ABJM Matrix Model and 2D Toda Lattice Hierarchy

It was known that one-point functions in the ABJM matrix model (obtained by applying the localization technique to one-point functions of the half-BPS Wilson loop operator in the ABJM theory) satisfy the Jacobi-Trudi formula, which strongly indicates the integrable structure of the system. In this paper, we identify the integrable structure of two-point functions in the ABJM matrix model as the two-dimensional Toda lattice hierarchy. The identification implies infinitely many non-linear differential equations for the generating function of the two-point functions.Comment: 35 pages, 7 eps figures; v2: references adde

Confidence intervals of prediction accuracy measures for multivariable prediction models based on the bootstrap-based optimism correction methods

In assessing prediction accuracy of multivariable prediction models, optimism corrections are essential for preventing biased results. However, in most published papers of clinical prediction models, the point estimates of the prediction accuracy measures are corrected by adequate bootstrap-based correction methods, but their confidence intervals are not corrected, e.g., the DeLong's confidence interval is usually used for assessing the C-statistic. These naive methods do not adjust for the optimism bias and do not account for statistical variability in the estimation of parameters in the prediction models. Therefore, their coverage probabilities of the true value of the prediction accuracy measure can be seriously below the nominal level (e.g., 95%). In this article, we provide two generic bootstrap methods, namely (1) location-shifted bootstrap confidence intervals and (2) two-stage bootstrap confidence intervals, that can be generally applied to the bootstrap-based optimism correction methods, i.e., the Harrell's bias correction, 0.632, and 0.632+ methods. In addition, they can be widely applied to various methods for prediction model development involving modern shrinkage methods such as the ridge and lasso regressions. Through numerical evaluations by simulations, the proposed confidence intervals showed favourable coverage performances. Besides, the current standard practices based on the optimism-uncorrected methods showed serious undercoverage properties. To avoid erroneous results, the optimism-uncorrected confidence intervals should not be used in practice, and the adjusted methods are recommended instead. We also developed the R package predboot for implementing these methods (https://github.com/nomahi/predboot). The effectiveness of the proposed methods are illustrated via applications to the GUSTO-I clinical trial

Duality Cascades and Parallelotopes

Duality cascades are a series of duality transformations in field theories, which can be realized as the Hanany-Witten transitions in brane configurations on a circle. In the setup of the ABJM theory and its generalizations, from the physical requirement that duality cascades always end and the final destination depends only on the initial brane configuration, we propose that the fundamental domain of supersymmetric brane configurations in duality cascades can tile the whole parameter space of relative ranks by translations, hence is a parallelotope. We provide our arguments for the proposal.Comment: 37 pages, 9 eps figures; v2: section 2.2 added, four figures adde

Brane Transitions from Exceptional Groups

It is a well-known result by Hanany and Witten that, when two five-branes move across each other, D3-branes stretching between them are generated. Later the same brane configurations played a crucial role in understanding the worldvolume theory of multiple M2-branes. Recently the partition function of multiple M2-branes was transformed to the Fredholm determinant for quantum algebraic curves, where the characteristic 3/2 power law of degrees of freedom is reproduced and the determinant enjoys a large symmetry given by exceptional Weyl groups. The large exceptional Weyl group reproduces the Hanany-Witten brane transitions and, besides, contains brane transitions unknown previously. Aiming at understanding the new brane transitions better, we generalize our previous study on the D5 quantum curve to the E7 case, which requires delicate handling of degeneracies. By combining the results of these two cases, we propose a "local" rule for the brane transitions.Comment: 33 pages, 8 eps figures; clarifications adde

NEDD8 Modification of CUL1 Dissociates p120CAND1, an Inhibitor of CUL1-SKP1 Binding and SCF Ligases

Cullin proteins assemble a large number of RING E3 ubiquitin ligases and regulate various physiological processes. Covalent modification of cullins by the ubiquitin-like protein NEDD8 activates cullin ligases through an as yet undefined mechanism. We show here that p120(CAND1) selectively binds to unneddylated CUL1 and is dissociated by CUL1 neddylation. CAND1 formed a ternary complex with CUL1 and ROC1. CAND1 dissociated SKP1 from CUL1 and inhibited SCF ligase activity in vitro. Suppression of CAND1 in vivo increased the level of the CUL1-SKP1 complex. We suggest that by restricting SKP1-CUL1 interaction, CAND1 regulated the assembly of productive SCF ubiquitin ligases, allowing a common CUL1-ROC core to be utilized by a large number of SKP1-F box-substrate subcomplexes

A Radial Sclerosing Lesion Mimicking Breast Cancer on Mammography in a Young Woman

A spiculated mass on a mammogram is highly suggestive of malignancy. We report the case of a 32-year-old woman with a radial sclerosing lesion that mimicked breast cancer on mammography. She visited her physician after palpating a lump in her left breast. Mammography showed architectural distortion in the upper inner quadrant of the left breast. Ultrasonography showed a low echoic area with an ambiguous boundary. Core needle biopsy was performed because of the suspicion of malignancy. Histological examination did not reveal any malignant cells. After 6 months, the breast lump became larger and the patient was referred to our hospital. Mammography performed in our hospital showed a spiculated mass, and therefore mammotome biopsy was performed. Histological examination revealed dense fibroelastic stroma with a wide variety of mastopathic changes, leading to a diagnosis of a radial sclerosing lesion. One year after the biopsy, the lump on her left breast had disappeared and mammography showed no spiculated mass

Image-based evaluation of contraction–relaxation kinetics of human-induced pluripotent stem cell-derived cardiomyocytes: Correlation and complementarity with extracellular electrophysiology

AbstractIn this study, we used high-speed video microscopy with motion vector analysis to investigate the contractile characteristics of hiPS-CM monolayer, in addition to further characterizing the motion with extracellular field potential (FP), traction force and the Ca2+ transient. Results of our traction force microscopy demonstrated that the force development of hiPS-CMs correlated well with the cellular deformation detected by the video microscopy with motion vector analysis. In the presence of verapamil and isoproterenol, contractile motion of hiPS-CMs showed alteration in accordance with the changes in fluorescence peak of the Ca2+ transient, i.e., upstroke, decay, amplitude and full-width at half-maximum. Simultaneously recorded hiPS-CM motion and FP showed that there was a linear correlation between changes in the motion and field potential duration in response to verapamil (30–150nM), isoproterenol (0.1–10μM) and E-4031 (10–50nM). In addition, tetrodotoxin (3–30μM)-induced delay of sodium current was corresponded with the delay of the contraction onset of hiPS-CMs. These results indicate that the electrophysiological and functional behaviors of hiPS-CMs are quantitatively reflected in the contractile motion detected by this image-based technique. In the presence of 100nM E-4031, the occurrence of early after-depolarization-like negative deflection in FP was also detected in the hiPS-CM motion as a characteristic two-step relaxation pattern. These findings offer insights into the interpretation of the motion kinetics of the hiPS-CMs, and are relevant for understanding electrical and mechanical relationship in hiPS-CMs