22,634 research outputs found
Transitive and self-dual codes attaining the Tsfasman-Vladut-Zink bound
A major problem in coding theory is the question of whether the class of cyclic codes is asymptotically good. In this correspondence-as a generalization of cyclic codes-the notion of transitive codes is introduced (see Definition 1.4 in Section I), and it is shown that the class of transitive codes is asymptotically good. Even more, transitive codes attain the Tsfasman-Vladut-Zink bound over F-q, for all squares q = l(2). It is also shown that self-orthogonal and self-dual codes attain the Tsfasman-Vladut-Zink bound, thus improving previous results about self-dual codes attaining the Gilbert-Varshamov bound. The main tool is a new asymptotically optimal tower E-0 subset of E-1 subset of E-2 subset of center dot center dot center dot of function fields over F-q (with q = l(2)), where all extensions E-n/E-0 are Galois
General Mass Scheme for Jet Production in DIS
We propose a method for calculating DIS jet production cross sections in QCD
at NLO accuracy with consistent treatment of heavy quarks. The scheme relies on
the dipole subtraction method for jets, which we extend to all possible initial
state splittings with heavy partons, so that the Aivazis-Collins-Olness-Tung
massive collinear factorization scheme (ACOT) can be applied. As a first check
of the formalism we recover the ACOT result for the heavy quark structure
function using a dedicated Monte Carlo program.Comment: 6 pages, 2 figure
Subquadratic time encodable codes beating the Gilbert-Varshamov bound
We construct explicit algebraic geometry codes built from the
Garcia-Stichtenoth function field tower beating the Gilbert-Varshamov bound for
alphabet sizes at least 192. Messages are identied with functions in certain
Riemann-Roch spaces associated with divisors supported on multiple places.
Encoding amounts to evaluating these functions at degree one places. By
exploiting algebraic structures particular to the Garcia-Stichtenoth tower, we
devise an intricate deterministic \omega/2 < 1.19 runtime exponent encoding and
1+\omega/2 < 2.19 expected runtime exponent randomized (unique and list)
decoding algorithms. Here \omega < 2.373 is the matrix multiplication exponent.
If \omega = 2, as widely believed, the encoding and decoding runtimes are
respectively nearly linear and nearly quadratic. Prior to this work, encoding
(resp. decoding) time of code families beating the Gilbert-Varshamov bound were
quadratic (resp. cubic) or worse
Almost isomorphism for countable state Markov shifts
Countable state Markov shifts are a natural generalization of the well-known
subshifts of finite type. They are the subject of current research both for
their own sake and as models for smooth dynamical systems. In this paper, we
investigate their almost isomorphism and entropy conjugacy and obtain a
complete classification for the especially important class of strongly positive
recurrent Markov shifts. This gives a complete classification up to entropy
conjugacy of the natural extensions of smooth entropy expanding maps, including
all smooth interval maps with non-zero topological entropy
Smallest snarks with oddness 4 and cyclic connectivity 4 have order 44
The family of snarks -- connected bridgeless cubic graphs that cannot be
3-edge-coloured -- is well-known as a potential source of counterexamples to
several important and long-standing conjectures in graph theory. These include
the cycle double cover conjecture, Tutte's 5-flow conjecture, Fulkerson's
conjecture, and several others. One way of approaching these conjectures is
through the study of structural properties of snarks and construction of small
examples with given properties. In this paper we deal with the problem of
determining the smallest order of a nontrivial snark (that is, one which is
cyclically 4-edge-connected and has girth at least 5) of oddness at least 4.
Using a combination of structural analysis with extensive computations we prove
that the smallest order of a snark with oddness at least 4 and cyclic
connectivity 4 is 44. Formerly it was known that such a snark must have at
least 38 vertices [J. Combin. Theory Ser. B 103 (2013), 468--488] and one such
snark on 44 vertices was constructed by Lukot'ka et al. [Electron. J. Combin.
22 (2015), #P1.51]. The proof requires determining all cyclically
4-edge-connected snarks on 36 vertices, which extends the previously compiled
list of all such snarks up to 34 vertices [J. Combin. Theory Ser. B, loc.
cit.]. As a by-product, we use this new list to test the validity of several
conjectures where snarks can be smallest counterexamples.Comment: 21 page
GoSam-2.0: a tool for automated one-loop calculations within the Standard Model and beyond
We present the version 2.0 of the program package GoSam for the automated
calculation of one-loop amplitudes. GoSam is devised to compute one-loop QCD
and/or electroweak corrections to multi-particle processes within and beyond
the Standard Model. The new code contains improvements in the generation and in
the reduction of the amplitudes, performs better in computing time and
numerical accuracy, and has an extended range of applicability. The extended
version of the "Binoth-Les-Houches-Accord" interface to Monte Carlo programs is
also implemented. We give a detailed description of installation and usage of
the code, and illustrate the new features in dedicated examples.Comment: replaced by published version and reference adde
A robust implementation of the Carathéodory-Fejér method
Best rational approximations are notoriously difficult to compute. However, the difference between the best rational approximation to a function and its Carathéodory-Fejér (CF) approximation is often so small as to be negligible in practice, while CF approximations are far easier to compute. We present a robust and fast implementation of this method in the chebfun software system and illustrate its use with several examples. Our implementation handles both polynomial and rational approximation and substantially improves upon earlier published software
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