scott and szewczyk in technometrics, 2001, have introduced a similarity measure for twodensities f1 and f2 , by1, 21 21 1 2 2( , ), ,f fsim f ff f f f< >=< >< >wheref1, f2 f1(x, θ1)f2(x, θ2)dx.+∞−∞< >=∫sim(f1, f2) has some appropriate properties that can be suitable measures for the similarity of f1 and f2 .however, due to some restrictions on the value of parameters and the kind of densities, ...

A forest is the clique complex of a strongly chordal graph and a quasiforest is the clique complex of a chordal graph. Kruskal–Katona type theorems for forests, quasi-forests, pure forests and pure quasi-forests will be presented. Introduction Recently, in commutative algebra, the forest ([5]) and the quasi-forest ([17] and [9]) have been extensively studied. Each of these concepts is, however,...

We recall that it is a famous result due to Harris, Mumford and Eisenbud thatMg is of general type for g ≥ 24 (cf. [HM], [H1], [EH]). On the other hand, a classical theorem due to Severi saysMg is unirational for g ≤ 10 (see [AC1] for a modern exposition). Similar results for higher g were proved in the 1980’s: Sernesi showed that M12 is unirational (cf. [Se]), then Chang and Ran settled the un...

we define and studyco-noetherian dimension of rings for which the injective envelopeof simple modules have finite krull-dimension. this  is a moritainvariant dimension that measures how far the ring is from beingco-noetherian. the co-noetherian dimension of certain rings,including commutative rings, are determined. it is shown that the class ${mathcal w}_n$ of rings with co-noetherian dimension...

We present a calculation of the two-loop anomalous dimension for the transversity distribution h1(x,Q ), γ n , in the MS scheme of the dimensional regularization. Due to the chiral-odd nature, h1 does not mix with the gluon distributions, and thus our result is the same for the flavor-singlet and nonsinglet distributions. At small n (moment of h1), γ h(1) n is significantly larger than γ n (the...

We introduce a new method for proving explicit upper bounds on the VC Dimension of general functional basis networks, and prove as an application, for the rst time, that the VC Dimension of analog neural networks with the sigmoidal activation function (y) = 1=1+e ?y is bounded by a quadratic polynomial O((lm) 2) in both the number l of programmable parameters, and the number m of nodes. The pro...

If a linear block code C of length n has a Tanner graph without cycles, then maximum-likelihood soft-decision decoding of C can be achieved in time O(n 2). However, we show that cycle-free Tanner graphs cannot support good codes. Specically, let C be an (n;k;d) linear code of rate R = k=n that can be represented by a Tanner graph without cycles. We prove that if R 0:5 then d 2, while if R < 0:5...