560 research outputs found
Super Rogers–Szegö polynomials associated with BCN type of Polychronakos spin chains
No full textAs is well known, multivariate Rogers–Szegö polynomials are closely connected with the partition functions of the AN−1 type of Polychronakos spin chains having long-range interactions. Applying the ‘freezing trick’, here we derive the partition functions for a class of BCN type of Polychronakos spin chains containing supersymmetric analogues of polarized spin reversal operators and subsequently use those partition functions to obtain novel multivariate super Rogers–Szegö (SRS) polynomials depending on four types of variables. We construct the generating functions for such SRS polynomials and show that these polynomials can be written as some bilinear combinations of the AN−1 type of SRS polynomials. We also use the above mentioned generating functions to derive a set of recursion relations for the partition functions of the BCN type of Polychronakos spin chains involving different numbers of lattice sites and internal degrees of freedom
Polychronakos-Frahm spin chain of BC_N type and the Berry-Tabor conjecture
No full text©2008 The American Physical Society.
This work was partially supported by the DGI under Grant No. FIS2005-00752, and by Complutense University and the DGUI under Grant No. GR74/07-910556. J.C.B. acknowledges the financial support of the Spanish Ministry of Science and Innovation through an FPU scholarship.We compute the partition function of the su(m) Polychronakos-Frahm spin chain of BC_N type by means of the freezing trick. We use this partition function to study several statistical properties of the spectrum, which turn out to be analogous to those of other spin chains of Haldane-Shastry type. In particular, we find that when the number of particles is sufficiently large the level density follows a Gaussian distribution with great accuracy. We also show that the distribution of (normalized) spacings between consecutive levels is of neither Poisson nor Wigner type but is qualitatively similar to that of the original Haldane-Shastry spin chain. This suggests that spin chains of Haldane-Shastry type are exceptional integrable models since they do not satisfy a well-known conjecture of Berry and Tabor, according to which the spacings distribution of a generic integrable system should be Poissonian. We derive a simple analytic expression for the cumulative spacings distribution of the BC_N-type Polychronakos-Frahm chain using only a few essential properties of its spectrum such as the Gaussian character of the level density and the fact that the energy levels are equally spaced. This expression is shown to be in excellent agreement with the numerical data.DGIComplutense UniversityDGUMinistry of Science and Innovation, EspañaDepto. de Física TeóricaFac. de Ciencias FísicasTRUEpu
An imprinted locus associated with transient neonatal diabetes mellitus
No full textRecently, we reported the localization of a gene for transient neonatal diabetes mellitus (TNDM), a rare form of childhood diabetes, to an approximately 5.4 Mb region of chromosome 6q24. We have also shown that TNDM is associated with both paternal uniparental disomy (UPD) of chromosome 6 and paternal duplications of the critical region. The sequencing of P1-derived artificial chromosome clones from within the region of interest has allowed us to further localize the gene and to investigate the methylation status of the region. The gene is now known to reside in a 300-400 kb region of 6q24 which contains several CpG islands. At one island we have demonstrated differential DNA methylation between patients with paternal UPD of chromosome 6 and normal controls. In addition, two patients with TNDM, in whom neither paternal UPD of chromosome 6 nor duplication of 6q24 have been found, show a DNA methylation pattern identical to that of patients with paternal UPD of chromosome 6. Control individuals show a hemizygous methylation pattern. These results show that TNDM can be associated with a methylation change and identify a novel methylation imprint on chromosome 6 associated with TNDM.</p
Studies on parental genomic imprinting of insulin-like growth factor-IImannose 6-phosphate receptor gene in humans : phenomenon, mechanism, and relevance to disease
No full text
The genetic and epigenetic regulation of insulin-like growth factor II gene expression in humans /
No full textThe human insulin-like growth factor-II is an important fetal mitogen with demonstrated effects on growth, proliferation and survival of a wide spectrum of cells and tissues in mice and humans. The transcriptional regulation of the gene (IGF2) is under developmental control and is subject to epigenetic and genetic effects. At the epigenetic level, the mouse gene is parentally imprinted with exclusive expression of the paternally-inherited gene copy in most of the tissues examined. In this work, we demonstrate that the human gene is also subject to genomic imprinting and that the trait is tissue-specific and polymorphic whose basis may be genotype-dependent. Additionally, we show that in culture, primary placental fibroblasts lose the ability to functionally imprint IGF2. In instances of biallelic IGF2 gene expression, both in human tissue as well as in culture, we observe that the adjacent, reciprocally-imprinted H19 gene, which is normally expressed from the maternally-transmitted allele, is undetectable.The imprinted IGF2 gene is located in close physical proximity to a variable number of tandem repeats (VNTR) sequence polymorphism that is found upstream of the insulin gene promoter, in humans. Alleles of the VNTR have demonstrated transcriptional effects on insulin gene expression in human fetal and adult pancreas in vivo and in pancreatic beta cells in vitro. In this work, we show that the VNTR also has allelic effects on IGF2 expression in human placenta in vivo and on INS-IGF2 reporter gene activity in human lymphoblasts, in vitro.Alleles of the 5' INS (VNTR) are associated with susceptibility to type I diabetes mellitus. The preferential transmission of paternal susceptibility haplotypes at this locus suggests the functional involvement of a nearby imprinted gene in the susceptibility to type I diabetes. The demonstration of allelic effects of the VNTR on IGF2 mRNA levels, in vivo and in vitro, makes IGF2 an attractive functional candidate
