389 research outputs found
Genetics of Chronic Lymphocytic Leukemia: Practical Aspects and Prognostic Significance
status: publishe
Holonomy of the Ising model form factors
We study the Ising model two-point diagonal correlation function by
presenting an exponential and form factor expansion in an integral
representation which differs from the known expansion of Wu, McCoy, Tracy and
Barouch. We extend this expansion, weighting, by powers of a variable
, the -particle contributions, . The corresponding
extension of the two-point diagonal correlation function, , is shown, for arbitrary , to be a solution of the sigma
form of the Painlev{\'e} VI equation introduced by Jimbo and Miwa. Linear
differential equations for the form factors are obtained and
shown to have both a ``Russian doll'' nesting, and a decomposition of the
differential operators as a direct sum of operators equivalent to symmetric
powers of the differential operator of the elliptic integral . Each is expressed polynomially in terms of the elliptic integrals and . The scaling limit of these differential operators breaks the
direct sum structure but not the ``Russian doll'' structure. The previous -extensions, are, for singled-out values ( integers), also solutions of linear differential
equations. These solutions of Painlev\'e VI are actually algebraic functions,
being associated with modular curves.Comment: 39 page
Nonintegrability of the two-body problem in constant curvature spaces
We consider the reduced two-body problem with the Newton and the oscillator
potentials on the sphere and the hyperbolic plane .
For both types of interaction we prove the nonexistence of an additional
meromorphic integral for the complexified dynamic systems.Comment: 20 pages, typos correcte
Basic Module Theory over Non-Commutative Rings with Computational Aspects of Operator Algebras
The present text surveys some relevant situations and results where basic
Module Theory interacts with computational aspects of operator algebras. We
tried to keep a balance between constructive and algebraic aspects.Comment: To appear in the Proceedings of the AADIOS 2012 conference, to be
published in Lecture Notes in Computer Scienc
Fuchs versus Painlev\'e
We briefly recall the Fuchs-Painlev\'e elliptic representation of Painlev\'e
VI. We then show that the polynomiality of the expressions of the correlation
functions (and form factors) in terms of the complete elliptic integral of the
first and second kind,
and , is a straight consequence of the fact that the differential
operators corresponding to the entries of Toeplitz-like determinants, are
equivalent to the second order operator which has as solution (or,
for off-diagonal correlations to the direct sum of and ). We show
that this can be generalized, mutatis mutandis, to the anisotropic Ising model.
The singled-out second order linear differential operator being replaced
by an isomonodromic system of two third-order linear partial differential
operators associated with , the Jacobi's form of the complete elliptic
integral of the third kind (or equivalently two second order linear partial
differential operators associated with Appell functions, where one of these
operators can be seen as a deformation of ). We finally explore the
generalizations, to the anisotropic Ising models, of the links we made, in two
previous papers, between Painlev\'e non-linear ODE's, Fuchsian linear ODE's and
elliptic curves. In particular the elliptic representation of Painlev\'e VI has
to be generalized to an ``Appellian'' representation of Garnier systems.Comment: Dedicated to the : Special issue on Symmetries and Integrability of
Difference Equations, SIDE VII meeting held in Melbourne during July 200
No Association Between MTHFR A1298C and MTRR A66G Polymorphisms, and MS in an Australian Cohort
Multiple sclerosis (MS) is a complex neurological disease that affects the central nervous system (CNS) resulting in debilitating neuropathology. Pathogenesis is primarily defined by CNS inflammation and demyelination of nerve axons. Methionine synthase reductase (MTRR) is an enzyme that catalyzes the remethylation of homocysteine (Hcy) to methionine via cobalamin and folate dependant reactions. Cobalamin acts as an intermediate methyl carrier between methylenetetrahydrofolate reductase (MTHFR) and Hcy. MTRR plays a critical role in maintaining cobalamin in an active form and is consequently an important determinant of total plasma Hcy (pHcy) concentrations. Elevated intracellular pHcy levels have been suggested to play a role in CNS dysfunction, neurodegenerative, and cerebrovascular diseases. Our investigation entailed the genotyping of a cohort of 140 cases and matched controls for MTRR and MTHFR, by restriction length polymorphism (RFLP) techniques. Two polymorphisms: MTRR A66G and MTHFR A1298C were investigated in an Australian age and gender matched case-control study. No significant allelic frequency difference was observed between cases and controls at the α = 0.05 level (MTRR χ^2 = 0.005, P = 0.95, MTHFR χ^2 = 1.15, P = 0.28). Our preliminary findings suggest no association between the MTRR A66G and MTHFR A1298C polymorphisms and MS
Improving Access to Mental Health Care and Psychosocial Support within a Fragile Context: A Case Study from Afghanistan
As one article in a series on Global Mental Health Practice, Peter Ventevogel and colleagues provide a case study of their efforts to integrate brief, practice-oriented mental health training into the Afghanistan health care system at a time when the system was being rebuilt from scratch
The Fuchsian differential equation of the square lattice Ising model susceptibility
Using an expansion method in the variables that appear in the
-dimensional integrals representing the -particle contribution to the
Ising square lattice model susceptibility , we generate a long series of
coefficients for the 3-particle contribution , using a
polynomial time algorithm. We give the Fuchsian differential equation of order
seven for that reproduces all the terms of our long series. An
analysis of the properties of this Fuchsian differential equation is performed.Comment: 15 pages, no figures, submitted to J. Phys.
