all G, m, and h. Here we prove that ρ±(G,m, h) equals ρ(G,m, h) when G is cyclic, a...