Composition of many spins, random walks and statistics
No full textAbstractThe multiplicities of the decomposition of the product of an arbitrary number n of spin s states into irreducible SU(2) representations are computed. Two complementary methods are presented, one based on random walks in representation space and another based on the partition function of the system in the presence of a magnetic field. The large-n scaling limit of these multiplicities is derived, including nonperturbative corrections, and related to semiclassical features of the system. A physical application of these results to ferromagnetism is explicitly worked out. Generalizations involving several types of spins, as well as spin distributions, are also presented. The corresponding problem for (anti-)symmetric composition of spins is also considered and shown to obey remarkable duality and bosonization relations and exhibit novel large-n scaling properties
Exome diagnostics: Already a reality?
No full text10.1136/jmedgenet-2011-100385Journal of Medical Genetics489579-579JMDG
Composition of many spins, random walks and statistics
No full textThe multiplicities of the decomposition of the product of an arbitrary number n of spin s states into irreducible SU(2) representations are computed. Two complementary methods are presented, one based on random walks in representation space and another based on the partition function of the system in the presence of a magnetic field. The large-n scaling limit of these multiplicities is derived, including nonperturbative corrections, and related to semiclassical features of the system. A physical application of these results to ferromagnetism is explicitly worked out. Generalizations involving several types of spins, as well as spin distributions, are also presented. The corresponding problem for (anti-)symmetric composition of spins is also considered and shown to obey remarkable duality and bosonization relations and exhibit novel large-n scaling properties. � 2016 The Author(s
Equivalence of two-dimensional QCD and the c = 1 matrix model
No full textWe consider two dimensional QCD with the spatial dimension compactified to a circle. We show that the states in the theory consist of interacting strings that wind around the circle and derive the Hamiltonian for this theory in the large limit, complete with interactions. Mapping the winding states into momentum states, we express this Hamiltonian in terms of a continuous field. For a gauge group with a background source of Wilson loops, we recover the collective field Hamiltonian found by Das and Jevicki for the matrix model, except the spatial coordinate is on a circle. We then proceed to show that two dimensional QCD with a gauge group can be reduced to a one- dimensional unitary matrix model and is hence equivalent to a theory of free nonrelativistic fermions on a circle. A similar result is true for the group , but the fermions must be modded out by the center of mass coordinate.We consider two dimensional QCD with the spatial dimension compactified to a circle. We show that the states in the theory consist of interacting strings that wind around the circle and derive the Hamiltonian for this theory in the large limit, complete with interactions. Mapping the winding states into momentum states, we express this Hamiltonian in terms of a continuous field. For a gauge group with a background source of Wilson loops, we recover the collective field Hamiltonian found by Das and Jevicki for the matrix model, except the spatial coordinate is on a circle. We then proceed to show that two dimensional QCD with a gauge group can be reduced to a one- dimensional unitary matrix model and is hence equivalent to a theory of free nonrelativistic fermions on a circle. A similar result is true for the group , but the fermions must be modded out by the center of mass coordinate.We consider two-dimensional QCD with the spatial dimension compactified to a circle. We show that the states in the theory consist of interacting strings that wind around the circle and derive the Hamiltonian for this theory in the large N limit, complete with interactions. Mapping the winding states into momentum states, we express this Hamiltonian in terms of a continuous field. For a U( N ) gauge with a background source of Wilson loops, we recover the collective field Hamiltonian found by Das and Jevicki for the c = 1 matrix model, except the spatial coordinate is on a circle. We then proceed to show that two-dimensional QCD with a U( N ) gauge group can be reduced to a one-dimensional unitary matrix model and is hence equivalent to a theory of N free nonrelativistic fermions on a circle. A similar result is true for the group SU( N ), but the fermions must be modded out by the center of mass coordinate
- …
