We study a gravitational model with curvature-squared R2 and curvature-quartic R4 nonlinearities. The effective scalar degree of freedom $\phi${} (the scalaron) has a multivalued potential U($\phi${}) consisting of a number of branches. These branches are fitted with each other in the branching and monotonic points. In the case of four-dimensional space-time, we show that the monotonic points are penetrable for the scalaron, while in the vicinity of the branching points, the scalaron has the bouncing behavior and cannot cross these points. Moreover, there are branching points where the scalaron bounces an infinite number of times with decreasing amplitude, and the Universe asymptotically approaches the de~Sitter stage. Such accelerating behavior we call bouncing inflation. For this accelerating expansion, there is no need for original potential U($\phi${}) to have a minimum or to check the slow-roll conditions. A necessary condition for such inflation is the existence of the branching points. This is a new type of inflation. We show that bouncing inflation takes place both in the Einstein and Brans-Dicke frames.

The major role of angiogenesis in cancer development has driven many researchers to investigate the prospects of noninvasive cancer imaging based on assessment of microvascular perfusion. The limited results so far may be caused by the complex and contradictory effects of angiogenesis on perfusion. Alternatively, assessment of ultrasound contrast agent dispersion kinetics, resulting from features such as density and tortuosity, has shown a promising potential to characterize angiogenic effects on the microvascular structure. This method, referred to as contrast-ultrasound dispersion imaging (CUDI), is based on contrast-enhanced ultrasound imaging after an intravenous contrast agent bolus injection. In this paper, we propose a new spatiotemporal correlation analysis to perform CUDI. We provide the rationale for indirect estimation of local dispersion by deriving the analytical relation between dispersion and the correlation coefficient among neighboring time-intensity curves obtained at each pixel. This robust analysis is inherently normalized and does not require curve-fitting. In a preliminary validation of the method for localization of prostate cancer, the results of this analysis show superior cancer localization performance (receiver operating characteristic curve area of 0.89) compared with those of previously reported CUDI implementations and perfusion estimation methods.