F2 is particularly interesting and useful to approximate. One reason that we might be interested is in understanding the quality of the output of the COUNT Sketch approximation, where |f̃j − fj| ≤ ε||f−j||2 ≤ ε √ F2. Since F1 is easy to compute exactly, the errors in the COUNT-MIN and MisraGries estimates are easy to compute. The F2 approximation lets us get good estimates of the (smaller) error...

Let Pc(x)={p?x|p,[pc]areprimes},c?R+?N and ?sym2f(n) be the n-th Fourier coefficient associated with symmetric square L-function L(s,sym2f). For any A>0, we prove that mean value of over Pc(x) is ?xlog?A?2x for almost all c??,(5+3)/8?? in sense Lebesgue measure. Furthermore, it holds c?(0,1) under Riemann Hypothesis. obtain asymptotic formula ?f2(n) ?p,qprimep?x,q=[pc]?f2(p)=xclog2x(1+o(1)),...

The one-dimensional quasilattices L lying in the square Fibonacci quasilattice F2 = F×F are classified; here F is the one-dimensional Fibonacci quasilattice. It is proved that there exists a countable set of similarity classes of quasilattices L in F2 (fine classification), and also four classes of local equivalence (rough classification). Asymptotic distributions of points in quasilattices L a...

Photolysis of ICN at 281.5, 266 and 249 nm produces CN X '2+ fragments in which the population of the F,(J"= N''+;) and F2(J"= "'-4) finestructure components vary markedly as a function of d', N" and dissociation wavelength. Population differences favour either F1 or F2, and can be > 2: 1. A model is proposed to explain this behaviour, in which out-of-plane, spin-dependent forces cause the elec...

We initiate a systematic study of linear sketching over F2. For a given Boolean function f : {0, 1}n → {0, 1} a randomized F2-sketch is a distributionM over d×nmatrices with elements over F2 such that Mx suffices for computing f(x) with high probability. We study a connection between F2-sketching and a two-player one-way communication game for the corresponding XOR-function. Our results show th...

We initiate a systematic study of linear sketching over F2. For a given Boolean function f : {0, 1}n → {0, 1} a randomized F2-sketch is a distributionM over d×nmatrices with elements over F2 such that Mx suffices for computing f(x) with high probability. We study a connection between F2-sketching and a two-player one-way communication game for the corresponding XOR-function. Our results show th...

We consider the hash function proposals by Mridul et al. presented at FSE 2005. For the proposed 2n-bit compression functions it is proved that collision attacks require Ω(2) queries of the functions in question. In this note it is shown that with O(2n/3) queries one can distinguish the proposed compression functions from a randomly chosen 2n-bit function with very good probability. Finally we ...