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

Neuroprotective Activity of Sibjeondaebo-tang on Aβ Peptide-Induced Damages

Background. Sibjeondaebo-tang (SJDBT) has been used to treat diverse disorders including neuropsychiatric disabilities in traditional Korean medicine. Objective. The present study aims to investigate the potential effects of SJDBT on neuroprotection against Aβ peptide-induced damage using in vitro culture and in vivo rat brain systems. Materials and Methods. PC12 cell viability was analyzed by MTT assay, and neurite arborizations and caspase 3 protein signals in cultured PC12 cells and in vivo cortical neurons were analyzed by immunofluorescence staining. Phospho-Erk1/2 protein was analyzed by immunofluorescence staining and western blot analysis. Results. In PC12 cells, atrophied cell body and reduced neurite extension by Aβ treatment were recovered by SJDBT treatment. Caspase 3 protein signals were increased in Aβ-treated PC12 cells, but SJDBT treatment decreased apoptotic cell death. Caspase 3 activation in cortical neurons, which was induced similarly by Aβ treatment, was reduced by SJDBT treatment. Furthermore, phospho-Erk1/2 protein levels, which had been decreased by Aβ treatment, were elevated in the cortical neurons by SJDBT treatment. Conclusion. These data show that SJDBT may play a role in protecting from damages induced by Aβ in neuronal tissue and further suggest that SJDBT can be explored as the potential therapeutic target for AD treatments in human

Two-gap and paramagnetic pair-breaking effects on upper critical field of SmFeAsO0.85_{0.85} and SmFeAsO0.8_{0.8}F0.2_{0.2} single crystals

We investigated the temperature dependence of the upper critical field [$H_{c2}(T)$] of fluorine-free SmFeAsO$_{0.85}$ and fluorine-doped SmFeAsO$_{0.8}$F$_{0.2}$ single crystals by measuring the resistive transition in low static magnetic fields and in pulsed fields up to 60 T. Both crystals show that $H_{c2}(T)$'s along the c axis [$H_{c2}^c(T)$] and in an $ab$-planar direction [$H_{c2}^{ab}(T)$] exhibit a linear and a sublinear increase, respectively, with decreasing temperature below the superconducting transition. $H_{c2}(T)$'s in both directions deviate from the conventional one-gap Werthamer-Helfand-Hohenberg theoretical prediction at low temperatures. A two-gap nature and the paramagnetic pair-breaking effect are shown to be responsible for the temperature-dependent behavior of $H_{c2}^c$ and $H_{c2}^{ab}$, respectively.Comment: 21 pages, 8 figure

Image-guided transcranial focused ultrasound stimulates human primary somatosensory cortex

Focused ultrasound (FUS) has recently been investigated as a new mode of non-invasive brain stimulation, which offers exquisite spatial resolution and depth control. We report on the elicitation of explicit somatosensory sensations as well as accompanying evoked electroencephalographic (EEG) potentials induced by FUS stimulation of the human somatosensory cortex. As guided by individual-specific neuroimage data, FUS was transcranially delivered to the hand somatosensory cortex among healthy volunteers. The sonication elicited transient tactile sensations on the hand area contralateral to the sonicated hemisphere, with anatomical specificity of up to a finger, while EEG recordings revealed the elicitation of sonication-specific evoked potentials. Retrospective numerical simulation of the acoustic propagation through the skull showed that a threshold of acoustic intensity may exist for successful cortical stimulation. The neurological and neuroradiological assessment before and after the sonication, along with strict safety considerations through the individual-specific estimation of effective acoustic intensity in situ and thermal effects, showed promising initial safety profile; however, equal/more rigorous precautionary procedures are advised for future studies. The transient and localized stimulation of the brain using image-guided transcranial FUS may serve as a novel tool for the non-invasive assessment and modification of region-specific brain functionopen43

Epileptic nystagmus: A case report and systematic review

AbstractPurposeWe aimed to define the characteristics of epileptic nystagmus and correlate those with other clinical findings in a large number of patients.MethodsWe report a patient with epileptic nystagmus and additionally reviewed the reported clinical features of 36 more patients through a systematic literature search. We analyzed the characteristics of epileptic nystagmus and attempted correlations of those with alertness of the patients and epileptic foci on EEG.ResultsAll 33 patients with unilateral horizontal nystagmus showed nystagmus beating away from the side of ictal discharges. Epileptic nystagmus was preceded by gaze deviation in 21 patients, with contraversive in 19 and ipsiversive in 2. Seizures associated with epileptic nystagmus were mostly focal (25/29, 86.2%) with or without loss of awareness. Ictal discharges originated from the occipital (n=16), parietal (n=9), temporo-occipital (n=6), frontal (n=4), and temporal (n=3) areas, and two patients had multiple epileptic foci. Seizures were usually symptomatic (24/37, 64.9%). The presence of preceding gaze deviation and midline crossing of the nystagmus did not correlate with the ictal onset zone or alertness of the patients. Recording of epileptic nystagmus was available only in 6 patients, and the epileptic nystagmus could be localized to the saccadic areas in two and to the smooth pursuit areas in another two. Two patients showed the features of epileptic nystagmus from both areas.ConclusionEven though the localizing value of epileptic nystagmus seems limited in previous reports, the fast phase of epileptic nystagmus was almost always directed away from the epileptic focus that mostly arose from the posterior part of the cerebral hemisphere