Product Subset Problem : Applications to number theory and cryptography

We consider applications of Subset Product Problem (SPP) in number theory and cryptography. We obtain a probabilistic algorithm that attack SPP and we analyze it with respect time/space complexity and success probability. In fact we provide an application to the problem of finding Carmichael numbers and an attack to Naccache-Stern knapsack cryptosystem, where we update previous results.Comment: 17 pages, 2 figures, LaTeX; references added, typos corrected, a new figure was inserted, sections 2.1, 2.2 improve

The effect of posterior subtenon methylprednisolone acetate in the refractory diabetic macular edema: a prospective nonrandomized interventional case series

BACKGROUND: To investigate the efficacy of posterior subtenon methylprednisolone acetate injection in treatment of refractory diffuse clinically significant diabetic macular edema (CSME). METHODS: In a prospective, nonrandomized, interventional case series, 52 eyes were diagnosed with CSME and treated with at least two sessions of laser photocoagulation according to Early Treatment Diabetic Retinopathy Study guidelines. At least 3 months after laser therapy, eyes with a residual central macular thickness were offered posterior subtenon injection of 40 mg methylprednisolone acetate. Main outcome measures were visual acuity, macular thickness and intraocular pressure. Potential complications were monitored, including intraocular pressure response, cataract progression and scleral perforation. RESULTS: Mean baseline visual acuity (in logMAR) improved significantly (p = 0.003) from 0.8 ± 0.36 to 0.6 ± 0.41 at 3 months. Mean foveal thickness decreased from 388 ± 78 μm at baseline to 231 ± 40 μm after 3 months (p < 0.0001). Visual acuity improvement in eyes with CSME with extrafoveal hard exudates was significant (p = 0.0001), but not significant in eyes with CSME with subfoveal hard exudates (p = 0.32). Intraocular pressure increased from 14.7 ± 2.0 mmHg (range, 12–18 mmHg) to a maximum value of 15.9 ± 2.1 mmHg (range, 12–20 mmHg) during the follow-up period. Complications in two eyes developed focal conjunctival necrosis at the site of injection. CONCLUSION: Posterior subtenon methylprednisolone acetate may improve early visual outcome in diffuse diabetic macular edema that fails to respond to conventional laser photocoagulation. Visual acuity improvement in eyes with CSME with extrafoveal hard exudates was significant; and this improvement is depends on location of hard exudates. Further study is needed to assess the long-term efficacy, safety, and retreatment

The combination of intravitreal triamcinolone and phacoemulsification surgery in patients with diabeticfoveal oedema and cataract

BACKGROUND: The management of diabetic patients with refractory macular oedema or patients with no adequate pre-operative view to administer laser treatment provide a challenge to the ophthalmologist. We wished to assess the use, safety and effect of intravitreal triamcinolone injection at the time of cataract surgery in patients with diabetic foveal oedema and sight limiting lens opacities. METHOD: This was a longitudinal non-randomised prospective pilot study in 18 eyes (12 patients). All patients had visually significant lens opacities and either persistent diabetic foveal oedema unresponsive to laser treatment-group A, or foveal oedema with no adequate pre-operative view for laser treatment- group B. The cataract surgery was carried out under full aseptic technique using a self-sealing temporal incision and a foldable acrylic lens. Intravitreal triamcinolone was given infratemporally pars plana at the completion of the cataract surgery. The patients were reviewed at day 5, 2 weeks, 2 months and then every 3 months as required. The Wilcoxin matched-pairs test was used to assess the significance of the improvement in visual acuity at 2 months. RESULTS: Twelve patients with a total of 18 eyes were included in the study. There were 10 patients (15 eyes) in group A and 3 patients (3 eyes) in group B. Preoperatively 16 of the 18 eyes had a visual acuity of 6/24 or worse. Postoperatively 83% of patients had completely dry foveae at 2 weeks. Best-corrected visual acuities at two months review ranged from 6/6 to CF with 9 eyes (50%) achieving 6/12 or better (7 eyes (47%) in group A and 2 eyes (67%) in group B). Three eyes had no recorded improvement in visual acuity, but no eyes had deterioration in acuity. The improvement in visual acuity was significant at p = 0.001. There were no significant sight threatening complications. CONCLUSION: Intravitreal triamcinolone has been shown to lead to an improvement in macular oedema and visual improvement in diabetic patients not undergoing cataract surgery but has not, to our knowledge, been previously used in a study like this one. We suggest that intravitreal injection at the time of cataract surgery could be carried out safely with encouraging visual outcomes in patients with diabetic foveal oedema and cataract

Intravitreal vs. subtenon triamcinolone acetonide for the treatment of diabetic cystoid macular edema

