Tau functions as Widom constants

We define a tau function for a generic Riemann-Hilbert problem posed on a union of non-intersecting smooth closed curves with jump matrices analytic in their neighborhood. The tau function depends on parameters of the jumps and is expressed as the Fredholm determinant of an integral operator with block integrable kernel constructed in terms of elementary parametrices. Its logarithmic derivatives with respect to parameters are given by contour integrals involving these parametrices and the solution of the Riemann-Hilbert problem. In the case of one circle, the tau function coincides with Widom's determinant arising in the asymptotics of block Toeplitz matrices. Our construction gives the Jimbo-Miwa-Ueno tau function for Riemann-Hilbert problems of isomonodromic origin (Painlev\'e VI, V, III, Garnier system, etc) and the Sato-Segal-Wilson tau function for integrable hierarchies such as Gelfand-Dickey and Drinfeld-Sokolov.Comment: 26 pages, 6 figure

Low Temperature Synthesis of Hexagonal Shaped α

This study demonstrates the low temperature synthesis of α-Al2O3 by solvothermal method using gibbsite alumina precursor in 1, 4-butanediol solvent according to various pH conditions. In acidic solution, an orthorhombic boehmite (AlOOH) structure was obtained after solvothermal reaction. A significant result in this study was that the solvothermally synthesized alumina in pH=9 at 300 °C for 36 h represented a rhombohedral α-Al2O3 structure hexagonal shaped with about 1.5~2.0 μm of particle size. Otherwise, the α-Al2O3 structure was rather changed to the mixture of a boehmite and α-Al2O3 structures above pH=11. In the case of α-Al2O3 synthesized at pH=9, the specific surface area was 26.18 m2/g, and the particles that were stable in acidic solution resulted in 61.80 mV of zeta potential

Analyzing the advantages of subcutaneous over transcutaneous electrical stimulation for activating brainwaves

Transcranial electrical stimulation (TES) is a widely accepted neuromodulation modality for treating brain disorders. However, its clinical efficacy is fundamentally limited due to the current shunting effect of the scalp and safety issues. A newer electrical stimulation technique called subcutaneous electrical stimulation (SES) promises to overcome the limitations of TES by applying currents directly at the site of the disorder through the skull. While SES seems promising, the electrophysiological effect of SES compared to TES is still unknown, thus limiting its broader application. Here we comprehensively analyze the SES and TES to demonstrate the effectiveness and advantages of SES. Beagles were bilaterally implanted with subdural strips for intracranial electroencephalography and electric field recording. For the intracerebral electric field prediction, we designed a 3D electromagnetic simulation framework and simulated TES and SES. In the beagle model, SES induces three to four-fold larger cerebral electric fields compared to TES, and significant changes in power ratio of brainwaves were observed only in SES. Our prediction framework suggests that the field penetration of SES would be several-fold larger than TES in human brains. These results demonstrate that the SES would significantly enhance the neuromodulatory effects compared to conventional TES and overcome the TES limitations.11Ysciescopu

Incidence, Predictors, Treatment, and Long-Term Prognosis of Patients With Restenosis After Drug-Eluting Stent Implantation for Unprotected Left Main Coronary Artery Disease

ObjectivesThe aim of this study was to evaluate the incidence, predictors, and long-term outcomes of patients with in-stent restenosis (ISR) after percutaneous coronary intervention (PCI) with drug-eluting stents (DES) for unprotected left main coronary artery (LMCA) disease.BackgroundFew data on the clinical course and management of patients experiencing restenosis after DES treatment for unprotected LMCA disease have appeared.MethodsBetween February 2003 and November 2007, 509 consecutive patients with unprotected LMCA disease underwent DES implantation, with 402 (80.1%) undergoing routine surveillance or clinically driven angiographic follow-up. A major adverse cardiac event was defined as the composite of death, myocardial infarction (MI), or target-lesion revascularization.ResultsThe overall incidence of angiographic ISR in LMCA lesions was 17.6% (71 of 402 patients, 57 with focal-type and 14 with diffuse-type ISR. Forty patients (56.3%) underwent repeated PCI, 10 (14.1%) underwent bypass surgery, and 21 (29.6%) were treated medically. During long-term follow-up (a median of 31.7 months), there were no deaths, 1 (2.2%) MI, and 6 (9.5%) repeated target-lesion revascularization cases. The incidence of major adverse cardiac event was 14.4% in the medical group, 13.6% in the repeated PCI group, and 10.0% in the bypass surgery group (p = 0.91). Multivariate analysis showed that the occurrence of DES-ISR did not affect the risk of death or MI.ConclusionsThe incidence of ISR was 17.7% after DES stenting for LMCA. The long-term clinical prognosis of patients with DES-ISR associated with LMCA stenting might be benign, given that these patients were optimally treated with the clinical judgment of the treating physician

