22,776 research outputs found
Strongly Regular Graphs Constructed from -ary Bent Functions
In this paper, we generalize the construction of strongly regular graphs in
[Y. Tan et al., Strongly regular graphs associated with ternary bent functions,
J. Combin.Theory Ser. A (2010), 117, 668-682] from ternary bent functions to
-ary bent functions, where is an odd prime. We obtain strongly regular
graphs with three types of parameters. Using certain non-quadratic -ary bent
functions, our constructions can give rise to new strongly regular graphs for
small parameters.Comment: to appear in Journal of Algebraic Combinatoric
Combinatorial Alphabet-Dependent Bounds for Locally Recoverable Codes
Locally recoverable (LRC) codes have recently been a focus point of research
in coding theory due to their theoretical appeal and applications in
distributed storage systems. In an LRC code, any erased symbol of a codeword
can be recovered by accessing only a small number of other symbols. For LRC
codes over a small alphabet (such as binary), the optimal rate-distance
trade-off is unknown. We present several new combinatorial bounds on LRC codes
including the locality-aware sphere packing and Plotkin bounds. We also develop
an approach to linear programming (LP) bounds on LRC codes. The resulting LP
bound gives better estimates in examples than the other upper bounds known in
the literature. Further, we provide the tightest known upper bound on the rate
of linear LRC codes with a given relative distance, an improvement over the
previous best known bounds.Comment: To appear in IEEE Transactions on Information Theor
Buildings and Hecke algebras
This paper investigates the connections between buildings and Hecke algebras
through the combinatorial study of two algebras spanned by averaging operators
on buildings. As a consequence we obtain a geometric and combinatorial
description of certain Hecke algebras, and in particular of the Macdonald
spherical functions and the center of affine Hecke algebras. The results of
this paper are used in later work to study spherical harmonic analysis on
affine buildings, and to study isotropic random walks on affine buildings
On the relationship between continuous- and discrete-time quantum walk
Quantum walk is one of the main tools for quantum algorithms. Defined by
analogy to classical random walk, a quantum walk is a time-homogeneous quantum
process on a graph. Both random and quantum walks can be defined either in
continuous or discrete time. But whereas a continuous-time random walk can be
obtained as the limit of a sequence of discrete-time random walks, the two
types of quantum walk appear fundamentally different, owing to the need for
extra degrees of freedom in the discrete-time case.
In this article, I describe a precise correspondence between continuous- and
discrete-time quantum walks on arbitrary graphs. Using this correspondence, I
show that continuous-time quantum walk can be obtained as an appropriate limit
of discrete-time quantum walks. The correspondence also leads to a new
technique for simulating Hamiltonian dynamics, giving efficient simulations
even in cases where the Hamiltonian is not sparse. The complexity of the
simulation is linear in the total evolution time, an improvement over
simulations based on high-order approximations of the Lie product formula. As
applications, I describe a continuous-time quantum walk algorithm for element
distinctness and show how to optimally simulate continuous-time query
algorithms of a certain form in the conventional quantum query model. Finally,
I discuss limitations of the method for simulating Hamiltonians with negative
matrix elements, and present two problems that motivate attempting to
circumvent these limitations.Comment: 22 pages. v2: improved presentation, new section on Hamiltonian
oracles; v3: published version, with improved analysis of phase estimatio
SPAD: a distributed middleware architecture for QoS enhanced alternate path discovery
In the next generation Internet, the network will evolve from a plain communication medium into one that provides endless services to the users. These services will be composed of multiple cooperative distributed application elements. We name these services overlay applications. The cooperative application elements within an overlay application will build a dynamic communication mesh, namely an overlay association. The Quality of Service (QoS) perceived by the users of an overlay application greatly depends on the QoS experienced on the communication paths of the corresponding overlay association. In this paper, we present SPAD (Super-Peer Alternate path Discovery), a distributed middleware architecture that aims at providing enhanced QoS between end-points within an overlay association. To achieve this goal, SPAD provides a complete scheme to discover and utilize composite alternate end-to end paths with better QoS than the path given by the default IP routing mechanisms
NLO electroweak corrections in extended Higgs Sectors with RECOLA2
We present the computer code RECOLA2 along with the first NLO electroweak
corrections to Higgs production in vector-boson fusion and updated results for
Higgs strahlung in the Two-Higgs-Doublet Model and Higgs-Singlet extension of
the Standard Model. A fully automated procedure for the generation of
tree-level and one-loop matrix elements in general models, including
renormalization, is presented. We discuss the application of the
Background-Field Method to the extended models. Numerical results for NLO
electroweak cross sections are presented for different renormalization schemes
in the Two-Higgs-Doublet Model and the Higgs-Singlet extension of the Standard
Model. Finally, we present distributions for the production of a heavy Higgs
boson.Comment: 47 pages, 29 figures, pdflatex, version to appear in JHE
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