A Z2Z4-additive code C ⊆ Z α 2 ×Z 4 is called cyclic if the set of coordinates can be partitioned into two subsets, the set of Z2 and the set of Z4 coordinates, such that any cyclic shift of the coordinates of both subsets leaves the code invariant. Let Φ(C) be the binary Gray image of C. We study the rank and the dimension of the kernel of a Z2Z4-additive cyclic code C, that is, the dimensions...

The purpose of this work is to reduce the workload of human experts in building systematic reviews from published articles, used in evidence-based medicine. We propose to use a committee of classifiers to rank biomedical abstracts based on the predicted relevance to the topic under review. In our approach, we identify two subsets of abstracts: one that represents the top, and another that repre...

With more data repositories constantly being published on the Web, choosing appropriate data sources to interlink with newly published datasets becomes a non-trivial problem. It is necessary to choose both the repositories to link to and the relevant subsets of these repositories, which contain potentially matching individuals. In order to do this, detailed information about the content and str...

In this paper, we construct a Hamiltonian Floer theory based invariant called relative symplectic cohomology, which assigns module over the Novikov ring to compact subsets of closed manifolds. We show existence restriction maps, and prove some basic properties. Our main contribution is identify natural geometric situation in cohomology two satisfy Mayer-Vietoris property. This tailored work und...

Let [n] = {1, 2, . . . , n} be a set with n elements, and let 2[n] denote the poset of all subsets of [n] ordered by inclusion. In other words, 2[n] is the Boolean lattice of order n or the n-dimensional hypercube. It is easy (for example using a symmetric chain decomposition [1, Theorem 3.1.1]) to find n disjoint skipless (saturated) symmetric chains of length n − 2, that is n disjoint chains ...

we characterize the rational subsets of a finite group and discuss the relations to integral cayley graphs.

We introduce and study simple supersimple independence relations in the context of AECs with a monster model. Theorem 0.1Let K be an AEC model.•If has relation, then does not have 2-tree property.•If relation (<?0)-witness property for singletons, tree property. 0.1 Let If The proof both facts is done by finding cardinal bounds to classes small Galois-types over fixed model that are inconsisten...

A geometric lattice is a frame if its matroid, possibly after enlargement, has a basis such that every atom lies under a join of at most two basis elements. Examples include all subsets of a classical root system. Using the fact that nitary frame matroids are the bias matroids of biased graphs, we characterize modular coatoms in frames of nite rank and we describe explicitly the frames that are...

We study multivariate integration of functions that are invariant under permutations (of subsets) of their arguments. We find an upper bound for the nth minimal worst case error and show that under certain conditions, it can be bounded independent of the number of dimensions. In particular, we study the application of unshifted and randomly shifted rank-1 lattice rules in such a problem setting...

Statistical analysis of rank data describing preferences over small and variable subsets of a potentially large ensemble of items {1, . . . , n} is a very challenging problem. It is motivated by a wide variety of modern applications, such as recommender systems or search engines. However, very few inference methods have been documented in the literature to learn a ranking model from such incomp...