18,774 research outputs found
Exact solutions for the two- and all-terminal reliabilities of the Brecht-Colbourn ladder and the generalized fan
The two- and all-terminal reliabilities of the Brecht-Colbourn ladder and the
generalized fan have been calculated exactly for arbitrary size as well as
arbitrary individual edge and node reliabilities, using transfer matrices of
dimension four at most. While the all-terminal reliabilities of these graphs
are identical, the special case of identical edge () and node ()
reliabilities shows that their two-terminal reliabilities are quite distinct,
as demonstrated by their generating functions and the locations of the zeros of
the reliability polynomials, which undergo structural transitions at
Equivalent String Networks and Uniqueness of BPS States
We analyze string networks in 7-brane configurations in IIB string theory. We
introduce a complex parameter M characterizing equivalence classes of networks
on a fixed 7-brane background and specifying the BPS mass of the network as
M_{BPS} = | M |. We show that M can be calculated without knowing the
particular representative of the BPS state. Based on detailed examination of
backgrounds with three and four 7-branes we argue that equivalent networks may
not be simultaneously BPS, an essential requirement of consistency.Comment: 28 pages, LaTeX, 18 eps figure
Similarity Renormalization, Hamiltonian Flow Equations, and Dyson's Intermediate Representation
A general framework is presented for the renormalization of Hamiltonians via
a similarity transformation. Divergences in the similarity flow equations may
be handled with dimensional regularization in this approach, and the resulting
effective Hamiltonian is finite since states well-separated in energy are
uncoupled. Specific schemes developed several years ago by Glazek and Wilson
and contemporaneously by Wegner correspond to particular choices within this
framework, and the relative merits of such choices are discussed from this
vantage point. It is shown that a scheme for the transformation of Hamiltonians
introduced by Dyson in the early 1950's also corresponds to a particular choice
within the similarity renormalization framework, and it is argued that Dyson's
scheme is preferable to the others for ease of computation. As an example, it
is shown how a logarithmically confining potential arises simply at second
order in light-front QCD within Dyson's scheme, a result found previously for
other similarity renormalization schemes. Steps toward higher order and
nonperturbative calculations are outlined. In particular, a set of equations
analogous to Dyson-Schwinger equations is developed.Comment: REVTex, 32 pages, 7 figures (corrected references
Maximum common subgraph isomorphism algorithms for the matching of chemical structures
The maximum common subgraph (MCS) problem has become increasingly important in those aspects of chemoinformatics that involve the matching of 2D or 3D chemical structures. This paper provides a classification and a review of the many MCS algorithms, both exact and approximate, that have been described in the literature, and makes recommendations regarding their applicability to typical chemoinformatics tasks
Differential Equations for Two-Loop Four-Point Functions
At variance with fully inclusive quantities, which have been computed already
at the two- or three-loop level, most exclusive observables are still known
only at one-loop, as further progress was hampered so far by the greater
computational problems encountered in the study of multi-leg amplitudes beyond
one loop. We show in this paper how the use of tools already employed in
inclusive calculations can be suitably extended to the computation of loop
integrals appearing in the virtual corrections to exclusive observables, namely
two-loop four-point functions with massless propagators and up to one off-shell
leg. We find that multi-leg integrals, in addition to integration-by-parts
identities, obey also identities resulting from Lorentz-invariance. The
combined set of these identities can be used to reduce the large number of
integrals appearing in an actual calculation to a small number of master
integrals. We then write down explicitly the differential equations in the
external invariants fulfilled by these master integrals, and point out that the
equations can be used as an efficient method of evaluating the master integrals
themselves. We outline strategies for the solution of the differential
equations, and demonstrate the application of the method on several examples.Comment: 26 pages, LaTeX; some explanatory comments added; several typos
correcte
Off-shell Currents and Color-Kinematics Duality
We elaborate on the color-kinematics duality for off-shell diagrams in gauge
theories coupled to matter, by investigating the scattering process , and show that the Jacobi relations for the kinematic numerators
of off-shell diagrams, built with Feynman rules in axial gauge, reduce to a
color-kinematics violating term due to the contributions of sub-graphs only.
Such anomaly vanishes when the four particles connected by the Jacobi relation
are on their mass shell with vanishing squared momenta, being either external
or cut particles, where the validity of the color-kinematics duality is
recovered. We discuss the role of the off-shell decomposition in the direct
construction of higher-multiplicity numerators satisfying color-kinematics
identity in four as well as in dimensions, for the latter employing the
Four Dimensional Formalism variant of the Four Dimensional Helicity scheme. We
provide explicit examples for the QCD process .Comment: Accepted version for publication in PLB. Manuscript extended: 19
pages, 15 figures; C/K duality for tree-level amplitudes in dimensional
regularization added; references added; title modifie
Choosing integration points for QCD calculations by numerical integration
I discuss how to sample the space of parton momenta in order to best perform
the numerical integrations that lead to a calculation of three jet cross
sections and similar observables in electron-positron annihilation.Comment: 25 pages with 8 figure
Predictive powers of chiral perturbation theory in Compton scattering off protons
We study low-energy nucleon Compton scattering in the framework of baryon
chiral perturbation theory (BPT) with pion, nucleon, and (1232)
degrees of freedom, up to and including the next-to-next-to-leading order
(NNLO). We include the effects of order , and , with
MeV the -resonance excitation energy. These are
all "predictive" powers in the sense that no unknown low-energy constants enter
until at least one order higher (i.e, ). Estimating the theoretical
uncertainty on the basis of natural size for effects, we find that
uncertainty of such a NNLO result is comparable to the uncertainty of the
present experimental data for low-energy Compton scattering. We find an
excellent agreement with the experimental cross section data up to at least the
pion-production threshold. Nevertheless, for the proton's magnetic
polarizability we obtain a value of fm, in
significant disagreement with the current PDG value. Unlike the previous
PT studies of Compton scattering, we perform the calculations in a
manifestly Lorentz-covariant fashion, refraining from the heavy-baryon (HB)
expansion. The difference between the lowest order HBPT and BPT
results for polarizabilities is found to be appreciable. We discuss the chiral
behavior of proton polarizabilities in both HBPT and BPT with the
hope to confront it with lattice QCD calculations in a near future. In studying
some of the polarized observables, we identify the regime where their naive
low-energy expansion begins to break down, thus addressing the forthcoming
precision measurements at the HIGS facility.Comment: 24 pages, 9 figures, RevTeX4, revised version published in EPJ
- …