A linear set view on KM-arcs

In this paper, we study KM-arcs of type t, i.e. point sets of size q + t in PG(2, q) such that every line contains 0, 2 or t of its points. We use field reduction to give a different point of view on the class of translation arcs. Starting from a particular F2-linear set, called an i-club, we reconstruct the projective triads, the translation hyperovals as well as the translation arcs constructed by Korchmaros-Mazzocca, Gacs-Weiner and Limbupasiriporn. We show the KM-arcs of type q/4 recently constructed by Vandendriessche are translation arcs and fit in this family. Finally, we construct a family of KM-arcs of type q/4. We show that this family, apart from new examples that are not translation KM-arcs, contains all translation KM-arcs of type q/4

Magnetic translation groups in n dimensions

Magnetic translation groups are considered as central extensions of the translation group T=Z^n by the group of factors (a~gauge group) U(1). The obtained general formulae allow to consider a magnetic field as an~antisymmetric tensor (of rank 2) and factor systems are determined by a transvection of this tensor with a tensor product t \otimes t'.Comment: 15 pages, Latex 2.09 Presenetd at Symp. "Quant. Group & Their Appl. in Phys.", Poznan, Oct. 17-20 199

Mac Lane method in the investigation of magnetic translation groups

Central extensions of the three-dimensional translation group T=Z^3 by the unitary group U(1) (a group of factors) are considered within the frame of the Mac~Lane method. All nonzero vectors t in T are considered to be generators of T. This choice leads to very illustrative relations between the Mac~Lane method and Zak's approach to magnetic translation groups. It is shown that factor systems introduced by Zak and Brown can be realized only for the unitary group U(1) and for some of its finite subgroups.Comment: 8 pages, 1 fig. in text, romp_sty.tex attached at the beginning Presented at 28 Symp. on Math. Phys., Torun 2-6 Dec 199

Periodic Motions in Banach Space and Applications to Functional-Differential Equations

In establishing the existence of periodic solutions for nonautonomous differential equations of the form x = g(x, t), where g is periodic in t of period for fixed x, it is often convenient to consider the translation operator T(x(t)) = x(t + ). If corresponding to each initial vector chosen in an appropriate region there corresponds a unique solution of our equation, then periodicity may be established by proving the existence of a fixed point under T. This same technique is also useful for more general functional equations and can be extended in a number of interesting ways. In this paper we shall consider a variable type of translation operator which is useful in investigating periodicity for autonomous differential and functional equations where the period involved is less obvious

Lexically Constrained Decoding for Sequence Generation Using Grid Beam Search

We present Grid Beam Search (GBS), an algorithm which extends beam search to allow the inclusion of pre-specified lexical constraints. The algorithm can be used with any model that generates a sequence $\mathbf{\hat{y}} = \{y_{0}\ldots y_{T}\}$, by maximizing $p(\mathbf{y} | \mathbf{x}) = \prod\limits_{t}p(y_{t} | \mathbf{x}; \{y_{0} \ldots y_{t-1}\})$. Lexical constraints take the form of phrases or words that must be present in the output sequence. This is a very general way to incorporate additional knowledge into a model's output without requiring any modification of the model parameters or training data. We demonstrate the feasibility and flexibility of Lexically Constrained Decoding by conducting experiments on Neural Interactive-Predictive Translation, as well as Domain Adaptation for Neural Machine Translation. Experiments show that GBS can provide large improvements in translation quality in interactive scenarios, and that, even without any user input, GBS can be used to achieve significant gains in performance in domain adaptation scenarios.Comment: Accepted as a long paper at ACL 201