Activity of users on Internet discussion forums is analyzed. The rank of users is shown to be approximated better by stretched-exponential function than by Zipfs law. Cumulative distribution function is found as an excellent tool in analysis of the dynamics of the collective social phenomena. We are able to approximate the number of blog comments with time by simple functions that resemble Ferm...

G02GDF Note: before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details. 1 Purpose G02GDF fits a generalized linear model with gamma errors. 3 Description A generalized linear model with gamma errors consists of the following elements: (a) a set of n observations, y i , from a gam...

A new scaling for the standard discrete Luria-Delbrück distribution is provided which leads to a weak convergence result as the parameter of the distribution tends to infinity. We show that the stable limiting probability measure has the Fourier transform t → exp(−π|t|/2−it log |t|). For the corresponding density an integral representation is derived, which differs from that found in a closely ...

A k-query locally decodable code (LDC) C : Σn → ΓN encodes each message x into a codeword C(x) such that each symbol of x can be probabilistically recovered by querying only k coordinates of C(x), even after a constant fraction of the coordinates have been corrupted. Yekhanin (2008) constructed a 3-query LDC of subexponential length, N = exp(exp(O(log n/ log log n))), under the assumption that ...

We consider the first descending ladder epoch τ = min { n ≥ 1 : S ≤ 0 } of a random walk ∑ ξ i , with i.d.d. summands having negative drift E − < . Let + max ( ) It is well-known that, for any α > finiteness implies and, λ exp that c where is, in general, another constant depends on distribution intermediate case, assuming g ∞ positive increasing function such lim inf x → / log and sup all Assu...

Abstract A positive radial singular solution for $$\Delta u+f(u)=0$$ Δ u + f ( ) = 0 with a general supercritical growth is constructed. An exact asymptotic expansion a...

Let { p j stretchy="false...