44,241 research outputs found
Data linkage algebra, data linkage dynamics, and priority rewriting
We introduce an algebra of data linkages. Data linkages are intended for
modelling the states of computations in which dynamic data structures are
involved. We present a simple model of computation in which states of
computations are modelled as data linkages and state changes take place by
means of certain actions. We describe the state changes and replies that result
from performing those actions by means of a term rewriting system with rule
priorities. The model in question is an upgrade of molecular dynamics. The
upgrading is mainly concerned with the features to deal with values and the
features to reclaim garbage.Comment: 48 pages, typos corrected, phrasing improved, definition of services
replaced; presentation improved; presentation improved and appendix adde
Interpolating between low and high energy QCD via a 5D Yang-Mills model
We describe the Goldstone bosons of massless QCD together with an infinite
number of spin-1 mesons. The field content of the model is SU(Nf)xSU(Nf)
Yang-Mills in a compact extra-dimension. Electroweak interactions reside on one
brane. Breaking of chiral symmetry occurs due to the boundary conditions on the
other brane, away from our world, and is therefore spontaneous. Our
implementation of the holographic recipe maintains chiral symmetry explicit
throughout. For intermediate energies, we extract resonance couplings. These
satisfy sum rules due to the 5D nature of the model. These sum rules imply,
when taking the high energy limit, that perturbative QCD constraints are
satisfied. We also illustrate how the 5D model implies a definite prescription
for handling infinite sums over 4D resonances. Taking the low energy limit, we
recover the chiral expansion and the corresponding non-local order parameters.
All local order parameters are introduced separately.Comment: Corresponds to published version, with some typos correcte
CHAMP: A Cherednik Algebra Magma Package
We present a computer algebra package based on Magma for performing
computations in rational Cherednik algebras at arbitrary parameters and in
Verma modules for restricted rational Cherednik algebras. Part of this package
is a new general Las Vegas algorithm for computing the head and the
constituents of a module with simple head in characteristic zero which we
develop here theoretically. This algorithm is very successful when applied to
Verma modules for restricted rational Cherednik algebras and it allows us to
answer several questions posed by Gordon in some specific cases. We could
determine the decomposition matrices of the Verma modules, the graded G-module
structure of the simple modules, and the Calogero-Moser families of the generic
restricted rational Cherednik algebra for around half of the exceptional
complex reflection groups. In this way we could also confirm Martino's
conjecture for several exceptional complex reflection groups.Comment: Final version to appear in LMS J. Comput. Math. 41 pages, 3 ancillary
files. CHAMP is available at http://thielul.github.io/CHAMP/. All results are
listed explicitly in the ancillary PDF document (currently 935 pages). Please
check the website for further update
A Complexity Preserving Transformation from Jinja Bytecode to Rewrite Systems
We revisit known transformations from Jinja bytecode to rewrite systems from
the viewpoint of runtime complexity. Suitably generalising the constructions
proposed in the literature, we define an alternative representation of Jinja
bytecode (JBC) executions as "computation graphs" from which we obtain a novel
representation of JBC executions as "constrained rewrite systems". We prove
non-termination and complexity preservation of the transformation. We restrict
to well-formed JBC programs that only make use of non-recursive methods and
expect tree-shaped objects as input. Our approach allows for simplified
correctness proofs and provides a framework for the combination of the
computation graph method with standard techniques from static program analysis
like for example "reachability analysis".Comment: 36 page
Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams
Nested sums containing binomial coefficients occur in the computation of
massive operator matrix elements. Their associated iterated integrals lead to
alphabets including radicals, for which we determined a suitable basis. We
discuss algorithms for converting between sum and integral representations,
mainly relying on the Mellin transform. To aid the conversion we worked out
dedicated rewrite rules, based on which also some general patterns emerging in
the process can be obtained.Comment: 13 pages LATEX, one style file, Proceedings of Loops and Legs in
Quantum Field Theory -- LL2014,27 April 2014 -- 02 May 2014 Weimar, German
Sum rules and three point functions
Sum rules constraining the R-current spectral densities are derived
holographically for the case of D3-branes, M2-branes and M5-branes all at
finite chemical potentials. In each of the cases the sum rule relates a certain
integral of the spectral density over the frequency to terms which depend both
on long distance physics, hydrodynamics and short distance physics of the
theory. The terms which which depend on the short distance physics result from
the presence of certain chiral primaries in the OPE of two R-currents which are
turned on at finite chemical potential. Since these sum rules contain
information of the OPE they provide an alternate method to obtain the structure
constants of the two R-currents and the chiral primary. As a consistency check
we show that the 3 point function derived from the sum rule precisely matches
with that obtained using Witten diagrams.Comment: 41 page
A UV completion of scalar electrodynamics
In previous works, we constructed UV-finite and unitary scalar field theories
with an infinite spectrum of propagating modes for arbitrary polynomial
interactions. In this paper, we introduce infinitely many massive vector fields
into a U(1) gauge theory to construct a theory with UV-finiteness and
unitarity.Comment: 25 page
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