j=1 hk,j |8(k, j) 2 [p]⇥[Nk], hk,j 2Hk , and the union of all such families GF,n = S |N|=n GF,N. Fix ⇢ > 0. For a fixed N, the Rademacher complexity of GF,N can be bounded as follows for any m 1: Rm(GF,N)  1 n Pp k=1 Nk Rm(Hk). Thus, the following standard margin-based Rademacher complexity bound holds (Koltchinskii & Panchenko, 2002). For any > 0, with probability at least 1 , for all g 2 GF,...

We investigate the decidability and computational complexity of (deductive) conservative extensions in fragments of first-order logic (FO), with a focus on the two-variable fragment FO and the guarded fragment GF. We prove that conservative extensions are undecidable in any FO fragment that contains FO or GF (even the three-variable fragment thereof), and that they are decidable and 2ExpTime-co...

We present a combinatorial characterization of sets of integers (rO,rl, ... ,TII-d, with OSri~"_2, " such that a'O,({1, ... ,a'·-1 fonn a basis of GF(q") over GF(q) for some ae GF'(q"). We use this characterization to prove the following generalization of the nonnal basis theorem fpr finite -fields of characteristic two: Let Ao.Al; ... ,A.,.-1 be integers in the range~<q, with at most one A.; e...

The guarded fragment with transitive guards, [GF+TG], is an extension of the guarded fragment of 9rst-order logic, GF, in which certain predicates are required to be transitive, transitive predicate letters appear only in guards of the quanti9ers and the equality symbol may appear everywhere. We prove that the decision problem for [GF+TG] is decidable. Moreover, we show that the problem is in 2...

Gleason has recently shown that the weight enumerators of binary and ternary self-dual codes are polynomials in two given polynomials. In this paper it is shown that classical invariant theory permits a straightforward and systematic proof of Gleason’s theorems and their generalizations. The joint weight enumerator of two codes (analogous to the joint density function of two random variables) i...

Griseofulvin (GF) is a widely used antifungal drug for the treatment of superficial dermatomycoses. However, because GF is carcinogenic and teratogenic in animal models there is considerable concern regarding its clinical application. Further, it produces numerical chromosome aberrations in human lymphocytes and cell lines. There are conflicting reports on the ability of GF to induce structural...

Tutte proved that a matroid is binary if and only if it does not contain a U2;4-minor. This provides a short proof for non-GF(2)-representability in that we can verify that a given minor is isomorphic to U2;4 in just a few rank evaluations. Using excluded-minor characterizations, short proofs can also be given of non-representablity over GF(3) and over GF(4). For GF(5), it is not even known whe...

Granuloma faciale (GF), also known as "eosinophilic granuloma," is a rare benign leukocytoclastic vasculitis which most commonly occurs on the face of middle-aged Caucasian males. Clinically, GF appears as single or multiple, slowly growing, reddish-brown papules, nodules or plaques which may be cosmetically unpleasant. Its pathogenesis is unknown and GF is notoriously resistant to treatments. ...