185 research outputs found
Lattice Green functions in all dimensions
We give a systematic treatment of lattice Green functions (LGF) on the
-dimensional diamond, simple cubic, body-centred cubic and face-centred
cubic lattices for arbitrary dimensionality for the first three
lattices, and for for the hyper-fcc lattice. We show that there
is a close connection between the LGF of the -dimensional hypercubic lattice
and that of the -dimensional diamond lattice. We give constant-term
formulations of LGFs for all lattices and dimensions. Through a still
under-developed connection with Mahler measures, we point out an unexpected
connection between the coefficients of the s.c., b.c.c. and diamond LGFs and
some Ramanujan-type formulae for Comment: 30 page
Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals
Lattice statistical mechanics, often provides a natural (holonomic) framework
to perform singularity analysis with several complex variables that would, in a
general mathematical framework, be too complex, or could not be defined.
Considering several Picard-Fuchs systems of two-variables "above" Calabi-Yau
ODEs, associated with double hypergeometric series, we show that holonomic
functions are actually a good framework for actually finding the singular
manifolds. We, then, analyse the singular algebraic varieties of the n-fold
integrals , corresponding to the decomposition of the magnetic
susceptibility of the anisotropic square Ising model. We revisit a set of
Nickelian singularities that turns out to be a two-parameter family of elliptic
curves. We then find a first set of non-Nickelian singularities for and , that also turns out to be rational or ellipic
curves. We underline the fact that these singular curves depend on the
anisotropy of the Ising model. We address, from a birational viewpoint, the
emergence of families of elliptic curves, and of Calabi-Yau manifolds on such
problems. We discuss the accumulation of these singular curves for the
non-holonomic anisotropic full susceptibility.Comment: 36 page
On the asymptotics of higher-dimensional partitions
We conjecture that the asymptotic behavior of the numbers of solid
(three-dimensional) partitions is identical to the asymptotics of the
three-dimensional MacMahon numbers. Evidence is provided by an exact
enumeration of solid partitions of all integers <=68 whose numbers are
reproduced with surprising accuracy using the asymptotic formula (with one free
parameter) and better accuracy on increasing the number of free parameters. We
also conjecture that similar behavior holds for higher-dimensional partitions
and provide some preliminary evidence for four and five-dimensional partitions.Comment: 30 pages, 8 tables, 4 figures (v2) New data (63-68) for solid
partitions added; (v3) published version, new subsection providing an
unbiased estimate of the leading for the leading coefficient added, some
tables delete
A Note on Computations of D-brane Superpotential
We develop some computational methods for the integrals over the 3-chains on
the compact Calabi-Yau 3-folds that plays a prominent role in the analysis of
the topological B-model in the context of the open mirror symmetry. We discuss
such 3-chain integrals in two approaches. In the first approach, we provide a
systematic algorithm to obtain the inhomogeneous Picard-Fuchs equations. In the
second approach, we discuss the analytic continuation of the period integral to
compute the 3-chain integral directly. The latter direct integration method is
applicable for both on-shell and off-shell formalisms.Comment: 61 pages, 5 figures; v2: typos corrected, minor changes, references
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Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order epsilon-expansion of generalized hypergeometric functions with one half-integer value of parameter
We continue the study of the construction of analytical coefficients of the
epsilon-expansion of hypergeometric functions and their connection with Feynman
diagrams. In this paper, we show the following results:
Theorem A: The multiple (inverse) binomial sums of arbitrary weight and depth
(see Eq. (1.1)) are expressible in terms of Remiddi-Vermaseren functions.
Theorem B: The epsilon expansion of a hypergeometric function with one
half-integer value of parameter (see Eq. (1.2)) is expressible in terms of the
harmonic polylogarithms of Remiddi and Vermaseren with coefficients that are
ratios of polynomials. Some extra materials are available via the www at this
http://theor.jinr.ru/~kalmykov/hypergeom/hyper.htmlComment: 24 pages, latex with amsmath and JHEP3.cls; v2: some typos corrected
and a few references added; v3: few references added
Large scale analytic calculations in quantum field theories
We present a survey on the mathematical structure of zero- and single scale
quantities and the associated calculation methods and function spaces in higher
order perturbative calculations in relativistic renormalizable quantum field
theories.Comment: 25 pages Latex, 1 style fil
Regional distribution of white matter hyperintensities in vascular dementia, Alzheimer's disease and healthy aging
Background: White matter hyperintensities (WMH) on MRI scans indicate lesions of the subcortical fiber system. The regional distribution of WMH may be related to their pathophysiology and clinical effect in vascular dementia (VaD), Alzheimer's disease (AD) and healthy aging. Methods: Regional WMH volumes were measured in MRI scans of 20 VaD patients, 25 AD patients and 22 healthy elderly subjects using FLAIR sequences and surface reconstructions from a three-dimensional MRI sequence. Results: The intraclass correlation coefficient for interrater reliability of WMH volume measurements ranged between 0.99 in the frontal and 0.72 in the occipital lobe. For each cerebral lobe, the WMH index, i.e. WMH volume divided by lobar volume, was highest in VaD and lowest in healthy controls. Within each group, the WMH index was higher in frontal and parietal lobes than in occipital and temporal lobes. Total WMH index and WMH indices in the frontal lobe correlated significantly with the MMSE score in VaD. Category fluency correlated with the frontal lobe WMH index in AD, while drawing performance correlated with parietal and temporal lobe WMH indices in VaD. Conclusions: A similar regional distribution of WMH between the three groups suggests a common (vascular) pathogenic factor leading to WMH in patients and controls. Our findings underscore the potential of regional WMH volumetry to determine correlations between subcortical pathology and cognitive impairment. Copyright (C) 2004 S. Karger AG, Basel
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