68 research outputs found
From "Dirac combs" to Fourier-positivity
Motivated by various problems in physics and applied mathematics, we look for
constraints and properties of real Fourier-positive functions, i.e. with
positive Fourier transforms. Properties of the "Dirac comb" distribution and of
its tensor products in higher dimensions lead to Poisson resummation, allowing
for a useful approximation formula of a Fourier transform in terms of a limited
number of terms. A connection with the Bochner theorem on positive definiteness
of Fourier-positive functions is discussed. As a practical application, we find
simple and rapid analytic algorithms for checking Fourier-positivity in 1- and
(radial) 2-dimensions among a large variety of real positive functions. This
may provide a step towards a classification of positive positive-definite
functions.Comment: 17 pages, 14 eps figures (overall 8 figures in the text
On the positivity of Fourier transforms
Characterizing in a constructive way the set of real functions whose Fourier
transforms are positive appears to be yet an open problem. Some sufficient
conditions are known but they are far from being exhaustive. We propose two
constructive sets of necessary conditions for positivity of the Fourier
transforms and test their ability of constraining the positivity domain. One
uses analytic continuation and Jensen inequalities and the other deals with
Toeplitz determinants and the Bochner theorem. Applications are discussed,
including the extension to the two-dimensional Fourier-Bessel transform and the
problem of positive reciprocity, i.e. positive functions with positive
transforms.Comment: 12 pages, 9 figures (in 4 groups
Delocalization transition for the Google matrix
We study the localization properties of eigenvectors of the Google matrix,
generated both from the World Wide Web and from the Albert-Barabasi model of
networks. We establish the emergence of a delocalization phase for the PageRank
vector when network parameters are changed. In the phase of localized PageRank,
a delocalization takes place in the complex plane of eigenvalues of the matrix,
leading to delocalized relaxation modes. We argue that the efficiency of
information retrieval by Google-type search is strongly affected in the phase
of delocalized PageRank.Comment: 4 pages, 5 figures. Research done at
http://www.quantware.ups-tlse.fr
Diffusion over a saddle with a Langevin equation
The diffusion problem over a saddle is studied using a multi-dimensional
Langevin equation. An analytical solution is derived for a quadratic potential
and the probability to pass over the barrier deduced. A very simple solution is
given for the one dimension problem and a general scheme is shown for higher
dimensions.Comment: 13 pages, use revTeX, to appear in Phys. Rev. E6
Endomyocardial Fibrosis: Still a Mystery after 60 Years
The pathologist Jack N. P. Davies identified endomyocardial fibrosis in Uganda in 1947. Since that time, reports of this restrictive cardiomyopathy have come from other parts of tropical Africa, South Asia, and South America. In Kampala, the disease accounts for 20% of heart disease patients referred for echocardiography. We conducted a systematic review of research on the epidemiology and etiology of endomyocardial fibrosis. We relied primarily on articles in the MEDLINE database with either “endomyocardial fibrosis” or “endomyocardial sclerosis” in the title. The volume of publications on endomyocardial fibrosis has declined since the 1980s. Despite several hypotheses regarding cause, no account of the etiology of this disease has yet fully explained its unique geographical distribution
The FANCM:p.Arg658* truncating variant is associated with risk of triple-negative breast cancer
