We study the operadic and categorical formulations of (conformal) full field algebras. In particular, we show that a grading-restricted R × R-graded full field algebra is equivalent to an algebra over a partial operad constructed from spheres with punctures and local coordinates. This result is generalized to conformal full field algebras over V L ⊗ V R , where V L and V R are two vertex operat...

Introduction: Modern radiotherapy (RT) techniques allow a highly precise deposition of the radiation dose in tumor. So, high conformal tumor doses can be reached while sparing critical organs at risk. Materials and Methods: This study was conducted in three phases. In the first phase; Fourteen patients with primary or recurrent prostate cancer receive Gallium-...

Some years ago, Polyakov [1] proposed constructing all conformally invariant quan tum field theories by using the constraint of conformal invariance to make concrete the fundamental principles of quantum field theory. This is the conformal boots t rap program. Conformal field theories describe the universality classes of critical phenomena, or equivalently the short distance limits of quantum f...

Trace anomaly for dilaton coupled conformal theories on curved background with non-zero dilaton is found from supergravity side as an IR e ect using AdS/CFT correspondence. For d = 2 it coincides with the conformal anomaly for dilaton coupled scalar (up to total derivative term which is known to be ambiguous). In four-dimensional case we get conformal anomaly for N = 4 super YM theory interacti...

Abstract A world-volume model of a non-critical 3-brane is quantized in a strong coupling phase in which fluctuations of the conformal mode become dominant. This phase, called the conformal-mode dominant phase, is realized at very high energies far beyond the Planck mass scale. We separately treat the conformal mode and the traceless mode and quantize the conformal mode non-perturbatively, whil...

Conformal prediction is a learning framework that produces models that associate with each of their predictions a measure of statistically valid confidence. These models are typically constructed on top of traditional machine learning algorithms. An important result of conformal prediction theory is that the models produced are provably valid under relatively weak assumptions—in particular, the...