<p>Abstract</p> <p>Background</p> <p>To assess the efficacy of the intravitreal (IVT) injection of Triamcinolone Acetonide (TA) as compared to posterior subtenon (SBT) capsule injection for the treatment of cystoid diabetic macular edema.</p> <p>Methods</p> <p>Fourteen patients with type II diabetes mellitus and on insulin treatment, presenting diffuse cystoid macular edema were recruited. Before TA injection all focal lakes were treated by laser photocoagulation. In the same patients one eye was assigned to 4 mg IVT injection of TA and the fellow eye was then treated with 40 mg SBT injection of TA. Before and one, three and six months after treatment we measured visual acuity with ETDRS chart as well as thickness of the macula with optical coherence tomography (OCT) and intraocular pressure (IOP).</p> <p>Results</p> <p>The eyes treated with an IVT injection displayed significant improvement in visual acuity, both after one (0.491 ± 0.070; p < 0.001) and three months (0.500 ± 0.089; p < 0.001) of treatment. Significant improvement was displayed also in eyes treated with an SBT injection, again after one (0.455 ± 0.069; p < 0.001) and three months (0.427 ± 0.065; p < 0.001). The difference between an IVT injection (0.809 ± 0.083) and SBT injection (0.460 ± 0.072) becomes significant six months after the treatment (p < 0.001).</p> <p>Macular thickness of the eyes treated with IVT injection was significantly reduced both after one (222.7 ± 13.4 μm; p < 0.001) and after three months (228.1 ± 10.6 μm; p < 0.001) of treatment. The eyes treated with SBT injection displayed significant improvement after one (220.1 ± 15.1 μm; p < 0.001) and after three months (231.3 ± 10.9 μm; p < 0.001). The difference between the eyes treated with IVT injection (385.2 ± 11.3 μm) and those treated with SBT injection (235.4 ± 8.7 μm) becomes significant six months after the treatment (p < 0.001).</p> <p>Intraocular pressure of the eyes treated with IVT injection significantly increased after one month (17.7 ± 1.1 mm/Hg; p < 0.020), three (18.2 ± 1.2 mm/Hg; p < 0.003) and six month (18.1 ± 1.3 mm/Hg; p < 0.007) when compared to baseline value (16.1 ± 1.402 mm/Hg). In the SBT injection eyes we didn't display a significant increase of intraocular pressure after one (16.4 ± 1.2 mm/Hg; p < 0.450), three (16.3 ± 1.1 mm/Hg; p < 0.630) and six months (16.2 ± 1.1 mm/Hg; p < 0.720) when compared to baseline value (16.2 ± 1.3 mm/Hg).</p> <p>Conclusion</p> <p>The parabulbar subtenon approach can be considered a valid alternative to the intravitreal injection.</p> <p>Trial registration</p> <p>Current Controlled Trials <b>ISRCTN67086909</b></p

Ocular-hypertensive response and corneal endothelial changes after intravitreal triamcinolone injections in Chinese subjects: A 6-month follow-up study

Purpose: To assess the intraocular pressure (IOP) and corneal endothelial changes, over a 6-month period, after a single injection of intravitreal triamcinolone (ivTA) in Chinese patients. Methods: A total of 43 eyes of 43 consecutive Chinese patients with various macular diseases received a single bolus injection of 4 mg ivTA, of which, 14 eyes with significant cataracts underwent simultaneous phacoemulsification and primary intraocular lens implantation. IOP was measured preoperatively and weekly in the first month, and then monthly until 6 months postinjection. Specular microscopy was performed on 24 of the 29 eyes without simultaneous cataract surgery, preoperatively and at months 1, 3, and 6. Results: All patients completed 6 months of follow-up. Nine out of 43 (20.9%) eyes had IOP >21 mmHg. Their mean maximum IOP was 29.2 mmHg (range 23.0-37.0), necessitating the use of 2.0 types of topical antiglaucomatous medications on average. The IOP elevation occurred at a mean of 5.2 weeks (range 1-17) postinjection. All IOPs returned to normal, without additional antiglaucomatous medications, by 6 months. There was no statistically significant difference (paired t-test, P < 0.05) in the corneal endothelial cell count and other specular microscopy parameters up to 6 months after the injections. Conclusion: A single 4 mg bolus injection of ivTA appeared to have no harmful effects on the corneal endothelium. IvTA caused transient IOP elevations in 20.9% of Chinese patients, similar to that observed in Caucasians. As the IOP rise can occur as early as 1 week after the injection, early monitoring will help its early detection and prevent optic nerve damage. © 2005 Nature Publishing Group All rights reserved.link_to_subscribed_fulltex