Composite Representation Invariants and Unoriented Topological String Amplitudes

Sinha and Vafa \cite {sinha} had conjectured that the $SO$ Chern-Simons gauge theory on $S^3$ must be dual to the closed $A$-model topological string on the orientifold of a resolved conifold. Though the Chern-Simons free energy could be rewritten in terms of the topological string amplitudes providing evidence for the conjecture, we needed a novel idea in the context of Wilson loop observables to extract cross-cap $c=0,1,2$ topological amplitudes. Recent paper of Marino \cite{mar9} based on the work of Morton and Ryder\cite{mor} has clearly shown that the composite representation placed on the knots and links plays a crucial role to rewrite the topological string cross-cap $c=0$ amplitude. This enables extracting the unoriented cross-cap $c=2$ topological amplitude. In this paper, we have explicitly worked out the composite invariants for some framed knots and links carrying composite representations in $U(N)$ Chern-Simons theory. We have verified generalised Rudolph's theorem, which relates composite invariants to the invariants in $SO(N)$ Chern-Simons theory, and also verified Marino's conjectures on the integrality properties of the topological string amplitudes. For some framed knots and links, we have tabulated the BPS integer invariants for cross-cap $c=0$ and $c=2$ giving the open-string topological amplitude on the orientifold of the resolved conifold.Comment: 1+17 pages, condensed version of arXiv/1003.5282 to appear in Nucl. Phys.

Hyperscaling violating geometry with magnetic field and DC conductivity

We consider black hole with magnetic field in hyperscaling violating Lifshitz theories arised in a four dimensional Einstein–Maxwell-dilaton system along with axion fields. Considering the linearised equation of relevant fluctuations in metric and gauge fields, we analytically compute thermoelectric conductivity of the dual theory using Dirichlet boundary condition and find agreement with conductivities obtained in near horizon analysis. We also study temperature dependence of the conductivities

Comparison of phacoemulsification versus phacotrabeculectomy in the treatment of patients with chronic angle closure glaucoma and concomitant cataract

Aims: Whether phacoemulsification or phacotrabeculectomy (with adjunctive mitomycin C) is the surgery of choice in eyes with chronic angle closure glaucoma (CACG) with concomitant cataract. Settings and Design: Prospective comparative case series. Materials and Methods: Patients with CACG and cataract were randomized into two groups, comparing phacoemulsification (Group A) versus combined phacotrabeculectomy with mitomycin C (Group B). Group A had 60 eyes of medically controlled CACG with cataract and 58 eyes of medically uncontrolled CACG with cataract. Group B had 53 eyes of medically controlled CACG with cataract and 61 eyes of medically uncontrolled CACG with cataract. The two groups had identical study designs. All patients were reviewed 3-monthly for 2 years after surgery. The primary outcome measure was to compare the surgical complications of phacoemulsification versus phacotrabeculectomy and the secondary outcome measures were intraocular pressure (IOP) control and disease progression in the two groups. Statistical analysis used: Fisher′s exact test and chi-square test. Results: There was no statistically significant difference in IOP control, glaucomatous progression, or final visual acuity, during the 24-month follow-up, between two groups. In Group A, 5 (4.2%) of 118 eyes reported four surgical complications while in Group B, 18 (15.8%) of 114 eyes had 16 surgical complications. The difference in the proportion of eyes with one or more surgical complications between the two groups was statistically significant [P = 0.003, 95% confidence interval (CI)FNx01]. In addition to this the risk of surgical complication with phacotrabeculectomy was significantly higher when compared to phacoemulsification [3.73 (P = 0.003, 95% CI, 1.43-9.70)]FNx01. Conclusions: Postsurgical complications were more frequently seen after phacotrabeculectomy. However, the data did not reveal statistically significant differences in IOP control, visual acuity, or disease progression between both groups

Retinal nerve fibre layer thickness by OCT3 provides direct assessment of axonal loss in optic neuritis and may help in the early diagnosis and progression analysis of multiple sclerosis

Context: Retinal nerve fibre layer (RNFL) being unmyelinated, RNFL thickness (RNFLT) provides direct evidence of axonal loss in optic neuritis (ON) and may prove to be a valuable diagnostic and prognostic tool in the development of multiple sclerosis (MS). Aims: Assessment of RNFLT by OCT3 in patients with recent onset retrobulbar ON, comparison of obtained values based on presence or absence of the periventricular white matter lesion (PVWML) on magnetic resonance imaging (MRI), comparison with the RNFLT of a control group, and analysis of the obtained results. Settings and Design: Cross-sectional study. Materials and Methods: Eighteen patients with <=3 weeks onset clinically diagnosed retrobulbar ON between 19 and 55 years were included. RNFLT was assessed on presentation by OCT3 for both the eyes. MRI of brain and spinal cord with gadolinium enhancement was also performed in all patients, after adequate medical clearance. Patients were divided into: group A (10 patients) with no MRI-proven PVWML and group B (8 patients) with one or more PVWML, operationally deemed to have MS. RNFLT analysis was also done in 18 age-matched controls who were assigned to group C. Statistical Analysis Used: ANOVA and Student′s t test. Results: ON eyes in group B had thinnest RNFLT (average temporal = 39.75 μ), followed by group A (average temporal = 44.3 μ), and finally by group C (average temporal-OU = 80.78 μ). Conclusions: Our study shows that patients with ON, irrespective of detection of PVWML on MRI, have thinner RNFL compared to age-matched controls (P < 0.001). The average RNFLT values are lowest in patients with PVWML. The aspect of RNFL thinning in non-ON eyes should be further studied as a possible subclinical indicator of MS

Glauco skills for the millennial glaucoma specialist

Clinical skills training in Glaucoma is an intergral for the Glaucoma specialist of tomorrow. We discuss the various modalities and resources for glaucoma skills training

Digital twins enable the quantification of the trade-offs in maintaining citrus quality and marketability in the refrigerated supply chain.

Supply chains of fresh fruit must maintain a very narrow window of hygrothermal conditions after harvest. Any excursions outside this range can markedly lower the consumer acceptability of the fruit. However, the loss in fruit quality and marketability largely remains invisible to stakeholders throughout the supply chain. Here we developed a physics-based digital twin of citrus fruit to pinpoint when, why and to what extent fruit quality and marketability are reduced. Sensor data on 47 commercial shipments are thereby translated into actionable metrics for supply chain stakeholders by mapping the variability using principal component analysis. We unveiled a large spread (between 3% and 60%) in the shipments for different metrics of quality and marketability. Half of the shipments currently lie outside the ideal trade-off range between maintaining quality, killing fruit fly larvae and avoiding chilling injury. The digital twin technology opens the possibility to obtain the real-time coupling with sensor data to monitor food quality and marketability