Genetics of human neural tube defects
Neural tube defects (NTDs) are common, severe congenital malformations whose causation involves multiple genes and environmental factors. Although more than 200 genes are known to cause NTDs in mice, there has been rather limited progress in delineating the molecular basis underlying most human NTDs. Numerous genetic studies have been carried out to investigate candidate genes in cohorts of patients, with particular reference to those that participate in folate one-carbon metabolism. Although the homocysteine remethylation gene MTHFR has emerged as a risk factor in some human populations, few other consistent findings have resulted from this approach. Similarly, attention focused on the human homologues of mouse NTD genes has contributed only limited positive findings to date, although an emerging association between genes of the non-canonical Wnt (planar cell polarity) pathway and NTDs provides candidates for future studies. Priorities for the next phase of this research include: (i) larger studies that are sufficiently powered to detect significant associations with relatively minor risk factors; (ii) analysis of multiple candidate genes in groups of well-genotyped individuals to detect possible gene–gene interactions; (iii) use of high throughput genomic technology to evaluate the role of copy number variants and to detect ‘private’ and regulatory mutations, neither of which have been studied to date; (iv) detailed analysis of patient samples stratified by phenotype to enable, for example, hypothesis-driven testing of candidates genes in groups of NTDs with specific defects of folate metabolism, or in groups of fetuses with well-defined phenotypes such as craniorachischisis
Lack of Association between Genetic Polymorphisms in Enzymes Associated with Folate Metabolism and Unexplained Reduced Sperm Counts
BACKGROUND: The metabolic pathway of folate is thought to influence DNA stability either by inducing single/double stranded breaks or by producing low levels of S-adenosyl-methionine leading to abnormal gene expression and chromosome segregation. Polymorphisms in the genes encoding enzymes in the folate metabolism pathway show distinct geographic and/or ethnic variations and in some cases have been linked to disease. Notably, the gene Methylenetetrahydrofolate reductase (MTHFR) in which the homozygous (TT) state of the polymorphism c.665C>T (p.A222V) is associated with reduced specific activity and increased thermolability of the enzyme causing mild hyperhomocysteinemia. Recently several studies have suggested that men carrying this polymorphism may be at increased risk to develop infertility. METHODOLOGY/PRINCIPAL FINDINGS: We have tested this hypothesis in a case/control study of ethnic French individuals. We examined the incidence of polymorphisms in the genes MTHFR (R68Q, A222V and E429A), Methionine synthase reductase MTRR; (I22M and S175L) and Cystathionine beta-synthase (CBS; G307S). The case population consisted of DNA samples from men with unexplained azoospermia (n = 70) or oligozoospermia (n = 182) and the control population consisted of normospermic and fertile men (n = 114). We found no evidence of an association between the incidence of any of these variants and reduced sperm counts. In addition haplotype analysis did not reveal differences between the case and control populations. CONCLUSIONS/SIGNIFICANCE: We could find no evidence for an association between reduced sperm counts and polymorphisms in enzymes involved in folate metabolism in the French population
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