Emergent Geometry of KP Hierarchy

We explain how to construct a quantum deformation of a spectral curve associated to a tau-function of the KP hierarchy.This construction is applied to Witten-Kontsevich tau-function to give a natural explanation of some earlier work.We also apply it to higher Weil-Petersson volumes and Witten’s r-spin intersection numbers.

Differentiation of Hepatocellular Carcinoma from Hepatic Hemangioma and Focal Nodular Hyperplasia using Computed Tomographic Spectral Imaging

Background and Aims:Hepatocellular carcinoma(HCC)is the most common primary hepatic malignancy.This study was designed to investigate the value of computed tomography(CT)spectral imaging in differentiating HCC from hepatic hemangioma(HH)and focal nodular hyperplasia(FNH).Methods:This was a retrospective study of 51 patients who underwent spectral multiple-phase CT at 40–140 keV during the arterial phase(AP)and portal venous phase(PP).Slopes of the spectral curves,iodine density,water density derived from iodine-and water-based material decomposition images,iodine uptake ratio(IUR),normalized iodine concentration,and the ratio of iodine concentration in liver lesions between AP and PP were measured or calculated.Results:As energy level decreased,the CT values of HCC(n=31),HH(n=17),and FNH(n=7)increased in both AP and PP.There were significant differences in IUR in the AP,IUR in the PP,normalized iodine concentration in the AP,slope in the AP,and slope in the PP among HCC,HH,and FNH.The CT values in AP,IUR in the AP and PP,normalized iodine concentration in the AP,slope in the AP and PP had high sensitivity and specificity in differentiating HH and HCC from FNH.Quantitative CT spectral data had higher sensitivity and specificity than conventional qualitative CT image analysis during the combined phases.Conclusions:Mean CT values at low energy(40–90 keV)and quantitative analysis of CT spectral data(IUR in the AP)could be helpful in the differentiation of HCC,HH,and FNH.