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

A Case of Radiation Retinopathy of Left Eye After Radiation Therapy of Right Brain Metastasis

A 37-year-old female, who had received modified radical mastectomy for cancer of her right breast, presented with decreased visual acuity in the left eye after radiation therapy for the management of the metastasis to her right brain 14 months ago. After ocular examination, we diagnosed her as radiation retinopathy. At the time of the first visit, the corrected best visual acuity was 0.4 in the left eye, and fundus examination revealed cotton wool spots and cystoid macular edema (CME). The findings in the right eye were normal except for cotton wool spots in the superior major arch. Fluorescein angiography (FA) showed marked telangiectasia and microaneurysms in her left eye but tiny microaneurysms in her right eye. Subsequent optical coherent tomography (OCT) showed CME. We injected intravitreal triamcinolone acetonide (TA). Two weeks after treatment, the visual acuity was improved to 0.6 and the retinal thickness was decreased. Three months later, the visual acuity in the left eye was dropped to 0.3 due to the recurrence of CME, so we injected intravitreal TA again. Five months later, visual acuity was improved to 0.5 and OCT revealed the improvement of CME. The incidence of radiation retinopathy is higher in the side nearer to radiation, but careful radiation blocking is also required on the opposite side of irradiation site considering the possibility of radiation retinopathy and careful observation is required on both sides of the eyes when performing fundus examination

Evaluation of the Efficacy of Vitrectomy for Persistent Diabetic Macular Edema and Associated Factors Predicting Outcome

PURPOSE: To evaluate the efficacy of vitrectomy for persistent diabetic macular edema after laser photocoagulation or intravitreal triamcinolone injections and to determine the demographic and ocular factors that influence functional and anatomical outcomes. METHODS: We retrospectively evaluated 55 eyes (51 patients) that had persistent diffuse macular edema after laser photocoagulation or intravitreal triamcinolone injections. We compared preoperative and postoperative best corrected visual acuity and macular thickness by Optical Coherence Tomography and investigated factors including patient's age, presence of vitreomacular traction, grade of diabetic retinopathy, and intraoperative internal limiting membrane removal that may influence the surgical results. RESULTS: The mean preoperative BCVA (log MAR) was 0.91+/-0.40 (0.8-1.2). The BCVA improved to 0.72+/-0.39 (0.3-1.2). The mean preoperative macular thickness was 440+/-130 (202-805) micrometer and the mean macular thickness decreased to 306+/-97 (136-580) micrometer postoperatively. The eyes showed statistically significant improvement in BCVA and central macular thickness (p<0.001). Preoperative better BCVA was associated with an improved postoperative visual acuity. (p=0.04). No other covariates were found to be statistically significant factors for prognosis of postoperative BCVA. CONCLUSIONS: In eyes with persistent diabetic macular edema after laser or IVTA injections, vitrectomy was effective for decreasing macular thickness and improvement of vision. The visual improvement after vitrectomy was associated with the preoperative better BCVA

Comparison of Combination Posterior Sub-Tenon Triamcinolone and Modified Grid Laser Treatment with Intravitreal Triamcinolone Treatment in Patients with Diffuse Diabetic Macular Edema

PURPOSE: To compare the efficacy of posterior sub-Tenon's capsule triamcinolone acetonide injection combined with modified grid macular photocoagulation (PSTI + MP) with intravitreal triamcinolone acetonide (IVTA) injection in the treatment of diffuse diabetic macular edema (DME). MATERIALS AND METHODS: Forty eyes of 33 patients with diffuse DME were randomly allocated into either PSTI + MP (20 eyes) or IVTA (20 eyes). Best corrected visual acuity (VA) and foveal thickness were measured. RESULTS: The ETDRS scores at baseline were 25.2 +/- 13.6 (mean +/- SD) letters in the PSTI + MP group, whereas 21.7 +/- 16.3 letters in the IVTA group. The ETDRS scores improved by 33.2 +/- 15.9, 34.7 +/- 16.6 and 30.9 +/- 19.0 letters in the PSTI + MP group whereas by 30.9 +/- 15.4, 30.1 +/- 17.9 and 31.5 +/- 15.0 letters in the IVTA group at 1, 3, and 6 months after the treatments, respectively. The VA improved significantly at 1 month and 3 months after both treatments (all p 0.05, Student's t-test). The foveal thicknesses at baseline and 1, 3, and 6 months after the treatments were 382.8 +/- 148.3, 309.1 +/- 131.3, 319.3 +/- 93.3, 340.4 +/- 123.5 microm (mean +/- SD) in the PSTI + MP group vs. 369.1 +/- 123.1, 241.4 +/- 52.3, 277.5 +/- 137.4, 290.2 +/- 127.9microm in the IVTA group, respectively. Pairwise comparisons revealed significant decrease in foveal thickness at 1 month (p = 0.01, paired t-test) for the PSTI + MP group, and at both 1 month (p 0.05, Student's t-test). In contrast to the PSTI + MP group, where no complications were noted, the elevation of intra-ocular pressure in 3 of 20 eyes (15%) and a significant increase in average cataract grading were observed in the IVTA group. CONCLUSION: PSTI + MP treatment provides significant improvement of vision in patients with diffuse DME over 3 months, and achieves outcomes comparable to those after IVTA treatment, however, with fewer complications.ope

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