Closed geodesics on orbifolds

In this paper, we try to generalize to the case of compact Riemannian orbifolds $Q$ some classical results about the existence of closed geodesics of positive length on compact Riemannian manifolds $M$. We shall also consider the problem of the existence of infinitely many geometrically distinct closed geodesics. In the classical case the solution of those problems involve the consideration of the homotopy groups of $M$ and the homology properties of the free loop space on $M$(Morse theory). Those notions have their analogue in the case of orbifolds (see [7]). The main part of this paper will be to recall those notions and to show how the classical techniques can be adapted to the case of orbifolds.Comment: Improved version which takes into account the comments of the refree. In particular, we extend to compact simply connected Riemannian orbifolds the result of Gromoll-Meye

Local cloning of Bell states and distillable entanglement

The necessary and sufficient amount of entanglement required for cloning of orthogonal Bell states by local operation and classical communication is derived, and using this result, we provide here some additional examples of reversible, as well as irreversible states.Comment: 5 pages, two columns, Latex. Few typos have been corrected. An explanation of the teleportation map (eqn. (3) in the manuscript) has been provide

Borderline Ovarian Malignancies : A Single Institute Retrospective Study.

Background: Borderline ovarian tumors are histologically characterized as epithelial tumors with a stratified growth pattern but without destructive stromal invasion. Little is known about the histological subtypes and outcome, role of fertility sparing surgery and role of postoperative therapy in advanced stage in Indian scenario. While there is ample data in the world literature about this disease, prognosis in Indian patients is largely unknown due to dearth of studies in our setting. Objective: To study the demographic profile, clinical features, imaging, treatment and outcome of borderline ovarian tumors. Methods: This is a retrospective study of eighty seven patients with pathologically proven diagnosis of borderline ovarian tumor, diagnosed and treated from January 2006 to October 2011 at our institution. Most patients underwent surgical staging which incuded total abdominal hysterectomy and bilateral salphingo-oophorectomy, infracolic omentectomy, bilateral pelvic and para aortic lymphadenectomy. Young patients who had not completed their family underwent fertility sparing surgery. Patients with invasive metastatic implants received adjuvant chemotherapy. The outcome of these patients was correlated with stage, type of peritoneal implant, type of surgical procedure and with histological subtype. Results: At a median follow-up of 48 months, 100 percent survival was noted. One patient with stage III disease had recurrence. Conclusions: Borderline ovarian tumors occur at a younger age compared to invasive tumors. In patients with early stage disease who wish to preserve fertility, hysterectomy and contralateral oophorectomy are not necessary. Serous tumors occur at a younger age. They can be associated with invasive peritoneal implants and raised CA125 values. Majority of the serous tumors are bilateral and smaller in size compared to mucinous and endometroid tumors. Raised CA125 values did not correlate with the stage of disease. These patients have an excellent prognosis even in Indian scenario where majority of patients present with big ovarian masses

Anti-chaperone [eszett]A3/A1102-117 peptide interacting sites in human aB-crystallin

Purpose: Our previous work identified 23 low molecular weight (<3.5 kDa) crystallin peptides in the urea-soluble fractions of normal young, normal aged, and aged cataract human lenses. We found that one of these crystallin fragments, [beta]A3/ A1102-117 peptide (SDAYHIERLMSFRPIC), that are present in aged and cataract lens, increased the scattering of light by [beta]- and [gamma]-crystallins and alcohol dehydrogenase (ADH) and also reduced the chaperone-like activity of [alpha][beta]-crystallin. The present study was performed to identify the interacting sites of the [beta]A3/A1102-117 peptide in [alpha]B-crystallin. Methods: [beta]A3/A1102-117 peptide was first derivatized with sulfo-succinimidyl-2-[6-(biotinamido)-2-{pazidobenzamido}- hexanoamido] ethyl-1-3 dithio propionate (sulfo-SBED), a photoactivable, heterotrifunctional biotincontaining cross-linker. The biotin-derivatized peptide was then incubated with [alpha]B-crystallin at 37 [degrees]C for 2 h to allow complex formation followed by photolysis to facilitate the transfer of the biotin label from the peptide to [alpha]B-crystallin. Label transfer was confirmed by western blot, and the labeled [alpha]B-crystallin was digested with trypsin. Tryptic peptides from [alpha]B-crystallin carrying the biotin label were purified by avidin affinity chromatography, and [beta]A3/A1102-117 peptide interacting sites in [alpha]B-crystallin were identified by matrix-assisted laser desorption ionization-time-of-flight mass spectrometry (MALDI-TOF MS) and nanospray quadrupole time-of-flight mass spectrometry (QqTOF MS/MS). Results: We found that the [beta]A3/A1102-117 peptide interacted with [alpha]B-crystallin regions 70LEKDR74, 83HFSPEELKVK92, 91VKVLGDVIEVHGK103, 93VLGDVIEVHGKHEER107, and 121KYR123, which are part of the [alpha]-crystallin domain, and were previously shown to be part of the functional chaperone site in [alpha]B-crystallin. The [beta]A3/A1102-117 peptide also interacted with regions at the COOH-terminal extension of [alpha]B-crystallin, 150KQVSGPER157, 164EEKPAVTAAPK174, and 164EEKPAVTAAPKK175. When two of the hydrophobic residues of [beta]A3/A1102-117 peptide were replaced with hydrophilic residues, the resulting substituted peptide, SDADHGERLMSFRPIC, did not show the anti-chaperone property. Conclusions: This study confirmed the interactions between a low molecular weight peptide derived from [beta]A3/A1- crystallin found in aged and cataract lenses and [alpha]B-crystallin. The binding of [beta]A3/A1102-117 peptide to the chaperone site and the COOH-terminal extension of [alpha]B-crystallin may explain its anti-chaperone property