Abstract Background: Acromegaly is a rare clinical syndrome caused by excessive production of growth hormone. The incidence rate 3 to 4 cases per million people year. It sporadic disease seen in middle-aged adults. Anterior pituitary adenoma secreting the hormone (GH) most common etiology. Other causes include hypothalamic and neuroendocrine tumors. Treatment modalities surgical, radiotherapeut...

We consider the half-line stochastic heat equation (SHE) with Robin boundary parameter $A = -\frac{1}{2}$. Under narrow wedge initial condition, we compute every positive (including non-integer) Lyapunov exponents of SHE. As a consequence, prove large deviation principle for upper tail KPZ under Neumann -\frac{1}{2}$ rate function $\Phi_+^{\text{hf}} (s) \frac{2}{3} s^{\frac{3}{2}}$. This confi...