Breast cancer is a common disease partially caused by genetic risk factors. Germline pathogenic variants in DNA repair genes BRCA1, BRCA2, PALB2, ATM, and CHEK2 are associated with breast cancer risk. FANCM, which encodes for a DNA translocase, has been proposed as a breast cancer predisposition gene, with greater effects for the ER-negative and triple-negative breast cancer (TNBC) subtypes. We tested the three recurrent protein-truncating variants FANCM:p.Arg658*, p.Gln1701*, and p.Arg1931* for association with breast cancer risk in 67,112 cases, 53,766 controls, and 26,662 carriers of pathogenic variants of BRCA1 or BRCA2. These three variants were also studied functionally by measuring survival and chromosome fragility in FANCM (-/-) patient-derived immortalized fibroblasts treated with diepoxybutane or olaparib. We observed that FANCM:p.Arg658* was associated with increased risk of ER-negative disease and TNBC (OR = 2.44, P = 0.034 and OR = 3.79; P = 0.009, respectively). In a country-restricted analysis, we confirmed the associations detected for FANCM:p.Arg658* and found that also FANCM:p.Arg1931* was associated with ER-negative breast cancer risk (OR = 1.96; P = 0.006). The functional results indicated that all three variants were deleterious affecting cell survival and chromosome stability with FANCM:p.Arg658* causing more severe phenotypes. In conclusion, we confirmed that the two rare FANCM deleterious variants p.Arg658* and p.Arg1931* are risk factors for ER-negative and TNBC subtypes. Overall our data suggest that the effect of truncating variants on breast cancer risk may depend on their position in the gene. Cell sensitivity to olaparib exposure, identifies a possible therapeutic option to treat FANCM-associated tumors
The FANCM:p.Arg658* truncating variant is associated with risk of triple-negative breast cancer
Breast cancer is a common disease partially caused by genetic risk factors. Germline pathogenic variants in DNA repair genes BRCA1, BRCA2, PALB2, ATM, and CHEK2 are associated with breast cancer risk. FANCM, which encodes for a DNA translocase, has been proposed as a breast cancer predisposition gene, with greater effects for the ER-negative and triple-negative breast cancer (TNBC) subtypes. We tested the three recurrent protein-truncating variants FANCM:p.Arg658*, p.Gln1701*, and p.Arg1931* for association with breast cancer risk in 67,112 cases, 53,766 controls, and 26,662 carriers of pathogenic variants of BRCA1 or BRCA2. These three variants were also studied functionally by measuring survival and chromosome fragility in FANCM−/− patient-derived immortalized fibroblasts treated with diepoxybutane or olaparib. We observed that FANCM:p.Arg658* was associated with increased risk of ER-negative disease and TNBC (OR = 2.44, P = 0.034 and OR = 3.79; P = 0.009, respectively). In a country-restricted analysis, we confirmed the associations detected for FANCM:p.Arg658* and found that also FANCM:p.Arg1931* was associated with ER-negative breast cancer risk (OR = 1.96; P = 0.006). The functional results indicated that all three variants were deleterious affecting cell survival and chromosome stability with FANCM:p.Arg658* causing more severe phenotypes. In conclusion, we confirmed that the two rare FANCM deleterious variants p.Arg658* and p.Arg1931* are risk factors for ER-negative and TNBC subtypes. Overall our data suggest that the effect of truncating variants on breast cancer risk may depend on their position in the gene. Cell sensitivity to olaparib exposure, identifies a possible therapeutic option to treat FANCM-associated tumors
A case-only study to identify genetic modifiers of breast cancer risk for BRCA1/BRCA2 mutation carriers
Breast cancer (BC) risk for BRCA1 and BRCA2 mutation carriers varies by genetic and familial factors. About 50 common variants have been shown to modify BC risk for mutation carriers. All but three, were identified in general population studies. Other mutation carrier-specific susceptibility variants may exist but studies of mutation carriers have so far been underpowered. We conduct a novel case-only genome-wide association study comparing genotype frequencies between 60,212 general population BC cases and 13,007 cases with BRCA1 or BRCA2 mutations. We identify robust novel associations for 2 variants with BC for BRCA1 and 3 for BRCA2 mutation carriers, P < 10−8, at 5 loci, which are not associated with risk in the general population. They include rs60882887 at 11p11.2 where MADD, SP11 and EIF1, genes previously implicated in BC biology, are predicted as potential targets. These findings will contribute towards customising BC polygenic risk scores for BRCA1 and BRCA2 mutation carriers
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