67 research outputs found
Minimum and maximum against k lies
A neat 1972 result of Pohl asserts that [3n/2]-2 comparisons are sufficient,
and also necessary in the worst case, for finding both the minimum and the
maximum of an n-element totally ordered set. The set is accessed via an oracle
for pairwise comparisons. More recently, the problem has been studied in the
context of the Renyi-Ulam liar games, where the oracle may give up to k false
answers. For large k, an upper bound due to Aigner shows that (k+O(\sqrt{k}))n
comparisons suffice. We improve on this by providing an algorithm with at most
(k+1+C)n+O(k^3) comparisons for some constant C. The known lower bounds are of
the form (k+1+c_k)n-D, for some constant D, where c_0=0.5, c_1=23/32=0.71875,
and c_k=\Omega(2^{-5k/4}) as k goes to infinity.Comment: 11 pages, 3 figure
Non-Coexistence of Infinite Clusters in Two-Dimensional Dependent Site Percolation
This paper presents three results on dependent site percolation on the square
lattice. First, there exists no positively associated probability measure on
{0,1}^{Z^2} with the following properties: a) a single infinite 0cluster exists
almost surely, b) at most one infinite 1*cluster exists almost surely, c) some
probabilities regarding 1*clusters are bounded away from zero. Second, we show
that coexistence of an infinite 1*cluster and an infinite 0cluster is almost
surely impossible when the underlying probability measure is ergodic with
respect to translations, positively associated, and satisfies the finite energy
condition. The third result analyses the typical structure of infinite clusters
of both types in the absence of positive association. Namely, under a slightly
sharpened finite energy condition, the existence of infinitely many disjoint
infinite self-avoiding 1*paths follows from the existence of an infinite
1*cluster. The same holds with respect to 0paths and 0clusters.Comment: 17 pages, 1 figur
Searching for Radio Pulsars in 3EG Sources at Urumqi Observatory
Since mid-2005, a pulsar searching system has been operating at 18 cm on the
25-m radio telescope of Urumqi Observatory. Test observations on known pulsars
show that the system can perform the intended task. The prospect of using this
system to observe 3EG sources and other target searching tasks is discussed.Comment: a training project about MSc thesi
Coupled oscillators as models of phantom and scalar field cosmologies
We study a toy model for phantom cosmology recently introduced in the
literature and consisting of two oscillators, one of which carries negative
kinetic energy. The results are compared with the exact phase space picture
obtained for similar dynamical systems describing, respectively, a massive
canonical scalar field conformally coupled to the spacetime curvature, and a
conformally coupled massive phantom. Finally, the dynamical system describing
exactly a minimally coupled phantom is studied and compared with the toy model.Comment: 18 pages, LaTeX, to appear in Physical Review
Novel genetic loci associated with hippocampal volume
The hippocampal formation is a brain structure integrally involved in episodic memory, spatial navigation, cognition and stress responsiveness. Structural abnormalities in hippocampal volume and shape are found in several common neuropsychiatric disorders. To identify the genetic underpinnings of hippocampal structure here we perform a genome-wide association study (GWAS) of 33,536 individuals and discover six independent loci significantly associated with hippocampal volume, four of them novel. Of the novel loci, three lie within genes (ASTN2, DPP4 and MAST4) and one is found 200 kb upstream of SHH. A hippocampal subfield analysis shows that a locus within the MSRB3 gene shows evidence of a localized effect along the dentate gyrus, subiculum, CA1 and fissure. Further, we show that genetic variants associated with decreased hippocampal volume are also associated with increased risk for Alzheimer's disease (rg =-0.155). Our findings suggest novel biological pathways through which human genetic variation influences hippocampal volume and risk for neuropsychiatric illness
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