Streaming algorithms for 2-coloring uniform hypergraphs

We consider the problem of two-coloring n-uniform hypergraphs. It is known that any such hypergraph with at most 1/10√n/ln n 2n hyperedges can be two-colored [7]. In fact, there is an efficient (requiring polynomial time in the size of the input) randomized algorithm that produces such a coloring. As stated [7], this algorithm requires random access to the hyperedge set of the input hypergraph. In this paper, we show that a variant of this algorithm can be implemented in the streaming model (with just one pass over the input), using space O(|V|B), where V is the vertex set of the hypergraph and each vertex is represented by B bits. (Note that the number of hyperedges in the hypergraph can be superpolynomial in |V|, and it is not feasible to store the entire hypergraph in memory.) We also consider the question of the minimum number of hyperedges in non-two-colorable n-uniform hypergraphs. Erdos showed that there exist non-2-colorable n-uniform hypegraphs with O(n2 2n) hyperedges and Θ(n2) vertices. We show that the choice Θ(n2) for the number of vertices in Erdös's construction is crucial: any hypergraph with at most 2n2/t vertices and 2nexp(t/8) hyperedges is 2-colorable. (We present a simple randomized streaming algorithm to construct the two-coloring.) Thus, for example, if the number of vertices is at most n1.5, then any non-2-colorable hypergraph must have at least 2n exp(√n/8) » n22n hyperedges. We observe that the exponential dependence on t in our result is optimal up to constant factors

Network-based dissolution

We introduce a novel graph-theoretic dissolution model which applies to a number of redistribution scenarios such as gerrymandering or work economization. The central aspect of our model is to delete some vertices and redistribute their "load" to neighboring vertices in a completely balanced way. We investigate how the underlying graph structure, the pre-knowledge about which vertices to delete, and the relation between old and new "vertex load" influence the computational complexity of the underlying easy-to-describe graph problems, thereby identifying both tractable and intractable cases

Parallel Sparse Matrix-Matrix Multiplication and Indexing: Implementation and Experiments

Generalized sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many high performance graph algorithms as well as for some linear solvers, such as algebraic multigrid. Here we show that SpGEMM also yields efficient algorithms for general sparse-matrix indexing in distributed memory, provided that the underlying SpGEMM implementation is sufficiently flexible and scalable. We demonstrate that our parallel SpGEMM methods, which use two-dimensional block data distributions with serial hypersparse kernels, are indeed highly flexible, scalable, and memory-efficient in the general case. This algorithm is the first to yield increasing speedup on an unbounded number of processors; our experiments show scaling up to thousands of processors in a variety of test scenarios

A complete classification of epistatic two-locus models

Background: The study of epistasis is of great importance in statistical genetics in fields such as linkage and association analysis and QTL mapping. In an effort to classify the types of epistasis in the case of two biallelic loci Li and Reich listed and described all models in the simplest case of 0/ 1 penetrance values. However, they left open the problem of finding a classification of two-locus models with continuous penetrance values. Results: We provide a complete classification of biallelic two-locus models. In addition to solving the classification problem for dichotomous trait disease models, our results apply to any instance where real numbers are assigned to genotypes, and provide a complete framework for studying epistasis in QTL data. Our approach is geometric and we show that there are 387 distinct types of two-locus models, which can be reduced to 69 when symmetry between loci and alleles is accounted for. The model types are defined by 86 circuits, which are linear combinations of genotype values, each of which measures a fundamental unit of interaction. Conclusion: The circuits provide information on epistasis beyond that contained in the additive × additive, additive × dominance, and dominance × dominance interaction terms. We discuss th

Roving librarian at a mid-sized, UK based University

Chapter 5 of Library Technology Reports (vol. 48, no. 8) “Rethinking Reference and Instruction with Tablets” details the “Roving Librarian” project carried out at a mid-sized UK university. All subject librarians have been equipped with iPads or Android tablets and sent out to rove. Regular times and places across the university have been arranged, primarily in social areas and working spaces where students congregate; a librarian takes a tablet computer and offers personalized assistance to students in these varied places. Alongside this, ad hoc support is offered to staff and students in meetings and casual encounters, facilitated by the constant access to the mobile devices. This chapter covers the benefits we have seen with the project and gives the results of a questionnaire carried out to determine whether a student would be likely to use the library more after their encounter with the Roving Librarian

ESR absorption spectrum of Gd3+ in single crystal Y2O3

Two electron-spin-resonance absorption spectra, each due to trivalent gadolinium, have been observed in single crystals of yttria, Y2O3. These spectra were observed at room temperature, 77 K, and 4.2 K with a spectrometer operating at 0.85-cm wavelength. One of these spectra exhibits trigonal symmetry with its principal direction being parallel to a crystal body diagonal. The other spectrum exhibits orthorhombic symmetry whose three mutually orthogonal directions are along a crystal cube edge and two crystal face diagonals. Both spectra exhibit resolved hyperfine structure. Fine-structure and hyperfine-structure parameters are given for both spectra. For the orthorhombic gadolinium ion, a slight displacement in the fine-structure spectrum of Gd157 from the spectrum due to the even-numbered isotopes is observed. This displacement can be expressed as a relative increase of about six parts in 104 in the value of B20. No analogous shift is observed in the trigonal spectrum of Gd157. © 1982 The American Physical Society