37 research outputs found
Singularities of -fold integrals of the Ising class and the theory of elliptic curves
We introduce some multiple integrals that are expected to have the same
singularities as the singularities of the -particle contributions
to the susceptibility of the square lattice Ising model. We find
the Fuchsian linear differential equation satisfied by these multiple integrals
for and only modulo some primes for and , thus
providing a large set of (possible) new singularities of the . We
discuss the singularity structure for these multiple integrals by solving the
Landau conditions. We find that the singularities of the associated ODEs
identify (up to ) with the leading pinch Landau singularities. The second
remarkable obtained feature is that the singularities of the ODEs associated
with the multiple integrals reduce to the singularities of the ODEs associated
with a {\em finite number of one dimensional integrals}. Among the
singularities found, we underline the fact that the quadratic polynomial
condition , that occurs in the linear differential equation
of , actually corresponds to a remarkable property of selected
elliptic curves, namely the occurrence of complex multiplication. The
interpretation of complex multiplication for elliptic curves as complex fixed
points of the selected generators of the renormalization group, namely
isogenies of elliptic curves, is sketched. Most of the other singularities
occurring in our multiple integrals are not related to complex multiplication
situations, suggesting an interpretation in terms of (motivic) mathematical
structures beyond the theory of elliptic curves.Comment: 39 pages, 7 figure
Notice nécrologique
Simon H., Racinet Philippe, Dubois Cl. Notice nécrologique. In: Revue archéologique de Picardie, n°1-2, 1985. p. 2
Notice nécrologique
Simon H., Racinet Philippe, Dubois Cl. Notice nécrologique. In: Revue archéologique de Picardie, n°1-2, 1985. p. 2
Is laparoscopy still the gold standard in infertility assessment? A comparison of fertiloscopy versus laparoscopy in infertility. Results of an international multicentre prospective trial: the 'FLY' (Fertiloscopy-LaparoscopY) study.
BACKGROUND: The aim of this prospective multicentre study was to compare the two endoscopic techniques of laparoscopy and fertiloscopy in routine evaluation of the pelvis in infertile women. METHODS: A total of 92 women was selected in 14 University Hospitals to undergo fertiloscopy followed by transabdominal laparoscopy by a team of two surgeons in each hospital. RESULTS: A high degree of concordance was observed between these two techniques, in that if fertiloscopy did not detect any abnormalities, this was also confirmed by laparoscopy. Discordance was observed in similar numbers of cases: eight after laparoscopy and nine after fertiloscopy. The diagnostic index for fertiloscopy and laparoscopy was calculated; sensitivity (86 and 87% respectively) and negative predictive value (64 and 67% respectively) were similar. The kappa index was also calculated for each of the six structures/regions (right/left tube; right/left ovary; peritoneum of pouch of Douglas; posterior uterus), and concordance (0.78 to 0.91) was considered almost complete. CONCLUSIONS: These results confirm fertiloscopy as a minimally invasive safe procedure that may be considered as an alternative to diagnostic laparoscopy in the routine assessment of women without clinical or ultrasound evidence of pelvic disease. On the basis of the additional advantages of fertiloscopy, namely salpingoscopy or microsalpingoscopy, it is considered that fertiloscopy could replace laparoscopy as a routine procedure in such women