Long-Term Clinical Outcomes of Sirolimus- Versus Paclitaxel-Eluting Stents for Patients With Unprotected Left Main Coronary Artery Disease Analysis of the MAIN-COMPARE (Revascularization for Unprotected Left Main Coronary Artery Stenosis: Comparison of Percutaneous Coronary Angioplasty Versus Surgical Revascularization) Registry

ObjectivesThe aim of this study was to evaluate long-term clinical outcomes after implantation of sirolimus-eluting stents (SES) or paclitaxel-eluting stents (PES) among patients with unprotected left main coronary artery (LMCA) disease.BackgroundThere have been few comparisons of long-term outcomes among currently available drug-eluting stents (DES) for the treatment of LMCA disease.MethodsA total of 858 consecutive patients with unprotected LMCA stenosis were treated with SES (n = 669) or PES (n = 189) between May 2003 and June 2006. Primary outcome was the composite of death, myocardial infarction (MI), or target vessel revascularization (TVR).ResultsBaseline clinical and angiographic characteristics were similar in the 2 groups. During 3 years of follow-up, the adjusted risk of primary composite outcome was similar among the groups (SES vs. PES: 25.8% vs. 25.7%, hazard ratio [HR]: 0.95, 95% confidence interval [CI]: 0.64 to 1.41, p = 0.79). The 2 groups also showed a comparable adjusted rate of each component of outcome: death (9.1% vs. 11.0%, HR: 0.92, 95% CI: 0.47 to 1.80, p = 0.82), MI (8.1% vs. 8.0%, HR: 0.80, 95% CI: 0.43 to 1.48, p = 0.47), and TVR (12.1% vs. 10.6%, HR: 1.10, 95% CI: 0.53 to 2.29, p = 0.81). The 3-year rates of definite or probable stent thrombosis were 0.6% in the SES group and 1.6% in the PES group (adjusted p = 0.18).ConclusionsIn consecutive patients with unprotected LMCA disease undergoing DES implantation, SES and PES showed similar long-term clinical outcomes in terms of death, MI, repeat revascularization, and stent thrombosis

Stent Thrombosis, Clinical Events, and Influence of Prolonged Clopidogrel Use After Placement of Drug-Eluting Stent Data From an Observational Cohort Study of Drug-Eluting Versus Bare-Metal Stents

ObjectivesThe purpose of this study was to evaluate the risk of stent thrombosis (ST), clinical outcomes, and the benefits of extended clopidogrel use after drug-eluting stent (DES) implantation.BackgroundData are limited regarding uniform evaluation of ST and the influence of clopidogrel continuation beyond 12 months on late events after DES treatment.MethodsWe identified 7,221 patients who received DES implantation (n = 3,160) or bare-metal stent (BMS) implantation (n = 4,061), and compared long-term adverse outcomes. Additionally, 2,851 patients with DES surviving 12 months without major events were analyzed according to clopidogrel continuation.ResultsThe adjusted-risk of overall ST was similar in the 2 groups. After 1 year, however, DES patients showed a higher risk of ST; definite/probable (hazard ratio [HR]: 3.55, 95% confidence interval [CI]: 1.26 to 9.99). The adjusted-risk of death (HR: 0.60, 95% CI: 0.46 to 0.79), death/myocardial infarction (HR: 0.63, 95% CI: 0.49 to 0.81), and target lesion revascularization (HR: 0.32, 95% CI: 0.24 to 0.43) were significantly lower in the DES group than in the BMS group. Continuing clopidogrel beyond 12 months was not associated with a reduced risk for ST (HR: 0.54, 95% CI: 0.07 to 4.23), death (HR: 1.20, 95% CI: 0.55 to 2.66), or death/myocardial infarction (HR: 1.16, 95% CI: 0.56 to 2.42) after DES implantation.ConclusionsAs compared with BMS, DES showed a similar risk of overall ST, but a higher risk of very late ST. The rates of death, death/myocardial infarction, and target lesion revasuclarization were significantly lower in the DES group. Clopidogrel continuation beyond 1 year did not appear to reduce ST and clinical events after DES implantation