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Local search is widely used to solve combinatorial optimisation problems and to model biological evolution, but the performance of local search algorithms on different kinds of fitness landscapes is poorly understood. Here we consider how fitness lan
Externí odkaz:
http://arxiv.org/abs/1907.01218
Publikováno v:
IEEE Transactions on Cognitive Communications and Networking, 5:2, June 2019
In the United States, the Federal Communications Commission has adopted rules permitting commercial wireless networks to share spectrum with federal incumbents in the 3.5~GHz Citizens Broadband Radio Service band. These rules require commercial syste
Externí odkaz:
http://arxiv.org/abs/1806.07745
We prove stable versions of trace theorems on the sphere in $L^2$ with optimal constants, thus obtaining rather precise information regarding near-extremisers. We also obtain stability for the trace theorem into $L^q$ for $q > 2$, by combining a refi
Externí odkaz:
http://arxiv.org/abs/1611.00928
Publikováno v:
Information and Computation 264 12-31 (2019)
The binary Constraint Satisfaction Problem (CSP) is to decide whether there exists an assignment to a set of variables which satisfies specified constraints between pairs of variables. A binary CSP instance can be presented as a labelled graph encodi
Externí odkaz:
http://arxiv.org/abs/1608.05358
Autor:
Cohen, David A., Cooper, Martin C., Jeavons, Peter G., Krokhin, Andrei, Powell, Robert, Zivny, Stanislav
Publikováno v:
SIAM Journal on Discrete Mathematics 31(4) (2017) 2279-2300
We study methods for transforming valued constraint satisfaction problems (VCSPs) to binary VCSPs. First, we show that the standard dual encoding preserves many aspects of the algebraic properties that capture the computational complexity of VCSPs. S
Externí odkaz:
http://arxiv.org/abs/1608.01628
We propose distributed algorithms for two well-established problems that operate efficiently under extremely harsh conditions. Our algorithms achieve state-of-the-art performance in a simple and novel way. Our algorithm for maximal independent set se
Externí odkaz:
http://arxiv.org/abs/1601.04306
Publikováno v:
Mathematika 62 (2016) 719-737
We prove a family of sharp bilinear space-time estimates for the half-wave propagator. As a consequence, for radially symmetric initial data, we establish sharp estimates of this kind for a range of exponents beyond the classical range.
Comment:
Comment:
Externí odkaz:
http://arxiv.org/abs/1506.04504
Autor:
Bez, Neal, Jeavons, Chris
We calculate the the sharp constant and characterise the extremal initial data in $\dot{H}^{\frac{3}{4}}\times\dot{H}^{-\frac{1}{4}}$ for the $L^4$ Sobolev--Strichartz estimate for the wave equation in four space dimensions.
Comment: 8 pages, no
Comment: 8 pages, no
Externí odkaz:
http://arxiv.org/abs/1407.1603
Publikováno v:
J. Math. Soc. Japan, Vol. 69, No. 2 (2017), pp. 1-18
We provide a comprehensive analysis of sharp bilinear estimates of Ozawa-Tsutsumi type for solutions u of the free Schr\"odinger equation, which give sharp control on $|u|^2$ in classical Sobolev spaces. In particular, we provide a generalization of
Externí odkaz:
http://arxiv.org/abs/1404.2466