Holonomy of the Ising model form factors

We study the Ising model two-point diagonal correlation function $C(N,N)$ 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 $\lambda$, the $j$-particle contributions, $f^{(j)}_{N,N}$. The corresponding $\lambda$ extension of the two-point diagonal correlation function, $C(N,N; \lambda)$, is shown, for arbitrary $\lambda$, 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 $f^{(j)}_{N,N}$ 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 $E$. Each $f^{(j)}_{N,N}$ is expressed polynomially in terms of the elliptic integrals $E$ and $K$. The scaling limit of these differential operators breaks the direct sum structure but not the ``Russian doll'' structure. The previous $\lambda$-extensions, $C(N,N; \lambda)$ are, for singled-out values $\lambda= \cos(\pi m/n)$ ($m, n$ 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

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

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 ${\bf S}^{2}$ and the hyperbolic plane ${\bf H}^{2}$. For both types of interaction we prove the nonexistence of an additional meromorphic integral for the complexified dynamic systems.Comment: 20 pages, typos correcte

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

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

Genetics of Chronic Lymphocytic Leukemia: Practical Aspects and Prognostic Significance

status: publishe

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, $K$ and $E$, 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 $L_E$ which has $E$ as solution (or, for off-diagonal correlations to the direct sum of $L_E$ and $d/dt$). We show that this can be generalized, mutatis mutandis, to the anisotropic Ising model. The singled-out second order linear differential operator $L_E$ being replaced by an isomonodromic system of two third-order linear partial differential operators associated with $\Pi_1$, 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 $L_E$). 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

Psycho-educational interventions for adults with severe or difficult asthma: a systematic review.

types: Journal Article; Research Support, Non-U.S. Gov't; ReviewThis is the author's version of the work that was accepted for publication in the Journal of Asthma. The final version can be accessed via the DOI in this record.Research highlights psychosocial factors associated with adverse asthma events. This systematic review therefore examined whether psycho-educational interventions improve health and self-management outcomes in adults with severe or difficult asthma. Seventeen controlled studies were included. Characteristics and content of interventions varied even within broad types. Study quality was generally poor and several studies were small. Any positive effects observed from qualitative and quantitative syntheses were mainly short term and, in planned subgroup analyses (involving < 5 trials), effects on hospitalizations, quality of life, and psychological morbidity in patients with severe asthma did not extend to those in whom multiple factors complicate management.UK NHS Health Technology Assessment Programm

Plasma-assisted ALD of LiPO(N) for solid state batteries

All solid state 3D batteries are pursued for their increased safety and high power capabilities. At present conformai coating of the solid electrolyte remains one of the key hurdles for the implementation of such devices. In the present work we investigate atomic layer deposition (ALD) as means of conformai deposition of lithium phosphate (Li3PO4) and nitrogen doped lithium phosphates (LiPON). These processes are characterized here to obtain the highest possible Li-ion conductivity. Li3PO4 is shown to yield a conductivity of 10-10 S/cm. On the other hand, an optimized LiPON process gave rise to a Li-ion conductivity of 510-7 S/cm. In addition, good conformality of the LiPON process was shown on high aspect ratio pillars. Furthermore, a solid state battery device was fabricated comprising a Li4Ti5O12 cathode, a 70 nm thick ALD LiPON solid electrolyte and a metallic lithium anode. The fabricated device is based on the thinnest solid electrolyte used so far as well as on the first ALD deposited solid electrolyte.</p

Comparison of bacterial microbiota of the predatory mite Neoseiulus cucumeris (Acari: Phytoseiidae) and its factitious prey Tyrophagus putrescentiae (Acari: Acaridae)

Neoseiulus cucumeris is a predatory mite used for biological control of arthropod pests. Mass-reared predators are fed with factitious prey mites such as Tyrophagus putrescentiae. Although some information on certain endosymbionts of N. cucumeris and T. putrescentiae exists, it is unclear whether both species share bacterial communities. The bacterial communities in populations of predator and prey mites, as well as the occurence of potential acaropathogenic bacteria were analyzed. The comparisons were based on the following groups: (i) N. cucumeris mass-production; (ii) N. cucumeris laboratory population with disease symptoms; (iii) T. putrescentiae pure populations and; (iv) T. putrescentiae from rearing units of N. cucumeris. Only 15% of OTUs were present in all samples from predatory and prey mite populations (core OTUs): the intracellular symbionts Wolbachia, Cardinium, plus other Blattabacterium-like, Solitalea-like, and Bartonella-like symbionts. Environmental bacteria were more abundant in predatory mites, while symbiotic bacteria prevailed in prey mites. Relative numbers of certain bacterial taxa were significantly different between the microbiota of prey mites reared with and without N. cucumeris. No significant differences were found in the bacterial communities of healthy N. cucumeris compared to N. cucumeris showing disease symptoms. We did not identify any confirmed acaropathogenic bacteria among microbiota